Remote Sensing from Air And Space (SPIE Press Monograph Vol. PM162)

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Remote Sensing from Air and Space

Remote Sensing from Air and Space R. C. Olsen

Bellingham, Washington USA

Library of Congress Cataloging-in-Publication Data Olsen, R. C. (Richard C.) Remote sensing from air and space / by R. C. Olsen p. cm. – (SPIE Press Monograph ; 162) Includes bibliographical references and index ISBN 978-0-8194-6235-0 1. Remote Sensing. I. Title G70.4.O47 2006 621.36’78—dc22 2006051183

Published by SPIE—The International Society for Optical Engineering P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: 360.676.3290 Fax: 360.647.1445 Email: [email protected] www.spie.org

Copyright © 2007 The Society of Photo-Optical Instrumentation Engineers All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher.

Printed in the United States of America.

The content of this book reflects the thought of the author(s). Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.

Contents

Preface Chapter 1 1.1

1.2

1.3 1.4 1.5

xii Introduction to Remote Sensing Order of Battle 1.1.1 Air order of battle 1.1.2 Electronic order of battle 1.1.3 Space order of battle 1.1.4 Naval order of battle Imagery Survey 1.2.1 Visible 1.2.1.1 GOES, whole Earth 1.2.1.2 DMSP (0.5 km), Earth at night 1.2.1.3 UoSAT (100m), San Francisco 1.2.1.4 Landsat 5 (30m), San Diego 1.2.1.5 Astronaut photography 1.2.1.6 SPOT (10 m) 1.2.1.7 IRS (5 m) 1.2.1.8 IKONOS—San Diego/Coronado Island 1.2.1.9 High-resolution airborne imagery 1.2.2 Infrared (IR) 1.2.2.1 GOES 9 1.2.2.2 Landsat—IR San Diego 1.2.2.3 DMSP—IR and microwave 1.2.3 Radar (SAR) 1.2.3.1 RADARSAT, Maui and the airport 1.2.3.2 SIRC—Multi-wavelength/polarization 1.2.3.2.1 Maui 1.2.3.2.2 SIRC, San Diego Harbor Three Axes Resources Problems

v

1 2 3 3 7 8 9 9 9 10 11 13 13 15 17 17 19 20 21 22 23 24 24 26 26 26 26 28 29

vi

Contents

Chapter 2 2.1 2.2 2.3

2.4

2.5

2.6 Chapter 3 3.1

3.2

3.3

3.4 3.5

3.6

3.7

Electromagnetic Basics The Electromagnetic Spectrum 2.1.1 Maxwell’s equations Polarization of Radiation Energy in Electromagnetic Waves 2.3.1 Photoelectric effect 2.3.2 Photomultiplier tubes Sources of Electromagnetic Radiatio 2.4.1 Line spectra 2.4.2 Blackbody radiation Electromagnetic Radiation (EMR)–Matter Interactions 2.5.1 Transmission 2.5.2 Reflection 2.5.3 Scattering 2.5.4 Absorption Problems

33 33 33 35 35 38 39 41 42 45 48 49 50 51 52 53

Visible Imagery The First Remote Sensing Satellite: Corona 3.1.1 A little history 3.1.2 The technology 3.1.3 Some illustrations Atmospheric Absorption, Scattering, and Turbulence 3.2.1 Atmospheric absorption: wavelength dependence 3.2.2 Atmospheric scattering 3.2.3 Atmospheric turbulence Basic Geometrical Optics 3.3.1 Focal length/geometry 3.3.2 Optical diagram: similar triangles, magnification 3.3.3 Aperture (f/stop) 3.3.4 Image formation by lens or pinhole Diffraction Limits: the Rayleigh Criterion Detectors 3.5.1 Film 3.5.2 Solid state 3.5.3 Focal plane arrays 3.5.4 Uncooled focal planes: Microbolometers Imaging System Types 3.6.1 Framing systems—mostly film systems (Corona) 3.6.2 Scanning systems 3.6.2.1 Cross track (Landsat MSS, TM; AVIRIS) 3.6.2.2 Along track (SPOT HRV) Hubble: The Big Telescope 3.7.1 The Hubble satellite

55 55 55 56 59 63 63 64 66 67 67 68 69 69 70 73 74 74 78 79 80 80 80 80 81 82 82

Contents

vii

3.7.2 The repair missions 3.7.3 Operating constraints 3.7.3.1 South Atlantic anomaly 3.7.3.2 Spacecraft position in orbit 3.7.4 The telescope itself 3.7.5 Detectors—Wide Field and Planetary Camera 2 3.7.5.1 Example: Diffraction and resolution limits 3.7.5.1.1 Rayleigh criteria 3.7.5.1.2 Geometric resolution 3.8 Commercial Remote Sensing—IKONOS and Quickbird 3.8.1 IKONOS 3.8.1.1 Imaging sensors and electronics for the IKONOS satellite 3.8.1.1.1 Camera telescope 3.8.1.1.2 Imaging sensors & electronics 3.8.2 NOB with IKONOS: Severodvinsk 3.9 DMSP: Visible Sensor, Earth at Night 3.10 Exposure Times 3.11 Problems Chapter 4 4.1 4.2

4.3 4.4

4.5

4.6

Orbital Mechanics Interlude Gravitational Force Circular Motion 4.2.1 Equations of motion 4.2.1.1 Example: A car is going around in a circle of 200 m radius at 36 km/hr. What is ω? 4.2.1.2 Example: A satellite is going around the Earth once every 90 minutes. What is ω? 4.2.2 Centripetal force Satellite Motion Kepler’s Laws 4.4.1 Elliptical orbits 4.4.2 Equal areas swept out in equal times 4.4.3 Orbital period: τ2 ∝ ρ3 Orbital Elements 4.5.1 Semi-major axis: a 4.5.2 Eccentricity: e or ε 4.5.3 Inclination angle: I 4.5.4 Right ascension of the ascending node: Ω 4.5.5 Closest point of approach (argument of perigee): ω A Few Standard Orbits 4.6.1 Low Earth orbit (LEO) 4.6.2 Medium Earth orbit (MEO) 4.6.3 Geosynchronous orbit (GEO)

84 86 86 86 86 88 90 90 92 92 95 95 95 96 97 98 99 101 103 103 104 104 104 105 105 105 106 106 107 108 108 108 108 108 109 109 109 110 111 111

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Contents

4.7 Chapter 5 5.1 5.2 5.3

5.4

5.5 5.6

5.7 Chapter 6 6.1

6.2

4.6.4 Molniya orbit (HEO) 4.6.5 Summary table—illustrations Problems

113 114 115

EO—Spectral Imagery Reflectance of Materials Human Visual Response Landsat 5.3.1 Orbit 5.3.2 Sensor: Thematic mapper 5.3.2.1 Optics 5.3.2.2 Focal planes 5.3.2.2.1 Prime focal plane 5.3.2.2.2 Cold focal plane 5.3.2.2.3 Spectral response 5.3.2.3 Spatial resolution—swath 5.3.2.4 Dynamic range 5.3.2.5 Data links Systeme Probatoire d’Observation de la Terre (SPOT) 5.4.1 HRV sensor, pan/spectral—both 60-km swath 5.4.1.1 Imaging modes—spatial and spectral resolution Spectral Responses for the Commercial Systems Imaging Spectroscopy 5.6.1 AVIRIS 5.6.2 Hyperion 5.6.3 MightySat II—FTHSI Problems

117 117 118 120 121 122 122 124 124 125 125 126 127 127 128 130 130 131 132 132 133 135 136

Image Analysis Interpretation Keys (elements of recognition) 6.1.1 Shape 6.1.2 Size 6.1.3 Shadow 6.1.4 Height (depth) 6.1.5 Tone or color 6.1.6 Texture 6.1.7 Pattern 6.1.8 Association 6.1.9 Site 6.1.10 Time Image Processing 6.2.1 Digital numbers: pixels and pictures, histograms 6.2.2 Dynamic range—snow and black cats

137 137 137 138 138 138 138 139 139 140 140 140 140 142 143

Contents

ix

6.3 6.4 6.5 6.6 Chapter 7 7.1

7.2

7.3 7.4

7.5

7.6 7.7

7.8 Chapter 8 8.1 8.2

6.2.3 Filters 6.2.3.1 Smoothing 6.2.3.2 Edge detection Histograms and Target Detection Histograms, Spectral Data, and Transforms Supplemental Notes on Statistics Problems

146 146 146 147 149 153 156

Thermal Infrared IR Basics 7.1.1 Blackbody radiation 7.1.2 Wien’s displacement law 7.1.3 Stefan-Boltzmann law T 4 7.1.4 Emissivity 7.1.5 Atmospheric absorption IR Concepts 7.2.1 Kinetic temperature 7.2.2 Thermal inertia, conductivity, capacity, diffusivity 7.2.2.1 Heat capacity (specific heat) 7.2.2.2 Thermal conductivity 7.2.2.3 Thermal inertia 7.2.2.4 Thermal diffusivity 7.2.2.5 Diurnal temperature variation Landsat Early Weather Satellites 7.4.1 TIROS 7.4.2 NIMBUS GOES 7.5.1 Satellite and sensor 7.5.2 Weather and storms—Hurricane Mitch 7.5.3 Volcanoes and ash clouds 7.5.4 Shuttle launch: vapor trail, rocket Defense Support Program—DSP SEBASS—thermal spectral 7.7.1 Hard targets 7.7.2 Gas measurements: Kilauea—Pu ‘u ‘O ‘o Vent Problems

157 157 157 158 158 159 159 159 159 160 160 161 161 161 162 163 165 166 166 167 167 169 170 171 172 175 175 176 178

Radar Imaging Radar Theory 8.2.1 Imaging radar basics 8.2.2 Radar range resolution 8.2.2.1 Signal shape

179 179 179 179 182 183

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Contents

8.3 8.4

8.5 8.6 8.7

8.8 Chapter 9 9.1

9.2

9.3

8.2.3 Radar azimuthal resolution 8.2.4 Beam pattern and resolution Synthetic-Aperture Radar Radar Cross Section (σ) 8.4.1 Dielectric coefficient: soil moisture 8.4.2 Roughness 8.4.3 Tetrahedrons/corner reflectors Polarization Wavelength Vehicles 8.7.1 Shuttle Imaging Radar (SIR) 8.7.1.1 Soil penetration 8.7.1.2 Oil slicks and internal waves 8.7.2 RADARSAT: ship detection 8.7.3 European radar satellites: ERS-1, ERS-2 8.7.3.1 Ship wakes 8.7.3.2 Multi-temporal images: Rome 8.7.3.3 SPAIN—MOROCCO—Strait of Gibraltar 8.7.4 Sandia Ku-band airborne radar Problems

185 186 188 191 192 194 194 195 196 197 197 199 200 201 202 203 204 204 206 208

Radar and LIDAR Radar Interferometry 9.1.1 Topographic mapping 9.1.2 The Shuttle Radar Topographic Mapping (SRTM) Mission 9.1.2.1 Mission design 9.1.2.2 Mission results: level-2 terrain-height datasets (digital topographic maps) LIDAR 9.2.1 Introduction 9.2.2 OPTECH: Airborne Laser Terrain Mapper (ALTM) 9.2.3 Bathymetry Exercise

211 211 211

Appendix 1 Derivations A1.1 Derivation of the Bohr Atom Assumption 1: The atom is held together by the Coulomb Force Assumption 2: The electron moves in an elliptical orbit around the nucleus (as in planetary motion). Assumption 3: Quantized angular momentum Assumption 4: Radiation is emitted only from transitions between the discrete energy levels

214 215 217 219 219 220 222 224 225 225 225 226 226 228

Contents

xi

A1.2 Dielectric Theory A1.3 Derivation of the Beam Pattern for a Square Aperture Appendix 2 A2.1 A2.2 A2.3 A2.4

CORONA Mission Overview Camera Data Mission Summary Orbits—An Example

Tracking and Data Relay Satellite System Relay Satellites—TDRSS White Sands TDRS 1 to 7 A3.3.1 Satellites A3.3.2 Payload A3.4 TDRS H A3.4.1 TDRS H, I, and J Payload Characteristics A3.4.1.1 S-Band Multiple Access A3.4.1.2 Single-Access (SA) Antenna (2) A3.4.1.3 Space-Ground-Link Antenna (Ku Band)

229 230 233 233 234 235 242

Appendix 3 A3.1 A3.2 A3.3

243 243 244 245 245 246 247 247 248 248 248

Appendix 4 Useful Equations and Constants EM Waves Bohr Atom Blackbody Radiation Reflection and Refraction Optics Orbital Mechanics and Circular Motion

249 249 249 249 250 250 250

Index

251

Preface

This text is designed to meet the needs of students interested in remote sensing as a tool for the study of military and intelligence problems. It focuses on the technology of remote sensing, both for students who will be working in systems acquisition offices and for those who might eventually need to be “informed consumers” of the products derived from remote sensing systems. I hope it will also be useful for those who eventually work in the remote sensing field. This text maintains as much as possible a focus on the physics of remote sensing. As a physicist, I’m more interested in the technology of acquiring data than the final applications. Therefore, this work differs from related textbooks that favor civilian applications, particularly geology, agriculture, weather (atmosphere), and oceanography. By contrast, I have concentrated on satellite systems, including power and telemetry systems, since this knowledge is important for those trying to develop new remote sensing systems. For example, one of the ongoing themes is how bandwidth constraints define what you can and cannot do in terms of remote sensing. From a tactical perspective, low-spatial-resolution systems are not very interesting, so this text focuses on systems of high spatial resolution. This is not to deny the utility of, say, weather systems for the military, but that is a domain of a different sort, and one I leave to that community. Similarly, although oceanography is clearly important to the navy, that too is a topic I leave to another community. Unlike earlier texts, this text avoids discussion of the older film-based imaging systems. When I started this text the IKONOS satellite had not yet been launched, so it is a curious thing that a document created in part due to the technological obsolescence of earlier textbooks may already be in some danger of falling behind! Remote sensing appears to be emerging as the third field, following communications and navigation, to become economically viable in space, and it is with great anticipation that we await the changes of a coming generation of imaging systems. This text is organized according to a fairly typical progression—basic physics first, then visible optical systems, followed by infrared and radar systems. The necessary physics is developed for each domain, followed by a look at a few operational systems that are appropriate for that section. Somewhat unusual for a text of this sort is a chapter on how orbital mechanics influences remote sensing.

xii

Preface

xiii

Finally, I will conclude the preface with a few basic questions. What is remote sensing? What is it good for? What do you need to know in order to use this technology? The text that follows will address these questions. R. C. Olsen Naval Postgraduate School, Monterey, CA November 2006

Chapter 1 Introduction to Remote Sensing

Remote sensing is a field of technology designed to enable people to look beyond the range of human vision. Whether it is over the horizon, beyond our limited human range, or in a spectral range outside human perception, we are in search of information. The focus here will be on imaging systems that extend our range of perception, particularly in the realms of intelligence, strategy, tactics, and military applications. To begin, consider one of the first remote-sensing images. Figure 1.1 shows a photograph by Gaspard-Félix Tournachon1 (Gaspard was also known by his pseudonym, Nadar). Gaspard took this aerial photo of Paris in 1868 from the Hippodrome Balloon, tethered 1700 ft above Paris. Contrast this with the cover photo taken by Apollo 17, just one hundred years later. This is a fairly classic remote-sensing image—a representation from a specific place

1

Figure 1.1 Nadar took his first aerial photographs in 1858, but those earlier images did not survive.2 Nadar applied for a patent for aerial surveying and photography in 1858. Aerial reconnaissance followed shortly, with significant work during the American Civil War.3

Tournachon was a notable portrait photographer from 1854 1860. Nadar made the first photographs with artificial light in 1861, descending into the Parisian sewers and catacombs with magnesium flares. He apparently was also an early experimenter in ballooning, even working with Jules Verne. http://www.getty.edu/art/collections/bio/a1622 1.html; http://histclo.hispeed.com/bio/n/bio nadar.html 2 John R. Jensen, Remote Sensing of the Environment: An Earth Resource Perspective, 2nd. ed. Prentice Hall, New York (2006). 3 Image courtesy of USGS: Earthshots, originally from the EROS Data Center of the U.S. Geolog ical Survey, a bureau of the U.S. Department of the Interior.

1

2

Chapter 1

and time of an area of interest. What sorts of things can be learned from such an image? Where, for instance, are the streets? What buildings are there? What are the purposes of those buildings? Which buildings are still there today? These are the elements of information that we want to extract from our imagery. In the material that follows, a model is established for extracting information from remote-sensing data. Following that section, remote-sensing data from a variety of systems is introduced to provide an early overview of the domains of the field.

1.1 Order of Battle Remote-sensing data, sans analysis, have a fairly modest value. What is really wanted, in general, is information appropriate to making a decision. To the extent we can obtain or understand what information can be derived from remote-sensing data, we begin to address a question posed in the preface: What is remote sensing good for? To answer, a paradigm is introduced, termed “order of battle” (OOB). This is largely associated with the counting of “things,” but not entirely. Indeed, one thing for which care must be taken: don’t limit the levels of information to simple “counting.” We also need to pay attention to nonliteral forms of information. OOB has a number of forms, depending on the area of interest, as indicated here: Air order of battle (AOB) Cyber order of battle (COB) Electronic order of battle (EOB) Ground order of battle (GOB), including logistics Industrial order of battle (IOB) Naval order of battle (NOB) Space order of battle (SOB) What items characterize these OOB types? What sort of information are we considering? Taking GOB as an example, one might like to know about vehicles—their numbers, locations, and types. Examples of types would be armored (e.g., tanks), transport (trucks), and personnel (high-mobility, multipurpose, wheeled vehicles, or HMMWVs). Having established types, further elements of information include operational status (fueled, hot, armed), capabilities, and armament (weapons). Other elements of GOB are troops (numbers, arrangement, types), defenses (for example, minefields, geography, missiles, chemical/biological, camouflage, and decoys) and infrastructure (such as roads and bridges). Three other OOB examples follow.

Introduction to Remote Sensing

3

Figure 1.2 SR-71 image, Bluefields, Nicaragua, New runway under construction, 2 January 1982.4

1.1.1 Air order of battle For air order of battle (AOB), the focus is primarily on aircraft and airfields. A tabular approach to compiling salient elements of information is shown below. The table is organized in increasing level of detail. There are several levels of detail that you will want to know about. Not all will be amenable to remote sensing, but the first step is to identify what you want to know. The next step is to determine which elements can be provided by available sensors. Two illustrations of AOB are given in Figs. 1.2 and 1.3. These are derived from SR-71 imagery, and show airfields in Nicaragua. Note that important elements such as the length and orientation (heading) of the runways are immediately apparent; further study shows elements of information such as the airfield defenses.

1.1.2 Electronic order of battle Electronic order of battle (EOB) is really the domain of the signals-intelligence (SIGINT) community, but imagery can shed light on the topic. Things you might

4

Courtesy of Federation of American Scientists: http://www.fas.org

4

Chapter 1 Table 1.1 Air order of battle—detail.

Planes

Type

Fighter

Weapons Sensors

Bomber Tanker Transport Trainer EW Reconnaissance Number Locations

Runways

Length Composition Direction Approach

Logistics POL*

Pilots

Defenses

Supply lines/lines of communication Fuel Tanks

Number Ranks Training Experience Weapons Radar

Locations * petroleum, oil, and lubrication ** field of view

Bunkers Runway Aprons (Material: asphalt, dirt, concrete) Terrain Lighting Weather Ground controllers

Capacity Type of fuel Fill factor

AA guns AA missiles Frequency Range Location Type FOV**

Civilian Military

Air-to-air Air-to-ground FLIR Radar Visible EW


5

Figure 1.3 SR-71 image, Punta Huete Airfield, Nicaragua.5

like to know about include defenses, such as surface-to-air missiles (SAMs) and radar installations. For radars, the technical details are admittedly more the domain of SIGINT than imagery intelligence (IMINT), because elements of information include frequencies, pulse-repetition frequency (PRF), scan type, and pulse width and mode. Still, location and the layout of radar tell you a lot, particularly with regard to access. The size of an antenna implies characteristics such as range. You may be able to determine operational patterns. The radars’ types can be identified by comparison to known systems, e.g., air search, surface search, fire control, and target trackers. You can find out something about their networking and communications, such as nodes or types (HF, microwave, fiber, etc.). You may also be able to determine the power source.

5

Courtesy of Federation of American Scientists: http://www.fas.org

6

Chapter 1

Figure 1.4 This Quickbird image (left) shows the Sary Shagan Hen House radar, Lake Balkhash, Kazakhistan. The image was taken on July 21, 2005. These large Soviet radar (260 m long) were designed to watch for ballistic missiles, in this case from the south and southwest.6 For context, the April 1991 image to the right is from the NASA Space Shuttle collection, from STS039, taken with the wide-angle 40 mm lens on a Hasselblad camera. The image shows Lake Balkhash. The lake is some 350 miles long.

Two illustrations are given here, one of a famous Soviet Cold War system, the other of a satellite communications station. In Fig. 1.4, the orientation of the Hen House radar is associated with its primary role of watching the horizon for ballistic missiles. Given the size and orientation of the radar, and some knowledge of the wavelength used, the resolution and field of view for the radar can be determined. The satellite communications station illustrated in Fig. 1.5 provides information both for EOB and space order of battle (SOB), discussed next.

6

©Digital Globe


7

Figure 1.5 Tactical Airborne Reconnaissance Pod System (TARPS) Umm al Aysh SATCOM.7

1.1.3 Space order of battle Space order of battle (SOB) is a relatively new area. It includes two components: space and ground systems. On the ground, elements of interest include launchers (boosters), launch pads and other infrastructure, and communications ground sites. Figure 1.6 illustrates the ground component with an image of a launch pad in Baikonur. In space, elements of information that are important are communications systems (relay satellites), operational payloads, and satellite orbital data. Figure 1.7 illustrates

7 8

Figure 1.6 U2 image of SS-6/Sputnik Launch Pad, Baikonur.8

Courtesy of Federation of American Scientists: http://www.fas.org Courtesy of Federation of American Scientists: http://www.fas.org

8

Chapter 1

space control issues. The XSS-10 satellite mission was a short-lived (about twelve hours of battery power) free-flyer deployed from a Delta II on January 29, 2003, following launch from Cape Canaveral Air Force Station, Florida (the primary payload was a GPS satellite). The 28-kg satellite was an AFRL mission, flown to within 100 m of the Delta II rocket. Surrey Satellite Technology did something similar with their SNAP-1 payload, imaging the Chinese Tsinghua satellite in 2001. They also imaged the Russian Nadezha search-and-rescue satellite, much to the surprise of the Russians.10 1.1.4 Naval order of battle Figure 1.7 This is an image of the Delta Naval order of battle (NOB) involves II rocket taken in space by the XSS-10 ships, of course. You want to know about satellite’s onboard camera. The satellite battle groups: their composition (types of transmitted the image back to Earth shortly after separating from the booster ships, numbers, arrangement in the group, to conduct its mission.9 steaming direction, velocity, etc). You want to know about ports: harbor characteristics, draft, piers, defenses, communication lines, and facilities. For ships in a harbor, you want to know their state of readiness. For individual ships, manpower, supplies, weapons, and sensors are important. In the case of carriers, you want to know about the aircraft aboard and how they are armed. Figure 1.8 illustrates a little of what can be seen by viewing a Russian naval base. You can count the submarines and to some extent identify them, by length and shape. You get some indication of readiness by looking at the ice: are the boats locked in or is there a path to open water? Note the level of activity on the docks around the submarines. In this case, things look pretty quiet. These illustrations for order of battle give us an idea of the types of information we would like to obtain. Next we briefly survey the various forms of remote-sensing data available historically and today. Visible, infrared, and radar imagery are illustrated.

9

Courtesy of Boeing: http://www.boeing.com Frank Morring, Jr., “At Surrey Satellite Technology, small and simple is beautiful,” Aviation Week & Space Technology 154(25), p 209 (2001).

10


9

Figure 1.8 Kamchatka Submarine Base, Russia. Located on the far-eastern frontier of Russia and the former Soviet Union, this peninsula has always been of strategic importance. Kamchatka is home to the Pacific nuclear submarine fleet, housed across Avacha Bay from Petropavlovsk at the secret Rybachy base. EROS, December 25, 2001, 1.8-m resolution.11

1.2 Imagery Survey To begin our study, we’ll take a look at some images that illustrate the range of data types found in remote sensing and show how what we can learn from remote sensing varies with spatial resolution and wavelength. The illustrations are chosen to suggest the variety of organizations involved with remote sensing—military and civil systems dominate, but there are also important private systems. A recurrent point of these examples is the tension between spatial resolution and coverage, and the competing interests of temporal sampling. We begin with (nearly) whole-Earth visible imagery. The cover image from Apollo 17 illustrates several important points—in particular a vexing one for remote sensing: clouds. Do you see indications of intelligent life? 1.2.1 Visible 1.2.1.1 GOES, whole Earth High-altitude satellites (such as weather satellites) image most of a hemisphere. The GOES-9 visible imager acquires an image of one hemisphere every 30 min, or the northern quad once every 15 min, with a spatial resolution of 1 km. The familiar weather news is frequently illustrated by images from GOES satellites.

11

EROS. A high resolution satellite image Courtesy of ImageSat International N.V.

10

Chapter 1

Figure 1.9 GOES-9 visible image, June 9, 1995, 18:15 UTC.12

What value do such data have for the military? For one thing, cloud coverage is revealed. Clouds are a major concern in modern warfare, directly affecting the ability of pilots and autonomous weapons to locate targets. This whole-Earth image also begins our illustration of the important tradeoffs between spatial resolution, frequency of coverage, and area of coverage. High-altitude satellites, such as geosynchronous weather satellites, provide large-area coverage, more or less continuously, producing an image every 15–30 min, at a spatial resolution of 1 km, as noted.

1.2.1.2 DMSP (0.5 km), Earth at night Similar spatial and temporal characteristics are found in a second example, from a complementary military weather system. The Defense Meteorological Satellite Program (DMSP) operates low Earth-orbiting satellites. These polar-orbiting satellites image the Earth at a resolution of 1 km during the day, with results similar to those from GOES. It provides coverage at high latitudes that cannot be obtained from geosynchronous systems, but with relatively poor temporal coverage; any

12

Credit: NASA Goddard Space Flight Center, data from NOAA GOES.


11

Figure 1.10 DMSP image of the U.S. East Coast at night.13

given low- to mid-latitude region will be imaged only a few times a day. A more unusual capability emerges after dark. The operational line-scan system, photomultiplier tube (OLS-PMT) sensor on DMSP sees clouds at night. DMSP’s low-light capability includes the ability to see city lights, large fires (as of oil wells and forests), and the aurora borealis, as well as less-obvious light sources such as those produced by industrial activity. The image here was obtained at a spatial resolution of 2.6 km. The imager is designed to see clouds at night via moonshine; the brightness of city lights saturates the photomultiplier tube detectors (or photon counters).

1.2.1.3 UoSAT (100 m), San Francisco The third illustration in our sequence, a TMSAT image, improves spatial resolution by a factor of 10. UoSAT shows the possibilities inherent in small satellite technologies at remarkably low cost. Figure 1.11 shows imagery from a small satellite built

13

C.D. Elvidge, K.E. Baugh, E.A. Kihn, H.W. Kroehl, and E.R. Davis, “Mapping of city lights us ing DMSP operational linescan system data,” Photogrammetric Engineering and Remote Sensing 63, pp. 727 734 (1997).

12

Chapter 1 Figure 1.11 TMSAT image of San Francisco Bay. Various manmade features are discernable, including the Bay Bridge connecting San Francisco and Oakland (though the Golden Gate Bridge is shrouded in fog), and the runways at San Francisco and Oakland airports, standing out as long straight lines on the bay shore. The variety of wavelengths gives additional information. Red areas indicate dense, healthy vegetation (due to the strong, near-IR reflectance of chlorophyll), mainly forests on the Santa Cruz and Diablo mountains. Urban areas are generally blue-gray. To the right, the intensive agriculture of the Sacramento and San Joaquin valleys is visible as a patchwork of fields, whose colors indicate vegetative status (bare soil, marsh, young or mature vegetation, etc.).14

by Surrey Satellite Technology, Ltd. (SSTL), one in a series of capable small satellites. SSTL is a commercial spin-off from the University of Surrey and the Surrey Space Centre. This image was taken by TMSAT, owned and operated by the Thai Microsatellite Company (TMSC), Bangkok, Thailand. The TMSAT micro-satellite captured the image shown here on August 29, 1998, at 18:54:15 UTC (38.3°N 122.6°W) over the cities of Oakland and San Francisco in California. This multispectral image was produced by combining the data from three narrow-angle cameras, sensing in the green, red, and near-IR spectra. Each image contains 1020 × 1020 pixels, covering an area of 100 × 100 km at a mean ground resolution of 98 m/pixel. Satellites like this run on the order of $2 million, delivered on orbit (as of the year 2000). This imagery is a remarkable testimony to the possibilities inherent in small satellites. More recent launches by UoSAT involve sensors with 10-m resolution in the panchromatic band and 32-m resolution in the multispectral (e.g., color) bands. These robust systems cost about $10 million (circa 2004). A fairly recent model was UoSat-12, launched for Algeria as AlSAT-1. UoSAT expects to orbit 2-m resolution systems in the near future, at a similar price. The main limitation in smaller systems is telemetry bandwidth, which limits overall coverage. Higher-bandwidth telemetry demands higher-power systems, and all such systems are considerably larger than the Surrey designs.

14

Courtesy of Surrey Space Centre: http://www.ee.surrey.ac.uk


13

1.2.1.4 Landsat 5 (30 m), San Diego Multiple wavelength images (or multispectral) are most commonly applied to Earth resources. Landsat has been the flagship system for Earth resources studies of the Earth for over three decades. The low-Earth orbiting satellites image the whole Earth once every sixteen days. The Thematic Mapper (TM) sensors provide 30-m resolution imagery in seven spectral bands.15 The image in Fig. 1.12 was taken from three visible-wavelength sensors and combined to make a “true” color image. The top frame is one complete Landsat scene. Figure 1.13(a) shows a small segment covering San Diego Harbor. This image chip has been extracted to illustrate the highest resolution of the TM sensor. Note that the Coronado Bridge is just visible crossing from San Diego to Coronado Island. Long linear features like bridges and roads show up well in imagery, even if they are narrow by comparison to pixel size. In comparison to an imager like GOES, the penalty paid for this high spatial resolution is a reduced field of view—nominally 185 km across in any image.

1.2.1.5 Astronaut photography16 Landsat imagery gives a fair idea of what can be seen from space by the human eye. To further illustrate this, two images by astronauts, taken with handheld Hasselblad cameras from aboard the space shuttle, are included. Shuttle astronauts have produced a variety of noteworthy images over the years. Spatial resolution in such photographic images is comparable to that of Landsat, but resolution varies with the satellite’s altitude and the lenses used. The standard telephoto, a (250 mm optic) yields resolution similar to that of Landsat, as illustrated in the photographic image of San Diego in Fig. 1.13(b), which is typical of the NASA film libraries’ astronaut photography. For the Hasselblad cameras, the 250 mm optic would be considered a 3× telephoto lens. Figure 1.14 shows the effect of altitude. This photographic image of Egypt and Saudi Arabia was chosen because it is taken from an unusually high altitude for the shuttle, and a fairly large area can be seen. We find that North Africa and the Middle East are mostly cloud free, as with many Earth images.

15

The most recent system, Landsat 7, also offers a higher resolution panchromatic image with 15 m pixels. The resolution for the long wave infrared sensor is only 60 m. 16 Space photography by astronauts can be used for remote sensing analysis under some condi tions; see Robinson et al, “Astronaut acquired orbital photographics as digital data for remote sens ing: spatial resolution,” Int. J. Remote Sensing 23, pp. 4403 4438 (2002).

14

Chapter 1

Figure 1.12 Landsat 5 image of San Diego, May 7, 1996.

Figure 1.13 (a) Landsat 5 image enlarged, (b) Photographic image, STS064-080-021 (STS064 launch September 9, 1994).


15

Figure 1.14 Eastern Egypt, the Red Sea, and Saudi Arabia in a single view of the Near East (26.5N, 36.5E) from a 330-nautical-mile orbit on April 29, 1990. Easily seen are eastern Egypt, the Nile River, Lake Nassar, the Red Sea, and almost half of Saudi Arabia.17

1.2.1.6 SPOT (10 m) For over a decade, the highest-resolution commercial imagery available came from the French SPOT satellite. Featuring a panchromatic sensor with 10-m resolution, SPOT has been the companion to Landsat since 1986.18 Here an image of San Diego County provides a full frame of data, and an image chip details the harbor area and downtown. Looking at Fig. 1.15(b), note that the Coronado Bridge is sharper than in previous images. Details of the airport are apparent, and elements of information relevant to AOB start to emerge. The piers have emerged as distinct objects, and one detects ships’ movement in the water—or at least their wakes. Notice that the implicit conflict between coverage and spatial resolution has by now emerged explicitly. The two high-resolution cameras on SPOT each provide imagery of 60-km-swath width. Combined, this is still down from the 185 km provided by Landsat. This comparison of resolution and coverage has to be made with similar satellite generations—in particular with telemetry systems of comparable capacity.

17 18

NASA Photo ID: STS031 79 01, Film type: 70 mm. See http://images.jsc.nasa.gov The most recent SPOT satellite, SPOT 5, offers 2.5 m spatial resolution.

16

Chapter 1

Figure 1.15(a) SPOT-3 image of San Diego County. (b) San Diego Harbor, SPOT image.19

19

© CNES 1994, Courtesy SPOT Image Corporation


17

1.2.1.7 IRS (5 m) The Indian remote-sensing satellite, IRS-1C, launched in December 1995, provided the highest-resolution images available commercially for a 4-year interval before IKONOS was launched in 1999. The IRS system is included next to illustrate the capability of the 5–6-m resolution the Indian system offers. Equally important, the IRS illustrates the global nature of remote sensing, and how capabilities fare outside the major western powers. India has labored for a number of years under a burden of technology-transfer limitations, and it is noteworthy that one result has been the evolution of an indigenous manufacturing capability.20 Israel has exhibited similar prowess, and Surrey Satellite Technology provides many smaller countries with assets they can control. Figure 1.16 shows San Diego Harbor again. The inset is the entire “scene.” Note the substantially reduced coverage compared to the Landsat scene in Fig. 1.12. Once again, images from a common technology era are confined to similar numbers of bits or pixels—in other words, coverage is traded for resolution. In fact, the problem emerges simply in showing this image: the Coronado Bridge has been left out for lack of room. Following the paradigm at the beginning of the chapter, consider this scene in relation to AOB and NOB. What can you see (and not see) at 5–10-m resolution? Ships are now clearly visible in the water; can you see ships at the piers? There is at least one carrier docked on the north side of Coronado Island, homeport for the Kitty Hawk and Constellation. Can you identify any ships? What can you tell about San Diego’s airport? Given the length of the runways at Lindbergh field, can you estimate the length of the runways at Coronado Naval Air Station?

1.2.1.8 IKONOS—San Diego/Coronado Island The launch of the IKONOS satellite in 1999 dramatically changed the world of remote sensing. For the first time, imagery comparable to that obtained from military systems was widely available to civilians. IKONOS offers 1-m-spatial-resolution panchromatic imagery, and 4-m-resolution multispectral (color) imagery. Shown in Fig. 1.17 is a color image of San Diego taken on November 17, 1999. The Coronado Bridge, heretofore a rather tenuous, thin line, is now clearly defined, as are the many small watercraft in the harbor. Direct comparison with earlier systems is a bit hard; not only does the modern system have higher bandwidth, it has the ability to look off-nadir (sideways), thus dramatically improving revisit time. IKONOS can image any spot on Earth at 1-m resolution at 3-day intervals. Of

20

Neelam Mathews and Frank Morring, Jr., “Space in India: India’s space pioneer president de signs his nation’s future,” Aviation Week & Space Technology, p. 51 (Nov. 22, 2004).

18

Chapter 1

Figure 1.16 San Diego Harbor, IRS image.21

course, the whole scene is only 10 km on a side, so there is still a conflict between area coverage and resolution. See if you can locate the Hotel Del Coronado with its red-tile roof and “Coronado” written in the sand.

21

Courtesy of Space Imaging, Inc.


19

Figure 1.17 Coronado Island, San Diego, California, IKONOS.22

1.2.1.9 High-resolution airborne imagery Still higher resolution is possible, primarily from airborne platforms. In the last few years, electronic cameras have begun to replace film cameras, but the latter are still heavily used in the commercial imaging world. An illustration is shown here from a recent flight over San Diego Harbor. The resolution is better than 1 foot. Note the relatively large file size, a consequence of the relatively large area being imaged at high resolution.

22


20

Chapter 1

Figure 1.18 Three successive images are shown from an aerial photograph taken over San Diego Harbor (2004). The figure at the top left is the full frame, the figure above (top right) is a small chip from the 21,000 × 21,000 pixel image scanned from the film image. A further zoomed-in view of the 1.3 gigabyte file is shown at bottom left. The resolution is between 6 and 12 inches. Note the glare on the water, and how the wind-driven water waves show from above. The carrier is the USS Midway, part of an exhibit at the San Diego Maritime Museum.23 Images from Lenska Aerial Images.

1.2.2 Infrared (IR) The previous sections showed familiar visible imagery in a succession of resolutions. The remaining images illustrate some other important modalities in remote sensing—in particular, infrared imaging and radar. Infrared imagery differs from visible in two big ways: thermal IR works at night, and mid-wave infrared (MWIR)

23

http://www.navsource.org


21

Figure 1.19 GOES infrared imagery, July 11, 1995, 1800 UTC. The cloud colors provide information about their height (which varies with temperature) and water content.

and long-wave infrared (LWIR) data allow for non-literal information—meaning, for example, that you can extract temperatures.

1.2.2.1 GOES 9 A companion figure to Fig. 1.9 is shown here in Fig. 1.19. Infrared images from the GOES weather satellite again show much of the western hemisphere. Wavelength bands 3.9, 11, and 12 microns (often abbreviated as µm or simply µ) are encoded as red, green, and blue. Note that per weather convention, the gray scales are inverted: cold is brighter, dark is hotter, so that cold clouds will appear white. This image was taken in daylight in the western hemisphere. The solid earth is hotter than the

22

Chapter 1

oceans during the day, thus appearing dark, particularly over the western United States. The drier western states, with less vegetation, are hotter than the eastern side of the country. The Earth’s atmosphere decreases monotonically in temperature with altitude within the troposphere (the region with weather), and the cloud temperatures vary along with the ambient atmosphere. The character of infrared emission varies in wavelength with temperature, so the apparent color of the clouds in this presentation reflects cloud temperatures, and therefore height. 1.2.2.2 Landsat—IR San Diego Reflective infrared and thermal infrared data from Landsat 5 (the same scene as in Fig. 1.12) are shown encoded as an RGB triple in Fig. 1.20. Note how the hot as-

Figure 1.20 Landsat image taken May 7, 1996 – infrared wavelengths (bands 6, 5, and 7). (Red: 11 µm, Green: 1.65 µm, Blue: 2.2 µm).


23

phalt and city features are bright in the red (thermal) frequencies, while parks are green (cool, and highly reflective in shortwave IR).

1.2.2.3 DMSP—IR and microwave Imagery from the DMSP satellite was shown above in Fig. 1.10. DMSP also carries an infrared sensor, as illustrated below, and a sensor that measures microwave emissions that reflect moisture content in the atmosphere. Combined, these sensors provide a more complete weather picture than any one sensor. The views in Fig. 1.21 are complementary. The infrared image (top left) shows the clouds (again, white is coded as cooler, dark as warmer). The low-light image at upper right shows city lights to the northwest and a line of lightning extending from

Figure 1.21 DMSP: Visible, infrared, and microwave wavelengths. Microwave wavelengths are also emitted by thermal or blackbody radiators. Here, the 85 GHz band (0.3 cm) gives additional information on atmospheric water content.

24

Chapter 1

Florida towards the Yucatan Peninsula. The microwave data shown at lower left reflect water content in the clouds. 1.2.3 Radar (SAR) The third major remote sensing modality is radar. Radar sensors offer a day or night, all-weather capability that is important not only to the military, but to much of the civilian world. Tropical regions, in particular, are often clouded over, and earth resources work in those areas is difficult to conduct with systems like Landsat. Three civilian radar systems are currently in operation, the Canadian Radarsat-1, the European satellite (ERS-2), and the recently launched Japanese mission, ALOS. NASA flew the Shuttle Imaging Radar-C (SIR-C) as an imaging mission twice (and then a third time as the topographic-mapping mission). 1.2.3.1 RADARSAT, Maui and the airport Canada launched RADARSAT on November 4, 1995. The spacecraft is equipped with a C-band (5.6 cm), HH polarization, synthetic-aperture radar (SAR) capable of acquiring reasonably high-resolution images (nominally 25 m, but ranging from 8–100 m, depending on mode). The images have a swath width in the 50–500 km range, again depending on mode. The SAR data look substantially different at high resolution, which bothers some people. Figure 1.22 is an image of Maui. The full scene at left looks some-

Figure 1.22 RADARSAT image of Maui, Hawaii.24

24

RADARSAT 1 data © Canadian Space Agency, 1996. Received by the Canada Centre for Re mote Sensing. Processed and distributed by RADARSAT International.


25

Figure 1.23 SIR-C image of Maui. This image was acquired by Spaceborne Imaging Radar-C/X-Band Synthetic Aperture Radar (SIR-C/X-SAR) aboard the space shuttle Endeavour on April 16, 1994. The image is 73.7 km by 48.7 km (45.7 miles by 30.2 miles) and is centered at 20.8° north latitude, 156.4° west longitude. North is toward the upper left. The colors are assigned to different radar frequencies and polarizations of the radar as follows: Red is L-band, horizontally transmitted and received. Green is C-band, horizontally transmitted and received.25 Blue is the difference of the C-band and L-band channels.

what like a regular optical image, but the enlarged figure at right reveals the speckled nature of most SAR imagery. Note that the airfield on Maui is black, because the runways are very smooth compared to the wavelength of the radar—the radar’s energy bounces away from the satellite rather than return. The levels of gray in the water of the left image indicate differing wind speeds on the surface, which cause variations in the scattering coefficient of the water. The prevailing winds from the southwest cast a wind shadow in the lees of the islands. The brightness of the water depends on the amplitude of small wind-driven capillary waves. Wind speed and direction can be derived from SAR imagery—wind speeds within ~ 2 m/s of true wind speed, and 30–40° of true wind direction.26

25

See http://www.jpl.nasa.gov/radar/sircxsar/maui.html. Also see http://satftp.soest.hawaii.edu/ space/hawaii/nav/sirc.maui.html 26 Karen Bannerman, “Use of Space Borne Radar Data for Oil Spill Management,” presentation at the International Oil Spill Conference, Miami, FL, May, 2005.

26

Chapter 1

1.2.3.2 SIRC—Multi-wavelength/polarization 1.2.3.2.1 Maui Radarsat and ERS are limited to single wavelengths. By contrast, the SIR-C mission carried multi-wavelength, multi-polarization capability. A scene similar to the RADARSAT view above is shown here for Maui, Hawaii. Resolution is similar to that of RADARSAT. Figure 1.23 shows the results from imaging at different radar wavelengths. Radar is very sensitive to surface roughness, on the scale of the radar wavelengths—here 6 cm and 24 cm for the C and L bands, respectively. The light blue and yellow areas in the lowlands near the center are sugarcane fields. Differences in the vegetation cover on the middle flanks of East Maui can also be identified. Rain forests appear in yellow, while grassland is shown in dark green, pink, and blue. West Maui Volcano, on the lower left, is 1800 m high (5900 ft), and considered extinct. The entire eastern half of the island consists of East Maui Volcano, which rises to 3200 m (10,500 ft) and features a spectacular crater, Haleakala, at its summit. East Maui Volcano’s most recent eruption took place near the coast at the southwestern end of the volcano in the late 1700s. The different lava types (and ages), are partly revealed by variations in radar response.

1.2.3.2.2 SIRC, San Diego Harbor To conclude, San Diego is again presented. Fig. 1.24(a) shows a full SIR-C image scene; Fig. 1.24(b) shows a subset of the image for comparison with the visible and infrared images above. Burned areas in the center of Fig. 1.24(a) are dark, and the vegetated areas to the east of San Diego are greenish. In Fig. 1.24(b), the Coronado Bridge shows up rather well, bright against the dark water. Shelter Island, a sandspit in Mission Bay, almost disappears because the damp sand absorbs radar imagery [compare with Figs. 1.15(b) and 1.20].

1.3 Three Axes The sequence of images presented above has demonstrated the three dimensions associated with remote sensing imagery: the spatial, spectral, and temporal. Figure 1.25 illustrates these three dimensions, which are in general somewhat mutually exclusive. You can have high spatial resolution, but only at low temporal coverage (like Landsat: decent pictures, but only once every 16 days or so). You can have high temporal coverage (like GOES, once every 30 min), but then your spatial resolution is only 1 km. If you want spectral coverage (multispectral or hyper-spectral), you will pay a penalty in the other dimensions.


27

Figure 1.24(a) This image was acquired on October 3, 1994, by the Spaceborne Imaging Radar-C/X- Band Synthetic Aperture Radar (SIR-C/X-SAR) aboard the space shuttle Endeavour (Image P48773).

Figure 1.24(b) San Diego image from the Shuttle Imaging Radar, L-band and C-band data. Subset of image P48773.

28

Chapter 1

Figure 1.25 Three Dimensions for remote sensing.

Similarly, there is a conflict between resolution and field of view: image a larger area, and in general you will have lower spatial resolution. A fourth axis, polarization, has started to appear in the remote-sensing community as an additional dimension of information.

1.4 Additional Resources There are some classic and modern textbooks to note: •

•

•

• •

•

Remote Sensing of the Environment: An Earth Resource Perspective, published in 2000 by John R. Jensen is an excellent book by one of the top people in remote sensing. The classic text by Charles Elachi, Introduction to the Physics and Techniques of Remote Sensing, 1987, long out of print, has recently been reissued in a new edition (2006). A classic text by Lillsesand and Kiefer has been updated: Remote Sensing and Image Interpretation, by Thomas M. Lillesand, Ralph W. Kiefer, and Jonathan W. Chipman, 2003. A fairly geology oriented, but still excellent text by Floyd F. Sabins is Remote Sensing, Principles and Interpretations, 3rd Edition, 1996. The classic text: Fundamentals of Remote Sensing and Airphoto Interpretation, by Thomas Eugene Avery and Graydon Lennis Berlin, is rather dated even in its 5th edition, 1992, but is still a great reference with many illustrations. Physical Principles of Remote Sensing, by W. G. Rees, 1990, is a good compact text, extending into geophysical topics not addressed here.


• • • •

29

Introduction to Remote Sensing, by James B. Campbell, 1996, provides a good qualitative view of remote sensing, without equations. Manual of Photographic Interpretation, 2nd Edition, American Society for Photogrammetry and Remote Sensing, 1997. By far the best book on the topic of data analysis is Remote Sensing Digital Image Analysis: An Introduction, by John A. Richards, Xiuping Jia, 1999. There is a web-based Remote Sensing Tutorial written by Dr. Nicholas M. Short: http://rst.gsfc.nasa.gov/start.html.

1.5 Problems 1. List 5–10 elements of information that could be determined for NOB from imagery. Typical main elements are battle group, ships, submarines, ports, weather, personnel, C3, and medical. 2. What wavelengths of EM radiation are utilized in the images shown in this chapter? (This is really a review question, best answered after completing Chapter 2.) 3. Construct a table/graph showing the relationship between ground resolution and area of coverage for the sensors shown in this chapter. (Also a review question.) 4. Compare the various images of San Diego Harbor. What are the differences in information content for the high-resolution panchromatic systems (SPOT, IRS-1C), the multispectral system (Landsat, visible, and infrared), and the radar system. Which is best for lines of communication? Terrain categorization? Air order of battle? NOB?

In the next two chapters, the progression of energy (light) will be followed from the source (generally the sun) to detectors that measure such energy. Concepts of target reflectance and atmospheric transmission are developed, and the problem of transmitting data to the ground is discussed.

Chapter 2 Electromagnetic Basics

2.1 The Electromagnetic Spectrum We have discussed various remote sensing modalities and some characteristics of modern systems; at this point, it is necessary to review some basic physics. The chief thing to understand is the electromagnetic (EM) spectrum and EM radiation, of which light, radar, and radio waves are examples. We’ll look at the physical equations that underlie EM waves, the wave equations that result, their energy in the context of the photoelectric effect, sources of EM radiation, and some fundamental interactions of EM waves with matter. 2.1.1 Maxwell’s equations The principles that define electricity and magnetism were codified by Maxwell in the late 1800s in four equations that bear his name: Q

∫∫ E ⋅ dS = ε o ∫∫ B ⋅ dS = 0

∇ ⋅E =

or

∇ ⋅B = 0

∂

∫ E ⋅ d l = − ∂t ∫∫ B ⋅ dS ∂

∫ B ⋅ d l = µ o i + µ o ε o ∂t ∫∫ E ⋅ dS

ρ εo

or

or

33

or

∇×E= −

[2.1(a)]

[2.1(b)] ∂B ∂t

∇ × B =µ ο J + µ oε o

[2.1(c)] ∂E . ∂t

[2.1(d)]

34

Chapter 2

These four equations, respectively, say the following: a) The electric flux through a Gaussian surface is equal to the charge contained inside the surface. b) In the absence of a magnetic point charge, the magnetic flux through a Gaussian surface is equal to zero. c) The voltage induced in a wire loop is defined by the rate of change of the magnetic flux through that loop (the equation that defines electrical generators). d) A magnetic field is generated by a current (typically in a wire), but also by a time-varying electric field. These equations can be manipulated in differential form to produce a new differential inline equation, the wave equation in either electric or magnetic fields: ∇ 2E − ε o µ o

∂ 2E = 0 and ∂t 2

∇ 2B − ε o µ o

∂ 2B = 0. ∂t 2

(2.2)

Maxwell understood that the solutions to these equations were defined by oscillating electric and magnetic fields (E and B). In particular, these equations immediately give the speed of light: c = 1 / ε o µ o . The complexity of the solutions vary, but there are some fairly simple ones involving plane waves propagating in a straight line. Like all wave phenomena, the solution involves the wavelength, frequency, and velocity of the radiation. In equation form, a typical solution looks like this: z  E( z , t ) = Ex$ cos 2π  − ft λ 

or E( z , t ) = Ex$ cos( kz − ωt ),

(2.3)

which is the equation for a wave propagating in the plus z$ direction, with an electric field polarized in the x$ direction (more on polarization below). The various terms in this equation are defined as follows: E λ f c

= = = = = k =

amplitude of the electric field wavelength (in m) frequency in Hz (cycles/s) phase velocity of the wave (in m/s) angular frequency, ω = 2πf the wave number, k = 2π / λ .

The solution depends upon the wavelength and frequency, which are related by: λf = c.

(2.4)

Electromagnetic Basics

35

Figure 2.1 Four cycles of a wave are shown, with wavelength λ, or period τ. The wave has an amplitude A equal to 3.

For EM waves in a vacuum, the value of c = 2.998 × 108 (m/s), an important constant of physics. Note that the period τ is the inverse of the frequency, because for a wave it must be true that ω ⋅ τ = 2π or f ⋅ τ = 1. The angular frequency and wave number are somewhat less intuitive than the frequency and wavelength, but are standard terminology in describing waves.

2.2 Polarization of Radiation A subtle but important point is that E and B are both vectors. This vector character to EM radiation becomes important when we consider the concept of polarization. Familiar to most as an aspect of expensive sunglasses, polarization shows up in both optical observations and radar. A brief illustration of how EM waves propagate becomes necessary at this point. Figure 2.2 shows how the electric and magnetic fields oscillate with respect to one another in an EM wave (in a vacuum). The electric and magnetic fields are perpendicular to one another and to the direction of propagation k. These waves are transverse as opposed to longitudinal (or compressional) waves. The orientation of the electric field vector in the plane perpendicular to k defines the polarization direction. Here, linear polarization is illustrated—other forms of polarization are possible, but harder to illustrate.

2.3 Energy in Electromagnetic Waves The wave theory of EM radiation (and light) explains a great deal about phenomena we observe in physics, but at the turn of the 20th century, it became obvious that a different perspective was needed to explain some of the interactions of light and matter—in particular, processes such as the photoelectric effect (and similar processes important for detection of light). The inadequacy of the wave theory led to a resurgence of the idea that light, or electromagnetic radiation, might better be thought of as particles, dubbed photons. The energy of a photon is given by

36

Chapter 2

Figure 2.2 Polarization in an electromagnetic wave. Note that the electric field is perpendicular to the magnetic field (E⊥B), and both are perpendicular to the direction of propagation k. Following a typical convention, E is in the x direction, B is in the y direction, and the wave is propagating in the z direction. This same convention is used in Eq. 2.3.

E = hf,

(2.5)

where f = frequency of the EM wave (in Hz), and 6 .626 × 10 −34 J ⋅ s  h = Planck’s Constant =  . −15 4 .136 × 10 eV ⋅ s The electron-volt (eV) is a convenient unit of energy related to the standard metric unit (Joule) by the relation 1 eV = 1.602 × 10 19 Joules. Note that the conversion factor is just the charge of the electron. This is not coincidental, but rather a consequence of the definition of the non-metric unit. Photon energy E is determined by the frequency of EM radiation: the higher the frequency, the higher the energy. Though photons move at the speed of light (as would be expected for electromagnetic radiation), they have zero rest mass, so the rules of special relativity are not violated. Is light a wave or a particle? The correct answer is “yes.” The stance we employ really depends upon the process being observed, or the experiment underway. The applicable perspective often depends upon the energies (frequencies) of the photons. It is generally found that wave aspects dominate at frequencies below about 1015 Hz; particle aspects dominate at higher frequencies. In the visible part of the spectrum, both descriptions are useful. Figure 2.3 summarizes the concepts developed so far. Wavelength, frequency, and energy are plotted vertically with the labels we routinely use to define wavelength regions. Common abbreviations for wavelength are given. Note that the unit that might be expected for 10 6 m, the micrometer (µm), is generally termed the micron instead. The Angstrom is a non-metric unit, but nevertheless widely used, particularly by older physicists. The nanometer (nm) needs to be carefully distinguished from a


37

Figure 2.3 The spectrum of electromagnetic radiation.

nautical mile. Visible-light wavelengths correspond to wavelengths of ~ 0.5µm, and energies of 2–3 electron volts (eV). Example: The energy of the photons making up an electromagnetic wave (light wave) in the visible part of the spectrum that is green is E = hf = (4.14 × 10

15

) (6 × 1014 ) = 2.48 eV.

This energy is on the order of (or slightly less than) typical atomic binding energies. Energies of typical x-ray photons are in the 104 to 105 eV range, while the photons of a 100 MHz radio signal are only about 4 × 10 7 eV.

38

Chapter 2

2.3.1 Photoelectric effect The concept of energy in photons is very important for detector technology. One illustration is the photoelectric effect, a concept that won Albert Einstein the Nobel Prize. The phenomenon is typically described in the context of an experiment, as illustrated below. If light hits a metal surface in a vacuum, electrons are liberated from the surface and can be collected on a second surface—here, the collector plate. You can measure the energy of the electrons by applying a back bias (a negative voltage) to the collector plate, repelling the electrons. Electric potentials of one to two volts are typically sufficient to zero out the current. Traditional wave theory predicts that the amplitude of the current will vary with the amplitude (intensity) of the light, which it does. But wave theory is not able to explain an observed dependence on the wavelength (frequency) of the light. The higher the light frequency (the bluer the light), the greater the electron energy. Einstein combined the above concept, E = hf, with the idea of a work function, a fixed amount of energy necessary to liberate electrons from a metal surface—typically a volt or two. A classical laboratory experiment in the photoelectric effect is illustrated in Fig. 2.4. Light of varying wavelength is shone on a metal plate in a sealed vacuum cylinder. If the frequency is high enough, photons are emitted from the surface and propagate across a short gap to the collector plate. The collected electrons can be measured as a current. A calibrated voltage source is placed in the circuit to oppose the flow of the current. As the voltage is varied, the current varies. In this illustration, a mercury lamp with several distinct spectral lines is used, with results in Fig. 2.5.

Figure 2.4 Layout for demonstration of the photoelectric effect. The convention for the current is that it flows in the direction opposite that of the electrons.1 1

Courtesy Daedalon Corporation, PO Box 202.8, Salem, MA 01970.


39

In our illustration, light at three wavelengths is used: λ = 435.8 nm, 546.1 nm, and 632.8 nm (blue, green, and red). Calculating the energies corresponding to these wavelengths, we get, for blue as an example: E = hf =

= =

hc λ

4 .136 × 10 −15 eVs ⋅ 3 × 10 8 435 .8 × 10 −9 m 1.24 × 10 −6 4 .358 × 10 −7

m s

Figure 2.5 Results from a demonstration of the photoelectric effect using a mercury (Hg) light source.2

= 2 .85 eV.

Similarly, we get E = 2.27 eV and E = 1.96 eV for wavelengths of 546.1 and 632.8 nm, respectively. The experimental data shown below show that the total photon energy equals the electron energy plus the work function, or 2 E = hf = qW + Φ.

(2.6)

Table 2.1 Observations of the photoelectric effect.

Wavelength (nm)

Photon energy (eV)

Electron stopping potential, W (in volts)

Work function, Φ(eV)

435.8

2.85

1.25

1.6

546.1

2.27

0.7

1.6

632.8

1.96

0.4

1.6

2.3.2 Photomultiplier tubes The photoelectric effect demonstrates the idea that light (photons) has energy and also leads to our first example of how detectors work: the photomultiplier tube. This old technology is still in use, having evolved into modern technological devices such as night-vision scopes.

2

Courtesy Daedalon Corporation, Po Box 202.8, Salem, MA 01970.

40

Chapter 2

Figure 2.6 Sternglass Formula for Secondary Electron Yield. The Sternglass formula is the standard description for the yield of secondary electrons, as a function of incident electron energy. Sternglass published an expression for the secondary current by electron impact using the yield function:  E  E δ(E) = 7.4 δ m   exp −2    Em   Em     where the maximum yield (δm) and the energy at which it occurs (Em) vary from material to material. Illustrative values for glass (SiO2), for example, are δm = 2.9; Em = 420 eV.3

The front surface of the photomultiplier tube is a very efficient photoelectron source within the spectral range (and photon energy) of interest. An initial-incident photon produces a single electron (statistically, only about 70–90% of photons produce an electron), and the electron is multiplied through secondary emission, a close cousin of the photoelectric effect. This is the technology used in the DMSP/OLS-PMT detector, illustrated in Figs. 1.10 and 3.45. As illustrated in Fig. 2.6, secondary emission is a process that can generate multiple electrons for each electron hitting a surface. The yield varies with material, but is generally two or more for electron energies of a few hundred volts. This enables a process of amplification to occur as the electrons from each stage are moved along. A fairly standard, end-illuminated, photomultiplier-tube design is shown in Fig. 2.7. A typical tube will have 10 stages or so, with a net acceleration of 1–2 kV distributed over the stages. A photon incident on the alkali window on the left will be multiplied until a measurable charge pulse of 105 to 106 electrons is carried out on the anode on the right. Photomultiplier-tube technology has evolved into new forms that use fiber-optic bundles where the thin fibers are replaced with channels, or hollow tubes, again exploiting the multiplication process provided by secondary emission. Figure 2.8 illustrates how this technology works. These devices are the core of night-vision technology.

3

E.J. Sternglass, “Theory of secondary electron emission,” Sci. Pap. 1772, Westinghouse Re search Laboratory, Pittsburgh, PA (1954).


41

Figure 2.7 Hamamatsu photomultiplier tube.4

Figure 2.8 Micro-channel plate (image intensifier) design. A standard Hamamatsu product will be 1–10 cm in diameter, 0.5–1 mm thick, and have a channel pitch of 10–30 µm. They can be (and are) ganged together to increase the multiplication factor (104 for one stage, 106 for two stages, 108 for three stages). To form an image, a phosphor plate is put at the end of the stack.5

2.4 Sources of Electromagnetic Radiation

Now that we’ve defined electromagnetic waves and have an indication of how photons might be detected, let’s look at how EM waves are created. There are several major sources of electromagnetic radiation, all ultimately associated in some form with the acceleration (change of energy) of charged particles (mostly electrons). For remote sensing, these can be divided into three categories:

4

Photomultiplier Tubes Sales Brochure, TPMO0005E01, June 2002, Hamamatsu Photonics, KK. Hamamatsu Photonics, KK: Rectangular MCP and Assembly Series TMCP 1006E02, Decem ber 1999, Circular MCP and Assembly Series, TMCP1007E04, December 1999, and Image Intensifi ers, TII0001E2, September 2001.

5

42

• • •

Chapter 2

Individual atoms or molecules that radiate line spectra; Hot, dense bodies that radiate a continuous “blackbody” spectrum; and Electric currents moving in wires (aka, antennas).

2.4.1 Line spectra Single atoms or molecules emit light in a form called line spectra. An atom or molecule that is reasonably isolated (such as in a gas at ordinary temperatures and pressures) will radiate a discrete set of frequencies called a line spectrum. Conversely, if we pass radiation exhibiting a continuous spectrum of frequencies through a gas, we find that a discrete set of frequencies is absorbed by the gas, leading to a spectrum of discrete absorption lines. The wavelengths radiated (and absorbed) are characteristic of the atom or molecule in question, and thus present a powerful tool for determining the composition of radiating (or absorbing) gases. Line spectra analysis accounts for much of our knowledge of the chemical composition of stars (including the sun). The processes of absorption and emission of photons is reasonably well explained by the Bohr model of the atom, developed at the beginning of the 20th century, which uses the familiar atom-as-solar-system construct. This model has a nucleus at the center of the atom composed of heavy protons (+) and neutrons. The lighter electrons (–) orbit the nucleus at well-defined radii, which correspond to different energy levels. The closer they orbit the nucleus, the lower (more negative) their energy levels. As energy is given to the electrons, the radii of their orbits increase until they finally break free. Bohr hypothesized that the radii of the orbits were constrained by quantum mechanics to have certain values (really, a constraint on angular momentum). This produces a set of discrete energy levels that are allowed for the electrons. Bohr also claimed that the emission and absorption of energy (light) by an atom could only occur for transitions between the discrete energy levels allowed to electrons. Figure 2.9 illustrates the concept that photons are emitted (or absorbed) in changes of these discrete energy levels. See Appendix 1 for more careful analysis of the Bohr model. A few pages of mathematics in the appendix give the formula for the energy of the electrons orbiting in hydrogen-like atoms: 2

E 1  Ze 2  m E=−  = Z 2 12 ,  2 2  4πε 0 h  n n

(2.7)

where n = the quantum number: 1, 2, 3, …., Z = the atomic number, m = the electron mass, and e = the electron charge. The remaining terms are constants, and for Z = 1, we find that for hydrogen,


E1 = −

me 4 32π 2ε 20 h− 2

43

= –13.58 eV.

Figures 2.10 and 2.11 illustrate energy levels in Bohr’s model of the hydrogen atom. We find that the ionization energy, the energy necessary to remove the electron from its “well,” is 13.58 eV. If the electron gains somewhat less energy, it may move up to an excited state, where n > 1. For example, if an electron beginning in the ground state gains 10.2 eV, it will move up to the n = 2 level. Figure 2.9 Bohr Postulate: Photons are proIf the electron gains an energy of duced/destroyed by discrete transition in en13.58 eV or more, the atom will be ergy. completely ionized. Dropping down from n = 2 to n = 1, it will emit a photon of 10.19 eV energy, at a wavelength λ=

hc = 121.6 nm = 1216 Å. ∆E

If ∆E is expressed in electron-volts (eV), which it usually is, then the constant “hc” in the numerator can be written as hc = 4 .14 × 10 −15 ⋅ 3 × 10 8 = 1.24 × 10 −6 (eV m ), and thus the wavelength λ (in m) is given by λ ( m) =

1.24 × 10 −6 ∆E(eV )

or

λ ( nm ) =

1240 . ∆E(eV )

(2.8)

In general, transitions will occur between different energy levels, resulting in a wide spectrum of discrete spectral lines. Transitions from (or to) the n = 1 energy level (the ground state) are called the Lyman series. The n = 2 to n = 1 transitions compose the Lyman alpha (α) transition. This ultraviolet (UV) emission is one of the primary spectral (emission) lines of the sun’s upper atmosphere. The emission (or absorption) lines in the visible portion of the sun’s spectrum are the Balmer series, transitions from n > 2 to n = 2. Higher-order series are of less importance for our purposes.

44

Chapter 2

Figure 2.10 An energy-level diagram of the hydrogen atom, showing the possible transitions corresponding to the different series. The numbers along the transitions are wavelengths in units of angstroms, where 1 nm = 10 Å.6

Figure 2.11 The Balmer series: Hydrogen spectra in the visible region, in emission and absorption.

6

Adapted from: Atam P. Arya, Fundamentals of Atomic Physics, Allyn and Bacon, Boston, MA (1971).


45

Though the Bohr model was ultimately replaced by the solution of the Schrödinger equation and a more general form of quantum mechanics, it successfully predicts the observed energy levels for one-electron atoms and illustrates the quantum nature of the atom and associated energy levels. It is also a good beginning for understanding the interesting spectral characteristics that reflected and radiated light may exhibit in remote sensing applications.

2.4.2 Blackbody radiation Blackbody radiation is emitted by hot solids, liquids, or dense gases and has a continuous distribution of radiated wavelength as shown in Fig. 2.12. The curves in this figure give the radiance L in dimensions of Power / unit area • wavelength • solid angle, or units of Watts / m 2 µ ster. The radiance equation is

Radiance = L =

2 hc 2 λ

5

1 e

hc λ kT

−1

,

(2.9)

where c = 3 × 10 8 ms ; h = 6 .626 × 10 −34 J ⋅ s; k = 1.38 × 10 −23 J / K. It is a little easier to decipher the nature of the formula if it is rewritten slightly:

L=

 hc     λ kT 

5

2 2 x5 5 ( kT ) = ( kT ) 5 , hc c 3 h 4 e λ kT − 1 c3h 4 ex − 1

where the dimensionless term: x = ( hc / λ kT ) is defined. We see that the shape of this function of wavelength λ is unchanging as temperature changes; only the overall amplitude changes (and of course, the location of the peak in wavelength). Real materials will differ from the idealized blackbody in their emission of radiation. The emissivity (ε) of a surface is a measure of the efficiency with

(2.10)

Figure 2.12 Blackbody radiation as a function of wavelength.

46

Chapter 2

which the surface absorbs (or radiates) energy and lies between 0 (for a perfect reflector) and 1 (for a perfect absorber). A body that has ε = 1 is called a “blackbody.” In the infrared, many objects are nearly blackbodies—in particular, vegetation. Materials with ε < 1 are called graybodies. Emissivity (ε) will vary with wavelength. Note that some textbooks employ another form of Planck’s Law, featuring an extra π: Radiant Exitance = M =

Watts 2πhc 2 1 . hc 5 2 λ e λ kT − 1 m µ

(2.11)

The difference is that the dependence on angle of the emitted radiation has been removed by integrating over the solid angle. You can do this for blackbodies because they are “Lambertian” surfaces by definition—the emitted radiation does not depend upon angle, and M = πL. For our purposes, two aspects of the Planck curves are of particular interest: the total power radiated, which is represented by the area under the curve, and the wavelength at which the curve peaks λmax. The power radiated (integrated over all wavelengths) is given by the StefanBoltzmann law:  Watts  R = σεT 4  ,  m2  where

(2.12)

R = Power radiated per m2 ε = Emissivity (taken as unity for a blackbody)  W  σ = 5 .67 × 10 −8  2 4  (Stefan’s Constant) m K  T = Temperature of the radiator (in K)

Wien’s Displacement Law gives the wavelength at which the peak in radiation occurs: λ max =

a , T

for a given temperature T. The constant a has the value a = 2 .898 × 10 −3 ( m K ) , which gives λmax in meters if T is in Kelvin.

(2.13)


47

Example: Assume that the sun radiates like a blackbody (which is not a bad assumption, although we must choose two slightly different temperatures to match the observed quantities). (a) Find the wavelength λmax at which this radiation peaks. The solar spectral shape in the visible is best matched by a temperature of ~ 6000 K. (b) Find the total power radiated by the sun. The Stefan-Boltzmann law is best served by an “effective temperature” of ~ 5800 K.

(a)

λ max

−3 a 2 .898 × 10 ( m K ) = = = 4 .83 × 10 −7 m 6000K T

The spectrum peaks at ~500 nm, as illustrated in Fig. 2.13. (b) Next we can calculate R, the power emitted per m2 of surface. We use: R = σεT 4 and we assume that ε = 1 (blackbody). Evaluating, we get: R = 5 .67 × 10 −8 ⋅1 ⋅ 5800 4 = 6 . 42 × 10 7

W m2

To find the total solar power output we must multiply by the solar surface area, S첐 = 4 π R첐2, where R첐 = 6.96 × 108 m is the mean radius of the sun. Hence the total solar power output is: P첐 = R (4 π R첐2) = 4 π (6.96 × 108)2 × (6.42 × 107) P첐 = 3.91 × 1026 W The sun’s spectrum is shown in Fig. 2.13 with the spectrum of a 5800 K blackbody superimposed.7

7

Kenneth Phillips, Guide to the Sun, Cambridge University Press, pp. 83 84 (1992).

48

Chapter 2

Figure 2.13 The solar spectrum, based on the spectrum of Neckel and Labs, “The solar radiation between 3300 and 12500 Angstrom,” Solar Physics, 90, 205–258, 1984. Data file courtesy of Bo-Cai Gao, NRL. The peak occurs at about 460 nm (blue).

Figure 2.14 Solar spectrum as observed on Mount Haleakala.8

A somewhat different perspective on the visible band of the solar spectrum is obtained from an illustration created at the University of Hawaii. The dark lines superimposed on the rainbow scale, known as Frauenhofer lines, are solar-absorption features, due to the cool hydrogen, helium, and other elements just above the surface of the sun. These correspond to the dips in the solar irradiation curve illustrated above.

2.5 Electromagnetic Radiation (EMR)–Matter Interactions9 EM radiation that impinges upon matter is called incident radiation. For the Earth, the strongest source of incident radiation is the sun. Such radiation is called insolation (a shortening of incoming solar radiation). The full moon is the next strongest

8

Courtesy of the University of Hawaii, Institute for Astronomy, C.E.K. Mees Solar Observatory: http://www.solar.ifa.hawaii.edu 9 This section is adapted from the classic text by Thomas Eugene Avery and Graydon Lennis Berlin, Fundamentals of Remote Sensing and Airphoto Interpretation, Macmillan Publishing Com pany, New York (1992).


49

Figure 2.15 The four interactions defined here are somewhat artificial from a pure physics perspective, but are nonetheless extremely useful.10

source, but its radiant energy is only about a millionth that of the sun. Upon striking matter, EMR may be transmitted, reflected, scattered, or absorbed in proportions that depend upon:10 • • •

the compositional and physical properties of the medium, the wavelength or frequency of the incident radiation, and the angle at which the incident radiation strikes a surface.

These four fundamental energy interactions with matter are illustrated in Fig. 2.15. 2.5.1 Transmission Transmission is the process by which incident radiation passes through matter without measurable attenuation; the substance is thus transparent to the radiation. Transmission through material media of different densities (e.g., air to water) causes radiation to be refracted or deflected from a straight-line path with an accompanying change in its velocity and wavelength; frequency always remains constant. In Fig. 2.15, it is observed that the incident beam of light (θ1) is deflected

10

Ibid. Figure used with permission.

50

Chapter 2

toward the normal in going from a low-density to a denser medium (θ2). Emerging from the far side of the denser medium, the beam is refracted from the normal (θ3). The angle relationships in Fig. 2.15 are θ1 > θ2 and θ1 = θ3. The change in EMR velocity is explained by the index of refraction (n), which is the ratio between the velocity of EMR in a vacuum (c) and its velocity in a material medium (v): c n= . v

(2.14)

The index of refraction for a vacuum (perfectly transparent medium) is equal to 1, or unity. Because v is never greater than c, n can never be less than 1 for any substance. Indices of refraction vary from 1.0002926 for the Earth’s atmosphere to 1.33 for water to 2.42 for diamond. The index of refraction leads to Snell’s Law: n1 sin θ1 = n 2 sin θ 2 .

(2.15)

2.5.2 Reflection Reflection (also called specular reflection) describes the process whereby incident radiation bounces off the surface of a substance in a single, predictable direction. The angle of reflection is always equal and opposite to the angle of incidence (θ1 = θ2 in Fig. 2.15). Reflection is caused by surfaces that are smooth relative to the wavelengths of incident radiation. These smooth, mirror-like surfaces are called specular reflectors. Specular reflection causes no change to either EMR velocity or wavelength. The theoretical amplitude reflectance of a dielectric interface can be derived from electromagnetic theory and can be shown to be 11 r⊥ =

n1 cos θ1 − n 2 cos θ 2 , n1 cos θ1 + n 2 cos θ 2

and

r| | =

n 2 cos θ1 − n1 cos θ 2 , n 2 cos θ1 + n1 cos θ 2

2.16

where ⊥ corresponds to E being polarized perpendicular to the plane of incidence and || corresponds to E being polarized parallel to the plane of incidence.

11

See, for example, Eugene Hecht, Optics, 4th Ed., Addison Wesley, Boston, MA (2001).


51

Here n1, θ1 and n2, θ2 are the refractive indices and angles of incidence and refraction in the first and second media, respectively. (Snell’s law defines θ2; other versions of these equations can be obtained as a function of the incident angle, but they are more tedious to present.) Here, r is the ratio of the amplitude of the reflected electric field to the incident field. The intensity of the reflected radiation is the square of this value. Figure 2.16 shows the intensity as a function of incident angle for typical air-to-glass values of the index of refraction. The difference between these numbers is why light reflected from surfaces like water becomes highly polarized. 2.5.3 Scattering Scattering (also called diffuse reflection) occurs when incident radiation is dispersed or spread out unpredictably in many directions, including the direction from which it originated (Fig. 2.15). In the real world, scattering is much more common than reflection. Scattering occurs with surfaces that are rough relative to the wavelengths of incident radiation. Such surfaces are called diffuse reflectors. The velocity and wavelength of electromagnetic waves are not affected by scattering. Variations in scattering manifest themselves in varying characteristics in the bidirectional reflectance distribution function (BRDF). For an ideal, Lambertian surface, this function would nominally be a cosine curve, but the reality generally varies quite a bit. Aside from the world of remote sensing, BRDF (also rendered BDRF) is also much studied in computer graphics and visualization. Figure 2.17 shows consequences of the variation in the scattering function from the NASA Terra satellite, orbiting at 700 km altitude, and the Multiangle Imaging Spectroradiometer (MISR). At left is a “true-color” image from the downward-looking (nadir) camera on MISR. This image of a snow-andice-dominated scene is mostly shades of gray. The false-color image at right is a composite of red-band data taken by the MISR’s forward 45.6°, nadir, and aft 45.6° cameras, displayed in Figure 2.16 Fresnel equations. Both curves 1 (100% reflection) as the incident blue, green, and red colors, respec- approach angle approaches 90°. Note that there is a tively. Color variations in the right im- range of incident angles for which the intenage indicate differences in angular sity of the parallel component is very small.

52

Chapter 2

Figure 2.17 Multiangle imaging spectroradiometer (MISR) images of Hudson Bay and James Bay, Canada, February 24, 2000. This example illustrates how multiangle viewing can distinguish physical structures and textures. The images are about 400 km (250 miles) wide with a spatial resolution of about 275 m (300 yards). North is toward the top. Photo credit: NASA/GSFC/JPL, MISR Science Team (PIA02603).

reflectance properties. The purple areas in the right image are low clouds, and light blue at the edge of the bay is due to increased forward scattering by the fast (smooth) ice. The orange areas are rougher ice, which scatters more light in the backward direction. 2.5.4 Absorption Absorption is the process by which incident radiation is taken in by a medium. For this to occur, the substance must be opaque to the incident radiation. A portion of the absorbed radiation is converted into internal heat energy, which is subsequently emitted or reradiated at longer thermal infrared wavelengths.


53

2.6 Problems 1. MWIR radiation covers the 3–5 µm portion of the EM spectrum. What energy range does this correspond to in eV? 2. Show that 1 µm corresponds to roughly 1 eV. This is a useful fact to memorize. 3. What frequency is an X-band radar? What wavelength (look in Chapter 8)? 4. What is the ground-state energy for an He+ ion in eV? Note that Z = 2. 5. Calculate the energy (in eV), frequency (in Hz), and wavelength (in m, µm, nm) for the n = 4 to n = 2 transition in a hydrogen atom (note that Z = 1). This is the Balmer-β transition. 6. Calculate the radiance L(λ) for T = 1000 K from λ = 0–20 µm, and plot. Note that this is a calculation exercise, and you should be sure you can obtain the correct answer with a hand calculator at a minimum of 2 wavelengths, say 3 and 10 µm. 7. Calculate the peak wavelength for radiation at T = 297 K, 1000 K, and 5800 K (in µm and nm). 8. Calculate the radiated power for a blackbody at 297 K in watts/m2. Assume a blackbody (ε = 1). Assume a surface area of 2 m2, and calculate the radiated power in watts. 9. From the formula for blackbody radiation, consider the element: x 5 / e x − 1. For what value of x does this function have a maximum? From that, can you obtain Wien’s Law? This turns out to be a difficult problem if you use calculus. A more straightforward approach is to plot the function of x using a calculator or computer. 10. Snell’s law problem: For an air-water interface, one can use typical values: n1 = 1; n2 = 1.33. For such values, calculate θ2 if θ1 = 30°. What is the speed of light in water? What is the angle for the reflected ray? 11. The formula for the amplitude of the reflectance of an incident EM wave, given in Eq. 2.16, simplifies nicely for normal incidence (θ = 0°). The equations both n − n2 . Now the intensity of the reflected EM wave (light) goes reduce to r = 1 n1 + n 2 as the square of the electric field, so for unpolarized incident light, the intensity of the light goes as 2

 n − n2  R= 1  .  n1 + n 2  For a light wave incident on glass, coming from air, calculate R. Use n1 = 1 for air, and n2 = 1.5 for glass. Does this correspond to your experience when looking out a window from a lit room at night?

Chapter 3 Visible Imagery

This chapter discusses remote sensing in the visible EM spectrum, beginning with images and technology from the first remote sensing satellites (the Corona spy satellites) and concluding with a look at several optical imaging satellites, particularly the Hubble Space Telescope (HST).

3.1 The First Remote Sensing Satellite: Corona 3.1.1 A little history Corona was America’s first operational space-reconnaissance project. It was developed as a highly classified program under the joint management of the CIA and USAF, a relationship that evolved into the National Reconnaissance Office (NRO). For context, note that the first Soviet satellite, Sputnik, was launched on October 14, 1957, and Van Allen’s Explorer spacecraft flew on a Redstone rocket on January 31, 1958. President Eisenhower approved the Corona program in February 1958. This proved to be farsighted, because when Francis Gary Powers was shot down in a U-2 on May 1, 1960, the president was forced to terminate reconnaissance flights over the Soviet Union (see the newspaper in Fig. 3.1). The first Corona test launch, on February 28, 1959, was the first of 12 failed missions in the Discover series (a cover name)—seven involving launch, five involving satellite and camera malfunctions. Mission 13 yielded the first successful capsule recovery from space on August 10, 1960.1 The first high-resolution images

1

The United States’ Explorer 6 transmitted the first (electronic) space photograph of Earth in Au gust 1959; the spin stabilized satellite had TV cameras. These images, apparently now lost, predate the more official first civilian images from space taken by TIROS 1, launched in April 1, 1960 (shown in Chapter 7). See http://msl.jpl.nasa.gov/Programs/explorer.html; and http://nssdc.gsfc.nasa.gov/, NSSDC ID: 59 004A 05.

55

56

Chapter 3

Figure 3.1 The New York Times, August 20, 1960. Note the other headlines at this time.2

from space were taken on the next mission, August 18, 1960. The last Corona mission, number 145, was launched May 25, 1972; the last images were taken May 31, 1972. Curiously, signals intelligence got a slightly earlier start; the launch of the first GRAB satellite on June 22, 1960, launched the electronic intelligence discipline into space. Early imaging resolution was on the order of 8–10 m, eventually improving to 2 m (6 ft). Individual images on average covered approximately 10 miles by 120 miles. The system operated for nearly 12 years, and over 800,000 images were taken from space. The declassified image collection includes 2.1 million ft of film in 39,000 cans. The subsequent KH-7 mission acquired imagery with resolutions of 2–4 ft beginning in July 1963, with much smaller imaging areas.3 3.1.2 The technology The Corona concept was to use film cameras to record images for a few days, then drop the film using a recovery vehicle. The film containers were de-orbited and re-

2 3

1960 The New York Times Company. Reprinted by permission. Jeffrey T. Richelson, “A ‘Rifle’ in Space,” AF Magazine 86 (June 2003).

Visible Imagery

57

covered by Air Force C-119 (and C-130) aircraft while floating to Earth on a parachute. The system adapted aerial-photography technology with a constantly rotating, stereo, panoramic-camera system [Figs. 3.2(a), 3.2(b), and 3.3]. The low orbital altitudes (typically less than 100 miles), and slightly elliptical orbits eased some of the problems associated with acquiring high-spatial-resolution imagery. The “Gambit” series of KH-7 satellites flew at even lower altitudes with initial perigees as low as 120 km. Appendix 2 provides details on the Corona missions. 4 The cameras, codenamed “Keyhole,” began as variants on products designed for aerial photography. The first cameras, the “C” series, were designed by Itek and built by Fairchild. Two counter-rotating cameras, pointing forward and aft and viewing overlapping regions, allowed for stereo views (Fig. 3.4). The cameras used long filmstrips, 2.2 in. × 30 in., and an f/5.0 Tessar lens with a focal length of 24 in. The first images had a ground resolution of 40 ft, based on a film resolution of 50–100 lines/mm. (Advances in film technology by Kodak were some of the most important technological advances in the Corona program. Kodak developed a special polyester base to replace the original acetate film.) Improved camera, lens, and film design led to the KH4 series cameras, with Petzval f/3.5 lenses, still at 24 in. focal length. With film resolutions of 160 lines/mm, it was possible to resolve ground targets of 6 ft. Corona (KH4) ultimately used film ranging in speeds from ASA 2 to 8—only a few percent of the sensitivity, or speed, of consumer film. This is the tradeoff for high film resolution and one reason that very large optics were needed.5 The great majority of Corona’s imagery was black and white (panchromatic). Infrared film was flown on Mission 1104; color film was flown on Missions 1105 and 1108.6 Photo-interpreters did not like the color film, however, because resolution was lower. Tests showed color as valuable for mineral exploration and other Earth resources studies, and its advantages led indirectly to the Landsat satellites. Note that the Soviet Union has maintained a film-return reconnaissance technology. Russia launched Kosmos 2410, a film return system, on September 24, 2004. The satellite was launched at an inclination of 67.12° with perigee on the order of 200 km, apogee of about 300 km. The satellite lifetime is only a few months at those altitudes.

4

Jeffrey T. Richelson, “A ‘Rifle’ in Space,” AF Magazine 86 (June 2003). See also www.lib. cas.cz/www/space.40/1963/028a.htm for old Corona satellite orbit parameters. 5 Dwayne A. Day, John M. Logsdon, and Brian Latell (Eds.), Eye in the Sky: The Study of the Co rona Spy Satellites, Smithsonian Institution Press (1998). 6 Ibid. Example: Mission 1108, KH 4B, 12/04/69. Cameras operate satisfactority. The mission carried 811 ft. of aerial color film added to the end of the film supply.

58

Chapter 3

Figure 3.2(a) KH4B, artist’s concept.7

Figure 3.3 A U.S. Air Force C-119, and later, a C-130 (shown here) modified with poles, lines, and winches extending from the rear cargo door captures a capsule ejected from a Discoverer satellite. Reportedly, this was considered by some to be the least likely part of the whole process—catching a satellite in midair.8

7

Figure 3.2(b) KH4B or J3 camera. DISIC= Dual Improved Stellar Index Camera.7

Figure 3.4 The KH4B cameras operated by mechanically scanning to keep the ground in focus. The paired cameras provided stereo images, which are very helpful for estimating the heights of cultural and natural features.

Courtesy of the National Reconnaissance Office (NRO): http://www.nro.mil Note that a subsequent NASA attempt to replicate this technique failed. The Genesis satellite crashed on September 8, 2004 because the parachute failed to deploy properly. It made a sizable hole in the Utah desert. AW&ST, Sept. 12, 2004; http://www.nasa.gov/mission pages/genesis/main/in dex.html

8

Visible Imagery

59

Figure 3.5 Corona satellite in the Smithsonian. The recovery vehicle is to the right.

3.1.3 Some illustrations The first Corona image was taken of the Mys Shmidta airfield. Figure 3.6 shows that the resolution was high enough to discern the runway and an adjacent parking apron. Eventually, systems got better, and higher resolution images were acquired. Figure 3.7 shows two relatively high-resolution images of the Pentagon and the Washington monument in Washington DC. Declassified imagery is available from the U.S. Geological Service (USGS).9 Of course, the whole point was to spy on the Soviet Union. Figure 3.8 shows the Severodvinsk Shipyard, a North Sea port for the USSR, on February 10, 1969. The large rectangular building in the center is the construction hall, and the square courtyard to its left is where vessels (submarines) are launched. The curved trail of disturbed snow and ice is where

9

See http://edc.usgs.gov/guides/disp1.html

Figure 3.6 Mys Shmidta Airfield, USSR. This August 18, 1960, photograph is the first intelligence target imaged from the first Corona mission. It shows a military airfield near Mys Shmidta on the Chukchi Sea in far northeastern Russia (Siberia, 68.900°N 179.367°W just across some forbidding water from Barrow, Alaska, at very similar latitude). North is at upper left. Credit: National Reconnaissance Office (NRO).

60

Chapter 3

Figure 3.7 Washington DC. (a) One always-popular target: the Pentagon. September 25, 1967. (b) Notice the shadow cast by the Washington Monument in September 1967. Credit: NRO.

Figure 3.8 Severodvinsk Shipyard, February 10, 1969, Corona (KH4).

submarines are floated into the river. The satellite is on a southbound pass over the port facility.10 The image of Severodvinsk is a chip from a much larger scene shown in Figs. 3.9 and 3.10. The strips are perpendicular to satellite motion, which in this frame must have been towards the southeast. Note the horizon images on the edges

10

Dwayne A. Day, John M. Logsdon, and Brian Latell (Eds.), Eye in the Sky: The Story of the Co rona Spy Satellites, Smithsonian Institution Press (1998).

Visible Imagery

61

Figure 3.9 Coverage map for Corona. Map derived from USGS.

Figure 3.10 Three consecutive Corona images. The shipyard in Fig. 3.8 is in the third frame, just under the word “Severodvinsk.” Note the ends of the film strips: “When the satellite’s main camera snapped a picture of the ground, two small cameras took a picture of the Earth’s horizon at the same time on the same piece of film. The horizon cameras helped interpreters calculate the position of the spacecraft relative to the Earth and verify the geographical area covered in the photo.”11

11

Courtesy of the Smithsomian National Air and Space Museum: http://www.nasm.si.edu

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Figure 3.11 (a) The arrows indicate the number of bombers compared to transport planes. (b) An image chip for the bombers indicated in the figure is displayed here. Credit: NRO.

of the film strips, showing the rounded Earth. These images from the horizon cameras provided reference/timing information as the system scanned from horizon to horizon. Figure 3.11 shows illustrations of a Soviet airfield, and a good example for AOB. This Corona mission on August 20, 1966, captured an image of Soviet heavy bombers at Dolon airfield in the Soviet Union. The 5–10 foot ground resolution of the Keyhole camera systems was sufficient to distinguish classes of aircraft, allow-

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ing them to be counted. Some indications of readiness state can be obtained by the locations of the aircraft and activity around the airframes.

3.2 Atmospheric Absorption, Scattering, and Turbulence In the previous chapter we looked at the illumination of objects by sunlight and the reflectance or scattering of light from those objects. As we follow the photons along their paths, we move in sequence from the atmosphere (in this section) through optical systems (in the next section) and then on to the detectors. There are three limiting factors that the atmosphere introduces into remote sensing. These are absorption (typically by atomic and molecular processes), scattering (primarily due to aerosols like dust, fog, and smoke), and turbulence (due to fluctuations in the temperature and density of the atmosphere). 3.2.1 Atmospheric absorption: wavelength dependence The atmospheric factor that most limits Earth observation is absorption—particularly absorption by water, carbon dioxide, and ozone, in roughly that order. Figure 3.12 shows atmospheric absorption calculated for a standard atmosphere at ground level (note that the horizontal axis is logarithmic). The calculations were done with MODTRAN, the standard USAF code for modeling atmospheric absorption and scattering. Regions shaded dark blue are atmospheric windows, that is, spectral regions that are largely transparent to EM radiation. By contrast, regions such as the spectral range from 5–7 µm are dominated by water absorption. The at-

Figure 3.12 Atmospheric absorption. Transmission curves calculated using MODTRAN 4.0, release 2. The U.S. standard atmosphere, 1976, is defined in the NOAA publication with that title, NOAA0S/T-1562, October 1976, Washington DC, stock # 003-017-00323-0.

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mosphere is opaque in this spectral range. Ozone shows its presence in a small spectral absorption band centered at 10 µm. 3.2.2 Atmospheric scattering Electromagnetic radiation (photons) is scattered by various particles in the Earth’s atmosphere. This scattering is caused by collisions between the photons and scattering agents that range from molecules (and atoms), suspended particulates (aerosols), and clouds (water droplets). Scattering is somewhat arbitrarily divided into three domains as a function of the relationship between the wavelength and the size of the scattering agents (atoms, molecules, and aerosols). Rayleigh, or molecular, scattering in the optical spectrum is primarily caused by oxygen and nitrogen molecules, whose effective diameters are much less than optical wavelengths of interest. Typical molecular diameters are 1–10 Å. The process of Rayleigh scattering is highly dependent on wavelength. The probability of scattering interactions is inversely proportional to the fourth power of wavelength (λ 4). This is illustrated in Fig. 3.13. The bottom-most (dashed) curve in the figure is the Rayleigh scattering term. The preferential scattering of blue wavelengths explains why the clear sky (i.e., with low humidity and few aerosols) appears blue in daylight. The blue wavelengths reach our eyes from all parts of the sky. This is why photographers who want to take clear panoramic photographs with black-and-white film use a yellow

Figure 3.13 Atmospheric scattering diagram.12 12

Adapted from P.N. Slater, “Photographic Systems for Remote Sensing,” in Manual of Remote Sensing, 2nd ed., R.N. Colwell (Ed.), American Society for Photogrammetry and Remote Sensing (ASPRS), Falls Church, VA, pp. 231 291 (1983).

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or red filter: it allows the less-scattered light to be captured on film for a sharper overall image. It is a strong motivating factor in choosing the wavelength response for satellite imagers, which typically exclude blue wavelengths. As the relative size of the scattering agent increases, the scattering processes evolve toward Mie scattering. The dependence of the scattering probability on wavelength decreases, and the scattering directionality evolves as well. For Rayleigh scattering, the probability of scattering is roughly equal in all directions; as the particle size increases, the probability of forward scattering increases. Mie scattering produces the almost white glare around the sun when a lot of particulate material is present in the air. It also gives the white light from mist and fog. Important Mie scattering agents include water vapor and tiny particles of smoke, dust, and volcanic ejecta—all particles comparable in size to the visible and infrared wavelengths used in remote sensing. Mie scattering is important in the determination of the performance of IR systems, particularly in littoral (coastal) environments. Depending upon the size distribution, shape, and concentration of scattering particles, the wavelength dependence varies between λ 4 and λ0. Scattering agents that are still larger (more than 10× the photon wavelength) cause particles to scatter independently of wavelength (non-selective in Fig. 3.13). This happens with the water droplets and ice crystals of which clouds and fog are composed, showing itself in the gray hues of fog. Such scattering causes the sunlit surfaces of clouds to appear a brilliant white. Large smog particles, if not possessing special absorption properties, turn the color of the sky from blue to grayish white. The combined effects of scattering and absorption are illustrated in Fig. 3.14. The figure is designed to indicate the impact of atmospheric absorption on light

Figure 3.14 Atmospheric absorption and scattering. Transmission curve calculated using MODTRAN 4.0, release 2. Conditions are typical of mid-latitudes, with the 1976 U.S. standard atmosphere assumed. The overall broad shape is due to scattering by molecular species and aerosols.

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transmitted from ground to space, as would be observed by a high-altitude satellite. Note that the spectral range is extended beyond that in the illustration above. The absorption due to ozone becomes very significant below 0.35 µm, and the atmosphere is opaque to sunlight below 0.3 µm, due to the ozone layer at altitudes of 20–40 km. Note that, overall, the atmosphere is more transparent in the long-wave infrared (11–12 µm) than in the visible spectrum (0.4–0.7 µm). 3.2.3 Atmospheric turbulence The third limiting factor in remote sensing through the atmosphere—atmospheric turbulence—is the answer to the question, why do the stars twinkle? Figures 3.15 and 3.16 illustrate. Light propagating through the atmosphere will encounter small perturbations of density and temperature, due to atmospheric turbulence. Small irregularities in density produce variations in the index of refraction, which in turn cause small fluctuations in the direction in which the light propagates (Snell’s law), on the order of one part in a milFigure 3.15 The apparent position of lion. These irregularities in the atmospheric a star will fluctuate as the rays pass boundary layer (the bottom of the atmothrough time-varying light paths. sphere) have characteristic scale sizes of tens of meters, and fluctuate on timescales of milliseconds to seconds. The impact of atmospheric turbulence is much greater for telescopes looking up through the atmosphere than for sensors looking down at Earth. Figure 3.16 shows how atmospheric turbulence affects stellar observations. Adaptive optics technology (not developed here), uses optical technology to compensate for the flickering direction of the incoming light. Figure 3.16 shows the “first light” image for the adaptive-optics system on the 3.5-m telescope at the Starfire Optical Range, taken in September 1997. The image on the left is the uncompensated image; the compensated image is on the right. In summary, three environmental factors constrain the resolution possible with an imaging system: absorption, scattering, and turbulence.

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Figure 3.16 This astronomical I band (850 nm) compensated image of the binary star Kappa-Pegasus (k-peg) was generated using the 756-active-actuator adaptive-optics system. The two stars are separated by 1.4544 µrad. The images are 128 × 128 pixels; each pixel subtends 120 nanoradians. The FWHM of the uncompensated spot is about 7.5 µrad —about 5 times the separation of the two stars.13 Note on nomenclature: Astronomy IR bands are H (1.65 µm), I (0.834 µm), J (1.25 µm), and K (2.2 µm).

3.3 Basic Geometrical Optics The sequence of physical processes considered here has followed the photons from the source (generally, the sun for visible imaging) and through the atmosphere. The energy now needs to be detected by a sensor. This requires an optical system and detectors. The simplest aspects of optical systems are considered here; our primary concern is the factors that define resolution. 3.3.1 Focal length/geometry The most fundamental equation in optics is the thin-lens equation: 1 1 1 = + . f i o

(3.1)

Here f is the focal length, an intrinsic characteristic of the lens determined by the radius of curvature and the index of refraction of the lens material (or materials). The

13

Courtesy of AFRL

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distances from the center of the lens to the object o and to the image i are the other two parameters. We see that the focal length defines the image distance when o, the object distance, is infinity (∞). In the illustration here, the object distance is twice the focal length, so the image distance is also twice the focal length (i = o = 2f ).

Figure 3.17 The thin-lens law.

3.3.2 Optical diagram: similar triangles, magnification The old geometry law holds that similar triangles determine the size of the image—the magnification is equal to the ratio of the image distance to the object distance. In the example above, the two are equal, so the image has the same size as the object. Normally, in remote sensing, the object distance is a large number, while the image distance is roughly the focal length. For example, the Hasselblad camera used by early astronauts was typically used with a 250 mm lens at an altitude of 150 km. So the ratio of image size to object is 250 × 10 −3 / 150 × 10 3 = 1.6 × 10 −6 , which is a pretty small number. The Monterey Peninsula (extending some 20 km from north to south in central California) would be imaged on a piece of film 32 mm

Figure 3.18 Magnification: similar triangles.

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in length (about half the width of the 70-mm film rolls). The Corona (KH4) missions introduced at the beginning of this chapter had 61-cm focal-length optics. 3.3.3 Aperture (f/stop) The light-gathering ability of a lens is defined by its diameter. More sensitive optical systems have larger (faster) optics. The effectiveness of a given aperture depends upon the focal length (the magnification). This dependence is defined by the concept of the f-number (f/#), or f/stop, as the ratio of the focal length to the lens (or mirror) diameter: f/# =

Focal Length . Diameter of the Primary Optic

(3.2)

Typical lenses found on amateur cameras will vary from f/2.8 to f/4. High-quality standard lenses will be f/1.2 to f/1.4 for 35 mm cameras. The longer the focal length (the higher the magnification), the larger the lens needs to be to maintain a similar light-gathering power. The longer the focal length, the harder it is to create a fast optic. A telephoto for a sports photographer might be 500 mm and might at best be f/8 (question: what is the diameter implied by that aperture?). Note that two different quantities are being referred to as “f” here, following optical convention. One is the focal length; the other is the aperture. As mentioned at the beginning of this chapter, the KH4-B cameras had a focal length of 24 inches and were 5–10 inches in diameter (see the appendix on Corona cameras). Apertures of f/4 to f/5.6 are typical of the early systems. By contrast, we’ll see that the Hubble Space Telescope is characterized by aperture values of f/24 and f/48, depending on the optics following the big primary mirror. Supplemental topic: Optical systems made with lenses need to pay attention to the transparency of the material in the spectral range of interest. Glass is transparent from ~400 nm into the infrared. UV sensors and MWIR/LWIR sensors need to be constructed from special materials making them much more expensive. 3.3.4 Image formation by lens or pinhole Once the image has formed on the focal plane (for example, on film), an image can be recorded. This is illustrated by a pair of images taken with a 35 mm camera. The image on the left in Fig. 3.19 was taken with a normally employed 50 mm lens.14

14

In photography, “normal” means that if you print the image on an 8 × 10 piece of paper, and hold it at arm’s length, it will appear as the scene did in real life.

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Figure 3.19 Two images of the shoreline. The pinhole is effectively a 50 mm lens stopped down to an aperture of approximately 0.57mm, or approximately f/100.

The image to the right was taken with the same camera, but without the lens. Instead, a piece of aluminum foil was pierced with a pinhole and fastened on a lens cap at the front of the camera, approximately 50 mm from the film plane. The pinhole’s diameter was approximately 1% that of the normal lens. The pinhole image obtained is fuzzy; the smaller the pinhole, the sharper the image will be. The problem with a small aperture is, of course, relatively long exposure time. A limit is eventually reached as diffraction effects emerge, as described in the next section.

3.4 Diffraction Limits: the Rayleigh Criterion In addition to geometrical issues in optics, we must consider the impact of physical principles that depend upon the wave character of light. One manifestation of this wave character is diffraction—the fact that light can diffuse around sharp boundaries. Diffraction applies equally to sound and ocean waves, which have scales of distance we’re more familiar with. Diffraction leads to a fundamental, defining formula for the limitation in angular (spatial) resolution for any remote sensing system: the Rayleigh criterion. The Rayleigh criterion is traditionally presented in the one-dimensional (1D) case, where an infinite single slit is considered. This is illustrated in Fig. 3.20. The somewhat out-of-scale figure shows light rays incident on a slit. For purely geometrical optics, there would be a white spot on the surface below, corresponding to the size of the slit. Instead, there is a central maximum with a width determined by the wavelength of the light, the width of the slit, and the distance from the slit to the surface below, or range.

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The intensity goes as: 2

ax  sin (Φ )  I ∝ , with Φ = 2π ;  Rλ  Φ 

(3.3)

a is the width the of the slit, x is the distance along the target surface away from the center line, R is the range, and λ is the wavelength. The function in brackets is the familiar sinc function, which has magnitude one at Φ = 0, then drops to zero at Φ = π. This occurs when:

2π

ax = π , or Rλ

x λ = . R 2a

Figure 3.20 Single slit diffraction pattern.

(3.4)

The width of the central maximum is just twice this value, and we get a wellknown result: that the angular width of the first bright region is ∆θ = 2x / R = λ / a. Note that the secondary maxima outside this region can be important, particularly in the radar and communications worlds—these are the sidelobes in the antenna pattern of a rectangular Figure 3.21 Single slit diagram for the geantenna. ometry of the diffraction pattern. What does this have to do with optical systems? The concept means that for a finite aperture, there is a fundamental limit to the angular resolution, which is defined by the ratio of the wavelength to the aperture width or diameter. The formula applies exactly to rectangular apertures, as will be seen in the radar section (Chapter 8): The Rayleigh criterion: ∆θ =

λ , D

(3.5)

where ∆θ is the angular resolution, and D is the aperture width. This formula needs to be modified for circular apertures. The result is effectively obtained by taking the

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Fourier transform of the aperture shape, which for a circular aperture results in a formula involving Bessel functions:  J (w)  I ∝ 1  ,  w  2

with w J1 a r R λ

= = = = = =

(3.6)

2πar / R λ , the J Bessel function of order 1, lens radius, distance from center line, distance from lens to screen, and wavelength.

This function is illustrated in Fig. 3.22. The first zero occurs where w = 3.832, which leads to a relatively famous result, that the radius of the “Airy disk” = 0.61λ × distance/lens radius, or that the angular resolution of a lens is:

∆θ = 0 .61 ⋅

λ , a

or

Figure 3.22 Airy pattern for diffraction from a circular aperture.

∆θ = 1.22 ⋅

λ . diameter

(3.7)

So what are the implications? As angular resolution improves, two adjacent objects become separable, as illustrated in Fig. 3.23. The concept is generally best understood in astronomical applications, where ∆θ is the angular separation between two stars. In the figure, it can be seen that the two stars can just be distinguished when their angular separation is ∆θ, as defined in Eq. 3.7. The concept extends directly into terrestrial applications, however, and defines the ground separation distance (GSD), which is the product of ∆θ and the range from sensor to target. Note that there are again secondary maxima outside the main beam, which again would be sidelobes for a circular antenna. Application: Consider a Hubble-like system orbiting at an altitude of 200 nautical miles, or 370 km, and assume it is nadir-viewing, so that the range is just the altitude.

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Figure 3.23 (a) Two objects (stars) separated by a distance x just corresponding to the Rayleigh Criteria for a cylindrical optic. (b) Here are two point targets at a range of 400 km. The objects are separated by 10 m, so the angular separation is ~25 µrad. The wavelength is 0.5 µm. The four images shown here illustrate what happens as the diameter of the optic (mirror or lens) varies over the range: 12.2, 24.4, 36.6, and 48.8 mm. The second image from the bottom matches the Rayleigh criterion—the objects are separated by ∆θ = 1. 22 ⋅ λ / D = 25. µrad and can just barely be distinguished. The two at top are separated by twice ∆θ.

Mirror diameter = 96 in. = 2.43 m Wavelength = 5000 Å = 5 × 10 7 m λR 5 × 10 −7 ⋅ 370 × 10 3 GSD = ∆x = 1.22 = 1.22 ⋅ = 9.3 × 10 −2 m a 2 . 43 = 9.3 cm or 3.7 in.

3.5 Detectors Following optics, the next primary element in any sensor system is the detector. There are two primary detection techniques: film and electronic. We’ll discuss film systems briefly, and then modern solid-state electronic systems.

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Figure 3.24(a) The silver bromide grains of an x-ray film emulsion (2,500 diameters).

Figure 3.24(b) Cross section of the unprocessed emulsion on one side of an x-ray film. Note the large number of grains as compared to the developed grains in the figure at right.

Figure 3.24(c) Cross section showing the distribution of developed grains in an x-ray film emulsion exposed to give moderate density.

3.5.1 Film15 Film is made up of two elements, a flexible, transparent base, and a light-sensitive emulsion, generally a gelatin containing a radiation-sensitive silver compound. These silver salts undergo subtle atomic changes when exposed to light. Treating the exposed film with a chemical solution called a developer causes a reaction to take place that results in the formation of black, metallic silver. It is this silver, suspended in a gelatin, that constitutes the image. Figure 3.24, taken from a Kodak illustration, shows how the grains appear and the range of grain sizes [Fig. 3.24(a)], and then how the grains change with exposure and development. The resolution of film depends on the size of these silver grains—higher resolution requires finer grain. The tradeoff is that faster, or more sensitive, films require larger silver-halide grains (think larger cross-section, and higher chance of a photon hitting the crystal). For the Corona missions, Kodak developed special films that had very high resolution (100–160 lines/mm), but were correspondingly slow. The large optics helped compensate for the low sensitivity. 3.5.2 Solid state Generally speaking, the detectors involved in remote sensing utilize arrays of solid-state detectors, much like the charge-coupled devices (CCDs) in modern video cameras and digital still cameras. This rather broad statement about the class of sensors also termed focal plane arrays (FPAs) does not properly account for the many sensors flying linear arrays (1D focal planes), as on SPOT, or even the ongoing use of single-detector sensors such as on GOES and Landsat. Still, the underlying physics is similar.

15

Used with permission of Eastman Kodak Company.

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Figure 3.25 This photograph was taken on Kodak Tri-x pan film—an old standby for action photography, which was characteristically grainy. The small box on the gutter defines the expanded region. The image was scanned at 4000 lines per inch, so the 135 pixels correspond to 0.857 mm (0.03375 in.).

There are a number of possible approaches to electronic detection of optical radiation. The focus here is on “intrinsic” (bandgap) detectors, which is the design used for most silicon (CCD) focal planes.16 Photo-emissive technology was introduced in Chapter 2 in the discussion of photomultiplier tubes and image intensifiers. As with Bohr atoms, solid materials (in Figure 3.26 Energy band gap illusparticular, semiconductors) have a distribution tration. of energy levels that may be occupied by electrons. Generally, electrons reside in a state corresponding to the ground state of an individual atom, termed the valence band. There is then a gap in energy (a

16

See Craig McCreight, “Infrared detectors for astrophysics,” Physics Today (February, 2005).

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“bandgap”) that represents a range of energies that are forbidden for the electron to occupy. If a photon hits the semiconductor, however, it can give energy to an electron in the valence band, exciting it up into the conduction band. The significance is that it is now possible for the electron to move as if in a conductor, and it can be collected and measured. This is the essence of the detection mechanism for most solid-state detectors. Their efficiency varies, but typically 40–80% of incident photons with sufficient energy can be detected. For silicon, the maximum efficiency occurs in the near infrared, from 0.9–1.0 µm. This simple description makes it possible to understand some of the more important constraints in the use of solid-state detectors. First, one must match the energy bandgap to the energy of the photons to be observed. The photon energy must be greater than the size of the bandgap, which varies with material.17,18 Table 3.1 Bandgap energies for common semiconductors.

Material

Bandgap energy (eV) at 300 K

Silicon (Si)

1.12

Germanium (Ge)

0.66

Gallium Arsenide (GaAs)

1.424

Indium Antimonide (InSb)

0.18

Platinum Silicide (PtSi)

0.22

Lead Sulfide (PbS)

0.35–0.40

Mercury Cadmium Telluride (HgCdTe)

0.1 to 0.3

How do these values limit the use of different materials as detectors? Taking silicon as the most common example, we recall from Chapter 2 the equation that relates wavelength to the energy in a transition: λ=

hc . ∆E

(3.8)

Here, ∆E is the bandgap energy (in eV) and we use: λ=

−6 hc 1.24 × 10 (eV m ) = = 1.1 × 10 −6 m, or 1.1 µm. 1.12 eV ∆E

17 George Rieke, Detection of Light From the Ultraviolet to the Submillimeter, 2nd edition, Cam bridge University Press (2003). 18 S.M. Sze, Physics of Semiconductor Devices, Wiley, New York (1981), and Charles Kittel, In troduction to Solid State Physics, Wiley, New York (1971).

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So, the visible and the first part of the near-infrared spectrum can be detected with silicon detectors. This is reflected in their common use in modern cameras. The detection of longer wavelength photons requires materials such as HgCdTe, or InSb. The relatively small band gaps cause a problem, however. At room temperature, the electrons tend to rattle around, and every now and then one will cross the gap, due to thermal excitation. This process is largely controlled by the exponential term that comes from the “Maxwell-Boltzmann” distribution (or bell-shaped curve), which describes the velocities, or energies, to be found in any collection of objects (whether electrons, atoms, or molecules) in a thermal equilibrium: N2 =e N1

E2 − E1 kT

bandgap energy

⇒ number ∝ e thermal energy (kT)

(3.9)

If these electrons are collected, this becomes part of a background noise known as the dark current. To prevent this, the materials must be cooled—typically to 50–70 K, which requires liquid nitrogen at least, and for some applications, liquid helium

Figure 3.27 Rough guide to the spectral ranges of use for different focal-plane materials. HgCdTe is abbreviated as MCT: MerCadTelluride.19

19

Courtesy of Boeing.

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(4 K). Mechanical refrigerators can also be used, but are problematic in space applications because they generally have relatively short lifetimes, and can introduce vibration into the focal plane, which is bad. Some recent NASA missions have used a long-lived pulse-tube technology developed by TRW, with apparent success. The importance of cooling is illustrated here with a calculation:

Use HgCdTe, assume a bandgap of 0.1 eV, and compare the nominal number of electrons above the bandgap at room temperature (300 K) and at 4 K. Note that the conversion factor k in the term kT is: 1.38 × 10 −23

Joules Kelvin

1.6 × 10 −19

Joules eV

= 8 .62 × 10 −5

eV Kelvin

T = 300 K: kT = 0 .026 eV ; T = 4 K , kT = 0 .00035 eV

number ∝ e

band gap energy thermal energy ( kT )

 − 0.1 −3. 8 = 0 .02 at 300 K e 0.026 = e = 0.1 e − 0. 00035 = e −286 ≈ 0 at 4 K 

At room temperature, the exponential is small, but reflects a non-negligible number of excitations of electrons above the bandgap energy. At the temperature of liquid helium, the electrons sit quietly below the band gap. Figure 3.27 shows the wavelength and temperature ranges that may be used for a variety of materials. Note how longer wavelengths fairly uniformly require lower temperatures.

Visible imaging cameras uniformly use silicon as the sensitive element. Typical commercial infrared imaging systems use InSb, PtSi, and HgCdTe (e.g., the FLIR Systems family of cameras). In addition, there are two popular new technologies: quantum-well (QWIP) and microbolometer detectors. The latter in particular offers a variety of advantages over the more traditional cooled semiconductor systems, as discussed below. 3.5.3 Focal plane arrays The photosensitive component of a detector can exist as a single element, and there are a number of operational systems that nominally have a single detector. A notable current example would be the GOES weather satellite, described later. Generally, however, newer systems feature either rectangular arrays (as in digital cameras) or

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linear arrays of pixels, as will be seen below for IKONOS, with an array of 1 × 13,500 pixels. A CCD is an array of sensitive elements. The CCD is an integrated circuit (IC) with the unique property that a charge held in one cell of the IC can be shifted to an adjacent cell by applying a suitable shift pulse. Information defined by the amount of charge can be shifted from cell to cell with virtually no loss. This characteristic allowed the devices to be used as a memory device. When it was further discovered that the construction could be altered so that individual cells also responded to incident light while retaining the ability to shift charges, the concept of a solid-state imager emerged. In a CCD, each picture element, or pixel, converts incoming light into an amount of charge directly proportional to the amount of light received. This charge is then clocked (shifted) from cell to cell, to be finally converted to a video signal that represents the original image, at the output of the CCD. The detector resolution is defined by the pitch, or spacing, between individual pixel elements on the focal plane, which is typically very close to the size of the pixel. Modern silicon sensors generally have a pitch on the order of 5–10 µm. More exotic materials generally have somewhat larger values for the detector pitch. 3.5.4 Uncooled focal planes: microbolometers20 One problem with the technology behind semiconductor detectors is the need for cooling. Either a coolant (e.g., liquid nitrogen) or a mechanical refrigerator is required. The former is awkward in the field and limited for space use, because only so much coolant can be brought along. Mechanical devices are generally troublesome and tend to fail in space applications. Consequently, there is significant motivation to develop alternatives. Energy detectors, as opposed to the photon detectors described above, are emerging as an important alternative for remote sensing systems.

20

Figure 3.28 Thermally isolated resistor (200 µm × 200 µm), used in a microscopic Wheatstone bridge. Current enters from top left and exits through the bottom right. As the sensor heats, changes in its resistance can be measured with great sensitivity.

For a purely mechanical approach, some people are working on micro cantilever systems. See, for example, http://www.sarcon.com/research & dev/ir sensor concept/slide1.htm

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Microbolometer techniques approach detection by sensing the change in temperature of a sensitive element, typically by measuring its resistance. This allows the direct detection of “heat,” as opposed to counting photons directly. Consequently, such detectors do not need to be cooled. Commercial IR cameras are now using these detectors, and they are very popular for applications such as firefighting. These cameras are not as sensitive as photosensitive technologies and may not offer the spatial resolution of traditional approaches, because the pixel pitch is generally fairly large, on the order of 50 µm with current detectors.

3.6 Imaging System Types Remote sensing systems can be divided into a handful of basic types, depending on the form of imaging technology used. These distinctions affect the resolution and sensitivity of the system, and to a certain extent, the quality of the data. 3.6.1 Framing systems—mostly film systems (Corona) Framing systems are those that snap an image, much like a common film camera or a digital camera (still or video). An image is formed on a focal plane and stored via chemical or electronic means (film or CCD, respectively). Variations on this technique are used by some air-photo systems, and in the early Corona satellites, where the film is moved in concert with the satellite motion for longer exposure and better focus. Figure 3.29(a) illustrates such a system. The wide-field planetary camera (WFPC) on the Hubble is an example of this approach, as well as the early UoSat cameras (Fig. 1.11). 3.6.2 Scanning systems 3.6.2.1 Cross track (Landsat MSS, TM; AVIRIS) Sensors such as those on the GOES weather satellite and Landsat system consist of a small number of detectors—from one to 32 or so in the systems described later in the text. The sensor is swept from side to side, typically via an oscillating mirror, while the system flies along a track. The image is built up by the combined motion of the optic and the platform (aircraft or satellite), as shown in Fig. 3.29(b). Such sensors are called “whiskbroom” sensors.

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Figure 3.29(b) Cross-track scanner.

Figure 3.29(a) Framing system.

3.6.2.2 Along track (SPOT HRV) Linear detector arrays are used in systems such as the SPOT HRV sensor, the IKONOS camera, and the Quickbird sensor. The cross-track dimension is covered by the linear array, while the along-track direction is covered by the motion of the satellite. This type of sensor is termed “push broom”; Fig. 3.29(c) illustrates its use. Note how the pixels in the detector map to a line on the ground. Geometrical optics defines the map from detector pixel to the spot on the ground.

21

Figure 3.29(c) Push broom system.21

From Thomas Eugene Avery and Graydon Lennis Berlin, Fundamentals of Remote Sensing and Airphoto Interpretation, Macmillan Publishing Company, New York, 1992.

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3.7 Hubble: The Big Telescope The science and technology of remote sensing involves the propagation of light from source to subject to sensor and relies on an understanding of the platform (or satellite bus) and the processes that transmit remotely sensed imagery to the ground. The Hubble Space Telescope serves to illustrate all these elements in the image chain. 3.7.1 The Hubble satellite The Hubble Space Telescope (HST) was deployed April 25, 1990, from the space shuttle Discovery (STS-31). Hubble is large, with a 2.4-m diameter mirror that allows remarkable access to the distant universe, unimpeded by atmospheric absorption, scattering, and turbulence. It is useful to ponder that the 100" Hooker Telescope installed at the Mt. Wilson Observatory was the largest telescope in the world from 1917–1948. Edwin Hubble used this telescope for decades. Seven decades later, a telescope of the same size was put in orbit. From a space-operations perspective, one of the remarkable things about the satellite has been the four missions flown to date by which the space observatory was repaired and updated.

Figure 3.30 The initial deployment of the Hubble Space Telescope.

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Figure 3.31 The Hubble satellite.

HST is roughly cylindrical, 13.1 m end-to-end and 4.3 m in diameter at its widest point. The ten-ton vehicle is three-axis stabilized. Maneuvering is performed via four of six gyros, or reaction wheels. Pointing can be maintained in this mode (coarse track) or through fine-guidance sensors (FGSs) that lock onto guide stars to reduce drift and assure pointing accuracy. Hubble’s pointing accuracy is 0.007 arc sec (0.034 µrad). Power to the system electronics and scientific instruments is provided by two 2.4 × 12.1 m solar panels, which provide a nominal total power of 5 kW. The power generated by the arrays is used by the satellite system (about 1.3 kW) and scientific instruments (1–1.5 kW), and to charge the six nickel-hydrogen batteries that power the spacecraft during the roughly 25 min/orbit in which HST is within the Earth’s shadow.22

22

Dr. J. Keith Kalinowski, NASA/GSFC, private communication, August 3, 1999.

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Communications with Hubble are carried on via the Tracking and Data Relay Satellites (TDRS) (see appendix A3). Observations taken during the time when neither TDRS is visible from the spacecraft are recorded and dumped during periods of visibility. The spacecraft also supports real-time interactions with the ground system during times of TDRS visibility. The primary data link is at 1024 kbps, using the S-Band link to TDRS.23 The system routinely transfers a few GB per day to the ground station. Data are then forwarded to NASA/GSFC via landlines. Table 3.2 Hubble Space Telescope launch and engineering characteristics.

Launch date/Time

1990-04-25 at 12:33:51 UTC

On-orbit dry mass

11600.00 kg

Nominal power output

5000 W (BOL)

Batteries

Six—60 Amp-hour NiMH

Orbital period

96.66 m

Inclination

28.48°

Eccentricity

0.00172

Periapsis

586.47 km

Apoapsis

610.44 km

Science data telemetry rate

TDRS, S-Band, SA, 1024 kbps

Engineering telemetry rate

TDRS, S-Band, MA, 32kbps

3.7.2 The repair missions Hubble has been serviced four times; first on the STS-61 shuttle mission launched on December 2, 1993, which was the fifth flight of the Endeavour orbiter. During several days of extra-vehicular activity (EVA), the crew installed corrective optics (COSTAR) in the light path after removing the high-speed photometer (HSP) instrument, replaced the older wide-field/planetary camera (WF/PC) with a newer version (WFPC 2), and replaced malfunctioning solar arrays. The COSTAR helped correct the effects of the unfortunate spherical aberration caused by incorrect grinding of the Hubble mirror. The next repair was made from shuttle mission STS-82, launched on February 11, 1997. The STS-82 mission again involved repairs and instrument swapping. During several days of EVA, the crew replaced a failed FGS, swapped one of the reel-to-reel tape recorders for a solid-state recorder, and exchanged the original Goddard High-Resolution Spectrograph (HRS) and the UCSD Faint Object Spec-

23

Daniel Hsu, Hubble Operations Center, private communication, January 7, 2005. Science data are all 1Mbps (real time or playback).

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Figure 3.32 From STS-82, the second service mission, February 19, 1997. New solar arrays have not been deployed yet (S82E5937, 07:06:57).

trograph (FOS) with the Space Telescope Imaging Spectrograph and the Near Infrared Camera and Multi Object Spectrometer (NICMOS). In addition to scheduled work, astronauts discovered that some of the insulation around the telescope’s light shield had degraded, so several thermal-insulation blankets were attached to correct the problem. Repair mission 3A was launched December 19, 1999. During three spacewalks, astronauts replaced all six Hubble gyroscopes. Four had failed, the fourth failing in November 1999, thus accelerating the launch schedule. With only two gyros, the satellite was nonoperational, and had been put in safe mode. Astronauts installed new battery-voltage regulators, a faster central computer, a fine-guidance sensor, a data recorder, and a new radio transmitter. The telescope was released from Discovery on Christmas day (5:03 p.m. CST). Shuttle Columbia was launched for the fourth service mission on March 1, 2002 (STS-109). New rigid solar arrays, coupled with the new power-control unit, were installed, generating 27% more electrical power, an increase that roughly doubled the power available to scientific instruments (curiously, the original control algorithms designed for satellite pointing became useful for the first time.) A new camera, the Advanced Camera for Surveys (ACS), was installed. The ACS replaced the Faint Object Camera, the last of Hubble’s original instruments. With a wider field of view and sensitivity to wavelengths ranging from ultraviolet to the far red (115–1050 nm), ACS supplanted the WFPC2 sensor as the primary survey instrument. A final service mission was scheduled for 2004, but the Columbia disaster in October 2003 has caused that mission to be significantly delayed, if not cancelled.

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3.7.3 Operating constraints There are two important constraints on satellite behavior, that will affect most LEO satellites.

3.7.3.1 South Atlantic anomaly Above South America and the south Atlantic Ocean lies a lower extension of the Van Allen radiation belts called the south Atlantic anomaly (SAA). No astronomical or calibration observations are possible during spacecraft passages through the SAA because of the high background induced in the detectors. SAA passages limit the longest possible uninterrupted exposures to about twelve hours (or eight orbits). This phenomenon compromises almost all low-Earth-orbit imaging systems, though not to the same extent as astronomical systems, which depend on very low background count rates in the detector.

3.7.3.2 Spacecraft position in orbit Because HST’s orbit is low, its atmospheric drag is significant, varying according to the orientation of the telescope and the density of the atmosphere (which depends on the level of solar activity). The chief manifestation of this effect is that it is difficult to predict where HST will be in its orbit at a given time. The position error may be as large as 30 km within two days of the last determination. This effect also impacts Earth-observing systems and can cause significant pointing errors for high-spatial-resolution systems. Systems such as Quickbird update their satellite ephemeris information once an orbit. 3.7.4 The telescope itself The Hubble is an f/24 Ritchey-Chretien Cassegrain system with a 2.4-m-diameter primary mirror and a 0.3 m secondary mirror. The Cassegrain design for the Hubble is very common among satellite systems. The primary mirror is constructed of ultra-low-expansion silica glass and coated with a thin layer of pure aluminum to reflect visible light. A thinner layer of magnesium fluoride is laid over the aluminum to prevent oxidation and reflect ultraviolet light. The secondary mirror is constructed from Zerodur, a very-low-thermal-expansion (optical) ceramic. The effective focal length is 57.6 m. Figure 3.33 illustrates the optical design for the telescope. The distance between the mirrors is 4.6 m, and the focal plane is 1.5 m from the front of the primary mirror. The angular resolution at 500 nm is 0.043 arc sec (0.21 µrad). The fine guidance sensors (FGS) view through the primary optic. The off-axis viewing geometry does not interfere with imaging, and allows use

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Figure 3.33 Hubble optics. The mirrors are hyperboloids, the secondary is convex. The primary has a focal length of 5.5 m and a radius of curvature of 11.042 m. The secondary has a focal length of –0.7 m and a radius of curvature of 1.358 m. The bottom image is an accurate ray trace for the Cassegrain telescope.24

of the large primary optic for the necessary detector resolution. Note that a requirement for the spacecraft was a pointing accuracy (jitter) of 0.007 arc sec. This was more easily achieved after the first set of solar arrays was replaced. The flexible array design vibrated rather badly every time the satellite moved from sun to shadow, or shadow to sun—that is, twice an orbit. This design error required redesign of the satellite pointing control algorithms.

24

Courtesy of Lambda Research (using OSLO): http://www.lambdares.com

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Figure 3.34 The primary mirror of the Hubble telescope measures 2.4 m (8 ft) in diameter and weighs about 826 kg (1820 lbs). By comparison, the Mt. Wilson 100 inch solid glass mirror weighs some 9000 pounds.25 The center hole in the primary mirror has a diameter of 0.6 m.

It was soon found that there was a more serious problem with the Hubble: the mirror was not ground to quite the right prescription, and it suffered from spherical aberration (too flat by about 4 µm at the edges.) As a consequence, new optics designs were created, and a corrective optic was added for the existing instruments (COSTAR). Subsequent scientific instruments, such as the WFPC2, built corrections into the optics. 3.7.5 Detectors—Wide Field and Planetary Camera 2 The Hubble normally carries four or five distinct sensors. The Wide Field and Planetary Camera 2 (WFPC2) is described below. Hubble’s scientific instruments are mounted in bays behind the primary mirror. The WFPC2 occupies one of the radial bays, with an attached 45° pickoff mirror that allows it to receive the on-axis beam. (The best image quality is obtained on-axis.)

25

Courtesy of Mt. Wilson Observatory: http://www.mtwilson.edu

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Figure 3.35 Top Left: A Faint Object Camera (FOC) image of a star taken prior to the STS-61 shuttle mission to service the HST, during which astronauts installed COSTAR. The broad halo (one-arc sec diameter) around the star is caused by scattered, unfocused starlight. Top Right: Following installation, deployment, and alignment of COSTAR, starlight is concentrated into a 0.1-arc sec diameter circle, STSci-PRC1994-08; Bottom Left: The central region of the Active Galaxy NGC 1068, FOC pre-COSTAR. Bottom Right: NGC 1068, with COSTAR, early January, 1994, at a distance of 60 million light years. STSci-PRC1994-07. Both courtesy of the Space Telescope Science Institute (STSci).26

26

See http://www.spacetelescope.org, http://www.hubblesite.org, and http://www.seds.org/messier/ more/m077 hst.html

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Figure 3.36 WFPC2 optics. Light enters the optical train from the main telescope at left.

The WFPC2 field-of-view is distributed over four cameras by a four-faceted pyramid mirror near the HST focal plane. Each of the cameras contains an 800 × 800 pixel Loral CCD detector. Three wide-field cameras operate at f/12.9, and each 15-µm pixel images a 0.10 arc sec portion of the sky. The three wide-field cameras cover an L-shaped field of view of 2.5 × 2.5 arc min. The fourth camera operates at 0.046" (0.22 µrad) per pixel (f/28.3) and is referred to as the planetary camera. This sensor is therefore operating at the full resolution of the telescope. The fourth camera observes a smaller sky quadrant: a 34" × 34" field (note that 34" is 34 arc sec, not 34 inches.) This is a sufficiently large field of view to image all the planets but Jupiter. The spectral range lies from approximately 1150C to 10,500C. Exposure times range from 0.11 to 3000 seconds. 3.7.5.1 Example: Diffraction and resolution limits 3.7.5.1.1 Rayleigh criteria The angular resolution for the telescope is given as 0.043" (arc sec), with the slightly larger value of 0.046" for the combined Hubble/WFPC2 system. These values include all the effects that are ignored in the simplest approximation to the Rayleigh criteria, ∆θ = 1.22 λ / lens (mirror) diameter. A few numbers are tested here, assuming a deep blue wavelength (410 nm): ∆θ =

1.22 ⋅ 4 .1 × 10 −7 m = 2 .08 × 10 −7 radians. 2. 4 m

Compare this to the given value

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91

Figure 3.37 This image of Mars was taken with the WFPC2 on March 10, 1997, just before Mars opposition, when the red planet made one of its closest passes to Earth (about 100 million km). At this distance, a single picture element (pixel) in WFPC2’s planetary camera spans 22 km on the Martian surface. The image is less than 335 pixels across—the Martian diameter is 6794 km. This picture was created by combining images taken with blue (433 nm), green (554 nm), and red (763 nm) filters. Credit: STScI-PRC97-09, March 20, 1997, David Crisp (JPL) and the WFPC2 Science Team.

∆θ =

0 .043 arc sec 2π rad ⋅ = 2 .08 × 10 −7 rad. s s ° 360 60 min 60 deg

Applying this value to the hypothetical problem of the ground resolution that Hubble would have if pointed down, we get:

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Figure 3.38 For the Hubble/WFPC2 combination, altitude is 600 km, detector size is 15 µm, and focal length is 57 m.

GSD = ∆θ ⋅ altitude = 2 .08 × 10 −7 ⋅ 600 × 10 3 (m) = 0 .12 m. If Hubble were pointed downward, you would get a GSD of 12 cm. The calculations can be repeated for 0.046 arc sec, but the increase is only a few percent.

3.7.5.1.2 Geometric resolution The above implies that the detector has infinite resolution. In reality, however, it does not. Using the concept of similar triangles shown previously and the values for the detector’s pixel size, given above, we can compare detector resolution to the best resolution offered by the telescope: GSD pixel size , = altitude focal length

GSD =

giving

(3.10)

pixel size 15 × 10 −6 ⋅ altitude = ⋅ 600 × 10 3 = 0 .16 m , focal length 57

which is slightly worse than the best the telescope can do—the airy disk from a distant star, or a small bright light on the ground, would not quite fill one detector pixel. The detector is undersampling the image.

3.8 Commercial Remote Sensing—IKONOS and Quickbird The world of remote sensing changed dramatically on September 24, 1999, with the successful launch of the IKONOS satellite by Space Imaging Corporation. The subsequent launch of the Quickbird satellite by Digital Globe on October 18, 2001 emphasized the dramatically new world that imaging reconnaissance had become.

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Figure 3.39 First light image from IKONOS of the Jefferson memorial, September 30, 1999.27

Images with spatial resolutions of 1 m or better were now available for any customer willing to pay for the imagery. Satellite and instrument characteristics for the two satellites are enumerated in the table below. IKONOS and Quickbird differ in design; Quickbird is unique for not using a Cassegrain. Both use store-and-dump telemetry systems. Space Imaging uses a large number of ground stations; Digital Globe uses one or two (northern) high-latitude ground stations. Both companies suffered system loss in their initial launches. Digital Globe, launching after Space Imaging, lowered the orbit of their satellite to provide higher spatial resolution and provide an economic advantage over its competitor. A larger focal plane allowed them to maintain a larger swath width.

27


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Chapter 3 Table 3.3 Commercial systems.

IKONOS

Launch information

Orbit

Quickbird

Date:

September 24, 1999

October 18, 2001

vehicle

Lockheed Martin Athena II rocket

Delta II

Location

Vandenberg Air Force Vandenberg Air Force Base, California Base, California

altitude

681 km

450 km

period

98 min

93.4 min

inclination

98.1 deg

98 deg

pan*

1-m (nominal at < 26 deg off nadir)

0.61 m at nadir

MSI**

4-m

2.44 m at nadir

Resolution (GSD) Swath width

11 km at nadir

16.5 km at nadir

Revisit frequency

2.9 days at 1-m resolution; 1.5 days at 1.5-m resolution for targets at 40° latitude

1 to 3.5 days at 70-cm resolution, depending on latitude

Metric accuracy

12-m horizontal and 10-m vertical accuracy with no control

14.0 m RMSE

726 kg at launch main body: 1.8 × 1.8 × 1.6 m

1024 kg (wet, extra hydrazine for low orbit), 3.04 m (10 ft) in length

Mass/size

Onboard storage 64 Gb

128 Gb payload data X-band downlink at 320 Mbps

Comms

X-band downlink at 320 Mbps

housekeeping X-band from 4, 16, and 256 kbps 2 kbps S-band uplink

* panchromatic Imagery ** multispectral Imagery

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95

3.8.1 IKONOS The IKONOS satellite was launched on September 24, 1999 from Vandenberg Air Force Base. Orbiting at 681 km, it provides 1-m-resolution, panchromatic (visible range) imagery, at a revisit time of 3 days. IKONOS also carries a 4-m-resolution multispectral sensor, covering the VNIR portion of the spectrum addressed by Landsat bands 1–4 and the 3 SPOT bands. One of the biggest advantages of this new generation of satellites is the ability to point significantly off nadir, dramatically reducing revisit time in comparison with earlier systems such as Landsat. A wider dynamic range makes the sensor more capable as well.29

Figure 3.40 Image of the IKONOS satellite in the acoustic test cell at Lockheed Martin Missiles and Space in Sunnyvale, CA.28

Figure 3.41 First light image from IKONOS, September 30, 1999. The Jefferson memorial is shown at higher resolution above in Fig. 3.39.29

3.8.1.1 Imaging sensors and electronics for the IKONOS satellite 3.8.1.1.1 Camera telescope The telescope design is a Cassegrain, with a central hole in the mirror and detectors behind. Three of the five telescope mirrors are curved, and used to focus the image

28

M. Mecham, “IKONOS launch to open new earth imaging era,” Aviation Week & Space Tech nology (October 4, 1999). 29 Courtesy of Space Imaging, Inc.

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onto the imaging sensors at the focal plane. Two flat mirrors, known as fold mirrors, bounce the imagery across the width of the telescope, thereby reducing overall telescope length from 10 m to about 2 m. The three-mirror anastigmat has a focal length of 10 m, and is an f/14.3 optic. The primary is 0.7 m in diameter × 0.10 m thick, massing 13.4 kg. Two of the optics can be adjusted for focusing by ground command, should correction be necessary. 3.8.1.1.2 Imaging Sensors and Electronics The camera’s focal-plane unit—attached to the back end of the telescope—contains separate sensor arrays for simultaneous capture of panchromatic (black-andwhite) and multispectral (color) imagery. The panchromatic sensor array consists of 13,500 pixels, with a pitch of 12 µm. (Three overlapping 4648 pixel linear arrays.)30 The multispectral array is coated with special filters, and the 3375 pixels have a pitch of 48 µm. The digital processing unit compresses digital image files from 11 bits per pixel (bpp) data to an average value of 2.6 bpp, at a speed of 115 million pixels/s. The lossless, real-time compression of the imagery is a capability that only recently has been made practical by modern computational resources. It is important that IKONOS

Figure 3.42 The IKONOS telescope, built by Kodak, features three curved mirrors. Two additional flat mirrors fold the imagery across the inside of the telescope, thereby significantly reducing telescope length and weight. The telescope is an obscured, three mirror anastigmat with two fold mirrors: a 70-cm diameter primary with 16-cm central hole; 10.00-m focal length, and 1.2-µrad instantaneous field-of-view (pixel).31

30

“Extraterrestrial: Watching the Earth from 400 miles above,” Insights in Imaging, Kodak (June 2003). 31 Courtesy of Space Imaging, Inc.

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and Quickbird offer the extended dynamic range represented by 11 bit data words (Digital number ranges from 0-2047). This topic will be developed in Chapter 6. 3.8.2 NOB with IKONOS: Severodvinsk Figures 3.43 and 3.44 illustrate the sort of imagery that can be obtained for regions of strategic interest. First we see a large scene, and then a zoomed view of the sub-

Figure 3.43 Severodvinsk, near metropolitan Arkhangelsk, southeast of Murmansk. This is the overview image for the 11740 pixels (Columns) × 12996 pixels (Rows) image. The 0.85-m resolution original was downsampled to 1.0-m resolution before delivery. The original satellite imaging license limited the company to 1-m resolution.32 32

Analysis of data courtesy of Space Imaging, Inc.

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Figure 3.44 Severodvinsk, as captured by IKONOS. Compare the Corona image in Fig. 3.8. Acquisition date/time: 2001-06-13 08:48 GMT, Nominal Collection Azimuth: 133.4306°, Nominal Collection Elevation: 79.30025°, Sun Angle Azimuth: 168.5252°, Sun Angle Elevation: 48.43104°33

marine facility. Compare this image to the Corona image shown at the beginning of the chapter.33

3.9 DMSP: Visible Sensor, Earth at Night Defense Meteorological Satellite Program (DMSP) satellites are primarily intended to gather weather data for military purposes. We’ll look at the system as an example of low-light imaging. This system consists of platforms in sun-synchronous orbits with dayside equatorial crossings at 6:00 AM and 10:30 AM, local time. The purpose is to help forecasters identify and track developing weather patterns. Characteristics of some recent Block 5D-2 missions are given here. The Operational Linescan System (OLS) instrument consists of two telescopes and a photomultiplier tube (PMT). The scanning telescope of the OLS has a 20-cm aperture with an effective collecting area of 239 cm2 and effective focal length of 1.22 m. Light is split into two channels by a beam splitter. The system is designed to produce constant high-resolution imaging rather than accurate radiometry. Some of the characteristics are given here. Note that the sensitivity of the low-light sensor is two to four orders of magnitude higher than that of the daylight sensor.

33

Analysis of data courtesy of Space Imaging, Inc.

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99 Table 3.4 DMSP satellite parameters.

Common name International number Launch date (YYYY/MM/DD) Launch time Mass Apogee Perigee Period Inclination

DMSP 5D-2-F14 1997-012A 1997/04/04 1647 850.0 kg 855 km 841 km 101.8 min 98.8°

Table 3.5 DMSP sensors.

Spectral channels OLS-L OLS-PMT OLS-T

Wavelength Wavelength Sensitivity (µm) (FWHM, µm) 0.40–1.10 0.58–0.91 10 3–10 5 Watts/cm2 per sterradian 0.47–0.95 0.51–0.86 10 5–10 9 Watts/cm2 per sterradian 10. 0–13.4 10.3–12.9 190–310 K

Spatial resolution 0.56 km* 2.7 km 5.4km

* stored data are resampled to 2.7 km

The DMSP detectors operate as whiskbroom scanners. The continuous analog signal is sampled at a constant rate making the Earth-located centers of each pixel roughly equidistant, i.e., 0.5 km apart. For high-resolution (fine mode) imaging, 7325 pixels are digitized across the 108° swath from limb to limb. The low-lightlevel sensor operates at lower spatial resolution. The low-light data are useful for a variety of purposes beyond weather; for example, Chris Elvidge at NOAA has been archiving DMSP data sets for tracking population trends. Figure 3.45 shows U.S. light patterns, based on cloud-free imagery. The sensor saturates when viewing city lights, so there is no dynamic range for this data.

3.10 Exposure Times We have neglected one final, rather important point. For high-spatial-resolution systems, satellite movement becomes an issue because of motion blur, just as occurs in regular photography of rapidly moving targets. A simple calculation can estimate exposure time. CCD arrays have sensitivity not unlike regular daylight film, with a standard speed defined as ISO 100. An old photographic rule of thumb is that the exposure time at f/11 to f/16 is 1/ISO, or in this case 1/100 s. The f/14 IKONOS optics provide sufficient light for 1/100 s (10 ms) exposure. The satellite moves ap-

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Figure 3.45 NGDC made a stable-lights dataset of the USA using 236 orbits of nighttime DMSP data from the dark half of lunar cycles over six months. The image is resampled to 1 km resolution.34

proximately 70 m in that time— much too far for a clear image. Modern sensors are somewhat more sensitive than given here, but the principle holds for systems like Quickbird and IKONOS. There are two approaches to the need for very short exposure times. One is to mechanically scan the optics to compensate for satellite motion or slew the spacecraft so as to reduce effective ground velocity. Landsat does this, as described in Chapter 5, with a scanning mirror system. The second is to counter the motion electronically. This is done on IKONOS and Quickbird with a technique called time-delay integration (TDI) on the focal plane, by which electrons are moved along the focal plane in the direction of satellite motion, accumulating until sufficient exposure time has been reached (the same technology is used on some flatbed scanners). The Kodak-built focal-plane on IKONOS has up to 32 steps of TDI. Typically, twenty steps of TDI are needed to build up sufficient charge. The Quickbird satellite implements both TDI and mechanical slew of the whole spacecraft to reduce effective ground velocity.

34

C.D., Elvidge, et al., “Mapping of city lights using DMSP operational linescan system data,” Photogramm. Eng. Rem. S., 63, pp. 727 734 (1997); See also http://dmsp.ngdc.noaa.gov

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3.11 Problems 1. When was the first Corona launch? 2. When was the first successful launch and recovery of a Corona capsule? Which number was it? 3. How many launches did it take before a film was successfully returned? 4. How did the date of this launch relate to that of the U-2 incident with Gary Powers? 5. What was the best resolution (GSD) of KH-4 cameras discussed here? 6. What was the swath width associated with the best-resolution KH-4 images? 7. How many Corona missions were there? 8. For a 24" focal length, f/3.5 lens, calculate the Rayleigh limit to GSD for a satellite at 115 km altitude. Assume nadir-viewing, visible light (500 nm). 9. What diameter mirror would be needed to achieve 12-cm resolution (GSD) at geosynchronous orbit (6.6 Re, geocentric—note that this is not the altitude). 10. What are the three factors that constrain the resolution obtainable with an imaging system? 11. What is the focal length, diameter, and f/# for the Hubble primary optic? 12. Adaptive optics: compare the Rayleigh criteria for the 3.5-m Starfire observations in Fig. 3.16 to results with and without the adaptive optics system. 13. What is the energy band gap for lead sulfide? What is the cutoff wavelength for that value? 14. The Corona lenses were f/5.0 Tessar designs with a focal length of 24". Calculate the diameter of these lenses. 15. For a 24"-focal-length camera, f/3.5, at an altitude of 115 km, calculate the GSD corresponding to a 0.01 mm spot on the film (100 lines/mm). Assume nadir-viewing. Note that this is a geometry problem. 16. What is the f/# for the 0.57 mm pinhole illustrated in Fig. 3.19? Note that the focal length is approximately 50 mm. 17. How large an optic (mirror) would you need on the moon to obtain 0.66-m GSD at the Earth’s surface? What is the angular resolution of this optic (∆θ in radians)? Assume visible radiation: λ = 0.5 µm = 5 × 10 −7 m. 18. For the PUEO system illustrated below, compare the observed FWHM of 0.10 arc sec to the Rayleigh limit for such a mirror. Repeat for the natural seeing conditions of 0.3 arc sec. 19. Kodak offers a commercial remote sensing effort under their CIITPIX program. Aircraft: Cessna Conquest 441 Flight altitude: Approximately 10,800 ft (3292 m) above mean terrain. Camera: Zeiss Rmk Top 30, equipped with gyro-stabilization mounts and forward-motion compensation units that ensure clearer, sharper images. The camera is equipped with Topar A3 normal-angle lens, focal length 305 mm (12"), angular field 56° (diagonal), aperture f/5.6–f/22 continuously, distortion # 3 µm. Film: Kodak Aerocolor II negative film 2445, a very fine grain, medium-speed color negative film with resolving power of 40–80 lines/mm depending on the

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Figure 3.46 (a) This is the center of the globular cluster M71 at I band (830 nm). FWHM is 0.10 arc sec (center) to 0.18 arc sec (edges). The natural seeing was 0.30 arc sec (excluding tracking errors and telescope fixed aberrations). This was taken with a 1200 seconds exposure. (b) Image of an 8.6 R magnitude star in the astronomical I band (850 nm). The FWHM is 0.068 arc sec. “To our knowledge, this is the crispiest long exposure image ever from ground-based observations.”35 This was a two-second exposure. May 3–8, 1996, Canadian-French-Hawaiian Telescope (CFHT) adaptive-optics-compensation system. Also called PUEO after the sharp-visioned Hawaiian owl. The telescope is 3.6 m in diameter. The observatory is atop Mauna Kea, a 4200 m, dormant volcano on the island of Hawaii.

contrast of the test target. Film and camera enable resolution of features as small as 5.3–10.6 in. (13.5–27 cm). The actual resolution will depend on factors such as atmospheric conditions, ground contrast, film processing, etc. The film is sensitive in the visual spectral band between 350 and 700 nm and is 9.5" in width. Rolls are 125, 200, or 400 ft. a) If the lens is used wide open (f/5.6), what will the physical optics limit (Rayleigh criterion) give for the best resolution at an altitude of 3292 m, assuming the camera is nadir-viewing? Use a wavelength in the middle of the spectral range for the film used here, e.g. 500 nm. b) How does this answer change if the lens is stopped down to f/22? c) The usable film width is 9.0" (22.9 cm). Assuming square pictures (9.0" × 9.0"), what is the field of regard on the ground (that is, how big is the ground area being imaged)? d) What physical distance on the film corresponds to 15 cm (6") on the ground?

35

Courtesy of University of Hawaii: http://www.cfht.hawaii.edu

Chapter 4 Orbital Mechanics Interlude

The design and operation of remote sensing systems depends on the orbital motion of the satellites they employ, and a proper understanding of how they work and how to exploit them requires knowledge of orbital mechanics. This chapter is designed to provide an understanding of orbital mechanics as it impacts remote sensing.

4.1 Gravitational Force Orbital mechanics for Earth-orbiting satellites is determined by the effects of gravity. Students should be familiar with the simple textbook case where force due to gravity is given by the formula f = mg, where m is mass (generally in kilograms), and g is acceleration due to gravity (approximately 9.8 sm2 ). Unfortunately, this simple form, while appropriate near the surface of the Earth, will not do for orbital motion—a more complex form must be used. The correct formula for this “central force problem” is F = −G

m1 m2 r2

r$ ,

(4.1)

where G = 667 . × 10 −11 N m2 / kg 2 (gravitational constant), m1 and m2 are the masses involved (the Earth and the satellite, usually), r is the separation between the center of the Earth and the satellite, and the vector elements (and sign) indicate that the force is along a line joining the centers (of mass) of the two bodies. As always, the force F is in Newtons and masses are in kilograms. At the surface of the Earth, this equation takes the familiar form: F = g o m,

103

(4.2)

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2 where g o = G ( mEarth / R Earth ) = 98 . sm2 is the acceleration due to gravity at the Earth’s

surface. Note that this can lead to a convenient form of Eq. 4.1: 2

R  F = g o m  Earth  ,  r 

(4.3)

where REarth = 6380 km, and we have used mEarth = 5.9736 × 1024 kg. [Although mEarth and G are not known to high accuracy, the product is: GMEarth = (3.98600434 ± 2 × 10 8) × 1014 m3s 2. The ±2 × 10 8 in the parentheses is the error in the last digit of the expression—the term has nine significant digits.]1

4.2 Circular Motion The force due to gravity results in a variety of possible solutions of the equations of motion, the simplest of which is circular orbits, which objects like the moon approximate. 4.2.1 Equations of motion The velocity of an object moving in a circular orbit is described by means of an angular velocity, which determines the relationship between the radius of the circular motion and the linear velocity v = ωr,

(4.4)

where v = velocity in m/s, r = distance from center of motion, ω = angular velocity (rad/s). The angular frequency ω is related to the usual frequency f by a factor of 2π: ω = 2πf. Frequency, in turn, is related to the period τ by the relation: τ=

1 2π = ω f

(4.5)

4.2.1.1 Example: A car is going around in a circle of 200 m radius at 36 km/hr. What is ? ω=

1

)

3 v (36 × 10 m / 3600 s = = 005 . rad / s 200 m r

W. G. Rees, Physical Properties of Remote Sensing, Cambridge University Press (1990).

Orbital Mechanics Interlude

105

4.2.1.2 Example: A satellite is going around the Earth once every 90 minutes. What is ? Period (τ) = 90 × 60 = 5400 seconds. f =

1 1 = = 1.85 × 10 −4 s −1 ; τ 5400

ω = 2πf = 1.16 × 10 −3 radians / s

4.2.2 Centripetal force Newton said that for a mass to move in a trajectory other than a straight line, a force must be applied. In particular, circular motion requires the application of centripetal force. The magnitude of this force is: Fcentripetal = m

v2 = mω 2 r . r

(4.6)

4.3 Satellite Motion For an object in circular motion, the consequence of the centripetal force applied to a satellite by gravity is the following balance: 2

Fcentripetal

v2 R  =m = Fgravity = g o m  Earth  .  r  r

(4.7)

Note that mass cancels out—orbital motion does not depend on satellite mass. 2

g R2 v2 R  = g o  Earth  ⇒ v 2 = o Earth ⇒  r  r r v=

(4.8)

go R Earth . r

There is a directly inverse relationship between the radius and velocity of a satellite in circular orbit around the Earth. This simple derivation serves to introduce some basic concepts of orbital motion, in particular Kepler’s laws.

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Illustration: Geosynchronous orbit What is the radius of the orbit of a geosynchronous satellite—that is, a satellite with an orbital period of 24 hours? First: ω =

2π 2π = 24 hours 86,400 s

v=

go v R Earth ⇒ ω = = r r

go r

R Earth ⇒ 3

g ω2 = o3 , or 2 R Earth r

3

go 1  r  ⇒   = 2 1  R Earth  ω R Earth r R Earth

 g 1  = o   R Earth ω 2 

1 3

1

1  9 .8 (86400) 2  3   3 = 6 . 62 ) 290 . 45 = = ( 6 2   6 .38 × 10 (2π ) 

so we see that geosynchronous orbit is 6.6 Earth radii (geocentric). What is the velocity of the satellite?

4.4 Kepler’s Laws Johannes Kepler (1571–1630) studied orbital motion of the planets using data obtained from Tycho Brahe. Starting from the Copernican theory of the solar system (that the sun was at the center), Kepler posited that the orbits of the planets were elliptical, not circular. Kepler’s three laws describing planetary motion apply equally to satellites: 1. Planetary orbits are ellipses, with one focal point at the center of the sun. 2. Equal areas are swept out in equal times. 3. The square of the orbital period is proportional to the cube of the semi-major axis. It was one of the great triumphs of Newtonian mechanics that Kepler’s laws could be derived from basic physics principles. 4.4.1 Elliptical orbits The first of Kepler’s laws stated that orbital motion would be elliptical—circular orbits are a special case of such orbits.


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An ellipse is characterized by the semi-major and semi-minor axes (a, b), or alternatively, the semi-major axis and the eccentricity (ε or e). In our case, the central point for orbital motion is the focus, which for satellite motion around the Earth is the center of the Earth. Some useful formulas: x2 y2 + = 1. a2 b2 ε=

(4.9)

a2 − b2 or a

ε = 1−

b2 . a2

(4.10)

Figure 4.1 r =

(

a 1− ε 2

).

1+ ε cos θ

The distance from the center to the focus is c = εa = a 2 − b 2 .Note that the sum of the perigee and apogee is just twice the semi-major axis. 4.4.2 Equal areas are swept out in equal times Kepler’s second law is a consequence of the conservation of angular momentum; L = mv × r; L = mvr sin θ is a constant. Hence, at each point along the orbit, the product of the velocity perpendicular to the radial vector v θ and the radius is a constant. Note that at perigee and apogee, the radial velocity is zero (by definition), and if one checks the values to the right, one can see that: 2 .709 × 6 .192 = 13 .277 × 1.263 In consequence of this law, a satellite spends most of its time at apogee.

Figure 4.2 Earth is at one focus, x = 5.29; the x range is –13.29 to 2.71 REarth.

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The instantaneous velocity is given by  2 1 v = GM  −  ,  r a where r is the instantaneous radius from the center of the Earth and a is the semi-major axis. 4.4.3 Orbital period:

2

r3

The orbital period depends only on the radius of the orbit, for circular orbits; the orbital period depends only on the semi-major access for elliptical orbits. Following the same calculation given above in the derivation of the period for a geosynchronous orbit, we find: v=

go v R Earth ⇒ ω = = r r

2π τ= R Earth

go r

3

R Earth =

2π ; or τ

(4.11)

4π 2 4π 2 r3 3 = r r 3. ⇒ τ2 = 2 M Earth G go g o R Earth

This result is obtained quickly here for a circular orbit, but is more generally true. Replace the radius of the circle with the semi-major axis, and you get the value of the orbital period.

4.5 Orbital Elements There are a handful of key parameters used to define the orbit of a satellite. These parameters define the energy and shape of the orbit, and the orientation of the orbit ellipse. 4.5.1 Semi-major axis: a The size of the orbit is determined by this parameter, as illustrated in the two figures above. The semi-major axis a is half of the longest axis of the ellipse. A related measure of size is the distance from the origin to the focus c (c = 8 and 5.29 in the two ellipses shown above). 4.5.2 Eccentricity: e or The eccentricity ε determines the shape of the orbit: ε = c/a. For a circle, ε = 0; for a straight line, ε = 1. The latter would be a ballistic missile: straight up and straight down. 4.5.3 Inclination angle: I The inclination angle is the angle between the orbit plane and the equatorial plane of the Earth. In the idealized case of a spherical Earth, a geostationary satellite at the


109

Earth’s equator would have an inclination of 0°. Reality differs slightly from this for modern geosynchronous satellites. A polar-orbiting satellite will have an inclination of 90° (more or less). The non-spherical Earth exerts a torque on the satellite’s orbit plane. For an inclination of less than 90°, the orbit will precess west; for an inclination greater than 90°, it will precess east. This rate of precession can be set to just balance the rotation of the Earth. For the right choice relative to altitude, a polar-orbiting satellite with the right inclination will be sun-synchronous—nominally 97–98° for LEO satellites. The remaining parameters determine the relative phase of the orbit. 4.5.4 Right ascension of the ascending node: The ascending node is the point at which the northbound (ascending) satellite crosses the equator. The right ascension of the ascending node (RAAN) is the celestial longitude of this point. (Right ascension is measured with respect to the fixed sky, not the Earth.) As an alternative definition, the RAAN is the angle between the plane of the satellite orbit and the line connecting the Earth and sun on the first day of spring, or vernal equinox. The right ascension can also be described as being measured from the point of Ares. A related definition—the descending node is the southbound equator crossing. 4.5.5 Closest point of approach (argument of perigee): This is the latitude for perigee, measured from the ascending node in the orbital plane in the direction of satellite motion. ω = 0° corresponds to perigee occurring over the equator, 90° puts perigee over the north pole. Because of the non-spherical Earth, in general, the argument of perigee will precess. Table 4.1 Satellite inclination.

Inclination < 63.4°

ω precesses opposite the satellite motion

Inclination = 63.4°

ω does not precess (Molniya orbit)

Inclination > 63.4°

ω precesses in the same direction as the satellite motion

4.6 A Few Standard Orbits There are a set of more-or-less standard orbits used in the satellite industry, most of which have some use in the remote sensing community. In altitude, they range from low-Earth-orbit (LEO) (altitudes of a few hundred miles), to geosynchronous orbit (altitudes of some 20,000 miles).

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Figure 4.3 Ground track for four orbits by a LEO satellite, Landsat 4, crossing the equator during each orbit at 0940 local time. Note the solar sub-point just above the coast of South America, corresponding to the time of the satellite crossing the equator. During the 98-minute orbit, the Earth has rotated 24.5°.

4.6.1 Low Earth orbit (LEO) LEO is the domain of a large fraction of remote sensing satellites of various kinds, including weather, Earth resources, and reconnaissance. These satellites are typically in a sun-synchronous orbit, meaning they cross the equator at the same local time to maintain a constant solar-illumination angle for observations. Figure 4.3 shows the ground track for Landsat 4, orbiting at an altitude of 705 km.

Figure 4.4(a) LEO illustration. The two white lines are for the orbit, and the ground track of the orbit.

Figure 4.4(b) The sensor on Landsat 4 sweeps along the orbit, aimed at the sub-satellite point (in the nadir direction). Over 16 days, the satellite will have observed the entire Earth.


111

4.6.2 Medium Earth orbit (MEO) MEO is the domain of the global positioning satellites (GPS). Though not directly used for remote sensing, they are increasingly important for mapping, and thus influence the interpretation of remotely sensed imagery. These satellites are in 4.15 RE circular (26378 km geocentric) orbits, with 12-hour periods. Figure 4.5 MEO orbit, illustrated for two GPS orbit planes.

Figure 4.6 Orbit ground tracks for three GPS satellites.

4.6.3 Geosynchronous (GEO) Geosynchronous orbit is standard for most commercial and military communications satellites, the NASA telemetry system (TDRSS), and weather satellites (GOES). There is some sloppiness in the usage of the term “geosynchronous,” and it is frequently interchanged with “geostationary.” Properly, the first really means an orbit with a 24-hour period, while the latter means that the satellite position with respect to the ground is unchanging. A truly geostationary orbit is difficult to obtain, and deviations from 0° inclination of a few degrees are typical. This leads to a modest amount of north-south motion during the day.

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Figure 4.7 The TDRSS orbit and the field of view from the satellite.

Figure 4.8 TDRS views the Earth. The GOES satellite views in Chapter 1 are similar to that shown here (Figs. 1.9, 1.19). TDRS 7, launched in 1995 Apogee 35809 km Perigee 35766 km Period 1436.1 min Inclination 3.0 deg

Figures 4.7 and 4.8 illustrate a TDRS satellite orbit and field of view as a typical geosynchronous satellite. Note that the poles are not in view. TDRS-1 has drifted enough away from the equator that it is no longer geostationary and can view the


113

Antarctic, supporting an NSF ground station. The image of the Earth taken from Apollo 17, as shown on the cover, was taken from near geosynchronous orbit. 4.6.4 Molniya orbit (HEO) The Molniya, or high Earth orbits (HEO) are useful for satellites that need to dwell at high latitudes for an extended period. The careful match of inclination and eccentricity allows a balance of forces that keeps the orbit plane from precessing; that is, the latitude at which apogee occurs does not vary. This is the standard orbit for Russian communications satellites. The 12 hour orbit ‘dwells’ for 8 or 9 hours at apogee, then sweeps through perigee in the southern hemisphere, ultimately coming back up over the northern pole over the opposite side of the Earth (Fig. 4.9). Note that the satellite can view the northern hemisphere on both legs of the orbit (Fig. 4.10).

Figure 4.9 Molniya orbit ground track. The sub-solar point is centered on India. Table 4.2 Orbital elements for Molniya orbit.

Semi-major axis: a

26553.375 km

apogee radius

46228.612 km

Eccentricity: e

0.74097

perigee radius

6878.137 km

Inclination: I

63.40°

perigee altitude

500.000 km

Argument of perigee

270.00°

RAAN

Longitude of Ascending node

230.043°

mean motion (revs per day)

335.58° 2.00642615

Period

43061.64 s

Epoch

July 1, 1999 00:00:00

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Figure 4.10(a) The view from Molniya orbit, corresponding to the location at apogee illustrated above (06:54 UT).

Figure 4.10(b) Some twelve hours later, the view from the apogee over the US. The sub-solar point is in the Caribbean (18:05 UT).

4.6.5 Summary table—illustrations Illustrative values for satellites in the above orbits are given in the summary table below. These numbers are primarily from the Satellite Tool Kit (STK) database. STK is a product of Analytical Graphics, Inc.


115 Table 4.3 Typical orbital parameters.

Orbit Typical satellite Launch date Altitude: apogee

LEO Landsat 7

MEO GPS 2-27

04/16/1999

09/12/1996

703 km

20,314 km

39,850 km

perigee Radius: apogee perigee Semi-major axis Period

701 km

20,047 km 4.15 RE

500 km 7.2 RE 46,228 km 6878.1 km 26,553.4 km

Inclination Eccentricity Mean motion (revs/day)

98.21° 0.00010760 14.5711

1.1 RE 98.8 min

4.15 RE 26378 km 12 hr 717.9 min 54.2° 0.00505460 2.00572

HEO (Molniya) Russian communications

GEO TDRS 7 07/13/1995

~12 hr 717.7 min 43,061 s 63.4 0.741 2.00643

5.6 RE 35,809 km 35,766 km 6.6 RE 6.6 RE 24 hr 1436.1 min 86,164 s 2.97° 0.000765 1.0027

4.7 Problems 1. Calculate the angular velocity with respect to the center of the Earth for a geosynchronous orbit in rad/s. 2. Calculate the period for a circular orbit at an altitude of one Earth radius. 3. Calculate the period for a circular orbit at the surface of the Earth. What is the velocity? This is a “Herget” orbit, and is considered undesirable for a satellite. 4. Look up the orbits for the nine planets and plot the period vs. the semi-major axis. Do they obey Kepler’s third law? This is best done by using a log-log plot. Even better, plot the two-thirds root of the period vs. the semi-major axis (or mean radius). 5. Derive the radius of the orbit for a geosynchronous orbit. 6. Can you see Antarctica from geosynchronous orbit? 7. A satellite is in an elliptical orbit, with perigee of 1.5 Earth radii (geocentric), and apogee of three Earth radii (geocentric). If the velocity is 3.73 km/s at apogee, what is the velocity at perigee (what is the semi-major axis)? Hint: Use conservation of angular momentum: L = mv × r = constant.

Chapter 5 EO—Spectral Imagery

The discussion of remote sensing up to this point has focused on panchromatic (black & white) imagery. Beyond recording obvious features of size and shape, remote sensing excels in capturing and interpreting color. Color systems also yield some spectacular imagery. For example, in this early “true-color” image from Landsat 7, we perceive the green hillsides and muddy runoff of the upper San Francisco bay (Fig. 5.1).

5.1 Reflectance of Materials The reflectance of most materials varies with wavelength. This allows spectral imagers, such as those on the Landsat missions, to distinguish different materials. Distinguishing between minerals is a fairly common goal for such work by geologists. In Fig. 5.2, different aspects of reflective spectra are illustrated. Spectra are the fingerprints of elements, deriving from their fundamental atomic characteristics, as indicated in our discussion of Bohr’s model of the hydrogen atom. One of the more important, and dramatic, spectral features found in remote sensing is the “IR ledge” at 0.7 µm, as found in Fig. 5.2.1 This dramatic rise in reflectance with wavelength makes vegetation appear bright in the infrared (old-style, black-and-white infrared film would show vegetation as white, for example). The military designs camouflage to mimic this behavior. The panchromatic sensors on Landsat, SPOT, IKONOS, and Quickbird extend well into the infrared, and as a result, vegetation is bright in their imagery.

1

Also occasionally termed the “red edge,” e.g., in D.N.H. Horler, M. Dockray, and J. Barber, “The red edge of plant leaf reflectance,” Int. J. Remote Sens. 4, pp. 273 288 (1983).

117

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Figure 5.1 Visible image of San Francisco from Landsat 7, April 23, 1999, flight day 9, orbit 117. ~1830Z With special thanks to Rebecca Farr, NESDIS/NOAA. The satellite is not yet in its final orbit, and not on the standard reference grid, WRS, so the scene is offset 31.9 km east of nominal scene center (Path 44, Row 34). Landsat has been the premier Earth resources satellite system for three decades.

5.2 Human Visual Response2 Before considering the spectral response of orbital systems, let’s consider human visual response. The sensitive elements of the eye are the rods and cones. Rods (which far outnumber cones) are sensitive to differences in brightness within the

2

See W.L. Teng, E.R. Loew, D.I. Ross, V.G. Zsilinsky, C. Lo, W.R. Philipson, W.D. Philpot, S.A. Morain, “Fundamentals of Photographic Interpretation,” 2nd ed. in Manual of Photographic In terpretation. W.R. Philipson (Ed.), American Society for Photogrammetry and Remote Sensing, Bethseda, MD, p. 67 (1997). Also see H.J.A. Dartnall, J.K. Bowmaker, and J.D. Mollon, “Microspectrophotogrammetry of Human Photorecepters,” in Color Vision: Physiology & Psychophysics, John Mollon, L. Ted Sharpe (Eds.), Academic Press, London (1983).

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Figure 5.2 Reflectance for some manmade and natural materials. Note how the olive-green paint mimics the grass spectrum in the visible to NIR, but then deviates.

Figure 5.3 Human vision: The white curves indicate the sensitivity level for the three types of cones. The black curve indicates the sensitivity of the rods.3

middle of the light spectrum. The rods’ peak sensitivity corresponds to the peak in solar illumination. If we had only rods, we would see in shades of grey.

3

See John E. Dowling, The Retina: An Approachable Part of the Brain, Harvard University Press, Cambridge, Mass., (1987). See also H.J.A. Dartnall, J.K. Bowmaker, and J.D. Mollon, “Human Vi sual Pigments: Microspectrophotometric Results from the Eyes of Seven Persons,” Proceedings of the Royal Society of London B, 220 (1218), pp. 115 130 (1983).

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Cones provide our color vision. There are three types of cones: L-cones are sensitive primarily to red in the visible spectrum. M-cones are sensitive to green. S-cones are sensitive to blue.

5.3 Landsat In late July 1972, NASA launched the first Earth-Resources Technology Satellite, ERTS-1. The name of the satellite, and those that followed, was soon changed to Landsat. These have been the primary Earth-resources satellites ever since, utilizing multispectral imagery (MSI) with a spatial resolution of 30 m. The most recent in the series, and perhaps the last, is Landsat 7. The table below shows some of the parameters for the sequence of missions. Note the evolution in data storage technology, bandwidth, and the changes in downlink technology. Resolution has gradually increased with time. Landsat 7 added a 15-m GSD panchromatic sensor to the MSI sensors. Figure 5.4 shows the satellite orbit, and illustrates the 185-km viewing swath for the Enhanced Thematic Mapper (ETM) sensor, described below. The figure also reflects the different downlink options, as the sensor communicates with the Landsat Ground Station (LGS). Table 5.1 Landsat sensors and orbits.

Satellite Landsat 1 (ERTS-A) Landsat 2

Landsat 3

On-Orbit/ Operating July 23, 1972– January 6, 1978 January 22, 1975–February 25, 1982 March 5, 1978– March 31, 1983 July 16, 1982–*

Sensors*** MSS RBV MSS RBV

MSS RBV Landsat 4 MSS TM Landsat 5** March 1, 1984– MSS to date TM Landsat 7 April 15, 1999–to ETM+ date (pan)

Resolution (m) 80 80 80 80 80 30 80 30 80 30 30 15

Altitude (km) 917

705

Data Link Direct downlink w/recorder (15 Mbps)

Direct downlink w/TDRSS (85 Mbps) Direct downlink w/solid state recorders (150 Mbps)

* TM data transmission failed in August 1993; satellite was used for maneuver testing. ** Landsat 6 failed due to a launching problem. *** RBV: Return Beam Vidicon; MSS: Multi Spectral Scanner; TM: Thematic Mapper

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Figure 5.4 The nadir-viewing satellite images a swath 185 km wide.

Figure 5.5 Subsequent orbits are displaced by some 2500 km to the west. There are 233 unique orbit tracks.

5.3.1 Orbit The Landsat missions have been sun-synchronous polar orbiters in circular orbits (LEO). The later missions operating at an altitude of 705 km. NASA’s Mission to Planet Earth has added several satellites in the Landsat 7 orbit—Terra, Aqua, SAC-C, and EO-1. They trail the older satellite by a few minutes in orbital sequence. An inclination of ~97° makes them sun-synchronous. Equatorial crossings were set at 9:30 am for Landsats 1, 2, and 3; 10:30 am for Landsats 4 and 5; and 10:00 am for Landsat 7. Landsats 4, 5, and 6 have orbit tracks set for 14.5 orbits per day. The repeat cycle is every sixteen days. Figure 5.5 shows the orbit track, and shows how the orbit shifts in local time (longitude). The orbit track for Landsat 7 is further illustrated in Fig. 5.6. The ground track is illustrated for 2 orbits. The satellite is on an ascending node on the night side, and descends southward on the day side.

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Figure 5.6 This orbit ground track corresponds to the San Francisco image above. The yellow spot just below Mexico City is the sub-solar point, April 23, 1999, ~1830Z.

5.3.2 Sensor: Thematic Mapper4 The first Landsats flew with a multispectral (MSS) imager and a TV-like sensor (the return-beam vidicon, or RBV). Beginning with Landsat 4, the primary instrument became the Thematic Mapper (TM), though the MSS was also carried to maintain continuity in archival, synoptic datasets. The TM sensor has provided seven bands of spectral information at 30-m resolution since 1982. On the most recent vehicle, Landsat 7, the instrument was revised as the Enhanced Thematic Mapper plus, or ETM+. The instrument features improved spatial resolution in the LWIR channel (60 m) and a new panchromatic band with higher spatial resolution (15 m). The discussion that follows addresses the ETM+ sensor. 5.3.2.1 Optics The optical design of Landsat predates large linear or rectangular arrays; it is of whiskbroom design. The telescope is a Ritchey-Chrétien Cassegrain, as seen with several earlier systems. The primary mirror (outer) aperture is 40.64 cm; the clear inner aperture is 16.66 cm. The effective focal length is 2.438 m, and the aperture is f/6. The instantaneous field of view (IFOV) for one pixel of the high-resolution panchromatic sensor is 42.5 µrad.

4

See http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook toc.html

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Figure 5.7 Landsat ETM+ optical path.

The relay optics consist of a graphite-epoxy structure containing a folding mirror and a spherical mirror that are used to relay the imaged scene from the prime focal plane to the band 5, 6, and 7 detectors on the cold focal plane. The characteristics of the relay optics are given in the table below. The relay optics provide a magnification of 0.5, used because of the reduced resolution of the band 6 detectors compared to the other detector elements. Table 5.2 Landsat Relay optics design parameters.

Folding mirror clear aperture outer diameter

7.98 cm

Folding mirror clear aperture inner diameter

1.364 cm

Spherical mirror clear aperture diameter

14.067 cm

Magnification

0.5

f/#

3.0

Mirror material

ULE glass

Mirror coating

Aluminum, SiO overcoat

There is a mechanical scanning mirror at the beginning of the optical path. It oscillates at 7 Hz, or a period of 142.925 milliseconds (ms). The mirror scans a range of 0.2686 rad (15.39°). (The mirror scans for 60.74 ms; it then takes 10.72 ms to reverse the motion.) In half a period, or 71.4 ms, the spacecraft moves 480 m down track (6.7 km/s). The scan correction mirrors compensate for the satellite’s forward motion as the sensor accumulates 6000 pixels in its whisk-broom cross-track sam-

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pling. The scan line correction mirror failed on Landsat 7, causing the satellite to collect spatially distorted data. 5.3.2.2 Focal planes The ETM+ scanner contains two focal planes that collect, filter, and detect the scene radiation in a swath (185 km wide), as it passes over the Earth. The primary (warm) focal plane consists of optical filters, detectors, and preamplifiers for five of the eight ETM+ spectral bands (bands 1–4 and 8). The second focal plane is the cold focal plane (90 K), which includes optical filters, infrared detectors, and input stages for ETM+ spectral bands 5, 6, and 7. This approach of dividing the sensor into two focal planes is common with sensors that must cover an extended wavelength range. It is difficult (and expensive) to build focal planes that extend from the visible into the shortwave infrared (SWIR).

Figure 5.8 Diagram of the Landsat 7 focal plane design.

5.3.2.2.1 Prime focal plane5 The prime focal-plane array is a monolithic silicon focal plane made of five detector arrays: band 1 through band 4 and the pan band (8). The arrays for bands 1–4 contain sixteen detectors divided into odd-even rows. The array for the pan band

5

With thanks to Dr. Carl Schueler, Director Advanced Concepts, Raytheon, May 1999, and http://ltpwww.gsfc.nasa.gov/IAS/handbook/

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contains thirty-two detectors, also in odd-even rows. The system focus is optimized for the panchromatic band, which has the highest spatial resolution. Table 5.3 Landsat prime focal plane assembly design parameters (silicon).

Parameter

Bands 1 through 4 Pan band

Number of detectors

16 per band

32

Detector Size

103.6 µm × 103.6 µm

51.8 µm × 44.96 µm

Detector Area

1.074 × 10 4 cm2

2.5 × 10 5 cm2

IFOV size

42.5 µrad

21.3 µm × 18.4 µrad

Center to center spacing along track

103.6 µm

51.8 µm

Center to center spacing between rows 259.0 µm

207.3 µm

5.3.2.2.2 Cold focal plane There are sixteen cooled indium antimonide (InSb) detectors for bands 5 and 7. Finally, for the LWIR, there are eight cooled mercury cadmium telluride (HgCdTe) photoconductive detectors for band 6. The detectors for bands 1–4, 5, and 7 each have 30-m resolution; the LWIR detector has 60 m resolution (an improvement over the 120 m resolution on TM). The detectors are arranged to have coincident 480-m coverage down track. Table 5.4 Landsat cold focal plane design parameters.

Parameter

Bands 5 and 7

Band 6

Number of detectors

16 per band

8

Detector Size

48.3 µm × 51.82 µm 104 µm × 104 µm

IFOV size

42.5 µm

42.5 µrad × 85.0 µrad

Center-to-center spacing along track

51.8 µm

104 µm

Center-to-center spacing between rows 130 µm

305 µm

5.3.2.2.3 Spectral response The spectral response of the Landsat sensors is important for understanding data from this and subsequent systems, because most subsequent sensors have adopted similar spectral sampling approaches. Figure 5.9 shows the spectral bands for Landsat 7. The plot color coding reflects the band colors. There are 4 reasonably contiguous bands in the visible and near-infrared (1–4), and then two short-wave

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Figure 5.9 The Landsat 7 spectral band base response functions are plotted here as a function of wavelength. These values are from the ground calibration numbers provided by NASA/GSFC. The higher-resolution pan-chromatic band covers the same region as bands 2, 3, and 4, but does not extend into the blue. This is to avoid the atmospheric scattering at shorter wavelengths.

infrared (SWIR) bands plotted. The band 6 response is plotted separately. IKONOS, Quickbird, and others all have very similar spectral bands to the Landsat bands 1–4. Note the sharp cutoff in the response of the silicon focal plane at 0.9 µm, as the silicon band gap is approached. The peculiar numbering scheme, with band 6 seemingly out of order, is due to the evolution of the TM design. 6 5.3.2.3 Spatial resolution—swath Table 5.5 Landsat spectral bands.

Band

1 2 3 4 5 6 7 Pan

Detector Si Si Si Si InSb HgCdTe InSb Si

Wavelength (nm) 450–520 (VIS, blue) 520–600 (VIS, green) 630–690 (VIS, red) 760–900 (NIR) 1550–1750 (SWIR) 10.40 to 12.5 µm, thermal 2090–2350 (SWIR) 520–900

Resolution (m) 30 30 30 30 30 60* 30 15

* 60 m resolution for band 6 on Landsat 7; 120 m on earlier missions.

6

Professor David Landgrebe, Private Communication, 2002. The original design was to include five reflective bands. When NASA allowed the additional reflective band at 2.1 µm, it became band 7. The most recently added band, band 8, is the high spatial resolution panchromatic channel.

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5.3.2.4 Dynamic range The dynamic range for the Landsat sensors is typical of the satellites flown in the first decades of remote sensing. The TM and ETM sensors have 8-bit dynamic range—meaning that the digital number varies from 0 to 255, thus defining the amount of data to be broadcast to the ground.

5.3.2.5 Data links7 The telemetry system for Landsat serves as a model for data-system requirements. Landsat 7 is primarily a “store and dump” system. Data are stored on a solid-state recorder (SSR) and transmitted primarily to the Landsat ground station (LGS) at Sioux Falls, South Dakota. The downlink is an X-band link at a combined aggregate rate of 150 megabits per second (Mbps).8 The data recorded on the SSR can be played back using one or two 150-Mbps bit streams and transmitted to the LGS via the X-band link. A rough calculation shows how the data rate evolves from such a sensor. A scan line is about 6000 pixels across, based on the 185 km swath, and 30-m pixels.

A 185-km swath ⇒

185-km = 6000 pixels / scan line or 3.36 × 105 bits per 30 m / pixel

scan line (56 × 6000). What is the time interval corresponding to one scan line? τ=

30 m 7 × 10 3 m / s

= 0 .0043 s or 4 .3 ms

(Compare to the 71.4 ms sweep time cross track, divided by 16 for the number of rows imaged in each sweep.) 3 .36 × 10 5 bits bits » 80 Mbps or 10 The implicit data rate: = 78 . 4 × 10 6 −3 s 4 .3 × 10 s Megabytes per second. The “correct” answer was 85 Mbps for Landsats 4 and 5. These systems used an 8.2 GHz (X-band) downlink.

7 8

See http://caster.gsfc.nasa.gov/lps/ExtIntFaces/satellite.html Note the importance of discriminating between upper and lower case for the “b” in Mbps.

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This sensor takes 6928 cross-track samples in a sweep, since the pixels overlap some. Considering only the seven spectral channels, there are nominally 56 bits per pixel.9 One can estimate the time required to acquire one line by dividing the pixel size by the satellite velocity. One can then estimate the data rate by dividing the number of bits per line by the time required to collect those pixels.

5.4 SPOT (Systeme Probatoire d’Observation de la Terre) The French also have a ‘flagship’ earth resources platform, the Systeme Probatoire d’Observation de la Terre, or SPOT (see Fig. 5.10). The spectral capability of SPOT is limited compared to Landsat, but SPOT carried the highest spatial resolution panchromatic sensor available to the civilian community for a number of years. The orbits for the SPOT satellites are ~822-km altitude, with a 26-day repeat cycle. As with Landsat, they are sun-synchronous Figure 5.10 SPOT-5 carries several cam(98.7° inclination), crossing the equator eras with varying resolution and pointing at 10:30 local time on a descending capabilities.10 node. The orbital period is 101.4 min. SPOTs 4 and 5 are working as of mid-2005. Imagery is all 8 bit. The evolving system, described in the table below, reflects the evolution of the technologies for data storage and transmission. SPOT data from San Diego were illustrated in Chapter 1 for the high-resolution panchromatic sensor. The spectral imagery from SPOT (see Fig. 5.12) is less widely used when Landsat data are available. With the advent of modern processors, SPOT-5 uses a discrete cosine transform to compress data. A factor of 2.8 is possible for the panchromatic channel, 2.28 for the multispectral bands. This allows for greater storage and effective data rate.

9

The lower spatial resolution LWIR data in channel 6 are sent in a low and high gain setting, so it ends up making a similar contribution to the bandwidth requirement, even though the resolution is lower than the reflective channels. 10 © Centre National d’Etudes Spatiales (CNES).

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129 Table 5.6 SPOT satellites and sensors.

Mission

Launch Data rate (Year/MM/DD)

Storage

Solar arrays

SPOT 1

1986/02/22

2 × 25 Mbits/s

Two 120-Gbit tape recorders; ~280 images on average, decompressed file size of 36 Mb.

1 KW

SPOT 2

1988/03/01

2 × 25 Mbits/s

SPOT 3

1993/09/26

2 × 25 Mbits/s

SPOT 4

1998/03/24

2 × 25 Mbits/s

SPOT 5

2002/05/04

2 × 50 Mbits/s, 90-Gbit (EOL) solid- 2.4 KW state memory. (16 MB Quadrature DRAM chips)11 phase-shift keying (QPSK)

Two 120-Gbit tape re- 2.1 KW corders 9-Gbit solid-state memory (experimental)

Figure 5.11 SPOT HRV fields of view.12 Figure 5.12 Spectral bands for SPOTS 1–3.12

11

Up to five images acquired simultaneously, two downlinked in real time and three stored onboard. See http://www.spotimage.fr/home/system/introsat/seltec/welcome.htm, http://spot5.cnes. fr/gb/satellite/45.htm 12 © CNES/Courtesy SPOT Image Corporation.

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5.4.1 HRV sensor, pan/spectral—both 60-km swath The first 4 SPOT HRV sensors used paired linear arrays of 6000 pixels each for the high-resolution panchromatic imager, with a spatial resolution of 10 m. With SPOT 5, they used revised optics and a clever offset pair of linear arrays to provide 2.5 m resolution over the same 60-km swath.13 The spectral channels use 3000 pixels each. The system uses push-broom scanning, but with a significant off-nadir pointing capability (about 23° off nadir). The two sensors can be pointed independently but apparently are normally operated to give a 120-km swath directly below the satellite (see Fig. 5.11). The ability to use off-nadir pointing enhances the ability to do stereo pairs and can be used to shorten revisit intervals.

5.4.1.1 Imaging Modes—Spatial and Spectral Resolution Note that on SPOT 4, an additional SWIR band was added, and a change in the spectral bandpass occurred for the panchromatic channel. On SPOT 4, the high-resolution mode is in the red band. With SPOT 5 (see figure 5.13), they resumed the earlier approach, using a high-resolution sensor with a broad spectral range. Compare the spectral sensitivity of SPOT to the Landsat 7 panchromatic band, and note that for SPOT 5, the panchromatic sensor is not sensitive to near-infrared. The lack of continuity in the sensor characteristics is detrimental to synoptic studies. Table 5.7 SPOT spectral bands.

Res.

SPOT 1, 2, 3 (XS) SPOT 4 (XI)

SPOT 5

Band 1

20 m

500–590 nm (green)

500–590 nm (green)

500–590 nm (green)

Band 2

20 m

610–680 nm (red)

610–680 nm (red)

610–680 nm (red)

Band 3

20 m

790–890 nm (IR)

790–890 nm (IR)

790–890 nm (IR)

Band 4

20 m

–

1580–1750 nm

1580–1750 nm (SWIR)

(SWIR)

Hi-res. M

13

10 m

Monospectral, P

P mode: 510–730 nm

M mode: 610–680 P: 480–710 nm nm 2.5-m resolution

Panchromatic

The “quincunx” design was necessary to compete with the new commercial data emerging from the United States, given a use license issued by the French government late in the design process.

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131

Figure 5.13 SPOT-5 spectral responses. Note that bands 2 and 3 are designed to distinguish the vegetation signature at the 700-nm IR ledge. The panchromatic sensor overlaps the green and red, but is not responsive to near infrared. This is in contrast to IKONOS and Quickbird.14

5.5 Spectral Responses for the Commercial Systems A major evolution in spectral imaging has occurred with the advent of three commercial remote sensing systems. IKONOS, Quickbird, and Orbview-3 provide spectral imagery at a resolution of 4 m or better15 and have similar spectral responses, all modeled after the first four Landsat spectral bands. The calibration values for IKONOS are given in Fig. 5.14. Note that the panchromatic-sensor spectral response extends well into the near infrared, and that the response in blue is relatively poor. The response functions for the other commercial sensors are all very similar. The subtle differences become important when spectral quantities are estimated, such as vegetation health or area coverage. The markets and applications for these sensors are still being created. Their improved spatial resolution (a factor of ten greater than Landsat) is ideal for studies of fields and forests by those who wish to observe and characterize vegetation; presently, the largest market is in agriculture.

14

© Centre National d’Etudes Spatiales (CNES). OrbView 3 was launched June 26, 2003. The sensor provides 4 m spectral data in an 8 km swath.

15

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Figure 5.14 The panchromatic sensor has almost no blue response, to avoid image degradation caused by atmospheric scattering. Note the fairly high NIR coverage of the panchromatic sensor. Blue: 0.45–0.52 µm; Green: 0.52–0.60 µm; Red: 0.63–0.69 µm; NIR: 0.76–0.90 µm.

5.6 Imaging Spectroscopy Imaging spectroscopy is the acquisition of images wherein for each spatial-resolution element of an image, a continuous spectrum of the energy arriving at the sensor is measured. These spectra are used to derive information based on the signature of the interaction of matter and energy expressed in the spectrum. Spectroscopy has been used in the laboratory and astronomical observatory for more than a hundred years. The AVIRIS sensor is the prototype imaging spectrometer for remote sensing. 5.6.1 AVIRIS AVIRIS is an acronym for airborne visible-infrared-imaging spectrometer. AVIRIS is a world-class instrument in the realm of Earth remote sensing, a unique optical sensor that delivers calibrated images of the upwelling spectral radiance in 224 contiguous spectral channels (also called bands), with wavelengths from 380 to 2500 nm. The instrument was designed to fly aboard a NASA ER-2 plane (a U2 modified for increased performance) at approximately 20 km above sea level, at about 730 km/hr. The AVIRIS instrument contains 224 detectors, each with a wavelength-sensitive range (also known as spectral bandwidth) of approximately 10 nm, allowing it to cover the range between 380 nm and 2500 nm. Plotted on a graph, the data from each detector yields a spectrum that, compared with the spectra of known substances, reveals the composition of the area under surveillance.

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Figure 5.15 AVIRIS line diagram. AVIRIS uses silicon (Si) detectors for the visible range and indium-antimonide (InSb) for the near infrared, cooled by liquid nitrogen. The sensor has a 30° total field of view (full 614 samples) and one milliradian instantaneous field of view (IFOV, one sample), calibrated to within 0.1 mrad. Dynamic range has varied; 10-bit data encoding was used through 1994, 12-bit data have been read out since 1995.

AVIRIS uses a scanning mirror to sweep whiskbroom fashion, producing 614 pixels for the 224 detectors on each scan. An individual pixel produced by the instrument flown at an altitude of 20 km covers an approximately 20-m square area on the ground (with some overlap between pixels), yielding a ground swath about 11 km wide.16 5.6.2 Hyperion The first major VNIR/SWIR hyper-spectral sensor to fly in space was the Hyperion sensor, on the NASA EO-1 platform. EO-1 is a test bed for Earth-resources instruments, launched in conjunction with Landsat 7 and designed to test follow-on technology for NASA systems. EO-1/SAC-C was launched November 21, 2000, from VAFB in a 705-km orbit, trailing just after Landsat 7. The Hyperion sensor is the TRW-built cousin to the payload of NASA’s ill-fated Lewis satellite effort. Hyperion offers 30-m spatial resolution covering a 7.5-km swath. The 0.4– 2.5 µm spectral range is analyzed at 10-nm spectral resolution (220 bands). Figure 5.17 contains a nice illustration of the spectral nature of the sensor and an

16

See http://aviris.jpl.nasa.gov/

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Figure 5.16 This image from AVIRIS shows elements of a scene acquired on August 20, 1992. The mission was flown on a NASA ER-2 plane at an altitude of 20,000 m (65,000 ft) over Moffett Field, California, at the southern end of the San Francisco Bay. The image is roughly true color. Blue: 458.46 nm; green: 557.07 nm; red: 655.84 nm (bands 10, 20, and 30). The red on the east side of the bay is correct, due to the presence of one-cm-long red brine shrimp in the evaporation pond.

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Figure 5.17 Mount Etna. Hyperion offers 12-bit dynamic range.17

unusual look at the beginnings of a blackbody curve for the hot lava of Mount Etna, glowing at some 800–1000 K. The lava curve (brown in the line plot) shows a spectrum that rises above the intensity of reflected sunlight beginning at about 1600 nm, and appears to be peak around 2.4 µm. By contrast, a vegetation signature (the green curve), shows the IR ledge expected of healthy vegetation at 700 nm. The small arrows along the bottom of the curve, at 1234, 1639, and 2226 nm, indicate the spectral bands used to construct the image on the right, coded as blue, green, and red, respectively. 5.6.3 MightySat II—FTHSI18 The first hyperspectral sensor to fly on a satellite was the Fourier transform spectrometer flown by AFRL on the USAF MightySat-II. It was launched from Vandenberg Air Force Base into a 550-km polar orbit by a Minotaur rocket on 19 July 2000. The Fourier transform hyper-spectral imager (FTHSI) can produce 150 narrowband images in

17

See http://eo1.gsfc.nasa.gov/Technology/Documents/InstrumentOverview.html; or Jay Pearl man, et al., “Development and operations of the EO 1 hyperion imaging spectrometer,” Proc. SPIE, 4135, pp. 243 253 (2000). 18 See http://www.afrl.af.mil/news/summer00/features/mightysat feature.pdf

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the 0.45–1.05-µm band. Image quality was modest—but it was the first. Air Force security games prevented anyone from seeing much of the data.19 From a space-systems design effort, the most interesting aspect of the sensor was the use of commercial, off-the-shelf parts. No radiation-hardened parts were used, though some additional shielding was placed around critical components. The sensor operated nominally until the satellite was shut down.20

5.7 Problems

Figure 5.18 RGB of first scene, taken near Keenesburg, CO. The data are presented as a false-color IR image—red regions are areas of vegetation.21

1. What wavelength does the IR ledge for vegetation occur at? Is this in the bandwidth of a silicon detector? 2. When was the first Landsat launched? 3. What wavelength ranges correspond to red, green, and blue? 4. How many spectral channels are used for a Thematic Mapper? Over what wavelength ranges? 5. How wide is a standard Landsat 7 image? What is the spatial resolution for the six reflective bands? What is the spatial resolution for the thermal band? How many pixels wide does this make an image in the reflective band? 6. How does SPOT differ from Landsat 7? Consider spatial resolution (spectral bands, high-resolution panchromatic band), wavelength for the high-resolution panchromatic band, orbit, and wavelengths of spectral bands. 7. What is the nominal orbit for Landsat 7 (include altitude, inclination, local time for equator crossing)? 8. How long is the repeat cycle for Landsat 7? 9. What is the dynamic range for visible detectors on Landsat 7 (six, eight, or ten bits)? (You may need to go to the NASA/GSFC Landsat site on the web.) 10. What is the nominal spectral resolution for AVIRIS (compared to Landsat)?

19

William Scott, “Mighty Sat takes first hyperspectial images,” Aviation Week & Space Technology 153(7), p. 57 (2000). 20 John Otten, Private Communication, 2004. 21 The first hyperspectral sensor to fly on a satellite was the Fourier transform spectrometer pro duced by the Kestral Corporation of Albuquerque, NM.

Chapter 6 Image Analysis

In the previous chapters, we discussed imaging technology and remote sensing systems. Once the data reach the ground, the next question is how to extract information from the images. We’ll begin with traditional photo-interpretation techniques, then move on to the manipulation of digital data. There are two techniques involved in image processing for remote sensing: enhancing images for presentation and extracting information. Most work at the pixel level and many make use of scene statistics. If the data inhabit more than one spectral dimension (that is, if they have color), then a broad range of techniques can exploit their spectral character and extract information.

6.1 Interpretation Keys (Elements of Recognition)1 Traditional image analysis makes use of certain key elements of recognition, ten of which are developed here. The first four—size, shape, height, and shadow—are related to the geometry of objects in the scene. 6.1.1 Shape Shape is one of the most useful elements of recognition. One classic shape-identified structure is the Pentagon, shown earlier in Fig. 3.7. In Fig. 3.6, shape alone can identify the airfield, though it is not well resolved. Other instantly recognizable shapes include oval racetracks and the pyramids of Egypt.

1

Thomas Eugene Avery & Graydon Lennis Berlin, Fundamentals of Remote Sensing and Air photo Interpretation, 5th ed., Macmillan Publishing Company, New York, NY, pp. 52 57 (1992). W.L. Teng, et al., “Fundamentals of photographic interpretation,” in Manual of Photographic Interpretation. W.R. Philipson (Ed.), American Society for Photogrammetry and Remote Sensing, Bethseda, MD, pp. 49 113 (1997). John R. Jensen, Remote Sensing of the Environment: An Earth Resource Perspective, Prentice Hall, Upper Saddle River, New Jersey, pp. 121 133 (2000).

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6.1.2 Size Relative size is helpful in identifying objects, and mensuration, the absolute measure of size, is extremely useful in extracting information from imagery. Illustrations at the beginning of Chapter 1 showed how runway length could be obtained from properly calibrated imagery. For example, the Hen House radar sites (Fig. 1.4) display characteristic shapes and sizes. 6.1.3 Shadow Shadows separate targets from background. They can also be used to measure height. See, for example, the Washington monument in Fig. 3.7(b). 6.1.4 Height (depth) Height is generally derived from shadows in nadir-viewing imagery, but can be derived directly from more oblique views. Stereo imagery has been used to distinguish height in aerial photography and the original Corona imagery. Modern alternatives include LIDAR and interferometric synthetic-aperture radar (IFSAR). 6.1.5 Tone or color Tone and color are the product of the target albedo and illumination. The Landsat images in Chapter 1 illustrate this element. Consider the difference in tone between the runway (asphalt?) and adjacent regions in Fig. 1.16. The green regions on the south end of Coronado Island (Fig. 1.17) are distinguished from regions of similar brightness by color. On a larger scale, the distinction between dirt and vegetation in San Diego County can also be made by color (Fig. 1.13).

2

Figure 6.1 SA-2 SAM Base, KH-4 CORONA Product.2

Courtesy of Federation of American Scientists, http://www.fas.org

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6.1.6 Texture Texture is concerned with the spatial arrangement of tonal boundaries. Texture is the spatial arrangement of objects that are too small to be discerned. Texture depends upon the image scale, but can be used to distinguish objects that may not otherwise be resolved. The relative coarseness or smoothness of a surface becomes a particularly important visual clue with radar data (Fig. 1.23). Agricultural and forestry applications are appropriate for this tool—individual trees may be poorly resolved, but clusters of trees will have characteristic textures. 6.1.7 Pattern Related to shape and texture is pattern, the overall spatial form of related features. Figure 6.1 shows a Russian SAM site, with characteristic patterns that help detect missile sites, such as the Russian propensity for erecting three concentric fences around important installations. In imagery from systems like Landsat (30-m resolution), irrigated fields form characteristic circular patterns in the American southwest (Fig. 6.2). Geological structures, too, reveal themselves in characteristic patterns, a concept applied in the search for water on Mars and for characteristic textures3 and patterns4 associated with mineral hydration and water flow.

3

Figure 6.2 Boulder, Colorado. Landsat TM image, bands 4, 3, and 2. The Bighorn Basin is located about 100 miles east of Yellowstone National Park in northern Wyoming. The circle is characteristic of irrigated crops. Bright red indicates the area is highly reflective in the near infrared (TM band 4), which indicates vegetation.

T.J. Parker, et al., “Petrogenetic Interpretations of Rock Textures at the Pathfinder Landing Site,” presented at the 29th Lunar and Planetary Science Conference, March 16 20, 1998. 4 “The strongest evidence for the Martian ocean comes from a unique pattern found in the rocks that indicate a flow of some sort of built up of layers in the rock. There are fine distinctions between wind flow and water, however, and the Mars science team directed Opportunity to take a series of close up pictures so they could assess the etchings.” “Ripples that formed in wind look different than ripples formed in water,” said John Grotzinger, a rover science team member from the Massachusetts Institute of Technology. “Some patterns seen in the outcrop that Opportunity has been examining might have resulted from wind, but others are reli able evidence of water flow.” From http://dsc.discovery.com/news/briefs/20040322/marswater.html

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6.1.8 Association Three elements of photo-interpretation are related to context, or the relationship between objects in the scene to each other and to their environment. These elements are site, association, and time. Association is the spatial relationship of objects and phenomena, particularly the relationship between scene elements. “Certain objects are genetically linked to other objects, so that identifying one tends to indicate or confirm the other. Association is one of the most helpful clues for identifying cultural features.”5 Thermal-power plants will be associated with large fuel tanks or fuel lines. Nuclear-power plants tend to be near a source of cooling water (though this can also be considered an example of site or location). A classic instance of cultural association from the Cold War was the detection of Cuban forces in Angola by the presence of baseball fields in the African countryside (1975–76). 6.1.9 Site Site is the relationship between an object and its geographic location or terrain. This can be used to identify targets and their use. A poorly resolved structure on the top of a hill might, for example, be a communications relay, based on its location. 6.1.10 Time The temporal relationships between objects can also provide information, through time-sequential observations. Crops, for example, show characteristic temporal evolutions that uniquely define the harvest. Change detection in general is one of the most important tasks in remote sensing, and follows from this interpretation key.

6.2 Image Processing Several important topics appear at this point. In the discussion of images above and the data from various space systems described in previous chapters, we have not yet defined at least one important concept: the relationship between the numbers that come from a satellite and the images that result from those numbers.

5

Thomas Eugene Avery & Graydon Lennis Berlin, Fundamentals of Remote Sensing and Air photo Interpretation, Macmillan Publishing Company, New York (1992).

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Figure 6.3 Model Susie Olsen. The image chip on the right is reduced in resolution to 20% of the original.

Table 6.1 The digital number (DN) values are given here for the image chip of the eye shown above. The DN values for 152 are highlighted. There are ten such values. Compare to the image above by locating the highest data value, DN = 210. 1

1

2

2

3

4

5

6

7

8

10

11

12

13

14

15

181 188 178 157 153 119 106 107 97

91

91

89

89

87

102 117 119 115 106 82

3

179 160 162 149 132 107 90

98

114 129 151 172 175 177 169 166 158 141

4

163 158 144 147 120 116 115 121 137 162 174 180 184 184 179 184 182 184 179 170

5

156 149 145 137 139 143 148 156 169 177 179 177 179 182 175 179 177 179 177 169

6

153 151 148 149 153 156 159 152 152 151 153 152 155 162 166 171 173 175 172 166

7

156 152 158 159 150 136 137 146 156 160 158 152 140 134 132 145 161 162 163 158

8

148 158 157 139 144 151 126 87

73

58

55

52

67

96

122 125 123 150 156 153

9

148 152 142 149 143 120 95

48

50

58

43

50

85

85

57

10

147 152 157 130 143 192 103 47

65

97

38

47

87

165 120 50

71

113 133 144

11

164 153 126 157 197 210 121 71

43

34

44

56

109 170 143 98

73

76

117 132

12

172 134 147 155 151 161 143 110 95

67

71

85

149 146 114 89

99

96

109 131

13

182 187 186 181 175 179 173 171 161 151 134 122 120 116 125 126 129 138 144 153

14

178 198 198 182 179 182 181 191 172 167 162 153 145 153 152 150 152 157 164 169

15

175 185 192 188 185 187 193 205 201 194 190 185 177 173 166 164 170 173 180 182

16

183 185 193 195 198 199 201 200 196 191 188 186 180 180 182 184 187 191 192 189

86

9

90

16

79

17

18

19

20

111 128 150 152

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6.2.1 Digital numbers: pixels and pictures, histograms In the world of remote sensing, the data from a sensor, as received on the ground, is termed “digital number,” or DN (admittedly a redundant terminology). The relationship between DNs and images is illustrated here using a photograph taken with a digital electronic camera. The subject of a face was chosen to provide an intuitive image. The resolution is high, so a small image chip of the eye is extracted for our purposes and shown expanded on the right, its resolution reduced to facilitate display in tabular form. The data values associated with each eye pixel are given in the table below the figure, with numbers running from 0 to 210, where 0 is a black pixel and 210 is nearly white. Many image-processing techniques begin with an examination of the statistics of the scene or image; in particular, an important technique is to examine the histogram of occurrences in a scene. In this case, there are ten occurrences of DN value 152 in the table, corresponding to a bright gray in the image. This point is indicated in Fig. 6.4 (10 at DN = 152) in the trace of occurrences for the values in the table. The curves above show the distribution of values at the original resolution for that region, and then for the full image. The last trace has been divided by ten to keep it on scale. The curves appear rather broad because of the logarithmic vertical axis. Note that the electronic camera’s electronic brain has done its job: there is a fairly broad range of DN (0-255), with the histogram fairly evenly distributed across the 8 bits of dynamic range.

Figure 6.4 Histogram of DN occurrences. The reduced-resolution curve corresponds to the image at the right of Fig. 6.3 and the table above. The full resolution statistics for the same region are given, along with those for the complete 847 × 972 image.

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Figure 6.5 Histogram of DN occurrences. The choppiness of distribution is because IRS is only a 6-bit system; the dynamic range is only 0-64. In the rescaled date, only every 4th value is present.

In remote sensing, such histograms can be used to partition imagery. A histogram is shown here for the IRS-1C image of San Diego illustrated in Fig. 1.16. In Fig. 6.5 we see a nice Gaussian shape over most of the dynamic range and a peak near zero DN for water. One quick potential scene partition would be to divide the scene into elements where the DN is below 10 (for water), and above 10 (for land). This is the beginning of the processes that lead to target detection. 6.2.2 Dynamic range—snow and black cats A black-and-white picture taken with a high-quality 2 ¼-inch roll film camera (6 × 6 cm) was scanned using a Nikon film scanner with 12 bits of dynamic range. The resulting image had a range of digital numbers from ~50–4000. The image, scaled in various ways, is displayed in Fig. 6.6. The histogram of data values is displayed in Fig. 6.7. Roughly speaking, three peaks appear. At far right are the snow values (DN ~ 3,600), at far left (DN ~ 340), the dark coats. The middle peak at DN ~ 1080 is the mid-tones of clothing and fog-shrouded background. In Figure 6.6, the data are initially shown scaled from ~50–4000 (top right). The data are next rescaled to encompass each of the three broad regions that define the histogram. The image at the top right is scaled to show detail in the foreground, particularly the man’s jacket (DN = 50–800). The bottom row shows the midrange (800–2500), and the snow (2500–4000) in much greater detail.

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Figure 6.6 The scanned film has a dynamic range of 12 bits or so.

Note that modern satellites, such as IKONOS and Quickbird, provide 11-bit data, with DN that range from 0 to 2047. As with the illustration here, the data must be scaled to 0–255 for display. That mapping requires the same considerations as the illustration given here. One last note: if you wanted to see detail in the face of the little girl at left, the data range from DN = 241 – 2116 should be scaled to 0–255 (Fig. 6.7). Now let’s consider a very dark target. This cat was photographed with a Canon digital camera (1600 × 1200) (Fig. 6.8a); the exposure was adjusted to compensate for the nearly black fur. Histograms for the three colors are shown (Fig. 6.8b). The

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Figure 6.7 Peaks at DN = 340, 1080, and 3660. Face is scaled from DN = 241–2116.

Figure 6.8(a) Black cat digital image.

Figure 6.8(b) Black cat histogram.

peak at DN ~30 is the very dark fur on the face—the lowest values are for the shadowed fur. The grass and brighter fur make up the mid-range, at around 100 or so. The red collar and white fur provide the peak, at DN ~ 250. Such histograms are key in distinguishing targets from backgrounds in both panchromatic and spectral imagery. This concept will be described below, but first a few words on filtering.

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6.2.3 Filters There are a number of standard ways to manipulate images for enhanced appearance or to make it easier to extract information. Simple smoothing filters reduce noise; more sophisticated filters can reduce ‘speckle’ in radar imagery. A few simple concepts are illustrated here with a Landsat panchromatic image from San Francisco taken on March 23, 2000 (Fig. 6.9). The data have a basic resolution of 15 m. A small chip has been extracted for the northeast corner of the peninsula, the Bay Bridge and Yerba Buena Island, as well as an image chip for San Francisco Airport. The filters are applied using an image kernel—a concept adapted from calculus and transform theory. 6.2.3.1 Smoothing Noisy images can be difficult to interpret. One approach is to smooth the image, averaging adjacent pixels together through a variety of approaches, with some specialized versions like the Lee filter used to reduce speckle in radar images. The illustration here is not particularly apt, since the data quality is good, but a three-by-three filter block has been applied, with even weights for each pixel. The kernel is illustrated here: the center of each 3 × 3 pixel block is replaced by the average of all nine pixels. 0.111

0.111

0.111

0.111

0.111

0.111

0.111

0.111

0.111

6.2.3.2 Edge detection High-pass filtering removes the low-frequency components of an image while retaining the high frequency (local variations). It can be used to enhance edges of adjoining regions as well as sharpen an image. This is accomplished using a kernel with a high central value, typically surrounded by negative weights. Here, the kernel takes the difference between the central pixel and its immediate neighbors in all directions. Note how the bridge is enhanced, as are the edges of the island. –1

–1

–1

–1

8

–1

–1

–1

–1

A small section of the bridge is shown in a magnified view to further illustrate the filter’s result. The original data are on the left [Fig. 6.9(d)], the filter output is on the right [Fig. 6.9(e)].

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Figure 6.9 Landsat panchromatic sensor (a) raw data, (b) smoothed image, (c) high-pass filter, (d) raw, (e) high-pass filter.

Figure 6.10 Landsat (a) raw data, (b) high-pass filter (edge detection).

The same high-pass filter is applied to the airport area, depicted in Fig. 6.10. The runways are pulled out, along with the edges of the terminal buildings. Similar approaches are used to sharpen images for analysis by the human eye.

6.3 Histograms and Target Detection The trick in target detection is to be able to distinguish the target from the background reliably. The jargon for this is “probability of detection” (you want this to

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Figure 6.11 Histogram and target image. A model image simulates what you might obtain from a 40 × 40 detector array attached to a telescope. The image is inset, and the small bright region is supposed to be the target.

be high), versus “probability of false alarms” (preferably low). In Fig. 6.11, a target has been superimposed on a randomly generated background. The nominal target has been circled. A subset of the image values are given in the table below, centered on the target. The target pixels in the table below are those have higher data values than the background noise. The standard deviation is the square root of the variance, or 24.1. This is roughly the half width at half maximum (HWHM). The target, which is from 175–180, is four sigma away from the center of the background noise. Table 6.2 Image values centered on the target.

93 59 132 96 97 80 92 36 72 66 79

91 97 79 95 76 63 107 78 73 60 66

74 85 77 52 85 10 62 96 58 104 50

87 110 114 96 91 59 54 112 37 63 76

68 88 113 58 67 175 176 87 84 109 88

85 71 75 81 176 180 178 142 54 91 110

94 102 87 65 176 178 49 100 38 43 60

37 47 61 96 88 63 58 82 111 62 88

72 50 99 54 52 91 113 75 116 79 112

94 96 86 64 75 100 89 43 101 105 84

110 98 80 75 41 111 78 73 69 93 31

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As an exercise, estimate the random-noise level (the width of the background distribution, aka “sigma”) from the histogram graph and compare to the numbers obtained via calculation: Mean

Variance

Skewness

Kurtosis

76.8

580.3

0.21

0.92

6.4 Histograms, Spectral data, and Transforms The previous sections of this chapter primarily deal with panchromatic imagery. Spectral imagery requires different techniques. A fairly artificial illustration has been constructed to make some of the important concepts in spectral analysis more obvious. The example has a red Zip™ disk on the grass. The data are displayed as an image, histogram, and two scatter plots. Figure 6.12 shows that although it’s easy enough to see the disk, it’s not immediately obvious how to tell a computer to distinguish the red pixels from the background. Figure 6.13 shows a new data format: a 2D scatter plot. The high correlation is apparent. Color

Mean

Standard deviation (σ)

Red

50.9

23.4

Green

50.0

23.6

Blue

21.3

17.1

Figure 6.12 (a) Red disk, grass background. (b) Histogram of red (1), green (2), and blue (3) bands from color image.

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Figure 6.13 Scatter plots of the occurrence of RGB triples: (a) Red vs. green, (b) blue vs. green.

This correlation, or redundancy, in the data is not a major problem here, but it becomes much more so when you have higher spectral dimensions to your data (six or seven bands with Landsat, 224 bands with AVIRIS). The trick is to use the power of statistical analysis to make use of redundancy in spectral data. The details for our example above show a very strong correlation between the three bands. The correlation is unusually high because of the homogeneity of the scene, but the concept is fairly general. Images taken at varying wavelengths will be highly correlated. This correlation can be very important in spectral analysis. Table 6.3 Correlation and covariance matrices.

Correlation R

G

B

R

1.00

0.96

0.92

G

0.96

1.00

0.91

B

0.92

0.91

1.00

Covariance R

G

B

R

547.86

530.06

369.36

G

530.06

557.58

368.14

B

369.36

368.14

291.49

The correlation calculation has a closely related term: the covariance. They are related by a normalization factor that is the square of the standard deviation. In the covariance matrix above the diagonals are just the squares of the standard deviations given above.

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Target detection and related goals in spectral imagery can be powerfully addressed by these statistics. The trick is to rotate the data space into a coordinate system in which the different bands are uncorrelated, which frequently leads to a very useful transformation that facilitates the detection of targets and other tasks. This rotation in color space can be accomplished by diagonalizing the covariance (or correlation) matrix. This can be done by means of a rotation matrix (a matrix built from the eigenvectors of the transformation that diagonalizes the covariance matrix). This transformation is called a principle-components transform, also variously termed the Karhuenen-Loeve transform and the Hotelling transform. The new coordinates are PC1, PC2, and PC3. Table 6.4 below is interpreted, for example, such that: PC3 = 0.767 × Red – 0.597 × Green – 0.236 × Blue. PC1 is the average brightness, weighted by the dynamic range (variance) of each band. The remaining PC bands are orthogonal to the first (and each other), and uncorrelated to each other. In this case, PC3 is the difference between the red and blue/green images. Table 6.4 Transform matrix.

R

G

B

PC 1

0.631

0.635

0.445

PC 2

0.116

0.490

–0.864

PC 3

0.767

–0.597

–0.236

Table 6.5 Covariance matrix.

PC 1

PC 2

PC 3

PC 1

1341.74

0.0

0.0

PC 2

0.0

33.35

0.0

PC 3

0.0

0.0

21.85

The covariance matrix is now diagonal and has an additional interesting characteristic: the bands are ordered by their variance. For high-dimensional data, this means that you can often reduce the effective dimensionality by means of this transform. This is because the dimensionality of an imaged scene is generally fairly modest, reflecting to some extent the spectrally different objects in the scene. For hyper-spectral imagers, with hundreds of bands, the data are highly redundant. In a PC transform, the first few bands in transform space have the highest variance, that is, most of the scene information. Higher-order bands are mostly noise. In fact, one way to remove noise from spectral imagery is to transform into PC space, eliminate

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Figure 6.14 Scatter plots in principal-component space. Note that in PC 3, the disk is now clearly distinguished from the grassy background.

the noise bands, and then invert the transform—a very powerful method for removing systematic sensor noise. Note that the eye performs a very similar transformation. The signals from the LMS cones (Fig. 5.3) are transformed in a manner much like a PC transform. The red-green and blue-yellow cones produce highly correlated imagery, along with the panchromatic rods. The first component is intensity, the second hue, and the third is basically saturation. Most of the information (and the highest spatial resolution) is in the intensity band (PC 1), while color is a small percentage of the information (PC2). One consequence is that the eye’s ability to resolve high-frequency components is much greater for variations in intensity than in color.

Figure 6.15 Histogram of PC 3. Note that the vertical scale is logarithmic—the background distribution is quite narrow here—with σ = 4.67, FWHM is approximately 10. The target (the disk) is over 10σ away from the center of the grass.

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Returning to our image of the disk, we now see that the target (the disk) is clearly differentiated from the background in our new coordinate system, or color space. Figure 6.15 shows the disk pixels peak at a DN of 70 or so, some 10 sigma away from the center of the background distribution of grass pixels.

6.5 Supplemental Notes on Statistics Remote sensing data are replete with great applications for powerful statistical analysis tools, which require at least a modest knowledge of statistics and probability. A few fundamental concepts are defined below. First, the mean or average value takes the sum of the DN values, and divides by the number of pixels: Mean = x =

N

1 N

∑ x j.

(6.1)

j =1

The variance addresses the range of values about the mean. Spatially homogeneous scenes will have a relatively low variance; scenes or scene elements with a wide range of DN will have a larger variance. The standard deviation σ is just the square root of the variance: Variance =

1 N ∑( xj − x N − 1 j =1

σ=

), 2

(6.2)

(6.3)

Variance.

The correlation coefficient and covariance are closely related – Correlation Coefficient = r N

N

j =1

j =1

N ∑ xj yj − ∑ xj =

 N  N   N ∑ x j2 −  ∑ x j   j =1   j =1 covariance =

2 1/ 2

  

N

∑ yj j =1

2  N  N   2 N ∑ y j −  ∑ y j    j =1    j =1

1 N 1 ∑ x j y j − N − 1  j =1 N N

1 = ∑ (x j − x N − 1 j =1

)( y

j

1/ 2

N

N



j =1

j =1



(6.4)

∑ xj ∑ yj 

)

−y .

(6.5)

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Figure 6.16 San Diego Harbor, IKONOS image, February 7, 2000.6

Note that the correlation coefficient and covariance are related by the standard deviation: covariance / σxσy6 A very simple example: X = [1, 2, 3] mean (x) = 2 variance (x) = 1 σ(x) = 1 correlation coefficient = 1

Y = [2, 4, 6] mean (y) = 4 variance (y) = 4 σ(y) = 2 covariance = 2

Figure 6.17 (a) Dark grey, cluttered background with bright target. (b) Histogram for DN occurrence. 6


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Figure 6.18 The Moss Landing Mineral Refractory was built ca. 1942. The white material may be dolomite from the Gabilan mountains, or magnesium residue from the material extracted from seawater.7 7

Satellite images courtesy of Digital Globe.

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6.6 Problems 1. This image of San Diego Harbor (Fig. 6.16) was taken on February 7, 2000 by the IKONOS satellite. What can you tell about the two ships? The carrier is 315-m long. What can you tell about the other ship? 2. How could you tell that a road or rail line was intended for missile transport? 3. For an otherwise uniform scene (Fig. 6.17), there is a target with higher DN. The variance is 5106.4. Calculate the standard deviation (σ). Estimate distance between the target and background, in units of σ. 4. In Fig. 6.18, three regions are identified: water, a bright soil, and the old Moss Landing refinery site (red), with some very bright white sand and soil. Describe what dynamic ranges you would use to display the scene so as to enhance each region of interest. As an example, the best display for the soil would be to scale the data so that DN = 250 – 450 mapped to a digital display range of 0–255. 5. For a scene with 4 pixels, calculate the correlation between the pixels, and the covariance. Pixel #

Red (DN)

Green (DN)

Blue (DN)

1

40

50

60

2

20

25

28

3

30

30

30

4

15

16

14

Chapter 7 Thermal Infrared

To remote sensors, the infrared portion of the electromagnetic spectrum is quite different from the visible. In the IR, sensors provide more than just an image—IR can give non-literal information which may have different value than a comparable panchromatic (visible) image. A large range of tactical and strategic sensors operate solely in the IR, sensing the emitted radiation from targets and backgrounds, as opposed to the reflected radiation we have focused on in earlier sections.

7.1 IR basics In the visible spectrum, we mostly see by reflected light—typically sunlight. In the IR, there is a reflected solar component (during the day), but much remote sensing is due to emitted IR energy, particularly in the midwave-infrared (MWIR, 3–5 µm), and longwave-infrared (LWIR, 8–13 µm) spectral ranges. Figure 2.12 showed how the location of the peak in the spectrum and the amplitude of the radiated energy changes with temperature. As a consequence of these curves, we can both see in the IR and obtain temperature measurements of remotely sensed nighttime scenes. 7.1.1 Blackbody radiation Blackbody radiation was introduced in Chapter 2, and the relationship between the temperature of a body and the wavelengths of the emitted radiation was developed. It was noted that for terrestrial targets at 300 K (room temperature), the peak in the radiated spectrum is at 10 µm. This is illustrated in Fig. 7.1. Note that in the MWIR, reflected solar radiation is comparable to the radiation emitted from a 300 K blackbody. The concept of blackbody temperatures shows up in daily life, in places as ordinary as your local hardware store, where GE fluorescent light bulbs are sold by color temperature. For example: GE Daylight Ultra, 3050 lumens, 6500K; GE Daylight, 2550 lumens, 6250K;

157

158

Chapter 7

Figure 7.1 Blackbody curves. If you look at radiation from the sun, the sun acts like a blackbody at about 6000 K. Of course, the radiation from the sun decreases as per the inverse square law, and the incident radiation observed at the Earth is decreased by that factor: (radiussun/radiusEarth orbit)2. As a consequence, if you look at the 3–5 µm wavelength range, it is in the middle of the transition region from dominance by reflected solar radiation to dominance by emitted thermal radiation for terrestrial targets.

GE Chrome 50, 2250 lumens, 5000K; GE Residential, 3150 lumens, 4100K; GE natural color fluorescent for kitchen & bath, 3350 lumens, 3000K. (Note that lumens is a measure of brightness.) Two laws define the shapes shown in Fig. 7.1. 7.1.2 Wien’s displacement law Wien’s displacement law says that the wavelength of the peak is inversely related to the temperature: λm =

a , T

(7.1)

where a is a constant: a = 2898 µm/K. 7.1.3 Stefan-Boltzmann law T4 The Stefan-Boltzmann law defines the total power: S = εσT 4,

(7.2)

where σ is again a constant: σ = 5.669 × 10 8 W m 2 K 4, and ε is the emissivity. For a blackbody, the emissivity is 1.

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159

7.1.4 Emissivity The assumption so far has generally been that emissive objects are blackbodies, which are perfect absorbers and emitters of radiation. Real objects all have an emissivity (ε) that is between zero and one. The table below shows some average values for the 8–12 µm wavelength range. Just as with reflective spectra, there are fine scale variations in emissivity, which are unique to the material. Note that gold emits poorly in the longwave infrared. Figure 7.2 shows the variation in emissivity that occurs as a function of wavelength in the longwave IR spectrum for some common minerals. Note how the dip in the emissivity just above 11 µm moves to the right as the material varies from magnesite to dolomite to calcite. This reflects changing bond strengths in the materials.

Figure 7.2 Emissivity spectra for minerals in the LWIR spectra are offset by additive factors to avoid overlap. This figure comes from data in the Arizona State University spectra library: http:// emma.la.asu.edu/speclib/

7.1.5 Atmospheric absorption In the infrared wavelength range, atmospheric absorption, due primarily to water and carbon dioxide, becomes a very important consideration (Figs. 3.12, 3.14).

7.2 IR concepts 7.2.1 Kinetic temperature Resuming now with newer material, the concept of kinetic temperature appears. In general, a remote sensing instrument will not be able to factor emissivity into the im4 , the sensor data age analysis. As a result, although the radiated quantity is εσT kinetic 4 . Here, T kinetic is the “real” temperature, must in general be interpreted as σT radiated meaning the temperature one would measure with a thermometer at the target. Set-

160

Chapter 7 Table 7.1 Emissivities of common materials. (Credit: Buettner and Kern.)*

Material

Emissivity

Gold, polished @ 8–14 µm

0.02

Aluminum foil @ 10 µm

0.04

Granite

0.815

Sand, quartz, large grain

0.914

Asphalt, paving

0.959

Concrete walkway

0.966

Water with thin layer of petroleum

0.972

Water, pure

0.993

* Buettner and Kern, J. Geophys. Res. 70, p. 1333.

4 4 4 4 , or T radiated . Note that ε ting the two equal, we obtain: σT radiated = εσT kinetic = εT kinetic

is a number less than one, so T kinetic > T radiated by a factor which is just the fourth root of ε: 1

T radiative = ε 4 TKinetic

(7.3)

7.2.2 Thermal inertia, conductivity, capacity, diffusivity Normal reflective observations depend primarily on the instantaneous values for the incident radiation, but thermal IR observations are very much dependent on the thermal history of the target region and the nature of the materials imaged.1 7.2.2.1 Heat capacity (specific heat) Thermal heat capacity is a measure of the increase in thermal-energy content (heat) per degree of temperature rise. It is measured as the number of calories required to raise the temperature of 1 g of material by 1oC. It is given the symbol: C(calories / gm ° C).

1

W. G. Rees, Physical Principles of Remote Sensing, Cambridge University Press (1990); Floyd F. Sabins, Remote Sensing, Principles and Interpretations (3rd Ed), W.H. Freeman, New York (1996).

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161

Thermal storage is a closely related quantity, modified by the mass density: c(calories / cm 3 ° C where c = ρ C, where ρ is the mass density in g / cm 3 .

)

7.2.2.2 Thermal conductivity Thermal conductivity is the rate at which heat passes through a material, measured as the amount of heat (calories) flowing through a cross-section area (cm2), over a set distance (thickness in cm), at a given temperature difference (°C). It is given the symbol: K (calories / cm s ° C), where the nominal value for rocks is 0.006 in these peculiar units (compare water, ~0.001, and copper at 0.941). Rocks are generally poor conductors of heat compared to metals, but are better than loose soil, which tends to have insulating air pockets.

7.2.2.3 Thermal inertia Thermal inertia is the resistance of a material to temperature change, indicated by the time-dependent variations in temperature during a full heating/cooling cycle:  calories  P = K ρC  . 1   cm 2 ° C s 2 

(7.4)

This quantity varies by a factor of four or five for the range of materials shown in the table below.

7.2.2.4 Thermal diffusivity Thermal diffusivity is a measure of the rate of internal heat transfer within a substance. It is related to conductivity: k = K / Cρ(cm 2 / s . In remote sensing, it relates

)

the ability of a substance to transfer heat from the surface to the subsurface during the day (heating period), and from the subsurface to the surface during the night (cooling period).

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Table 7.2 Thermal parameters for various materials.2

 calories   P  1  2 2 cm ° C s  

Material

 calories  K   cm s ° C 

 calories  C   g °C 

ρ

Water

0.0014

1.0

1.0

0.038

Wood (oak)

0.0005

0.33

0.82

0.012

Sand Soil

0.0014

0.24

1.82

0.024

Basalt

0.0045

0.21

2.80

0.053

Aluminum

0.538

0.215

2.69

0.544

Copper

0.941

0.092

8.93

0.879

Stainless steel

0.030

0.12

7.83

0.168

g cm 3

7.2.2.5 Diurnal temperature variation The application of the above concepts is in the variation in temperature which occurs over the day for the illuminated Earth surface. Materials with high thermal inertia (such as metallic objects) change temperature by fairly modest amounts. Low-thermal-inertia materials (such as vegetation) change more quickly. Figure 7.3 illustrates some consequences. Note that different objects will reach equal radiative temperatures in the dawn and dusk intervals. This can cause targets to “disappear” as their temperatures match the background. This is more directly illustrated by some observations taken by Captain Aimee Mares in Hawaii. Figure 7.4 shows a visible image and IR camera observations taken over the Hale Koa hotel, from high up in the adjacent Hilton Hawaiian Village Hotel. The IR images were converted to temperatures, with time profiles as shown in Fig. 7.5. The variation in ocean temperature is probably less than shown here—the water surface is largely constant in temperature, and these variations generally reflect measurement error. By comparison to Fig. 7.3, shadows cause different objects to change temperature at different times through the day. Still, thermal crossover is fairly obvious for the crushed-rock roof and the vegetation below at 1800 hrs. Note that the greenery of the trees will be very close to the ambient air temperature, minus a bit for the effects

2

From http://eerst.gsfc.nasa.gov/Sect9/Sect9 3.html; See also Avery and Berlin, p. 28, Campbell, Thomas Eugene Avery & Graydon Lennis Berlin, Fundamentals of Remote Sensing and Airphoto In terpretation, Macmillan Publishing Company, New York (1992). Floyd F. Sabins, Remote Sensing, Principles and Interpretations, 3rd Ed, W. H. Freeman, New York (1996).

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Figure 7.3 Illustration of the temporal variations in temperature for various materials over a day.3

of evaporative cooling. This information can be very useful for the temperature calibration of remotely sensed IR images. Sabins (1986, 1996) gives a great deal of useful information on the interpretation of such scenes, including the impact of wind on surfaces.

7.3 Landsat Infrared data from Landsat were shown in Chapter 1 for a San Diego view. Here, a second example shows the Landsat 7 thermal band in use. The illustration is from over northern Greenland, at Thule AFB. In the color picture (Fig. 7.6), the 60-m resolution data from band 6 were resampled using cubic convolution to an effective pixel size of five meters, as part of a sensor-calibration study. This was then combined with panchromatic band data into an RGB picture, as shown in Fig. 7.6. Band 6 data is red and panchromatic-band data are assigned to the green and blue channels. Note how some features are revealed as warmer than the surrounding snow, due to heating from the 24-hour sunlight at this high northern latitude. The runway and various buildings on the base show relative warmth, with the southern sides of the storage tanks near the base somewhat warmer than the northern sides. Exposed rock on the hillsides to the north are emitting greater thermal radiation than the snow.

3

Floyd F. Sabins, Remote Sensing, Principles and Interpretations (3rd Ed), W. H. Freeman, New York (1996).

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Figure 7.4 Visible camera image and microbolometer IR-camera images, 3/23/2002. Taken at 0600, 1100, 1500, and 1800 local time.

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165

Figure 7.5 Temperature profiles for the scene in Fig. 7.4.

Figure 7.6 Landsat 7: The figure to the left is the merged IR and panchromatic image; to the right is the panchromatic (reflective) image. The frozen ocean is at upper left. The fuel tanks and runway are warmer than the background. North is up. Jim Storey of the EROS Data Center resampled and enhanced this image.

7.4 Early Weather Satellites Weather satellites are some of the primary IR platforms. Historically, the first were small polar-orbiting platforms (TIROS, NIMBUS), followed by the first geosynchronous platforms (ATS). The first illustrations here, in the visible wavelengths, add perspective on whether surveillance can be done at the tactical or the strategic level from high altitudes.

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7.4.1 TIROS The Television Infrared Observation Satellite (TIROS) was the first series of meteorological satellites to carry television cameras to photograph cloud cover and demonstrate the value of spacecraft for meteorological research and weather forecasting. The first TIROS was launched on April 1, 1960, and returned 22,952 cloud-cover photos. The satellite was tiny by modern standards. Mass: 120 kg. Perigee: 656 km. Apogee: 696 km. Figure 7.7 TIROS, April 1, Inclination: 48.4 deg. RCA built the small cylindri1960.4 cal vehicle: 42" in diameter, 19" in height. Figure 7.7, taken by TIROS, is one of the first images of the Earth taken from space. TIROS has a complicated history of name changes and aliases, sensor packages, and parameters. Between 1960 and 1965, 10 TIROS satellites were launched. They were 18-sided cylinders covered on the sides and top by solar cells, with openings for two TV cameras on opposite sides. Each camera could acquire 16 images per orbit at 128-second intervals. 7.4.2 NIMBUS Named for a cloud formation, Nimbus, a second-generation meteorological satellite, was larger and more complex than the TIROS satellites. Nimbus 1 was launched on August 28, 1964, and carried two television and two infrared cameras. Nimbus 1 had only about a one-month lifespan; six subsequent missions were launched, with Nimbus 7 operating from 1978 through 1993. The spacecraft carried an advanced vidicon camera system for recording and storing remote cloud-cover pictures, an automatic-picture-transmission camera for real-time cloud cover images, and a lead selenide detector (3.4 to 4.2 µm) to complement the daytime TV coverage and measure nighttime radiative temperatures of cloud tops and surface terrain. The radiometer had an instantaneous field of view of about 1.5°, which at a nominal spacecraft altitude corresponded to a ground resolution of approximately 8 km at nadir. Some of these early IR images are shown in Fig. 7.8. Observe that in the daytime image at left, land is hot (white) and water cool (dark).

4

See http://earthobservatory.nasa.gov/Library/RemoteSensing/remote 09.html

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Figure 7.8 IR images from NIMBUS. The left image is from NIMBUS III, taken June 5, 1969.

7.5 GOES 7.5.1 Satellite and sensor The Geostationary Operational Environmental Satellite (GOES) mission provides the now-familiar weather pictures seen on newscasts worldwide. Each satellite in the series carries two major instruments, an imager and a sounder, which acquire high-resolution visible and infrared data, as well as temperature and moisture profiles of the atmosphere. The GOES I-M system serves a region covering the central and eastern Pacific Ocean; North, Central, and South America; and the central and western Atlantic Ocean. Pacific coverage includes Hawaii and the Gulf of Alaska. This is accomplished by two satellites, GOES West, located at 135° west longitude, and GOES East, at 75° west longitude. A common ground station, the CDA station in Wallops, Virginia, supports the interface to both satellites. Figure 7.9 shows the GOES imager. A familiar Cassegrain design provides the primary optic, and the sensor is a single pixel swept mechanically over the visible hemisphere. This design allows the visible hemisphere to be imaged once every 30 min. This design, selected partly for heritage reasons, simplifies sensor calibra-

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Figure 7.9 GOES: The 120-kg module uses 120 W power, outputs 10-bit data at less than 2.62 Mbps.5

tion: calibrating a larger array to the required accuracy would be time consuming. Five channels are used, as illustrated in Fig. 7.10 and further defined in Table 7.3. Note the wide range of spectral channels, detector materials, and spatial resolution. Table 7.3 Specifications for GOES I, J, K, and L.6

Channel Wave- Wave length number (cm 1) (µm)

Detector type

S/N or Scene Purpose NEdT temperature

1

0.65

15,385

Silicon

150:1

N/A

Chlorophyll absorption & cloud mapping

2

3.9

2,564

In-Sb

1.4K

300K

Fires, volcanoes, & night mapping

3

6.75

1,481

Hg-Cd-Te 1.0K

230K

Moisture imaging & water vapor, winds

4

10.6

943

Hg-Cd-Te 0.35K 300K

5

12.0

833

Hg-Cd-Te 0.35K 300K

5 6

Courtesy ITT. Courtesy ITT.

Land & sea thermal mapping

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Figure 7.10 GOES-8 spectral response functions. Spatial resolution: Visible: 1 km (28 µrad); Channels 2, 4, 5: 4 km (112 µrad); Channel 3: 8 km (224 µrad).

The bandpass selections for GOES are mirrored by the polar-orbiting NOAA Tiros satellites and the upcoming NPOESS satellite system. They allow observations of clouds, cloud and water temperatures, and atmospheric water. Channel 3, at 6.7 µm, is at a wavelength that is absorbed by atmospheric water. The atmosphere is opaque at this wavelength (Fig. 3.12); the sensor is responding to energy radiated from water vapor at the top of the atmosphere. 7.5.2 Weather and storms—Hurricane Mitch Some feeling for the relative utility of the different bands is given by Fig. 7.11. Views in the visible and mid-wave infrared are given for Hurricane Mitch in 1998. The two bottom views at 2045 UTC (Zulu) show the reflective (sunlit) cloud tops (on the left) and the water emission from the storm clouds (at right).

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Channel 1—Visible, October 25, 1998, Channel 3—IR water vapor band, October 18:15 Z 26, 1998, 00:15 Z

Channel 1—Visible

Channel 3—Water vapor band Figure 7.11 Weather—layers of information.7

7.5.3 Volcanoes and ash clouds Two additional classes of phenomena revealed in the infrared are shown in Fig. 7.12. The importance of atmospheric water vapor is apparent in the top panels. The hot spots are dark in these panels because the traditional choice in presentation is to earmark white for cold so that clouds will appear white. At 4 µm, the atmosphere in the left image is reasonably transparent, and the hot lava flow from Kilauea is revealed. The right-hand panel shows the volcanoes on Hawaii and Maui extending above the water vapor layer. It is paradoxical that the value of the observatories on these islands surrounded by water is that the peaks extend into very dry atmosphere above the water layer.

7

See http://rsd.gsfc.nasa.gov/goes/text/goes8results.html

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Figure 7.12 Volcanoes and volcanic ash clouds.

The bottom panels in Fig. 7.12 show volcanic-ash plumes from Popocatepetl, near Mexico City. Volcanic ash clouds are a hazard for aviation, and are not easily detected other than by IR. The use of infrared bands allows the sensor to distinguish between water vapor and the silicon (or glass) particles. 7.5.4 Shuttle launch: vapor trail, rocket The GOES satellite makes a nice analog for a missile-warning satellite. Figure 7.13 shows GOES-8 images of the space-shuttle launch of June 21, 1996, a little after 1445 UTC (1045 EDT). The vapor trail can be seen in the visible image (present as the white cloud you see from the ground). The hot sub-pixel target is visible in all four infrared channels. The long-wave channels (11, 12 µm) don’t show good contrast because the Earth is already bright at that wavelength. The highest contrast is in the 6.7 µm channel, because the atmospheric water vapor prevents the sensor from seeing the extensive ground clutter. Visible plumes had been seen before by GOES, but this is the first time the unresolved heat from the rocket was seen in the 4- and 8-km IR pixels. The window channels at 3.9 and 11 µm are consistent with a 493 K blackbody occupying 0.42% of a 2-km square pixel. The water-vapor channels are consistent with a 581K

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Figure 7.13 The wavelength ranges used here were illustrated in Fig. 7.12. The third frame, from the 6.7 µm channel, shows the greatest signal-to-background ratio.8

blackbody occupying 0.55% of a 2-km pixel. The shuttle burns liquid hydrogen and oxygen to create a hot exhaust that appears bright in the water-vapor bands.8

7.6 Defense Support Program—DSP9 The missile-launch capability illustrated using the GOES data above is in use with the geosynchronous platforms termed DSP. These satellites, and their mission, are not as highly classified as they once were, and elements of their mission can be discussed.

8

See http://goes.gsfc.nasa.gov/text/goes8results.html Dwayne Day, “Origins and evolution of the defense support program” Spaceflight Magazine, Part 1 pp. 22 26 38(1), Part 2 pp. 59 63 38(2), Part 3 pp. 95 99 38(3); Craig Covault, “New missile warn ing satellite to be launched on First Titan 4,” Aviation Week & Space Technology, pp. 34 40 (February 20, 1989); Craig Covault, “Astronauts to launch warning satellite,” pp. 65 69 (November 18, 1991); Craig Covault, “Shuttle deploys DSP satellite, crew performs reconnaissance tests,” Aviation Week & Space Technology, p. 23 (December 2, 1991); Craig Covault, “Titan 4B to inaugurate new USAF launch operations,” Aviation Week & Space Technology, p. 90 (February 10, 1997); David Hughes, “JTAGS to expedite space based warnings,” Aviation Week & Space Technology, p. 61 (March 3, 1997); William B. Scott, “Funding fracas imperils ‘Nudet’ sensor,” Aviation Week & Space Technol ogy, p. 29 (January 5, 1998); Craig Covault, “USAF missile warning satellites provide 90 sec. scud attack alert,” Aviation Week & Space Technology, pp. 60 61 (January 21, 1991). 9

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The last generation of DSP satellites, termed Block 14, continued a sequence that began with the launch of the first operational DSP spacecraft in May, 1971. The satellites were built by TRW, with focal planes by Aerojet. The last block was characterized by a satellite that massed ~2400 kg and was 10-m in length and 6.7-m in diameter. The vehicle rotates about the long axis at 6 rpm. Solar arrays provide 1.5 KW power. The axis of the telescope is off the main rotation axis, allowing the telescope to sweep the whole Earth. The 6000-element focal plane is made from lead-sulfide detectors, designed to work at 2.7 µm. These detectors provide good sensitivity at the comparatively elevated temperature of 193K. This permitted passive, radiative cooling. The focal plane mass was ~540 kg (1200 pounds). Later generaFigure 7.14 The satellites were usually sent tions (1985) added a 4.3 µm HgCdTe aloft by the various generations of Titan launchfocal plane. The first ground station was ers. Here is the one shuttle launch: DSP Flight in Woomera, Australia—others were 16, “DSP Liberty,” launched by the shuttle added with time. The satellites also host Atlantis (STS-44) on November 24, 1991. The shuttle crew deployed the 37,600-lb DSP/IUS NUDET functions. stack at 0103 EST. The operational constellation is nominally four or five satellites. To quote Aviation Week & Space Technology: The existing four-spacecraft DSP constellation routinely detects, tracks, and pinpoints the launch location of small ballistic missiles such as the Scud. DSPs observed about 2,000 Soviet Scud launches directed at Afghan rebels and another 200 during the Iran/Iraq war. During the Persian Gulf war, the three DSP spacecraft above the Indian Ocean and eastern Atlantic region helped cue Patriot missile batteries, providing 5-min warning of 88 Iraqi Scud ballistic missile launches against Israel and Saudi Arabia. In addition, the DSP’s infrared tracking of the Scud rocket plumes was accurate enough to locate the Iraqi launch sites within 2.2 nautical miles. These detailed DSP data were then used to guide Air Force E-8 Joint-STARS aircraft toward the Scud launch sites for final launch-site identification and bombing by coalition forces.10

10

Craig Covault, “Astronauts to Launch Warning Satellite,” Aviation Week & Space Technology, Vol. 135, No. 20, pp. 65 69, (Nov. 18, 1991).

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Figure 7.15 Observations of two Titan II ICBM test launches.11

The IR sensor data from DSP are not currently releasable, though some results have surfaced in studies of natural phenomena such as meteorites. Two illustrations of what can be obtained from these high-temporal resolution, non-imaging sensors are shown here. IR data from MIDAS satellite tests are shown in Fig. 7.15. MIDAS was a DSP precursor, conducting tests in the 1960s. The sensors are lead sulfide, with filters designed to limit the response to the water-absorption band (2.65–2.80 µm). The initial variation in radiant intensity is due to the decrease in atmospheric absorption as the rocket rises in the atmosphere. The subsequent decline is due to plume effects in the exhaust. (Simmons, 2000).11 The visible sensor data from DSP are illustrated in Fig. 7.16. This plot shows the energy observed in a bolide—a meteor impact. The event is distinguishable both from other natural phenomena (such as lightning), and the sensor’s primary concern, ICBMs. Note that the calculations for power are based on an assumption that the target has a temperature of 6000 K. A temperature assumption is necessary because the broadband sensor only gives power—we don’t know where the peak in the spectrum occurs. Note the high temporal resolution—a domain not normally exploited in remote sensing. The IR sensors are also able to observe events like forest fires (Defense Daily, 4-29-1999) and jet aircraft on afterburners, and have some capabilities in battlefield damage assessment (BDA).

11

Frederick Simmons, Rocket Exhaust Plume Phenomenology, Aerospace Press, Los Angeles, CA (2000).

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Figure 7.16 Visible sensor data from DSP.12

7.7 SEBASS—Thermal Spectral 7.7.1 Hard targets Spectral imagery has been an important tool in the reflective domain; it is now emerging in the emissive domain. The image in Fig. 7.17 was taken from a tower during an experiment in Huntsville, Alabama, using the SEBASS instrument, which measures radiance as a function of wavelength. The spectra at three locations are shown below. The trees are nominally at air temperature and have essentially unity emissivity (they are blackbodies). The tank spectrum has a noticeable depression at about 9 µm (Fig. 7.18), though it is at the same tem- Figure 7.17 SEBASS data inteperature as the early morning air and the trees. The grated over LWIR spectral range. ground is cooler and darker in this image. Long wave infrared (LWIR) imagery like that shown here has the advantage of being a day-night capability. LWIR spectral imagery has some very useful applications in detecting gasses, as well, as shown in the next section.

12

E. Tagliaferri et al., “Detection of meteoroid impacts by optical sensors in Earth orbit,” in Hazards Due to Comets and Asteroids, T. Gehrels, et al. (Ed.), University of Arizona Press, Tucson, AZ (1994).

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Figure 7.18 SEBASS spectra.

7.7.2 Gas measurements: Kilauea—Pu ‘u ‘O ‘o Vent13 Volcanoes provide a high-temperature extreme for thermal spectral measurements. An experimental test flight using the University of Hawaii AHI sensor over a volcanic vent on the island of Hawaii provides the montage in Figs. 7.19–7.21. Figure 7.19 shows a visible image of the crater, and a rough view of the longwave infrared data on the right side, roughly corresponding to a strip through the vent area imaged on the left. Modeling IR data such as these requires a fairly complex model—most of the essential elements are illustrated in Fig. 7.20. MODTRAN calculations were done to define the processes shown there, and the results compared to the data. In Fig. 7.21, the smooth curves are blackbody fits to the long wavelength data. Deviations from the smooth curve from 8–9.5 µm are due to absorption by sulfur dioxide in a plume emitted by the volcano. The top curve in Fig. 7.21 is based on an estimated ground temperature of 342 K. The other two samples were taken over slightly cooler ground. The analysis of the data in Fig. 7.21 showed that AHI observed concentrations of SO2 could be successfully modeled at a few hundred parts per million (ppm), in a layer estimated to be 150 m in thickness, at the same temperature as the background air. This resulted in estimated plume concentrations of 1 to 5 × 104 ppm-m.

13

These illustrations come from thesis work at the Naval Postgraduate School by Captain Aimee Mares (USMC).

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Figure 7.19 Photograph of Kilauea, with LWIR data from over the volcano on the right (AHI).

Figure 7.20 Modeling the SO2 concentration requires a fair amount of information that must be estimated or modeled.

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Figure 7.21 The spectra are reasonably blackbody above 10 µm, and the background temperature can be estimated from this portion of the spectrum. At shorter wavelengths, the SO2 absorbs the upwelling radiation (AHI).

7.8 Problems 1. At what wavelength does the radiation for targets at 300 K peak? What is the ratio of the total power-per-unit area emitted by a person (300 K) and a hot vehicle (1000 K)? 2. What are the tradeoffs between using MWIR (3–5 µm) vs. LWIR (8–13 µm) Consider radiated energy, detector technology (cooling issues), and Rayleigh criterion concerns. 3. Of the materials in Table 7.2, which will show the largest temperature fluctuation during a 24-hour heating/cooling cycle; which will show the smallest? 4. A target has a “real” or kinetic temperature of 513.345 K. It has an emissivity of 0.900. What temperature would be estimated for the target if the (incorrect) assumption is made that it has an emissivity of one?

Chapter 8 Radar

8.1 Imaging Radar Radar, specifically imaging radar, provides a powerful tool for remote sensing, with the advantages of round-the-clock capability (due to independence from solar illumination) and all-weather performance (due to cloud penetration). Radar can penetrate modest depths into the Earth and allow glimpses below the surface of the Earth—useful in detecting buried objects such as pipelines or mines. Imaging radar is an essential tool for maritime concerns, from tracking ships to tracking sea ice. This chapter develops the physics and nature of imaging radar. Figure 8.1 illustrates some of the radar characteristics we will be interested in. The image from an airborne sensor combines observations at two wavelengths. Shades of yellow and blue differentiate regions of different surface roughness, and vegetated areas (golf courses and city parks) show up particularly well.

8.2 Theory 8.2.1 Imaging radar basics Radar systems have a unique set of terms, so new definitions are needed before we proceed. Not all will be used here, but all show up fairly regularly in the use of modern systems and in the literature. These definitions relate to an imaging platform (aircraft or satellite), and the velocity vector of that platform. Figure 8.2 illustrates this reference vector, which defines the along-track direction, which is also the azimuthal direction. The orthogonal direction is defined as the across-track, or range, direction. The angles are determined by the flight-line of the aircraft or satellite. A horizontal line perpendicular to the flight line allows for the definition of the depression angle β, measured from a horizontal plane downward to the radar beam. The depression angle varies across the image swath, the angle is small for far range, and

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Figure 8.1 San Francisco, California, JPL AIRSAR, C and L band, VV polarization. October 18, 1996, 71351 seconds GMT. 10 m GSD, aircraft tack –135°.

large for near range. The depression angle would be 90° for a nadir view, though imaging radar cannot view directly below the platform. The look angle θ is the complementary angle (β + θ = 90°) measured up from the local vertical. Similar angles are defined with respect to the ground. The incidence angle φ is the angle between the radar beam and a line perpendicular to the local ground surface; for horizontal terrain, the incidence angle equals the look angle (θ = φ). The complement of the incidence angle is called the grazing angle γ. Again, for horizontal terrain, the depression angle equals the grazing angle (β = γ). Finally, a set of distances is defined. Slant range is the line-of-sight distance measured from the antenna to the ground or target. Ground range is the horizontal distance measured along the surface from the ground track, or nadir, to the target. The

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Figure 8.2 Definitions of terms for imaging radar.1

area closest to the ground track at which a radar pulse intercepts the terrain is the near range, and the area of pulse termination farthest from ground track is the far range. The concept of resolution has been developed previously in the context of optical systems with fairly intuitive meanings. The ground resolution of an optical system, or GSD, is defined by the optical performance and detector characteristics. Resolution for radar systems behaves in a somewhat different way, and the definition of resolution, though similar, differs as well. Radar resolution is defined as the minimum separation between two objects of equal reflectivity that will enable them to appear individually in a processed radar image. Within the radar community, the

1

Thomas Eugene Avery & Graydon Lennis Berlin, Fundamentals of Remote Sensing and Airphoto Interpretation, Macmillan Publishing Company, New York (1992).

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impulse-response function defines resolution. Radar systems are generally used to distinguish point targets; the impulse response defines their ability to do so. The peculiar nature of radar is that the resolution in range and azimuth derive from different physical processes, and in general need not be the same. These relationships are discussed in the following sections. 8.2.2 Radar range resolution Range, or across-track, resolution is determined by the physical length of the radar pulse that is emitted from the antenna; this is called the pulse length. The pulse length can be determined by multiplying the pulse duration τ in time by the speed of light (c = 3 × 108 m/s); Pulse length = c τ.

(8.1)

Note that in some radar texts the pulse length, a distance, may be expressed as τ, which is more properly a time. In this work, the above definition will be used, but be aware that this is not a universal choice. For a radar system to discern two targets in the across-track dimension, all parts of their reflected signals must be received at the antenna at different times, or they will appear as one large pulse return, or spot in an image. In Fig. 8.3, it is seen that objects separated by a slant-range distance equal to or less than cτ/2 will produce reflections that arrive at the antenna as one continuous pulse, dictating that they be imaged as one large object (targets A, B, and C). If the slant-range separation is greater than cτ/2, the pulses from targets C and D will not overlap, and their signals will be recorded separately. Thus, slant-range resolution measured in the across-track dimension is equal to one-half the transmitted pulse length: R sr =

cτ . 2

(8.2)

To convert Rsr to ground-range resolution R gr, the formula is: R gr =

cτ , 2cos β

(8.3)

where τ is the pulse length, c is the speed of light, and β is the antenna depression angle. Note that radar imagery can be processed in both slant range and ground range. This is a technical choice, based to some extent on the imaging problem addressed.

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Figure 8.3 Radar range resolution is a function of pulse length.2

It can be noted from the equation that ground-range resolution improves as the distance from the ground track increases (i.e., across-track resolution is better in far range than in near range because β is smaller). Resolution can be improved by shortening the pulse length. However, a point will be reached when a drastically shortened pulse will not contain sufficient energy for its echoes to be detected by the receiver. As a practical matter, the minimum pulse length is a few microseconds, for a range resolution of hundreds of meters. A closely related concept to the pulse duration is the pulse-repetition rate, or frequency (PRF). This corresponds to the interval between pulses, and is relatively long compared to the pulse duration. Figure 8.4 illustrates the signals used for the SIR-C X-band radar. Here, the pulse width is 40 µs, the PRF is 1240–1736 Hz, or about fifteen times the width of the pulses illustrated here. 8.2.2.1 Signal shape Our ability to resolve targets basically revolves around the length of the radar pulse—but there is a problem in balancing the needs for suitable amounts of power broadcast and for range resolution. The solution comes in the concept of pulse modulation, which requires an additional concept: the relationship between the shape of a signal in the time domain and its distribution in the frequency domain. Figure 8.5 illustrates some basic features of signals and associated concepts. Basically, if you have a very short pulse, a wide spectrum of frequencies is implicit, while a monochromatic signal implies a very long pulse. Simple Fourier analysis

2

D.J. Barr, Use of Side Looking Airborne Radar (SLAR) Imagery for Engineering Soil Studies, Technical Report 46TR, U.S. Army Engineer Topographic Laboratories, Fort Belvoir, VA (1969).

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Figure 8.4 SIR-C X-SAR pulses recorded by a ground calibration receiver, sampling at 4 µs (250 kHz). Data take 30 of SRL-1 (April, 1994). The slight variation in power seen over this interval is due to the progress of the shuttle over the ground site. Note that without signal shaping, the best range resolution which could be obtained from such pulses would be 6 km. The resolution obtained via the techniques described below is 12–25 m, corresponding to the 9.5 or 19 MHz bandwidth.3

theory tells us a few important points about these relationships. In particular, the transform of a square pulse is a sinc function—the ratio of sin(x) to x. The pulse width in frequency is just the inverse of the pulse width in time, as indicated in the bottom half of Fig. 8.5. Note that for a square pulse, modulated by a carrier frequency, the center of the sinc function is shifted, but otherwise the shape of that function is unchanged. This concept allows a slightly different definition of radar range resolution, as follows: ∆ range =

cτ c = , 2 2B

(8.4)

where τ is the pulse length, and the bandwidth B is the inverse of τ, and c is the speed of light. This definition, purely formal at first, allows us to provide a simple way to understand the next step, which is to modulate the frequency of the pulse. The concept of frequency modulating the pulse, now termed “FM chirp,” was devised by Suntharalingam Gnanalingam while at Cambridge after World War II

3

M. Zink and R. Bamler, “X SAR calibration and data quality,” IEEE TGARS 33(4), pp. 840 847 (1995). Figure © 1995, IEEE.

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(1954). The technique was developed to study the ionosphere. Figure 8.6 illustrates the chirp concept—the pulse is modulated with a frequency that increases linearly with time. The value of this is that objects that are illuminated by the pulse can still be distinguished by the difference in frequencies of the returns, even if they overlap in Figure 8.5 Continuous wave and pulsed signals. time. Gnanalingam realized that Note that bandwidth = 1/pulse length. the transform of a chirped pulse would have a bandwidth in frequency space that was defined by the frequency range of the modulation. Without proof of any form, it is asserted here that by analogy to a finite pulse of constant frequency, the bandwidth is replaced by the range of the frequency sweep. As a result, the effective spatial resolution is: ∆ range =

c 2∆ f

(8.5)

This allows significantly better spatial resolution, because the frequency sweep can be much larger than the inverse of the pulse-width. (Example from the SIR-C X-band system—the 9.61 GHz signal had a 9.5 MHz chirp bandwidth—or about a 15-m range resolution).

Figure 8.6 A pulse varies linearly in frequency from f to fo + ∆f; the power is then localized in frequency space (bandwidth).

8.2.3 Radar azimuthal resolution Azimuth, or long-track resolution, Ra is determined by the width of the terrain strip illuminated by a radar pulse, which is a function of the beam width of a real-aperture radar (RAR). As shown in Fig. 8.7, the beamwidth increases with range. Thus, two tank-like objects (at the same range) are in the beam simultaneously, and their echoes will be received at the same time. Consequently, they will appear as one extended object in an image. Two other objects, an A7 jet and T72 tank, are located outside the beam width as shown here. Since a distance greater than the beam width separates them, their returns will be received and recorded separately. Thus, to separate two objects in the along-track direction, it is necessary that their separation on the ground be greater than the width of the radar beam. What determines the beam width? Basically, the length of the antenna.

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Figure 8.7 Imaging radar beam illumination.

8.2.4 Beam pattern and resolution We need to look at the nature of the antenna-radiation pattern briefly to get a handle on the resolution characteristics of an imaging radar system. Recalling the original discussion of the Rayleigh criterion (Chapter 2), we find that the same applies for a rectangular or cylindrical radar antenna. The beam pattern is derived in Appendix A1.3. Here, we simply claim the result, which is that the beam pattern is the Fourier transform of the aperture. For a square aperture, the pattern is the square of the sinc function. 2 Figure 8.8 shows this characteristic (sin α / α ) shape, where α = (kL sinθ)/2. L is the diameter of the aperture, or in our case, the length of the antenna. This function has zeros where the argument of sin is mπ, or: kL sin

θ = mπ ⇒ kL sin θ = 2mπ. 2

(8.6)

This leads to: 2π L sin θ = 2mπ ⇒ L sin θ = λ , λ

or

λ = sin θ. L

(8.7)

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This is effectively the same result given for the resolution of diffraction-limited optics. This is not an accident; it follows from the derivation of the far field (range >> aperture size and wavelength) behavior of any aperture. The equation for determining azimuth resolution Ra is Ra =

λ Rs L

(8.8) Figure 8.8 The square of the sinc function: (sin α / α).

where: λ = operating wavelength, Rs = slant range to the target, and L = length of the antenna.

The relationships expressed in Eq. 8.8 show that azimuth resolution decreases in proportion to increasing range (i.e., resolution is best in near range, where the width of the beam is narrowest), and a long antenna or a short operating wavelength will improve azimuth resolution. This concept applies to all radar, but in particular to RAR. In the case of RAR, the practical limit of antenna length for aircraft stability is about 5 m, and the all-weather capability of radar is effectively reduced when the wavelength is decreased below about 3 cm. Because of these limitations, RARs are best suited for low-level, short-range operations. The azimuthal resolution of a real-aperture imaging radar, in the along-track direction given above, can be rewritten as:

Ra =

λh . L cos θ

(8.9)

For ordinary-space kinds of numbers (antenna length L = 10 m, λ = 3 cm, θ = 20°, h = 800 km) we get a resolution of 2.5 km. It seems we need a bigger antenna. Before proceeding to the method by which a long synthetic antenna can be constructed, let’s look briefly at some real-antenna patterns, again from the SIR-C X-SAR instrument. Figure 8.9 shows what certainly appears to be a sinc2 pattern, per the theory described above (note that the use of dB as a unit means that we have a logarithmic vertical axis). A companion figure, Fig. 8.10, shows the data on a linear vertical scale (bottom), and divided by the expected factor of sinc 2 (ϕ / 0 .151°) on the

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Figure 8.9 SIR-C X-SAR azimuthal antenna pattern as observed from ground observations along the beam centerline (the center of the range antenna pattern).4 Be aware that the vertical axis in this figure is implicitly logarithmic (being in decibels); this allows the side lobes (secondary maxima) to be visible in this plot. The figure below uses a vertical axis that is truly linear.

top. Here, the model is for the 3-cm (9.6 GHz) waves, given the 12-m antenna length ( λ / L = 2 .64 milliradians = 0 .151°). For comparison, the range (or elevation) antenna pattern, synthesized from a number of observations like those in Fig. 8.9, is given in Fig. 8.11. Note that the width is considerably greater, given the relatively narrow dimension of the antenna in the corresponding direction (0.75 m).

8.3 Synthetic-Aperture Radar The principal disadvantage of real-aperture radar is that its along-track or azimuth resolution is limited by antenna length. Synthetic-aperture radar (SAR) was developed to overcome this disadvantage. SAR produces a very long antenna synthetically or artificially by using the forward motion of the platform to carry a relatively short real antenna to successive positions along the flight line. The longer antenna is simulated by exploiting the coherence of radar signals. For a sensor with an antenna length L, the main beam footprint on the surface has a characteristic length

4

Ibid. Figure © 1995, IEEE.

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Figure 8.10 SIR-C X-SAR azimuthal antenna pattern on a linear scale, and compared to sinc. Note that the portion of the data processed come from the region between the dashed lines, for which the model is very accurate.4

Figure 8.11 SIR-C X-SAR range antenna pattern. This beam pattern needs to cover the entire cross-track range of the system—here, 20–70 km as illuminated from 222 km altitude.5

l = 2 λ h / L. Data are accumulated for as long as a given point on the ground is in view (see Fig. 8.12).

5

Ibid. Figure © 1995, IEEE.

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Magically, the synthesized collection of measurements will have a beamwidth equal to θs =

L λ = , l 2h

(8.10)

and the resulting ground resolution is: Ra = h θ s =

L . 2

(8.11)

This very counter-intuitive result is due to the fact that for a smaller antenna (small L), the target is in the beam for a longer time. The time period that an object is illuminated increases with in- Figure 8.12 The ship is illuminated by the creasing range, so azimuthal resolution radar for a time interval which depends on is range independent. the altitude of the radar, and the beam width. The above discussion is correct for “scan-mode” SAR, where the antenna orientation is fixed. If the antenna is rotated (physically or electronically) in such a way as to continuously illuminate the target, a third result is obtained. In spotlight mode, radar energy is returned from the target for an interval defined by the operator. This allows an arbitrarily large antenna. For example, if the shuttle radar illuminated a target for 10 s, the effective antenna length would be some 75 km: Ra =

h λ λ ⋅ Rs = ⋅ , where Leff Leff cos θ

Leff = v platform ⋅ Tobserve .

(8.12)

In processing, the azimuth details are determined by establishing the position-dependent frequency changes or shifts in the echoes that are caused by the relative motion between terrain objects and the platform. To do this, a SAR system must unravel the complex echo history for a ground feature from each of a multitude of antenna positions. For example, if we isolate a single ground feature, the following frequency modulations occur as a consequence of the forward motion of the platform: • •

The feature enters the beam ahead of the platform and its echoes are shifted to higher frequencies (positive Doppler). When the platform is perpendicular to the feature’s position, there is no shift in frequency (zero Doppler).

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Figure 8.13 The synthetic antenna’s length is directly proportional to range: as across-track distance increases, antenna length increases. This produces a synthetic beam with a constant width, regardless of range for scan-mode SAR.6 Figure courtesy Goodyear Aerospace Corp.

•

As the platform moves away from the feature, the echoes have lower frequencies (negative Doppler) than the transmitted signal.

The Doppler-shift information is then obtained by electronically comparing the reflected signals from a given feature with a reference signal that incorporates the same frequency of the transmitted pulse. The output is known as a phase history, and it contains a record of the Doppler frequency changes plus the amplitude of the returns from each ground feature as it passed through the beam of the moving antenna. A consequence of this analysis approach is that objects that are moving will appear to be shifted in the along-track direction. 6

8.4 Radar Cross Section (σ) The radar cross section σ is generally defined as the ratio of the backscattered energy to the energy that the sensor would have received if the target surface had scattered the energy incident on it in an isotropic fashion. The backscatter cross section is usually expressed in dB (decibels), which is given by σ = 10 log (energy ratio).

6

Thomas Eugene Avery & Graydon Lennis Berlin, Fundamentals of Remote Sensing and Airphoto Interpretation, Macmillan Publishing Company, New York (1992).

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The cross-section σ depends on any number of surface characteristics, with a strong dependence on the incident angle and scattering angle. At scattering angles larger than about 30°, the surface scattering is dominated by the effect of small-scale roughness (small scale compared to the wavelength). The “point-scatterer” model is invoked here, and the small scatterers are assumed to make up a Lambertian distribution (an optics term): σ(θ ) ∝ cos 2 θ.

(8.13)

This gives some idea of the type of functional dependence on angle one might obtain. The details are much messier. The point of this portion of the discussion is that the radar return has a strong dependence on the angle of incidence on the target surface. This differs fairly substantially from the optical case, where there are modest effects due to the illumination angle, aside from shadows. Note also that a sun-synchronous satellite (e.g., Landsat) always observes under roughly the same illumination, whereas a radar satellite will not (θ varies).

8.4.1 Dielectric coefficient: soil moisture7 The amplitude of the radar return depends strongly on the dielectric coefficient of the surface material (this follows from the index of refraction in normal optics, n ~ ε r —the index of refraction varies as the square root of the relative dielectric constant). Radar returns vary substantially as the surface materials go from insulator to conduc-

7

Figure 8.14 The real (ε') and imaginary (ε'') components of the dielectric coefficient for a silty loam mixture, as a function of water content. Absorption increases with moisture content. Reflection (scattering) will increase as ε' increases.7

Charles Elachi, Introduction to the Physics and Techniques of Remote Sensing, Wiley, New York (1987).

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Figure 8.15 SIR-A observations of subsurface geological structures (soil penetration). The diagonal stripe is the SIR-A data, the gray background is the Landsat (visible) image. Work by Victor R. Baker and Charles Elachi.

tor—which in the dielectric coefficient shows up as the imaginary component ε''. In the illustration here, we see that soil moisture drives the imaginary term up, causing increased absorption of radar energy. Note the wavelength dependence of this variation: higher frequencies (lower wavelengths) are affected more. This means lower frequencies are better for penetrating ground and foliage. Backscatter is also sensitive to an illuminated area’s electrical properties, including water content. Wetter objects will appear bright and drier objects will appear dark. The exception is a smooth body of water, which will act as a flat surface and reflect incoming pulses away from a mapping area. These bodies will appear dark. Radar’s ability to penetrate dry soil is apparent in a variety of desert observations. Here, ancient riverbeds under the sand are shown for the eastern Sahara. The location is the Selima Sand Sheet region in northwestern Sudan. A 50-km-wide path from the Shuttle Imaging Radar-A (SIR-A) mission over the Sahara is shown superimposed on a Landsat image of the same area. The radar penetrated 1–4 m beneath the desert sand to reveal subsurface prehistoric river systems invisible on the Landsat image.

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Figure 8.16 The concept of rough and smooth needs to take into account the wavelength of the radiation.8 Figure courtesy Goodyear Aerospace Corp.

8.4.2 Roughness The effect of surface roughness is illustrated by Fig. 8.16.9 The figure is somewhat schematic, but it emphasizes the variation in radar return with angle and surface roughness. Note that roughness is relative to wavelength, so smooth means surfaces like concrete walls (e.g., cultural objects) and rough tends to mean things like vegetation. The rule of thumb in radar imaging is that the brighter the backscatter on the image, the rougher the surface being imaged. Flat surfaces that reflect little or no microwave energy always appear dark in radar images. Vegetation is usually moderately rough on the scale of most radar wavelengths and appears gray or light gray in a radar image. Surfaces inclined toward the radar will have a stronger backscatter than surfaces that slope away. 8.4.3 Tetrahedrons/corner reflectors Hard targets, meaning most manmade artifacts, generally have sharp corners and flat surfaces. These produce extremely bright returns, often saturating the images produced from SAR systems. The SIR-C flight over Death Valley included calibration sequences with retro-reflectors, which characteristically return all incident radiation back in the direction of incidence—that is, they are nearly perfect reflectors. Figure 8.17 shows some SIR-C observations rendered in line graphics. In the SAR images, these correspond to a small white dot against the relatively flat background.

8

Thomas Eugene Avery & Graydon Lennis Berlin, Fundamentals of Remote Sensing and Airphoto Interpretation, Macmillan Publishing Company, New York (1992). 9 Charles Elachi, Introduction to the Physics and Techniques of Remote Sensing, Wiley, New York (1987).

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Figure 8.17 SAR impulse response, Death Valley, CA, and retroreflectors. Credit: NASA.

8.5 Polarization The above discussion ignores the important topic of polarization. Radar transmissions are polarized, with components normally termed vertical (V) and horizontal (H). Vertical means that the electric vector is in the plane of incidence; horizontal means the electric vector is perpendicular to the plane of incidence.10 The receiving antenna can be selected for either V or H returns. This leads to a possible matrix of return values:

10

Charles Elachi, Introduction to the Physics and Techniques of Remote Sensing, Wiley, New York (1987).

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 σ HH σ=  σ VH

σH V  , σ VV 

(8.14)

where the first subscript is determined by the transmit state and the second by the receive state. These four complex (amplitude and phase) components of the scattering matrix give a wealth of information, much more than can be obtained from an optical system. Generally speaking, scatterers that are aligned along the direction of polarization give higher returns, and rough surfaces produce the cross-terms. Water gives almost zero scattering in the cross terms; vegetation, a relatively large cross-term.

8.6 Wavelength11 Choices for radar wavelength vary according to the goals of the system. In general, of course, radar penetrates clouds, smoke, rain, and haze. There is some wavelength dependence for rain penetration: at 15 cm and longer (2 GHz and below), rain is not a problem. At 5 GHz (6 cm), significant rain shadows are seen. At 36 GHz (0.8 cm) moderate rainfall rates can cause significant attenuation. Foliage penetration is enhanced with longer wavelengths. Shorter wavelengths (X and C band) primarily interact with the surface, while longer wavelengths (L and P band) penetrate forest canopies and soil. Table 8.1 Radar bands.

Band designation*

Wavelength (cm)

Frequency (GHz)

Ka (0.86 cm)

0.8–1.1

40.0–26.5

K

1.1–1.7

26.5–18.0

Ku

1.7–2.4

18.0–12.5

X (3.0, 3.2 cm)

2.4–3.8

12.5–8.0

C

3.8–7.5

8.0–4.0

S

7.5–15.0

4.0–2.0

L (23.5, 25 cm)

15.0–30.0

2.0–1.0

P

30.0–100.0

1.0–0.3

* Wavelengths commonly used in imaging radars are indicated in parenthesis.

11

RADARSAT/PCI notes, pp. 11, 43.

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8.7 Vehicles 8.7.1 Shuttle imaging radar (SIR) The shuttle imaging radar has flown in several versions (A, B, and C). The C payload flew twice as an imaging mission in 1994. The SIR-C missions were carried by the Endeavour orbiter, the first as SRL-1: STS-59, on April 9–20, 1994, and the second as SRL-2: STS-68, on September 30–October 11, 1994. Both missions were conducted with highly-inclined (57°), 222-km altitude, circular orbits. SIR-C included X-, C-, and L-band radar, and was capable of various modes, including full polarimetric (VV, VH, HV, and HH polarization). SIR-C flew a third time as the Shuttle Radar Topography Mission (SRTM) on February 11, 2000 (STS-99). C-band and X-band data were taken on the SRTM flight. Spatial resolution varied among the sensors and with operating mode, but was generally from 10–25 m, with a spatial extent of 30–50 km. The Figure 8.18 The X-, C-, and L-band antennas are all 12 m in length. In width, the X band (on combined SIR-C/X-SAR payload had the bottom of the figure) is 0.4 m wide, the a mass (instruments, antennas, and L-band is 2.95 m, and the C-Band panel is electronics) of 10,500 kg, filling 0.75 m. nearly the entire cargo bay of the shuttle. Enormous data rates are implicit in these missions. Launched April 9, 1994, the STS-59 mission for SIR-C/X-SAR collected a total of 65 hours of data during the 10-day mission, corresponding to roughly 66 million km2. All data were stored onboard the shuttle using high-density, digital, rotary-head tape recorders. The data filled 166 digital-tape cartridges (similar to VCR tapes). The mission returned 47 terabits of data (47 ×1012 bits). When all radars are operating, they produce 225 million bits of data per second. The raw data was processed into images using JPL’s digital SAR processor and by processors developed by Germany and Italy for the X-SAR data. The L- and C-band SARs allow multi-frequency and multi-polarization measurements. Parallel image generation can be done in L-band and C-band with HH, VV, HV, or VH polarization. The look angle was variable from 20–55°. The data

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Figure 8.19(a) The phased-array C- and Figure 8.19(b) The antenna is 4 m × 12 m L-band antennas are steered electronically. overall. Credit: NASA.

rate was 90 Mbit/s for L-band and 90 Mbit/s for C-band (a total of four streams of V and H data, each data stream with a data rate of 45 Mbit/s). Table 8.2 Shuttle imaging radar.

Parameter Wavelength (cm) Frequency Aperture length Aperture width Architecture Polarization Polarization isolation Antenna gain Mechanical steering range Electronic steering range Elevation beam width Azimuth beam width Peak radiated power System noise temperature Mass of structure

L-Band C-Band Antenna Antenna 23.5 5.8 1.250 GHz 5.3 GHz 12.0 m 12.0 m 2.95 m 0.75 m Active-phased array H and V H and V 25 dB 25 dB 36.4 dB 42.7 dB N/A N/A ±20° ±20° 5–16° 5–16° 1.0° 0.25° 4400 W 1200 W 450 K 550 K 3300 kg

X-Band Antenna 3.1 9.6 GHz 12.0 m 0.4 m Slotted waveguide V 39 dB 44.5 dB ±23° N/A 5.5° 0.14° 3350 W 551 K 49 kg

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The German X-band SAR was provided by DARA/DLR and ASI. The X-SAR uses only vertical polarization (VV). The look angle (off nadir) varied from 15–55° and the data rate was again 45 Mbit/s. The ground area illuminated by the antenna is an ellipse of about 60 km × 0.8 km (for an altitude of 222 km). The traveling-wave tube (TWT) amplifier generates 1736 pulses/s at a peak transmit power of 3.35 kW; the pulses are frequency modulated (chirp) with a pulse length of 40 µs and a programmable bandwidth of 9.5 or 19 MHz. The signal echoes are amplified in a coherent receiver, digitized (4 or 6 bit) and recorded together with auxiliary data. 8.7.1.1 Soil penetration One of the more fascinating aspects of radar imagery is its ability to look below the surface of dry soil such as deserts. Figure 8.15 above showed the results of an early shuttle flight; Fig. 8.20 shows imagery taken in a region of the Sahara Desert in North Africa by the space-shuttle orbiter Endeavour on October 4, 1994. This area is near the Kufra Oasis in southeast Libya, centered at 23.3° north latitude, 22.9° east longitude.12 This SIR-C image reveals a system of old, now inactive stream valleys, called “paleodrainage systems,” visible here as the two darker patterns converging at the top of the figure. During periods of wetter climate, these carried running water northward across the Sahara. The region is now hyper-arid, receiving only a few millimeters of rainfall per year, and the valleys are now dry “wadis,” or channels,

Figure 8.20 North is toward the upper left. Red is L-band, horizontally transmitted, horizontally received. Blue is C-band horizontally transmitted, horizontally received. Green is the average of the two HH bands. (a) JPL Image P45719.13 (b) Expanded view of Kufra Oasis.

12

http://www.photovault.com/Link/Universe/Planets/dEarthData/UPDVolume01/UPDV01P03 11.html 13 NASA/JPL Planetary Photojournal, http://photojournal.jpl.nasa.gov/PIADetQuery.html

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mostly buried by windblown sand. Prior to the SIR-C mission, the west branch of this paleodrainage system, known as the Wadi Kufra (the dark channel along the left side of the image), was recognized and much of its course outlined. The broader east branch of Wadi Kufra, running from the upper center to the right edge of the image, however, was unknown until the SIR-C imaging radar instrument was able to observe the feature here. The east branch is at least 5 km wide and nearly100 km long. The two branches of Wadi Kufra converge at the Kufra Oasis, at the cluster of circular fields at the top of the image [Fig. 8.20(b)]. The farms at Kufra depend on irrigation water from the Nubian Aquifer System. The paleodrainage structures suggest that the water supply at the oasis is a result of episodic runoff and the movement of groundwater in the old stream channels.

8.7.1.2 Oil Slicks and internal waves Maritime applications of radar include ship detection and oil-slick detection. Figure 8.21 shows the sensitivity of radar to surface disturbances on water, even though water is a poor reflector of radar energy. Normally, small wind-waves (over 3–4 m/s) produce radar returns. The amplitude of these small waves depends on wind speed and the surface tension of the water, which is modified slightly by oil. This modifies the return sufficiently to produce a characteristic signature, as shown

Figure 8.21 NASA/JPL figure P-46293 October 9, 199414 The image is located at 19.25° north and 71.34° east and covers an area 20 km by 45 km (12.4 miles by 27.9 miles). Note the complementary color scheme: yellow regions reflect relatively higher energy in the L-band, blue areas show relatively higher reflectance in C-band. Both bands are observed in VV polarization.

14

See http://photojournal.jpl.nasa.gov/catalog/PIA01803

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below. We also observe the influence of water temperature on the relative amplitude of the returns at different wavelengths. 15 Figure 8.21 is a radar image of an offshore drilling field about 150 km west of Bombay, India, in the Arabian Sea. The dark streaks are extensive oil slicks surrounding many of the drilling platforms, which appear as white spots. The narrower streaks are more recent leaks; the spread areas have dispersed over time. Eventually, the oil slick may be as thin as a single molecule thick. Oil slicks may result from natural seepage from the ocean floor as well as manmade sources. There are two forms of ocean waves shown in this image. The predominating, large waves (center right) are internal waves, formed below the surface at the boundary between layers of warm and cold water. They appear in the radar image because of the way they modify the surface. (Figure 8.27 also shows a dramatic example of internal waves.) These waves have characteristic wavelengths of 200–1600 m.16 Ocean swells, which are also generated by winds, are shown throughout the image but most distinctly in the blue area adjacent to the internal waves. 8.7.2 RADARSAT: ship detection17 RADARSAT data were briefly illustrated in Fig. 1.22. RADARSAT carries a C-band synthetic-aperture radar and operates in HH polarization. Launched on November 4, 1995, it had a five-year design life that has been significantly exceeded (still operating after 10 years). There are seven beam modes, offering a wide range

Figure 8.22 Ship detection, Singapore, January 8, 1996, ascending-orbit pass. RADARSAT-1, fine-beam position 2.18 Scene center: N 01 deg 17'', E 103 deg 42''. Incidence angle: 39–42°.

15

High resolution wind fields from ERS SAR, K. Mastenbroek, http://www.esa.int/esapub/eoq/ eoq59/MASTENBROEK.pdf 16 See http://www.gisdevelopment.net/aars/acrs/1999/ps1/ps1227pf.htm 17 http://www.rsi.ca/classroom/cl rsat.htm 18 RADARSAT 1 data © Canadian Space Agency 1996. Received by the Canada Centre for Remote Sensing. Processed and distributed by RADARSAT International.

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of resolutions (8–100 m) and swath widths (50–500 km). Incidence angles vary from 20–59°. RADARSAT 2 is to be launched in 2006. The satellite is in a circular, sun-synchronous (dawn-dusk) orbit at 798-km altitude, 98.6° inclination, and with a 100.7-min period. This orbit allows users to revisit a scene at the same local time, and the ascending node at 18:00 minimizes conflict in downlinking data to ground stations. It also simplifies maintaining the solar array pointing and maximizes power (no eclipse intervals). The circular orbit is maintained as accurately as possible to maintain repeatability in the imaging. The radar has a power transmission of 5 kW peak and 300 W average, and a duty cycle of up to 28% (28 min/orbit). The solar arrays produce 2.5 kW of power. The antenna is a 15 m × 1.5 m phased array. The pulse-repetition frequency (PRF) varies with mode, from 1270 Hz to 1350 Hz. The range bandwidth (chirp) varies from 11.6 to 30 MHz. The pulse length is 40 µs. The RADARSAT data shown in Fig. 8.22 provide an example of ship detection. The civil systems currently used on satellites have relatively poor spatial resolution, but the inset image chip in Fig. 8.22 shows a large cargo carrier. Higher intensity returns at the bow and stern are evident, and there is a superstructure amidships. The curious extensions to the sides may be smaller vessels off-loading cargo for transport to Singapore.19 Radarsat is considered better for ship detection than its European competitors, discussed next, because the HH-polarized signals are less sensitive to ocean-surface roughness than the VV-polarized transmit/receive signals.20 8.7.3 European radar satellites: ERS-1, ERS-2 The European radar satellites ERS-1 and ERS-2 are also polar-orbiting SAR systems at a mean altitude of about 780 km. ERS-1 was launched on July 17, 1991 from Kourou, French Guiana by an Ariane 4. The inclination is 98.52°, the period about 100 min. The instrument payload included active and passive microwave sensors and a thermal infrared radiometer. The satellite (Fig. 8.23) is large, weighing 2400 kg and measuring 12 m × 12 m × 2.5 m. ERS-1 ceased operation on March 10, 2000; ERS-2, launched April 21, 1995, continues to operate. Like RADARSAT, the radar is C-band (5.3 GHz), but ERS operates in VV polarization. The incidence angle is 20–26°. It is somewhat more powerful than RADARSAT, with the peak power supplied to the payload at 2600 W and the maximum payload average power is 550 W—but the payload requires almost double that power when active.

19

http://www.crisp.nus.edu.sg/~research/#early Karen Bannerman, “Use of Space Borne Radar Data for Oil Spill Management,” presentation at the International Oil Spill Conference, Miami, FL, May, 2005.

20

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Figure 8.24 ESA’s ERS-1 satellite was photographed by the Spot-4 Earth-observation satellite of the French space agency, CNES, at 0956 UT on May 6, 199821. From its 820-km orbit, SPOT-4 recorded ERS-1 passing by 41 km below, at a relative speed of 250 km/hr, over the Tenere Desert of Niger, Africa. Resolution of the ERS-1 spacecraft is 0.5 m. The image was taken by one of the HRVIR (high-resolution visible-infrared) cameras during SPOT’s testing phase. The feat was repeated a few years later: SPOT-5 imaged ERS-2.

Figure 8.23 ERS-2.21

8.7.3.1 Ship wakes ERS data are used in ship and ship-wake detection. Figure 8.25 shows two ships and their wakes. The displacement between the ships and their wakes indicates their velocities. The ship velocity can be estimated by the formula: VShip = VSat

∆x , R cos(ϕ )

(8.15)

where VShip is the ship’s velocity, VSat is the satellite’s orbit speed, ∆x is ship’s displacement from its wake, R is the slant range, and ϕ is the angle between the ship’s velocity vector and the SAR look-direction. The velocity component is effectively in the along-track direction, and is just that when the squint angle is zero.

21

Images courtesy of European Space Agency (ESA).

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Figure 8.25 The ERS-2 SAR image shows two moving ships and their wakes.22 From the ship on the left, the speed is estimated at 6 m/s. For the right ship, the turbulent wake, Kelvin envelopes, and transverse waves can be observed. Its speed is estimated to be around 12.5 m/s. ERS-2; 3 April 1996 – 03:29:29; Incident Angle: 23.0; Lat/Long +01.64/102.69.

8.7.3.2 Multi-temporal images: Rome Figure 8.26 illustrates a remote-sensing technique for which radar imagery is particularly well suited. This multi-temporal image of Rome and the Castelli Romani hills to its southeast shows, through color, a variety of changes in the agricultural fields of the lowlands and the grasslands and forests of the hills. The city, however, has not changed in the short interval between the first and the last of images and thus appears gray, because equal values of the RGB colors from which the image is made give a range of grayscales rather than of colors.

8.7.3.3 SPAIN—MOROCCO—Strait of Gibraltar The spectacular image of the Strait of Gibraltar in Fig. 8.27 shows internal waves that seem to move from the Atlantic Ocean to the Mediterranean Sea, at the east of Gibraltar and Ceuta. The waves have a wavelength of about 2 km. Internal waves are usually created by the presence of two different layers of water combined with a certain configuration of relief and current. At the Strait of Gibraltar, the two layers

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Figure 8.26 ERS-1 multitemporal image of Rome. Incidence angle, 23 °; spatial resolution, 30 m; swath width: 100 km. Three color bands are encoded: Green: January 3, 1992, Blue: March 6, 1992, and Red: June 11 1992; Copyright ESA, 1995. Original data distributed by Eurimage.22

feature different salinities, whereas the current is caused by the tide passing through the strait. As this current meets the ascending ocean bottom, the internal waves generated reach the surface some kilometers behind the strait. They are not directly visible, but produce a perturbation at the surface that appears as strips of rough and calm water. ERS-1 gives scientists the opportunity to observe and map such phenomena. The image has been artificially colored: land encoded as shades of brown, water as shades of blue. Normally, the land would be much brighter than the ocean, and ocean features would be invisible. The data were acquired at the Fucino ground station on July 1, 1992. The area covered is 90 km × 100 km.23

22

Images courtesy of European Space Agency (ESA). A more detailed description of the physics can be found here: http://www.ifm.uni hamburg.de/ ers sar/Sdata/oceanic/intwaves/gibraltar/intro/

23

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Figure 8.27 Straits of Gibraltar. Area covered is 90 km x 100 km; C-VV; resolution is 30 m.24

8.7.4 Sandia Ku-band airborne radar One concluding illustration from an airborne sensor shows what is possible if a spot-mode imaging approach is used. The radar developed by Sandia National Laboratories provides 1-m resolution at ranges of 2–15 km. The 15 GHz SAR is generally carried by the Sandia Twin Otter aircraft, but can operate on modestly sized UAVs. Figures 8.28 and 8.29 show data taken over Washington DC, showing a relatively broad area of coverage, and then a detailed image of the U.S. Capitol. Note that the upcoming RADARSAT-2 will have 2-m resolution and similar image quality. A recently developed evolution of the Sandia radar (May 2005) is now offering 0.1-m resolution. This airborne system rivals the imagery from optical systems. 25

24

Image courtesy of European Space Agency (ESA).

25

http://www.sandia.gov/radar/sar.html

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Figure 8.28 Washington DC, imaged by the Sandia Ku-band airborne SAR.26

Figure 8.29 Washington DC, the U.S. Capitol building.26

26

Credit: Sandia National Laboratory, particular thanks to Armin Doerry; Doerry, Gutierrez, and Wells, “A portfolio of fine resolution SAR images,” Proc. SPIE 5410A, pp. 12 16 (2004). See also http://www.sandia.gov/RADAR/imageryku.html

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8.8 Problems 1. For a SAR system such as SIR-C, does the nominal 12.5-m azimuthal resolution for the German X-band system correspond well to the nominal antenna width? What pulse length would be required to match that in range resolution? Compare to the actual pulse width. 2. What wavelengths and polarizations are used for commercial SAR systems (Radarsat, ERS)? 3. For a spotlight-mode SAR system, what azimuthal resolution could be obtained with X-band for a 10-second integration interval [assume v = 7.5 km/s, take the range (altitude) to be 500 km]? 4. The amplitude of the electric field for a 1D aperture is given by the formula 2 Intensity (θ) = [sin( kL sin θ / 2) / kL sin θ / 2] . The zeros of this equation then define the beam pattern, as shown in Fig. 8.8. Plot this function for an L-band antenna (λ = 24 cm). Take the antenna length to be 15 m (L = 15m, k = 2π / λ = 2π / 0 .23 m), and plot for an angular range of θ = 0 to 0.05 radians (about 3°). At what values of θ do the first few zeroes occur? 5. For the conditions illustrated in Fig. 8.11, the shuttle was at 222 km altitude and the antenna (shuttle) attitude was 27.1°. What range does the angular range (measured from nadir) correspond to? 6. During the SIR-B flight, observations similar to those shown in Figs. 8.9 to 8.11 were made. Fig. 8.30 shows the SIR-B measurements. Given a vehicle velocity of 7.5 km/s, convert the variations in time displayed here into a beam width in degrees. The wavelength is 23.5 cm. The local angle of incidence is 31°. (The incidence angle is measured down from the vertical.) What is the anFigure 8.30 SIR-B azimuth (along track) antenna length implied by this antenna pattern.27 tenna pattern?

27

M. C. Dobson, et al., “External calibration of SIR B imagery with area extended and point targets,” IEEE TGRS 24(4), pp. 453 460 (1986). Figure © 1986, IEEE.

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SIR-B Mission parameters Shuttle orbital altitudes

(360, 257), 224 km

Shuttle orbital inclination

57°

Mission length

8.3 days

Radar frequency

1.275 GHz (L-band)

Radar wavelength

23.5 cm

System bandwidth

12 MHz

Range resolution

58 to 16 m

Azimuth resolution

20 to 30 m (4-look)

Swath width

20 to 40 km

Antenna dimensions

10.7 m x 2.16 m

Antenna look angle

15 to 65 ° from vertical

Polarization

HH

Transmitted pulse length

30.4 microseconds

Minimum peak power

1.12 kW

Additional References for soil penetration • •

•

•

J.F. McCauley et al., “Subsurface valleys and geoarcheology of the Eastern Sahara revealed by shuttle radar,” Science 218, pp. 1004–1020 (1982). J.F. McCauley et al., “Palaeodrainages of the Eastern Sahara-The radar rivers revisited (SIR-A/B implications for a mid-tertiary trans-African drainage system),” IEEE Trans Geoscience & Remote Sensing GE-24, pp. 624–648 (1986). T.L. Sever, “Remote Sensing,” in Benchmarks in Time and Culture: An Introduction to Palestinian Archaeology, J.F. Drinkard, G.L. Mattingly, and J.M. Miller (Eds.), Scholars Press, pp. 279–305 (1988). Nicholas M. Sr. Short, and Robert W. Blair, Jr., Geomorphology From Space: A Global Overview of Regional Landforms, NASA (1986).

See also: • http://disc.gsfc.nasa.gov/geomorphology • http://ourworld.compuserve.com/homepages/mjff/rad rivs.htm • http://disVc.gsfc.nasa.gov/geomorphology/GEO 1/GEO PLATE I-3. HTML

Chapter 9 Radar and LIDAR

So far, we have focused on remote sensing techniques that are associated with imaging. In this concluding chapter, well consider some remote sensing techniques that are non-imaging, particularly those used for measuring elevation. This can be done with radar of the sort described in the previous chapter or with laser radar (LIDAR). In the first case, elevation is generally developed using interferometry.

9.1 Radar Interferometry Radar interferometry is the study of interference patterns created by combining two sets of radar signals. This technique allows for a number of powerful additional uses for SAR data beyond the formation of literal images. Two of the more important applications are topographic mapping and change detection. Both exploit the fundamental concept that SAR images contain both amplitude and phase information. 9.1.1 Topographic mapping Topographic mapping makes use of pairs of images acquired over a fairly modest spatial baseline (typically on the order of kilometers), over relatively short time intervals. The latter is defined by the need to have relatively few changes in the scene between observations. For satellites such as ERS-1 and 2 and RADARSAT, these conditions are normally obtained by comparing data from observations within a few days of one another, from nearly identical orbits. The desirability of producing such products adds to the demand for strict constancy in the near-circular orbits of these satellites. The geometry is illustrated by Fig. 9.1. Targets 1 and 2 are imaged on two separate orbits as illustrated. Given the offset in the satellite location (by a distance indicated here as a baseline), there will be a relative difference in the paths to the targets (s 2′ − s 2 ≠ s1′ − s1 ) that can be accurately determined to within a fraction of a wavelength. This difference in phase can then be translated into elevation differences.

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The concept is illustrated in Fig. 9.2 by means of phase difference observations from the SIR-C mission in October 1994. The complex images taken a day apart are highly correlated—the differences are due to elevation. Interferometry from multiple observations separated in time require that the scene not change in any significant way between observations—the two complex images need to be very highly correlated. A technique has been developed to obtain interferometric images taken simultaneously. In Fig. 9.3, the geometry used by the shuttle topographic mission (described in detail below) is shown. There is an antenna in the shuttle Figure 9.1 Interferometry basics. bay, and a second on a boom 60 m out. Images are formed from the radar energy received at the two antennas, and the interferometric phase is determined by calculating the difference between the two complex images. Figure 9.3 illustrates how ground elements at different heights will produce different radar returns. The differential distance of each of these targets to the ends of the antenna baseline depends on the height of the target. For the higher target (Target 2), the differential distance is greater than that of the lower one (Target 1). The interferometric phase for Target 2 is therefore larger than that for Target 1. Note that the differential distance gets larger as the incidence angle (θ1 < θ2) in the picture to the target gets larger. The interferometric phase, Φ, can be related to the incidence angle by the very nearly exact formula, Φ=B

sin(θ ) , λ

(9.1)

where B is the baseline length and θ is the incidence angle. The phase Φ is in cycles. For a given target height, θ can be calculated and the interferometric phase calculated using Eq. 9.1. This equation can be revised to obtain the height from the phase Φ, solving for θ, yielding the topographic height. 1

1

html

Text adapted from Robert Treuhaft, JPL; http://www2.jpl.nasa.gov/srtm/instrumentinterfmore.

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Figure 9.2 This image of Fort Irwin in California’s Mojave Desert shows the difference in phase between two (complex) SAR images, taken on October 7–8, 1994 by the SIR-C L- and C-band sensors. The image covers an area of about 25 km by 70 km. The color contours shown are proportional to topographic elevation. With a wavelength one-fourth that of the L-band, the results from the C-band cycle through the color contours four times faster for a given elevation change. So what does one color cycle mean? One (C-band) cycle corresponds to 2.8 cm ground displacement parallel to the satellite line of sight for interferometric SAR2.

As a quick illustration, consider a phase shift of 0.01 cycles (three degrees, per Fig. 9.2). Take the baseline as 60 m, the range as 310 km (222 km altitude, depression angle of 45°), and a wavelength of 24 cm: λ ; altitude difference = range ⋅ sin(θ), B 0 .24 altitude = 0.01 ⋅ ⋅ 310 × 103 = 12 m. 60

sin (θ ) = Φ

2

Image courtesy of NASA. See also Chao Wang et al., “Applying SAR Interferometry for Ground Deformation Detection in China,” Photogrammetric Engineering and Remote Sensing (PERS), ASPRS, Bethesda, MD, pp. 1157 1165 (2004).

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Figure 9.3 The geometry of the shuttle’s radar topographic mission.

In the case of SRTM (described below), vertical resolution of about 10 m can be obtained.3 9.1.2 The Shuttle Radar Topographic Mapping (SRTM) mission The SRTM flew on the space shuttle Endeavour, launched Friday, February 11, 2000 at 1743 Z. The 11-day mission collected an astonishing amount of data. The SIR-C hardware flew for a third time, though only the C- and X-band systems were used. The C-band radar (λ = 5.6 cm), with a swath width of 225 km, scanned about eighty percent of the land surface of the Earth (HH and VV). The German X-band radar (λ = 3 cm, VV), with a swath width of 50 km, allowed for topographic maps at a somewhat higher resolution than the C-band data, but did not have the near-global coverage of the American system. Some mission parameters of note4: Data Acquisition: 222.4 hours total duration of mapping phase, 99.2 hours C-band operation (8.6 Terabytes), 90.6 hours X-band operation (3.7 Terabytes), 12.3 Terabytes total data.

3

See also Soren Madsen and Howard Zebeker, “Imaging Radar Interferometry,” in Principles and Applications of Imaging Radar, Manual of Remote Sensing, 3rd ed., Floyd Henderson and An thony Lewis (Eds.), Wiley, New York, pp. 361 336 (1998). 4 See http://shuttlepresskit.com/STS 99

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9.1.2.1 Mission design Normally, the interferometric techniques described above require either two satellites or one satellite making multiple passes over a target. In the SRTM mission, a novel approach, in which a second antenna was deployed on a mast extending 60 m from the payload bay, provided sufficient baseline for the technique and dramatically reduced problems associated with changes in the target area, including changes as subtle as wind blowing in the trees. The mission also provided a very instructive illustration of satellite technology and the unique capability of the space shuttle. The challenge was that the structure had to maintain an almost perfect attitude with respect to the shuttle. Fluctuations in mast length of about 1 cm were expected. Uncompensated mast-tip motion of 1 cm with respect to the shuttle would result in a height error at the Earth’s surface of 60 m. Knowledge of the mast position with respect to the shuttle was therefore needed to better than 1 mm. The mast used on the SRTM mission was the Able Deployable Articulated Mast (ADAM) built by the Able Engineering Company of Goleta, California. The mast consisted of a truss comprising 87 cube-shaped sections called bays. Unique latches on the diagonal members of the truss allowed the mechanism to deploy bay-by-bay out of the mast canister to a length of 60 m (200 ft). The canister housed the mast during launch and landing and also deployed and retracted the mast. The mast supported a 360-kilogram antenna structure at its tip and carried 200 kilograms of stranded copper, coaxial, fiber-optic cables, and thruster gas lines along its length. Table 9.1 The Shuttle Radar Topography Mapping mission mast.

Mast length

60 m

Nominal mast diameter

1.12 m

Nominal bay width at longerons

79.25 cm

Nominal bay length

69.75 cm

Number of bays

87

Stowed height/bay

1.59 cm

Total stowed height

128 cm

This remarkable technology worked largely as planned. The mast deployed successfully, as illustrated in Fig. 9.6. Unfortunately, the attitude-control jet at the end of the mast clogged, and it was only through a remarkable bit of flying by shuttle astronauts that the system was able to acquire useful data. Data analysis was slowed by this problem, and accuracy of products reduced somewhat.

216

Chapter 9

Figure 9.4 SRTM mission overview.

Figure 9.5(a) Mast fully deployed at AEC. Figure 9.5(b) Mast with first few bays deShown from tip.5 ployed from canister at AEC.5

5

Images courtesy of ATK Space Systems.

Radar and LIDAR

217

Figure 9.6 SRTM mast, deployed. Shuttle glow is seen around the orbiter tail and along the mast in the left figure; this is due to interactions between atomic oxygen in the upper atmosphere and the surfaces of the spacecraft and antenna.

9.1.2.2 Mission results: level-2 terrain-height datasets (digital topographic maps) The level-2 terrain-height datasets contain the digital topography data processed from C-band data collected during the mission. Each posting in a level-2 terrain-height dataset represents a height measurement (posting) in meters relative to the WGS84 ellipsoid surface, a standard reference coordinate for elevation models. The absolute horizontal accuracy (90% circular error) is 20 m. The absolute vertical accuracy (90% linear error) is 16 m. For data from the equator to 50 ° latitude, the postings are spaced at 1 arc sec latitude by 1 arc sec longitude. At the equator, these are spacings of approximately 30 × 30 m. Figures 9.7 and 9.8 illustrate some of the products of the mapping mission. Starting from known elevation (sea level), altitude is obtained by unwrapping the variation in phase. Figure 9.7 shows how the phase varies over Lanai and a portion of Maui. This can be compared to the difference image from Ft. Irwin in Fig. 9.2. Once altitude has been determined, it can be used in a variety of applications. Figure 9.8 illustrates a pair of Canadian islands, with a visible (Landsat) image draped over the elevation model in a perspective view. This sort of perspective view is particularly useful for pilots training for low-level flight.

218

Chapter 9

Figure 9.7 Digital elevation models (DEMs) for some Hawaiian islands. Credit: NASA.

Figure 9.8 Typical graphical display format for preliminary SRTM results. The top figure illustrates the DEM model with Landsat 7 imagery draped over the perspective model. The lower portion shows a gray-scale-encoded DEM model. Visible Earth: 3D Perspective of Saint Pierre and Miquelon Islands. Credit: NASA.

Radar and LIDAR

219

9.2 LIDAR 9.2.1 Introduction Light detection and ranging, or LIDAR, uses the same principles as radar, but its shorter wavelengths make the data useful in quite different ways. There are a variety of LIDAR types; the form of interest here are those designed for remote sensing of the Earth. Other configurations are useful for studying the atmosphere, and in particular aerosols and dust in Figure 9.9 A pulse of laser light is emitted from the atmosphere. the aerial platform. A sensor records the reA typical LIDAR system consists turning energy as a function of the xy position, of a laser, typically operating in the providing then the z, or elevation component. near infrared (~1.05 µm), a scan mir- Such systems are occasionally designated 3D ror to sweep the laser beam cross- imagers. The imager depends on a very accurate knowledge of the platform position, genertrack, and a detector designed to mea- ally obtained from GPS.6 sure the return time with an accuracy of a few nanoseconds. The returning light pulse is observed with range gates, that is, the detector is sampled in a time sequence, and those times correspond to range. Airborne systems currently fly at modest altitudes (a few thousand feet), and the laser forms a spot on the ground of less than a meter in diameter, perhaps only a few tens of centimeters. (The beam divergence is typically a few tenths of a milliradian.) The sensor orperates in a ‘whisk-broom’ mode, sweeping cross-track with an angular extent defined by the hardware capabilities, but on the order of the –40 ° range illustrated here in Fig. 9.9. The spacing between pulses is typically larger than the spot size—typically 1–3 m. Pulse-repetition frequencies (PRF) determine the sweep rate (and angular range) which is practical for a given sensor. Initial rates were rather low. The chart below shows the evolution of the Optech sensors. The PRF being used depends somewhat on the altitude of the flying platform, so the specifications depend on altitude. Optech has manufactured most of the commercial systems in use today, so this chart reflects the field as a whole rather well. As the PRF goes up, the cost of flying a given area decreases. In a recent commercial effort, a 10 km × 20 km area north of Monterey was imaged in about a day

6

K. Kraus and N. Pfeifer, “Determination of terrain models in wooded areas with airborne laser scanner data,” ISPRS Journal of Photogrammetry and Remote Sensing 53, pp. 193 203 (1998); with thanks to David Evans, MSU, Dept of Forestry.

220

Chapter 9

Figure 9.10 Evolution of the Optech sensors

of flying. By contrast, a Quickbird image of this area takes approximately 8 seconds to acquire.7 As with radar, fine range (altitude) resolution depends on the pulse length, at first glance. As with radar, the pulse length is really too long in time to give the sort of resolution (cm), that modern systems need to provide. As a consequence, the LIDAR systems are designed to capture the leading edge of the light pulse, which can be resolved to very high temporal resolution. 9.2.2 OPTECH: Airborne Laser Terrain Mapper (ALTM) The ALTM is a terrain-mapping system for rapid, digital, elevation-data generation. A recent model generates up to 50,000 dual elevation measurements every second. As a marker for the market, in early 2004 Optech sold their fiftieth ALTM system. Other Optech products are designed for bathymetry, and use lasers modified to work in the blue-green, which is necessary for laser energy to penetrate water. The ALTM 3033 is shown in Fig. 9.11. Several images from an Optech system are shown next. Data were acquired by Airborne 1 Corporation, flying over Exposition Park in Los Angeles, imaging the Coliseum and the Sports Arena (the ellipse to the lower right, Fig. 9.12). Figure 9.13 shows a horizontal transect through the scene, roughly along the long center line of the football stadium. The sloping stadium walls lead down to a field that is below the level of the ground outside the stadium. Temporary seats (bleachers)

7

See http://www.alsm.ufl.edu/pubs/applications/apps.htm

Radar and LIDAR

221

Figure 9.11 The ALTM 3033 fits fairly comfortably in a small airplane. The laser is a diode-pumped Nd YAG, producing a near-IR beam at a 1064-nm wavelength. The output energy depends on pulse rate, but fewer than 7 watts or 100 microJoules/pulse with a less than 12-ns pulse width. The receiver is a single avalanche photon detector (APD).8

have apparently been set up in the peristyle end of the stadium. The intensity image from the 1.06-µm laser is shown in Fig. 9.14. In Fig. 9.15, the scattered returns from throughout the canopy show how the laser penetrates through the leaves, reaching the ground and returning. One of the more vexing problems in remote sensing is power and telephone lines, which are generally sub-pixel for any reasonable detector—the wires simply do not show up in optical imagery. The LIDAR, with a relatively small spot size, illuminates the wires at a fairly regular interval, and Fig. 9.16 shows the wires detected against quite accurately.

Figure 9.12 Los Angeles Coliseum, digital elevation model.

8

Image courtesy of Optech.

222

Chapter 9

Figure 9.13 LIDAR taken over the Los Angeles Coliseum. Note the goal posts are 120 yards apart. Bleachers are at the 420 m mark. Data courtesy of Airborne 1, Los Angeles, Ca.

Figure 9.14 Intensity image from LIDAR active illumination at 1.06 µm.

Figure 9.15 Detailed view of First/Last returns, bare soil, and extracted feature returns over a few trees to the west of the Coliseum.

9.2.3 Bathymetry One powerful capability offered by LIDAR is the ability to survey for water depth, that is, to conduct bathymetric surveys. An older system, the ocean-water LIDAR (OWL) was flown in the early 1990s. NPS student Charles Cassidy worked on this topic in 1995. An illustration of the sort of data obtained by this sensor is given in Fig. 9.17. The sensor detects light reflected from the surface, then the bottom. The difference gives a very accurate depth measure.

Radar and LIDAR

223

Figure 9.16 Power lines in three sections of corridor, in profile mode. Individual laser data points on wires, towers, and ground are clearly distinguished. Trees are clearly visible. Product: ALTM 1020 Location: Toronto, Canada. Altitude: 380 m AGL Laser Pulse Freq.: 5 kHz9

Figure 9.18 shows the results from a modern Optech system. The water depth is about 16.5 m. A cube has been placed in the water, and a smaller target placed on top of that. The figure illustrates the ability to accurately resolve depth for such test conditions.

Figure 9.17 The intensity plot shows a return from fairly near shore—water depth is a few tens of meters.

9


224

Chapter 9

Figure 9.18 Laser soundings, showing target, close-up of target soundings (soundings filtered). Targets: 10 × 10 m cube with 1 × 1 m cube suspended above it. General depth: 16.5 m. Large-target strikes: 100. Target depth: 6.5 m. Small-target strikes: 5 (two strongest shown).10

9.3 Exercise 1. For a LIDAR to have a vertical resolution of 5 cm, what is the upper limit on the pulse-length, in time? Assume a square pulse, as with a radar.

10


Appendix 1 Derivations

A1.1 Derivation of the Bohr Atom The existence of line spectra can be explained by means of the first “quantum” model of the atom, developed by Bohr in 1913. Although the Bohr model of the hydrogen atom was eventually replaced, it yields the correct values for the observed spectral lines, and gives a substantial insight into the structure of atoms in general. The following derivation has the objective of obtaining the energy levels of the Bohr atom. If we can obtain the energy levels, we can reproduce the hydrogen atom spectra. The derivation proceeds with three major elements: first, use force balance to relate the velocity to the radius of the electron orbit, then use a quantum assumption to get the radius, then solve for the energies. Assumption 1: The atom is held together by the Coulomb Force It is an experimental fact that the force F between two point charges q1 and q2 separated by a distance r is given by: F=

q1 q 2 4π ε 0 r 2

)

,

(A1.1)

1 = 8.99 × 109 (N m 2 / C 2 and q1 and q2 are in units of Coulombs. The 4π ε o distance, r, is in meters, of course. Note that the charges may be positive or negative. For a single electron atom, we take the charge of the nucleus, q1, to be +Ze, where Z is the atomic number of the atom (the number of protons in the nucleus). Z equals 1 for hydrogen. The charge of the electron, q2, is –e. Substituting the values into Eq. A1.1 above we obtain: where

225

226

Appendix 1

F=−

Ze 2 . 4πε 0 r 2

(A1.2)

The minus sign on the force term means the force is “inward,” or attractive. Assumption 2: The electron moves in an elliptical orbit around the nucleus (as in planetary motion). Let us assume that the electron moves in a circular orbit around the nucleus. We apply Newton’s second Law (F = ma) here by setting the Coulomb force equal to the centripetal force. The result can be written as − Ze 2 = − m v 2/ r , 4πε 0 r 2

(A1.3) Figure A1.1 Bohr atom model, Z = 3.

and we can now solve for the radius vs. velocity. Assumption 3: Quantized angular momentum Bohr now introduced the first of his two new postulates, namely that the only allowed orbits were those for which the angular momentum L was given by: L = mvr = nh− ,

(A1.4)

where m = electron mass; v = velocity; r = radius of the orbit; n = an integer (1,2,3,..); and h=

h = 1.054 × 10 −34 (Joule-seconds) = 0.658 × 10 −15 (eV-seconds), 2π

where h is simply Planck’s constant, as before. (One suggestion for a physical basis for this assumption is that if you view the electron as a wave, with wavelength λ = h/p = h/mv, then an integral number of wavelengths have to fit around the circumference defined by the orbit, or n • h/mv = 2πr. Otherwise, the electron “interferes” with itself. This all follows as a corollary

Derivations

227

to the idea that an electromagnetic wave is a particle with energy E = hf as above, and hence the momentum of a photon is p = E/c = hf/c = h/λ.) This is sufficient to give us vn =

nh mr n

(A1.5)

for the velocity of the electron in its orbit. Note that there is an index n, for the different allowed orbits. It follows that mvn2 Ze 2 mn 2 h 2 . = = rn m2 rn3 4π ε 0 rn2

(A1.6)

Upon solving for the radius of the orbit (rn), we get rn =

2   n 2 h 2 4π ε 0 2 4π ε 0 h × = n ,  2 2 m Ze  Zme 

rn (m) = n2 × 0.528 ×

or

(A1.7)

10 −10 . Z

This only works for one-electron atoms (H and He+ as a practical matter), but within that restriction, it works fairly well. For hydrogen (Z = 1) we get the Bohr radius, r1 = 0.528 × 10 10 m as the radius of the smallest orbit. The radius of the Bohr hydrogen atom is half an Angstrom. What is the radius of the orbit for the sole electron in He+ (singly ionized helium, Z = 2)? Now we can solve for the energy levels. The potential energy associated with the Coulomb force is: U =

q1 q 2 . 4π ε 0 r

(A1.8)

Taking U (r = ∞) = 0, and plugging in for the charges, we get U =−

Ze 2 . 4π ε 0 r

(A1.9)

A negative potential energy means the electron is in a potential ‘well.’ Given this expression for the potential energy, we need a similar expression for kinetic energy.

228

Appendix 1

The kinetic energy T is easily obtained from Eq. A1.3: 1 1 Ze 2 T = mv 2 = . 2 2 4π ε 0 r

(A1.10)

Therefore, the total energy of the electron is obtained: E =U + T = −

1 Ze 2 Ze 2 1 Ze 2 + =− . 4π ε 0 r 2 ( 4π ε 0 )r 2 ( 4π ε 0 )r

(A1.11)

The total energy is negative—a general characteristic of bound orbits. This equation also tells us that if we know the radius of the orbit (r) we can calculate the energy E of the electron. Substituting the expression for rn (Eq. A1.7) into Eq. A1.11, we obtain 1 Ze 2 1 Zme 2 E=− × 2 , or 2 4π ε 0 n 4π ε 0 h 2

2

m 1  Ze 2  2 E1 E=−   × 2 = Z 2 , (A1.12) 2  4π ε 0 h  n n

where E1 = −

me 4 = − 13.58 eV 32π 2ε 20 h 2

is the energy of the electron in its lowest or “ground” state in the hydrogen atom. Assumption 4: Radiation is emitted only from transitions between the discrete energy levels The second Bohr postulate now defines the nature of the spectrum produced from these energy levels. This postulate declares that when an electron makes a transition from a higher to a lower energy level, a single photon will be emitted. This photon will have an energy equal to the difference in energy of the two levels. Similarly, a photon can only be absorbed if the energy of the photon corresponds to the difference in energy of the initial and final states.

Derivations

229

A1.2 Dielectric Theory Why does the complex dielectric coefficient imply absorption? The answer goes back to Maxwell’s equations, and the solution for propagating waves. Two elements of the solution are claimed here: 1) For a plane wave, the electromagnetic field propagates according to the form

E n = Eo e − i ( kx −ωt )

or

Eo e

 2 πx  −i  − 2π f t   λ 

(A1.13)

ω 2π , where ω = 2πf, and k = . k λ 2) The velocity is V = 1 / ε µ; with c = 1 / ε o µ o = 3 × 10 8 ms in vacuum. c Hence, v = ; and n = ε µ / ε o µ o » ε / ε o = ε r , where we make use of n the fact that the permeability µ is generally equal to the vacuum value. Here εr is the relative dielectric coefficient (not just the real component). Such waves propagate at a velocity V = λ f =

Note that if εr is complex, εr = ε' + iε'', then so is the velocity, since it depends on the square root of εr. This raises a problem of interpretation, since it is not really meaningful for the wave velocity to be complex. Still, we can persist by returning to the definition of v, as the ratio of ω and k. One of the two, at least, must be complex. For radar purposes, it is best to take the frequency as real—making k complex. This has the following effect on our equation above: E = Eo e − i ( kx − ωt ) = Eo e − i [( k r + ik i ) x − ωt ] = Eo e − i ( k r x + ωt )e − k i x .

(A1.14)

Our traveling wave is now multiplied by an exponentially decreasing term, which is just the absorption of the radar energy by water, or another absorbing element.

230

Appendix 1

A1.3 Derivation of the beam pattern for a square aperture The beam pattern for a square antenna is derived here. It is shown that the beam pattern is basically the Fourier transform of the aperture. This is a general result that extends beyond the current illustration. Returning to a geometry that may remind the reader of Young’s double slit experiment, Fig. A1.2 shows a cut in the plane for a stylized phased-array anFigure A1.2 Each of the array elements is tenna. Each of the small elements on the the source of a spherically expanding wave, left hand side represents the source of a which reaches the “screen” at the right after radar pulse, which then propagates to traveling a distance that depends on y. the right. The array elements are separated by a distance d, in the y direction. Each array element is responsible for an electric field element defined by the equation for a spherically expanding wave: En ≈

Eo rn2

( a n e iϕ ) e − ikr , n

(A1.15)

n

where En = Electric field component due to nth array element, Eo = Electric field magnitude defined by the sources (all the same in this case), an = amplitude contribution from the nth array element, here with the dimensions of the length squared, φn = phase for the nth array element, rn = distance from nth array element to observation point, and k = 2π / λ is the wavenumber. A classic principle of electricity and magnetism says that the total electric field can be obtained by adding up all of the components, keeping track of the phase, of course. The total field from all the radiators is the sum of the elements: E total = ∑ n

Eo rn2

(a n e iϕ ) e − ikr . n

n

(A1.16)

Though accurate, this form is difficult to deal with analytically. Therefore, we will make some assumptions that allow us to simplify it. The primary one is that the observation point is a large distance from the array, rn >> d. We can then make use of the fact that the variation in amplitude with distance varies slowly in the y direction,

Derivations

231

compared to the relatively rapid changes in phase. For simplicity, we’ll take an = a constant, and φn = 0 (the emitters are all in phase). This leads to the simplified equation E total =

Eo rn2

∑ e − ikr

n

(A1.17)

,

n

where we have factored out the slow inverse square variation in amplitude. Now we play some tricks with the complex term inside the summation, addressing the question of how the exponent varies as n varies. If we take y0 = 0 to correspond to the n = 0 element, we get for r ro = x 2 + y 2 ; rn = x 2 + ( y + nd ) 2 .

(A1.18)

The above form is exact, the trick is to factor out the ro term from the rn terms. We can do this because d is small. First we expand the term inside the square root: rn = ro

x 2 + ( y + nd ) 2 x2 + y2

= ro

x 2 + y 2 + 2 ynd + n 2 d 2 x2 + y2

.

(A1.19)

Without any special tricks—yet—we expand and divide out:

rn = ro

x 2 + y 2 + 2 ynd + n 2 d 2 x2 + y2

= ro 1 +

2 ynd n2d 2 . (A1.20) + x2 + y2 x2 + y2

Now come the tricks—first taking the third term as very small, and then using an approximation for the square root, where the second term is small: rn = ro 1 +

 ynd   2 ynd ynd  = ro 1 + 2  . + 0 ≈ ro 1 + 2 2 2 2 x +y ro   x +y  

(A1.21)

(Reader exercise: check that the third term is small by plugging in some typical numbers: d = 1 cm, y = 500 m, x = 2000 m). Note that we can now turn to the family and simplify the remaining terms: iar polar form sin θ = ro

232

Appendix 1

E total =

Eo r02

∑ e − ikr

n

Eo

=

r02

n

E

∑ e − ikr − iknd sin θ = r o2 o

n

0

e − ikro ∑ e − iknd sin θ . (A1.22) n

This defines the zeroes in the beam pattern. For a continuous antenna element, the sum is replaced by an integral over an antenna of length L = nd: E total (θ ) =

Eo r02

e

− ikro

∑e

− ikro ( nd sin θ )

=

Eo

n

r02

e

− ikro

L 2

a o − iky sin θ dy , e L −L

∫

(A1.23)

2

where the sum over the elements has been replaced by an integral over y = –L/2 to L/2, and the amplitude factor has been put back in for a moment, along with an inverse length to go with the integration variable. The integral on the right side is simply the Fourier transform of the square aperture of length L: E total (θ ) =

Eo r02

e

− ikro

L 2

1

∫ Le

− L2

− iky sin θ

dy =

Eo r02

e − ikro

sin[( kL sin θ ) / 2]

(kL sin θ ) / 2

.

(A1.24)

The power at any particular location will then be proportional to the square of the electric field strength. The resulting function is then proportional to the square of the sinc function: sin 2 α / α 2 .

Appendix 2 CORONA

A2.1 Mission Overview KH-1

KH-2

KH-3

KH-4

KH-4A

KH-4B

Period of Operation

1959–60 1960–61 1961–62 1962–19 1963–19 1967–72 63 69

Number of RVs

1

1

1

1

2

2

Mission Series

9000

9000

9000

9000

1000

1100

Life

1 day

2–3 days 1–4 days 6–7 days 4–15 days

Altitude (nm) Perigee Apogee

103.5 (e) 136.0 (e) 117.0 (e) 114.0 (e) u/a 441.0 (e) 380.0 (e) 125.0 (e) 224.0 (e)

u/a

Avg Ops

u/a

u/a

u/a

110 (e)

100 (e)

81 (e)

Missions Total Successful

10 1

10 4

6 4

26 21

52 49

17 16

(e) estimated (u/a) unavailable (RV) re entry vehicle

233

19 days

234

Appendix 2

A2.2 Camera Data KH-1

KH-2

KH-3

KH-4

KH-4A

KH-4B

Model

C

C'

C''

Mural

J-1

J-3

Type

mono

mono

mono

stereo

stereo

stereo

Scan angle

70°

70°

70°

70°

70°

70°

30°

30°

30°

u/a

u/a

focal plane

focal plane

Stereo angle 1

u/a

Shutter

u/a

Lens2

f/5 f/5 Tessar Tessar

f/3.5 Petzval

f/3.5 Petzval

f/3.5 Petzval

f/3.5 Petzval

40

12–25

10–25

9–25

6

50–100

50–100

120

160

u/a

u/a

10.6 × 144 nm

8.6 × 117 nm

Resolution3 ground (ft)

25

film (lines/mm) 50–100 50–100 Coverage

u/a

u/a

Film base

acetate polyester polyester polyester polyester polyester

Film width

2.10"

2.10"

2.25"

2.25"

2.25"

2.25"

Image format

2.10" (est.)

2.19" (est.)

2.25 × 29.8"

2.18 × 29.8"

2.18 × 29.8"

2.18 × 29.8"

Camera

u/a

u/a

u/a

u/a

8,000'

8,000'

RV

u/a

u/a

u/a

u/a

16,000'

16,000'

Mission

u/a

u/a

u/a

u/a

32,000'

32,000'

Film load

1 2 3

unavailable 24'' focal length estimated

CORONA

235

A2.3 Mission Summary Date

Success1

Mission

Designator

Remarks

28 Feb

1959-002A

(β)

Discoverer I, Thor Agena A, orbited for 5 days. One year after Explorer 1 (2/21/58).

13 April

1959-003A

(γ1)

Discoverer II2, Thor rocket Agena A.

1959

3 June

Failed to Orbit.

25 Jun

9001

KH-1

no

Discoverer IV Agena did not orbit.

13 Aug

9002

KH-1

no

Discoverer V; camera failed on Rev 1: RV not recovered.

19 Aug

9003

KH-1

no

Discoverer Vl; camera failed on Rev 2; retrorocket malfunction; RV not recovered.

7 Nov

9004

KH-1

no

Discoverer VII Agena failed to orbit.

20 Nov

9005

KH-1

no

Discoverer VIll; bad orbit; camera failure; no recovery.

4 Feb

9006

KH-1

no

Discoverer IX; Agena failed to orbit.

19 Feb

9007

KH-1

no

Discoverer X; Agena failed to orbit.

15 Apr

9008

KH-1

no

Discoverer Xl; camera operated; spin rocket failure; no recovery.

29 Jun

N/A

N/A

N/A

Discoverer XII diagnostic flight; Agena failed to orbit.

10 Aug

N/A

N/A

N/A

Discoverer XIII diagnostic flight Successful.3

18 Aug

9009

KH-1

yes

Discoverer XIV; first successful KH-1 mission; first successful air recovery of object sent into space.

1960

236

Date

Appendix 2

Mission

Designator

Success1

Remarks

1960 continued 13 Sep

9010

KH-1

no

Discoverer XV; camera operated; wrong pitch attitude on reentry: no recovery (capsule sank).

26 Oct

9011

KH-2

no

Discoverer XVI; Agena failed to orbit.

12 Nov

9012

KH-2

no

Discoverer XVII; air catch: payload malfunction.

7 Dec

9013

KH-2

yes

Discoverer XVIII; first successful KH-2 mission: air catch.

20 Dec

N/A

N/A

N/A

Discoverer XIX radiometric mission (Midas missile detection test).

17 Feb

9014A

KH-5

no

Discoverer XX; first ARGON flight: orbital programmer failed, camera failed, no recovery.

18 Feb

N/A

N/A

N/A

Discoverer XXI radiometric mission.

30 Mar

9015

KH-2

no

Discoverer XXII; Agena failure; no orbit.

8 Apr

9016A

KH-5

no

Discoverer XXIII; camera OK; no recovery.

8 Jun

9018A

KH-5

no

Discoverer XXIV; Agena failure, power & guidance failure; no recovery.

16 Jun

9017

KH-2

yes

Discoverer XXV; water landing, recovery.

7 Jul

9019

KH-2

partial

Discoverer XXVI; camera failed on Rev 22: successful recovery.

21 Jul

9020A

KH-5

no

Discoverer XXVII; No orbit; Thor problem.

3 Aug

9021

KH-2

no

Discoverer XXVIII; No orbit; Agena guidance failure.

1961

CORONA

Date

237

Mission

Designator

Success1

Remarks

1961 continued 30 Aug

9023

KH-3

yes

Discoverer XXIX; 1st KH-3 flight; Air recovery.

12 Sep

9022

KH-2

yes

Discoverer XXX; air recovery (fifth).

17 Sep

9024

KH-2

no

Discoverer XXXI; no recovery, power failure.

13 Oct

9025

KH-3

yes

Discoverer XXXII; air recovery.

23 Oct

9026

KH-2

no

Discoverer XXXIII; Agena failed to orbit.

5 Nov

9027

KH-3

no

Discoverer XXIV; no recovery.

15 Nov

9028

KH-3

yes

Discoverer XXXV.

12 Dec

9029

KH-3

yes

Discoverer XXXV.

13 Jan

9030

KH-3

no

Discoverer XXXVII; Agena failed to orbit.

27 Feb

9031

KH-4

yes

Discoverer XXXVIII; first KH-4 flight: air recovery.

18 Apr

9032

KH-4

yes

Air recovery.

28 Apr

9033

KH-4

no

No recovery; failed to eject parachute.

15 May

9034A

KH-5

yes

30 May

9035

KH-4

yes

2 Jun

9036

KH-4

no

23 Jun

9037

KH-4

yes

28 Jun

9038

KH-4

yes

21 Jul

9039

KH-4

yes

28 Jul

9040

KH-4

yes

2 Aug

9041

KH-4

yes

29 Aug

9044

KH-4

yes

1 Sep

9042A

KH-5

yes

17 Sep

9043

KH-4

yes

29 Sep

9045

KH-4

yes

1962

No recovery; torn parachute.

238

Date

Appendix 2

Mission

Designator

Success1

Remarks

1962 continued 9 Oct

9046A

KH-5

yes

5 Nov

9047

KH-4

yes

24 Nov

9048

KH-4

yes

4 Dec

9049

KH-4

yes

On October 26, 1962, a non-photoreconnaissance engineering mission was flown. Richelson says the first KH4A camera flight was May 18, 1963. 1963 14 Dec

9050

KH-4

yes

8 Jan

9051

KH-4

yes

28 Feb

9052

KH-4

no

Separation failure.

18 Mar

8001

KH-6

no

First KH-6 flight; no orbit; guidance failure (Agena).

1 Apr

9053

KH-4

yes

26 Apr

9055A

KH-5

no

No orbit; attitude sensor problem.

18 May

8002

KH-6

no

Orbit achieved; Agena failed in flight.

13 Jun

9054

KH-4

yes

26 Jun

9056

KH-4

yes

18 Jul

9057

KH-4

yes

31 Jul

8003

KH-6

partial

Camera failed after 32 hrs.

24 Aug

1001

KH-4A

partial

First KH-4A flight;5 2 RV’s; RV-2 lost.

29 Aug

9058A

KH-5

yes

23 Sep

1002

KH-4A

partial

29 Oct

9059A

KH-5

yes

9 Nov

9060

KH-4

no

Failure, unstable launching.

27 Nov

9061

KH-4

no

Agena failed in flight; prevented recovery.

21 Dec

9062

KH-4

yes

Last KH-4 mission.

15 Feb

1004

KH-4A

yes

24 Mar

1003

KH-4A

110

RV-1 recovered; RV-2 lost.

1964 No orbit: Agena power failure.

CORONA

Date

239

Mission

Designator

Success1

Remarks No on-orbit operation: Agena failure: RV impacted in Venezuela.

1964 continued 27 Apr

1005

KH-4A

no

4 Jun

1006

KH-4A

yes

13 Jun

9063A

KH-5

yes

19 Jun

1007

KH-4A

yes

10 Jul

1008

KH-4A

yes

5 Aug

1009

KH-4A

yes

21 Aug

9064A

KH-5

yes

14 Sep

1010

KH-4A

yes

5 Oct

1011

KH-4A

partial

No RV-2 recovery.

17 Oct

1012

KH-4A

yes

RV-2 water recovery because of bad weather.

2 Nov

1013

KH-4A

partial

Both cameras failed on Rev 52.

18 Nov

1014

KH-4A

yes

19 Dec

1015

KH-4A

yes

15 Jan

1016

KH-4A

yes

25 Feb

1017

KH-4A

yes

25 Mar

1018

KH-4A

yes

29 Apr

1019

KH-4A

partial

18 May

1021

KH-4A

yes

9 Jun

1020

KH-4A

yes

19 Jul

1022

KH-4A

yes

17 Aug

1023

KH-4A

partial

Forward camera failed.

2 Sep

N/A

no

Destroyed on launching by range safety.

22 Sep

1024

KH-4A

yes

5 Oct

1025

KH-4A

yes

28 Oct

1026

KH-4A

yes

9 Dec

1027

KH-4A

yes

24 Dec

1028

KH-4A

yes

1965

No RV-2 recovery. Water recovery on RV-2.

Control-gas loss.

240

Appendix 2

Mission

Designator

Success1

2 Feb

1029

KH-4A

yes

9 Mar

1030

KH-4A

yes

7 Apr

1031

KH-4A

yes

3 May

1032

KH-4A

no

24 May

1033

KH-4A

yes

21 Jun

1034

KH-4A

yes

9 Aug

1036

KH-4A

yes

20 Sep

1035

KH-4A

yes

8 Nov

1037

KH-4A

yes

14 Jan

1038

KH-4A

yes

22 Feb

1039

KH-4A

yes

30 Mar

1040

KH-4A

yes

9 May

1041

KH-4A

yes

16 Jun

1042

KH-4A

yes

7 Aug

1043

KH-4A

yes

15 Sep

1101

KH-4B

yes

2 Nov

1044

KH-4A

yes

9 Dec

1102

KH-4B

yes

2 Jan

1045

KH-4A

yes

14 Mar

1046

KH-4A

yes

1 May

1103

KH-4B

yes

20 Jun

1047

KH-4A

yes

7 Aug

1104

KH-4B

yes

18 Sep

1048

KH-4A

partial

3 Nov

1105

KH-4B

yes

12 Dec

1049

KH-4A

yes

Degraded film.

1106

KH-4B

partial

Aft camera failed.

Date

Remarks

1966

Agena failed to separate from booster.

1967

Water pick-up on RV-2. First KH-4B mission (PERS).

1968

Forward camera failed.

1969 5 Feb

CORONA

Date

241

Mission

Designator

Success1

Remarks

1969 continued 19 Mar

1050

KH-4A

partial

Terminated; Agena failure.

2 May

1051

KH-4A

yes

Degraded film.

24 Jul

1107

KH-4B

partial

Forward camera failed; RV-1 water recovery.

22 Sep

1052

KH-4A

yes

Last KH-4A mission.

4 Dec

1108

KH-4B

yes

4 Mar

1109

KH-4B

yes

20 May

1110

KH-4B

yes

23 Jul

1111

KH-4B

yes

18 Nov

1112

KH-4B

yes

17 Feb

1113

KH-4B

no

24 Mar

1114

KH-4B

yes

10 Sep

1115

KH-4B

yes

19 Apr

1116

KH-4B

yes

25 May

1117

KH-4B

yes

1970

1971 Failure of Thor booster.

1972

1

Final Corona mission.

The assessment in this column is subjective.

2

Due to error, the capsule landed on the island of Spitzbergen, and was apparently recovered by the Soviet Union. Ref: Richelson, Jeffrey T., America’s Secret Eyes in Space, Harper & Row, New York (1990).

3

This was the first successful diagnostic flight in the Discoverer series. Its mission ended with the first successful recovery of an object sent into space. The recovery vehicle (RV) capsule was recovered from the Pacific Ocean, and the RV resides in the Smithsonian’s National Air and Space Museum.

242

Appendix 2

A2.4 Orbits—An Example1 Data are given here showing orbital parameters for an early Corona mission. Note the low altitude, elliptical (as opposed to circular) orbit, and the rapid drop in altitude. Inclination was 80.0°. 1959-005A (ε1)—Discoverer-5 Název objektu

SSC Start

Discoverer-5 KH-1 Mission 9003 (key hole) Agena 1028 FTV-1028 (flight test vehicle) Corona 5 18 1959-08-13 19:00:08 UT, Western Test Range, Thor Agena A

Parametry dráhy Epocha

P (min)

hP (km)

hA (km)

59-08-13.8

94.19

217

739

59-08-14.36

94.07

215

732

59-08-20.29

93.59

193

707

59-08-28.39

92.94

215

622

59-09-02.23

92.60

215

588

59-09-05.44

92.31

215

560

59-09-08.64

91.96

215

526

59-09-10.23

91.85

215

515

59-09-15.01

91.39

185

501

59-09-18.18

91.00

185

462

59-09-21.33

90.45

163

430

59-09-24.46

89.67

163

354

59-09-26.32

89.10

137

323

Význam parametrů: Epocha—Datum (rok, měsíc, den a zlomek dne), pro ně platí uvedené parametry. P—Perioda (doba oběhu). hP—Výška dráhy v pericentru. hA—Výška dráhy v apocentru. [?]

1

From http://www.lib.cas.cz/www/space.40/1959/005A.HTM

Appendix 3 Tracking and Data Relay Satellite System

A3.1 Relay Satellites—TDRSS In the early phases of the space age, NASA and the Air Force maintained a large array of ground stations to communicate with their satellites. The ground stations were expensive, and did not provide continuous coverage, particularly for the low-Earth-orbiting satellites. NASA developed the idea for a global system of communication satellites that culminated with the launch of TDRS-1 on April 4, 1983. Following the loss of TDRS-2 in the Challenger accident in 1986, five more TDRS satellites were launched over the next nine years. The original TRW-built satellites are now being supplemented (replaced) by Boeing built satellites, beginning with TDRS-H. TDRS-H (now known as TDRS-8), the first of the replenishment spacecraft, was launched on June 20, 2000. Note that the satellite names change from letter to number after launch. The complete system, known as the Tracking and Data Relay Satellite System or TDRSS, consists of the satellites, two ground terminals at the White Sands Complex, a ground terminal extension on the island of Guam, and customer and data handling facilities. This constellation of satellites provides global communication and data relay services for the Space Shuttle, International Space Station, Hubble Space Telescope and a multitude of low-Earth orbiting satellites, balloons, and research aircraft.1

1

See http://tdrs.gsfc.nasa.gov/tdrsproject/about.htm

243

244

Appendix 3

A3.2 White Sands The White Sands Complex (WSC) is located near Las Cruces, New Mexico and includes two functionally identical satellite ground terminals. Figure A3.1 shows the ground station. These terminals are known as the White Sands Ground Terminal (WSGT) and the Second TDRSS Ground Terminal (STGT). The ground stations include three 18.3-m Ku-band antennas, three 19-m Ku-band antennas and two 10-m S-band tracking, telemetry, and command (TT&C) antennas.

Figure A3.1 White Sands Ground Station, Second TDRSS Ground Terminal.

Figure A3.2 There are four nominal stations for the active TDRS constellation: TDE (TDRS East), TDW (TDRS West), TDZ [TDRS Zone of Exclusion (ZOE)], and TDS (TDRS Spare). The original plan involved only the two stations, TDE and TDW. A zone of exclusion existed in the original plan; eventually the third station was added.2

2

Jeff Glass, NASA/GSFC, Private Communication, January 2005; http://msp.gsfc.nasa.gov/ tdrss/new.html

Tracking and Data Relay Satellite System

245

Table A3.1 Satellite locations as of August 2005.

Satellite

Launch Date

Location

TDRS-1

April 4, 1983 STS-6 (Challenger)

49° W, provides South Pole support, McMurdo Station

TDRS-2

January 27, 1986 STS 51-L (Challenger)

TDRS-3

September 29, 1988 STS-26 (Discovery)

275.0° W—Designated TDZ*

TDRS-4

March 13, 1989 STS-29 (Discovery)

46° W—Designated TDS

TDRS-5

August 2, 1991 STS-43 (Atlantis)

171° W—Designated TD172

TDRS-6

January 13, 1993 STS-54 (Endeavour)

173° W—Designated TDS

TDRS-7

July 13, 1995 STS-70 (Discovery)

150° W—Storage Mode

TDRS-8

June 30, 2000 Atlas IIA

174° W—Designated as TDW

TDRS-9

March 8, 2002 Atlas IIA

62° W

TDRS-10

December 5, 2002 Atlas IIA

40.9° W—Designated TDE

* Controlled from Guam Remote Ground Terminal (GRGT)

A3.3 TDRS 1 to 7 A3.3.1 Satellites The Tracking and Data Relay Satellite series began with a TRW-built vehicle illustrated in Fig. A3.3. The system is fairly typical of communications satellites of this era (early 1980s). The total power output of the solar array is approximately 1800 watts. Spacecraft telemetry and commanding are performed via a Ku-band communications system, with emergency backup provided by an S-band system. 3

3

From http://tdrs.gsfc.nasa.gov/tdrsproject/tdrs1.htm#1

246

Appendix 3

Figure A3.3 TDRS 1–7 Spacecraft. Dimensions: 45 ft wide, 57 ft long, 5000 lbs. Power (EOL): 1800 watts.

A3.3.2 Payload4 The satellite payload is an ensemble of antennas designed to support the relay mission. •

•

4

Two Single Access (SA) antennas: Each antenna is a 4.9-m-diameter molybdenum wire mesh antenna that can be used for Ku-band and S-band links. Each antenna is steerable in 2 axes and communicates with one target spacecraft at a time. One Multiple Access (MA) S-band antenna array: This is an electronically steerable phased array consisting of 30 fixed helix antennas. The MA array can receive data from up to 20 user satellites simultaneously, with one electronically steerable forward service (transmission) at a time. Twelve of the helices can transmit and receive, with the remainder only able to receive. Relatively low data rates are supported—100 bps to 50 kbps. 5

See http://msl.jpl.nasa.gov/QuickLooks/tdrssQL.html NASA Press Release, “Tracking and Data Relay Satellite System (TDRSS) Overview;” Release No. 91 41 (June 7, 1991).

5

Tracking and Data Relay Satellite System

•

•

247

One Space to Ground Link antenna (SGL): This is a 2-m parabolic antenna operating at Ku-band that provides the communications link between the satellite and the ground. All customer data is sent through this dish, as are all regular TDRS command and telemetry signals. The antenna is gimbaled on two axes. One S-band omni antenna: a conical log spiral antenna used during the satellite’s deployment phase and as a backup in the event of a spacecraft emergency. This antenna does not support customer links.

A3.4 TDRS H The next generation of TDRS spacecraft are based on the body-stabilized Boeing (Hughes) 601 satellite. This is a standard communications bus which is heavily used in the telecommunications industry. The attitude control subsystem has an on-board processor, providing some measure of autonomy over the existing fleet. It also provides tighter pointing capability, which is required for the narrow bandwidth, used for the new Ka-band service. The power system is more robust. Two wings provide a 15-year end of life power of approximately 2300 watts. Nickel hydrogen batteries are used, by contrast with the older nickel cadmium batteries used in earlier satellites.

Figure A3.4 TDRS H.

A3.4.1 TDRS H, I, and J payload characteristics6 The TDRS H, I, and J provide 18 service interfaces to user spacecraft. The onboard communications payload can be characterized as bent-pipe repeaters, in that no processing is done by the TDRS.

6

See http://spaceflightnow.com/atlas/ac139/000626tdrsh.html

248

Appendix 3

A3.4.1.1 S-band multiple access The multiple access (MA) array consists of two antennas, one each for transmitting to and receiving from users. The phased array antennas are designed to receive signals from five spacecraft at once, while transmitting to one. A3.4.1.2 Single-access (SA) antenna (2) These two large (15-foot diameter) very light antennas are pointed at individual user satellites to transmit and receive data using one or two radio frequency (RF) channels (S-band and either Ku-band or Ka-band). The S-band access is used to support manned missions, science data missions including the Hubble Space Telescope, and satellite data dumps. The Ku band higher bandwidth supports high-resolution digital television including all space shuttle video communications. Recorders aboard NASA satellites can dump large volumes of data at rates of up to 300 million bits per second (300 Mb/s). The Ka band is a new tunable, wideband, high frequency service offered by the 15-foot antennas providing data rates up to 800 Mb/s. A3.4.1.3 Space-ground-link Antenna (Ku band) This smaller (2-m-diameter) antenna always points at the TDRS ground station at White Sands, New Mexico. Baseline service

Service

TDRS 1–7

TDRS H,I,J

Single access (SA)

S-Band

Forward

300 kbps

300 kbps

Return

6 Mbps

6 Mbps

Forward

25 Mbps

25 Mbps

Return

300 Mbps

300 Mbps

Forward

N/A

25 Mbps

Return

N/A

800 Mbps

Number of links per spacecraft

2 S SA 2 Ku SA

2 S SA 2 Ku SA 2 Ka SA

Forward

1 at 10 kbps

1 at 300 kbps

Return

5 at 100 kbps

5 at 3 Mbps

150 m 3 sigma

150 m 3 sigma

Ku-Band Ka-Band

Number of multiple access links per spacecraft (MA) Customer tracking

Appendix 4 Useful Equations and Constants

EM Waves λf = c; E = hf; λ =

hc ; c = 2.998 × 108; 1 eV = 1.602 × 10 ∆E

19

J

6 .626 × 10 −34 J ⋅ s  h = Planck’s Constant =   −15 4 .136 × 10 eV ⋅ s 1.24 × 10 −6 1.24 ∆ E(eV ) = = λ ( m) λ (µm )

Bohr Atom rn (m) = n 2 × 0 .528 × 10 −10 / Z. 2

1  Ze 2  m me 4 2 E1 ; En = −  = E = − = − 13.58 eV; Z  1 2  4 π ε 0h n 2 32 π 2ε 20 h 2 n2

Blackbody Radiation J W ; σ = 5 .67 × 10 −8 2 4 ; a = 2 .898 × 10 −3 mK K m K 2hc 2 1 Radiance = L = 5 hc λ λ kT e −1  W Stefan-Boltzmann law: R = σ ε T 4  2  m  k = 1.38 × 10 −23

249

250

Appendix 4

Wien’s law: λ max = Tradiance = ε 1/ 4Tkinetic

a T

Reflection and Refraction n=

c v

n1 sin θ1 = n 2 sin θ 2

n cos θ1 − n 2 cos θ 2 r⊥ = 1 n1 cos θ1 + n 2 cos θ 2

r| | =

n 2 cos θ1 − n1 cos θ 2 n 2 cos θ1 + n1 cos θ 2

 n − n2  R= 1   n1 + n 2 

Optics 1 1 1 = + ; f i o

f /# =

focal length diameter

Rayleigh criteria: GSD = ∆θ ⋅ range =

1.22 × λ ⋅ range diameter

Orbital Mechanics and Circular Motion v = ω r ; ω = 2π f ; τ = Fcentripetal = m F = −G go = G

m1 m2 r2 mEarth 2 R Earth

1 2π = ω f

v2 = mω 2 r r

2

m2 R  r$ ; F = g o m  Earth  ; G = 6 .67 × 10 −11 N 2 ;  r  kg m = 9 .8 2 s

REarth = 6.38 × 106 m, mEarth = 5.9736 × 1024 kg. go circular motion: v = R Earth r  2 1 Elliptical orbit: v = GM  −   r a τ2 =

4π 2 4π 2 3 r = r3 2 M Earth G g o R Earth

2

Index

A

covariance, 150 cross track, 80, 81

absorption, 52 adaptive optics, 66, 67, 102 Advanced Camera for Surveys (ACS), 85 Aerojet, 173 AHI, 176, 177 air order of battle (AOB), 3, 4,62 airborne, 19, 20 Airy disk, 72 aperture, 69 astronaut photography, 13 atmospheric absorption, 63 atmospheric scattering, 64 atmospheric turbulence, 66 AVIRIS, 132, 133, 134 azimuthal antenna pattern, 188, 189

D Defense Meteorological Satellite Program (DMSP), 10, 11, 23, 98 100 Defense Support Program (DSP), 172, 173, 174 dielectric coefficient, 192, 229 diffraction, 70, 72 Digital Elevation Model (DEM), 218 Digital Number (DN), 142, 143 dynamic range, 127, 143, 144

E Earth Resources Technology Satellite (ERTS 1), 120 electronic order of battle (EOB), 3 elements of recognition, 137 140 association, 140 height, 138 pattern, 139 shadow, 138 shape, 137 sight, 140 size, 138 texture, 139 time, 140 tone, 138 emissivity, 158, 159, 160 energy, 35 Enhanced Thematic Mapper (ETM), 120, 122 EROS, 9 European Radar Satellite (ERS), 202, 203 exposure time, 99

B bandgap, 75, 76 bathymetry, 222, 223, 224 beam pattern, 186, 189, 230 blackbody, 45, 158 Bohr atom, 42, 225 228

C Cassegrain, 86, 87, 93, 95, 122 central force problem, 103 centripetal force, 105 chirp, 184, 185 circular motion, 104 corner reflectors, 194 corona, 55, 59, 61, 233 242 correlation, 149, 150

251

252 F f/#, 69 Faint Object Camera (FOC), 85, 89 film, 74 filters, 146 framing system, 80, 81 frequency modulation, 184 FTHSI, 135, 136

Index

keyhole, 57 kinetic temperature, 159 KH4, 57 KH4B, 58

L Landsat, 13, 14, 22, 120, 163, 164 LIDAR, 219 low earth orbit (LEO), 110, 121

G gambit, 57 geometric resolution, 92 geosynchronous orbit (GEO), 106, 111, 112, 115 Gnanalingam, Suntharalingam, 184 GOES, 9, 21,167 169,172 GRAB, 56 gravity, 103

H Hasselblad, 13 histogram, 142, 143, 145, 147 149 Hubble telescope, 82 90 human vision, 118, 119 hydrogen atom, 42, 44 Hyperion, 133, 135

I IKONOS, 17, 19, 92 98, 100, 131, 132 image intensifier, 41 imaging radar, 179, 181 inclination, 108, 109 Indian Remote Sensing Satellite (IRS), 17, 18 indium antimonide (insb), 76, 125, 133 infrared, 20, 157 interferometry, 212 internal waves, 200, 204 interpretation keys (See elements of recognition), 137 140

K Kepler’s laws, 106 108 kernel, 146

M magnification, 68 Maxwell’s equations, 33 medium earth orbit (MEO), 111, 115 mercury cadmium telluride (HgCdTe), 76, 125 microbolometer, 79 MIDAS, 174 Molniya orbit (HEO), 113, 115 Multiangle Imaging Spectroradiometer (MISR), 52 Mys Schmidta, 59

N Nadar, 1 naval order of battle (NOB), 8, 97 NIMBUS, 166

O oil slicks, 200 Optech, 219 222 orbital elements, 108 orbital period, 108 order of battle (OOB), 2

P photoelectric effect, 38, 39 photomultiplier tube, 40, 41 pinhole, 69, 70 Planck’s law, 45, 46 polarization, 35, 36, 195 principle components (PC) transform, 151 pushbroom, 81

Index Q Quickbird, 6, 92 94, 131

253

statistics, 153 Stefan Boltzmann, 46, 157, 158 Sternglass formula, 40 Synthetic Aperture Radar (SAR), 188 191 Surrey Satellite Technology, Ltd. (SSTL), 12

R radar, 24, 179 radar azimuthal resolution, 185 188 radar cross section, 191 radar range resolution, 182 184 RADARSAT, 24, 201, 202 range antenna pattern, 189 Rayleigh criteria, 70, 71, 73, 90, 102, 186 Rayleigh scattering, 64 reflectance, 117, 119 reflection, 50 Ritchey Chretien Cassegrain, 86, 122

T Thematic Mapper (TM), 120, 122 thermal crossover, 162, 163 thermal inertia, 161 thin lens equation, 67, 68 time delay integration (TDI), 100 TIROS, 166 TMSAT, 12 Tournachon, 1 Tracking and Data Relay Satellite System (TDRSS), 84, 243 248 Transmission, 49

S Sary Shagan, 6 scattering, 51 SEBASS, 175, 176 Severodvinsk, 59 61, 97, 98 ship detection, 201, 202 ship wakes, 203gg Shuttle Imaging Radar (SIR), 25 27, 197, 198 Shuttle Radar Topographic Mapping (SRTM) Mission, 214 218 silicon, 76, 124, 133 Snell’s law, 50 spectral response, 126, 129 132 soil penetration, 193, 199, 209 solar spectrum, 48 space order of battle (SOB), 7 SPOT, 16, 17,128 130 Sputnik, 55 South Atlantic anomaly, 86 SR 71, 5

U UoSAT, 11

W wave equation, 34 wavelength, 35 weather satellites, 165, 170 wide field/planetary camera (WF/PC), 84, 88, 90 Wien’s displacement law, 46, 158 wiskbroom, 80

X XSS 10, 8

About the author

Dr. R. C. Olsen received his degrees at the University of Southern California (B.S.) and the University of California at San Diego (M.S., PhD). His graduate work in San Diego and early career in Huntsville, Alabama, were in the area of space plasma physics, with a particular emphasis on satellite charging behavior and the control of satellite charging. At the Naval Postgraduate School, he moved into the field of remote sensing, working with both optical and radar systems but in particular with spectral imaging systems. He teaches courses in remote sensing and classified military systems, and works to develop new methods of exploiting both civil and military systems for terrain classification and target detection. He has directed the thesis efforts of over 90 students working for their master’s degrees, more than half of those in the area of remote sensing.

255

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Fundamentals of Polarimetric Remote Sensing (SPIE Tutorial Text Vol. TT81)

EUV Sources for Lithography (SPIE Press Monograph Vol. PM149)

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Near-Space Remote Sensing: Potential and Challenges

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The Art of Radiometry (SPIE Press Monograph Vol. PM184)

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High-Operating-Temperature Infrared Photodetectors (SPIE Press Monograph Vol. PM169)

Geoscience and Remote Sensing

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The Remote Sensing of Tropospheric Composition from Space

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Remote Sensing and Image Interpretation

The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press Monograph Vol. PM01) (Press Monographs)

The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press Monograph Vol. PM01) (Press Monographs)

Remote Sensing: Applications

Optical Remote Sensing

Laser Remote Sensing

Atmospheric ultraviolet remote sensing

Introduction to Remote Sensing

Atmospheric Ultraviolet Remote Sensing

Remote Sensing Image Processing

Remote Sensing of Coastal Environments (Remote Sensing Applications Series)

Optical Clearing of Tissues and Blood (SPIE Press Monograph Vol. PM154)

Advances in Information Optics and Photonics (SPIE Press Monograph Vol. PM183)

Remote Sensing from Air And Space (SPIE Press Monograph Vol. PM162)

EUV Lithography (SPIE Press Monograph Vol. PM178)

Fundamentals of Polarimetric Remote Sensing (SPIE Tutorial Text Vol. TT81)

EUV Sources for Lithography (SPIE Press Monograph Vol. PM149)

Computational Color Technology (SPIE Press Monograph Vol. PM159)

Principles of Lithography, Third Edition (SPIE Press Monograph, Vol. PM198)

Near-Space Remote Sensing: Potential and Challenges

Tutorials in Complex Photonic Media (SPIE Press Monograph Vol. PM194)

Polymer Photovoltaics: A Practical Approach (SPIE Press Monograph Vol. PM175)

The Art of Radiometry (SPIE Press Monograph Vol. PM184)

Optical Lithography: Here is Why (SPIE Press Monograph Vol. PM190)

Optical Design for Biomedical Imaging (SPIE Press Monograph Vol. PM203)

High-Operating-Temperature Infrared Photodetectors (SPIE Press Monograph Vol. PM169)

Geoscience and Remote Sensing

Space Remote Sensing of Subtropical Oceans

The Remote Sensing of Tropospheric Composition from Space

Digital and Analog Fiber Optic Communications for CATV and FTTx Applications (SPIE Press Monograph Vol. PM174) (Press Monograph)

Remote Sensing and Image Interpretation

The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press Monograph Vol. PM01) (Press Monographs)

The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press Monograph Vol. PM01) (Press Monographs)

Remote Sensing: Applications

Optical Remote Sensing

Laser Remote Sensing

Atmospheric ultraviolet remote sensing

Introduction to Remote Sensing

Atmospheric Ultraviolet Remote Sensing

Remote Sensing Image Processing

Remote Sensing of Coastal Environments (Remote Sensing Applications Series)

Optical Clearing of Tissues and Blood (SPIE Press Monograph Vol. PM154)

Advances in Information Optics and Photonics (SPIE Press Monograph Vol. PM183)

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