Tutorial Texts Series • Optical Engineering Fundamentals, Second Edition, Bruce H. Walker, Vol. TT82 • Fundamentals of Polarimetric Remote Sensing, John Schott, Vol. TT81 • Radiation Thermometry: Fundamentals and Applications in the Petrochemical Industry, Peter Saunders, Vol. TT78 • Matrix Methods for Optical Layout, Gerhard Kloos, Vol. TT77 • Fundamentals of Infrared Detector Materials, Michael A. Kinch, Vol. TT76 • Practical Applications of Infrared Thermal Sensing and Imaging Equipment, Third Edition, Herbert Kaplan, Vol. TT75 • Bioluminescence for Food and Environmental Microbiological Safety, Lubov Y. Brovko, Vol. TT74 • Introduction to Image Stabilization, Scott W. Teare, Sergio R. Restaino, Vol. TT73 • Logic-based Nonlinear Image Processing, Stephen Marshall, Vol. TT72 • The Physics and Engineering of Solid State Lasers, Yehoshua Kalisky, Vol. TT71 • Thermal Infrared Characterization of Ground Targets and Backgrounds, Second Edition, Pieter A. Jacobs, Vol. TT70 • Introduction to Confocal Fluorescence Microscopy, Michiel Müller, Vol. TT69 • Artificial Neural Networks: An Introduction, Kevin L. Priddy and Paul E. Keller, Vol. TT68 • Basics of Code Division Multiple Access (CDMA), Raghuveer Rao and Sohail Dianat, Vol. TT67 • Optical Imaging in Projection Microlithography, Alfred Kwok-Kit Wong, Vol. TT66 • Metrics for High-Quality Specular Surfaces, Lionel R. Baker, Vol. TT65 • Field Mathematics for Electromagnetics, Photonics, and Materials Science, Bernard Maxum, Vol. TT64 • High-Fidelity Medical Imaging Displays, Aldo Badano, Michael J. Flynn, and Jerzy Kanicki, Vol. TT63 • Diffractive Optics–Design, Fabrication, and Test, Donald C. O’Shea, Thomas J. Suleski, Alan D. Kathman, and Dennis W. Prather, Vol. TT62 • Fourier-Transform Spectroscopy Instrumentation Engineering, Vidi Saptari, Vol. TT61 • The Power- and Energy-Handling Capability of Optical Materials, Components, and Systems, Roger M. Wood, Vol. TT60 • Hands-on Morphological Image Processing, Edward R. Dougherty, Roberto A. Lotufo, Vol. TT59 • Integrated Optomechanical Analysis, Keith B. Doyle, Victor L. Genberg, Gregory J. Michels, Vol. TT58 • Thin-Film Design: Modulated Thickness and Other Stopband Design Methods, Bruce Perilloux, Vol. TT57 • Optische Grundlagen für Infrarotsysteme, Max J. Riedl, Vol. TT56 • An Engineering Introduction to Biotechnology, J. Patrick Fitch, Vol. TT55 • Image Performance in CRT Displays, Kenneth Compton, Vol. TT54 • Introduction to Laser Diode-Pumped Solid State Lasers, Richard Scheps, Vol. TT53 • Modulation Transfer Function in Optical and Electro-Optical Systems, Glenn D. Boreman, Vol. TT52 • Uncooled Thermal Imaging Arrays, Systems, and Applications, Paul W. Kruse, Vol. TT51 • Fundamentals of Antennas, Christos G. Christodoulou and Parveen Wahid, Vol. TT50 • Basics of Spectroscopy, David W. Ball, Vol. TT49 • Optical Design Fundamentals for Infrared Systems, Second Edition, Max J. Riedl, Vol. TT48 • Resolution Enhancement Techniques in Optical Lithography, Alfred Kwok-Kit Wong, Vol. TT47 • Copper Interconnect Technology, Christoph Steinbrüchel and Barry L. Chin, Vol. TT46 • Optical Design for Visual Systems, Bruce H. Walker, Vol. TT45 • Fundamentals of Contamination Control, Alan C. Tribble, Vol. TT44 • Evolutionary Computation: Principles and Practice for Signal Processing, David Fogel, Vol. TT43 • Infrared Optics and Zoom Lenses, Allen Mann, Vol. TT42 • Introduction to Adaptive Optics, Robert K. Tyson, Vol. TT41 • Fractal and Wavelet Image Compression Techniques, Stephen Welstead, Vol. TT40 • Analysis of Sampled Imaging Systems, R. H. Vollmerhausen and R. G. Driggers, Vol. TT39 • Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, Valery Tuchin, Vol. TT38
Tutorial Texts in Optical Engineering Volume TT83
PRESS Bellingham, Washington USA
Library of Congress Cataloging-in-Publication Data Mann, Allen, 1929Infrared optics and zoom lenses / Allen Mann. -- 2nd ed. p. cm. -- (Tutorial texts in optical engineering ; v. TT83) Includes bibliographical references and index. ISBN 978-0-8194-7667-8 1. Infrared equipment. 2. Zoom lenses. I. Title. TA1570.M34 2009 621.36'2--dc22 2009010126
Published by SPIE P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1 360 676 3290 Fax: +1 360 647 1445 Email:
[email protected] Web: http://spie.org Copyright © 2009 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. The content of this book reflects the work and 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. Printed in the United States of America.
Introduction to the Series Since its inception in 1989, the Tutorial Texts (TT) series has grown to more than 80 titles covering many diverse fields of science and engineering. The initial idea for the series was to make material presented in SPIE short courses available to those who could not attend and to provide a reference text for those who could. Thus, many of the texts in this series are generated by augmenting course notes with descriptive text that further illuminates the subject. In this way, the TT becomes an excellent stand-alone reference that finds a much wider audience than only short course attendees. Tutorial Texts have grown in popularity and in the scope of material covered since 1989. They no longer necessarily stem from short courses; rather, they are often generated by experts in the field. They are popular because they provide a ready reference to those wishing to learn about emerging technologies or the latest information within their field. The topics within the series have grown from the initial areas of geometrical optics, optical detectors, and image processing to include the emerging fields of nanotechnology, biomedical optics, fiber optics, and laser technologies. Authors contributing to the TT series are instructed to provide introductory material so that those new to the field may use the book as a starting point to get a basic grasp of the material. It is hoped that some readers may develop sufficient interest to take a short course by the author or pursue further research in more advanced books to delve deeper into the subject. The books in this series are distinguished from other technical monographs and textbooks in the way in which the material is presented. In keeping with the tutorial nature of the series, there is an emphasis on the use of graphical and illustrative material to better elucidate basic and advanced concepts. There is also heavy use of tabular reference data and numerous examples to further explain the concepts presented. The publishing time for the books is kept to a minimum so that the books will be as timely and up-to-date as possible. Furthermore, these introductory books are competitively priced compared to more traditional books on the same subject. When a proposal for a text is received, each proposal is evaluated to determine the relevance of the proposed topic. This initial reviewing process has been very helpful to authors in identifying, early in the writing process, the need for additional material or other changes in approach that would serve to strengthen the text. Once a manuscript is completed, it is peer reviewed to ensure that chapters communicate accurately the essential ingredients of the science and technologies under discussion. It is my goal to maintain the style and quality of books in the series and to further expand the topic areas to include new emerging fields as they become of interest to our reading audience. James A. Harrington Rutgers University
Contents Preface ................................................................................................................. xi 1. System Considerations................................................................................... 1 1.1 Radiometry .................................................................................................. 1 1.1.1 Blackbody radiation.............................................................................. 1 1.1.2 Planck's equation ................................................................................. 1 1.1.3 Stefan-Boltzmann law .......................................................................... 2 1.1.4 Wien displacement law ........................................................................ 2 1.2 Atmospheric Transmission .......................................................................... 3 1.2.1 Scattering ............................................................................................. 3 1.2.2 Absorption ............................................................................................ 4 1.2.3 Infrared windows .................................................................................. 4 1.2.4 Computer calculation ........................................................................... 4 1.3 Lens Transmission ...................................................................................... 5 1.3.1 Transmittance ...................................................................................... 5 1.3.2 Reflectance .......................................................................................... 5 1.4 Coatings ...................................................................................................... 7 1.4.1 Single-layer coatings............................................................................ 7 1.4.2 Multilayer coatings ............................................................................... 8 1.5 Infrared Detectors ....................................................................................... 9 1.5.1 Basic relations...................................................................................... 9 1.5.2 Types ................................................................................................... 9 1.5.3 Arrays ................................................................................................. 11 1.5.4 Matching the detector with the optics ................................................ 11 1.6 References ................................................................................................ 12 2. Optics Fundamentals .................................................................................... 13 2.1 Lens Equation ........................................................................................... 13 2.2 Stops and Pupils ....................................................................................... 13 2.3 Optical Formulas ....................................................................................... 15 2.4 Optical Performance Criteria ..................................................................... 16 2.5 Telescopes ................................................................................................ 17 2.6 Primary Aberrations .................................................................................. 19 2.6.1 Definition of the Seidel aberrations .................................................... 19 2.6.2 Variation of primary aberrations with aperture and field height ......... 19 2.6.3 Stop shift equations ........................................................................... 20 2.7 Achromatism ............................................................................................. 21 2.7.1 Primary achromatism ......................................................................... 21 2.7.2 Secondary spectrum .......................................................................... 22 2.8 Principal Planes ........................................................................................ 22
vii
2.9 Problems ................................................................................................... 24 2.10 References .............................................................................................. 24 3. Unique Features of the Infrared Region ...................................................... 25 3.1 Optical Materials ....................................................................................... 25 3.1.1 Materials for the infrared .................................................................... 25 3.1.2 Calculation of index of refraction ....................................................... 27 3.2 Thermal Compensation ............................................................................. 28 3.2.1 Focus shift with temperature .............................................................. 28 3.2.2 Athermalization .................................................................................. 28 3.2.3 Athermalization methods ................................................................... 29 3.3 Cold Stop and Cold Shield ........................................................................ 30 3.4 Narcissus .................................................................................................. 30 3.4.1 Types of retroreflections .................................................................... 30 3.4.2 Reduction techniques ........................................................................ 30 3.5 Glass Substitution ..................................................................................... 31 3.6 References ................................................................................................ 32 4. Optical Design Techniques .......................................................................... 35 4.1 Optical Design Starting Point .................................................................... 35 4.2 Scaling ...................................................................................................... 35 4.3 Optical Materials Selection ....................................................................... 37 4.4 Techniques for Compactness ................................................................... 37 4.5 Symmetry Principle ................................................................................... 37 4.6 Bending ..................................................................................................... 38 4.7 Aplanatic Condition ................................................................................... 38 4.8 Adding an Element .................................................................................... 39 4.9 Field Lens Utilization ................................................................................. 39 4.10 Conics and Aspheres .............................................................................. 40 4.11 Diffractive Surfaces ................................................................................. 41 4.12 Aperture Stop Location ........................................................................... 41 4.13 Computer Optimization ........................................................................... 41 4.14 Global Search ......................................................................................... 42 4.15 Tolerances .............................................................................................. 44 4.16 References .............................................................................................. 44 5. Zoom Lenses ................................................................................................. 45 5.1 Types of Zoom Lenses.............................................................................. 45 5.1.1 Optically compensated zoom lens ..................................................... 45 5.1.2 Mechanically compensated zoom lens .............................................. 48 5.2 Infrared Zoom Lens Specifications ........................................................... 50 5.2.1 Spectral region ................................................................................... 51 5.2.2 Optical system performance .............................................................. 51 5.2.3 Aperture ............................................................................................. 51 5.2.4 Effective focal length .......................................................................... 51 5.2.5 Magnification range............................................................................ 51 5.2.6 Size constraints.................................................................................. 51 5.2.7 Operating environment ...................................................................... 51 5.2.8 Distortion ............................................................................................ 52
viii
5.2.9 Transmission ...................................................................................... 52 5.2.10 Narcissus ......................................................................................... 52 5.2.11 Vignetting ......................................................................................... 52 5.3 Extenders .................................................................................................. 52 5.4 References ................................................................................................ 53 6. Refractive Infrared Zoom Lenses ................................................................ 55 6.1 Target Simulators ...................................................................................... 55 6.1.1 CI Systems ......................................................................................... 55 6.1.2 Hughes Aircraft Company .................................................................. 56 6.1.3 Lockheed Martin ................................................................................ 60 6.1.4 Optics 1 .............................................................................................. 63 6.2 Scanning Systems .................................................................................... 65 6.2.1 Barr & Stroud ..................................................................................... 65 6.2.2 Pilkington P.E. .................................................................................... 67 6.2.3 Optics 1 .............................................................................................. 70 6.2.4 Precision-Optical Engineering ........................................................... 71 6.2.5 Zhejiang University, Department of Optical Engineering ................... 73 6.2.6 Electrooptical Industries, Ltd. ............................................................. 74 6.2.7 Scotoptix ............................................................................................ 76 6.2.7.1 Boresighted zoom lens ............................................................... 76 6.2.7.2 Athermalized zoom lens ............................................................. 76 6.2.7.3 Optically compensated zoom lens.............................................. 81 6.2.8 Optimum Optical Systems ................................................................. 81 6.2.9 Royal Institute of Technology ............................................................ 83 6.2.10 Fuji Photo Optical Company ............................................................ 83 6.2.11 Carl Zeiss ......................................................................................... 84 6.3 Charge-Coupled Device Imaging Systems ............................................... 84 6.3.1 Angenieux .......................................................................................... 84 6.3.2 University of Alabama, Huntsville ...................................................... 87 6.3.3 National First University of Science and Technology ........................ 87 6.3.4 Industrial Technology Research Institute........................................... 88 6.4 Laser Beam Expanders............................................................................. 88 6.4.1 Carl Zeiss ........................................................................................... 88 6.4.2 University of Twente .......................................................................... 89 6.5 Diffractive Optics ....................................................................................... 93 6.5.1 Optics 1 .............................................................................................. 94 6.5.2 Optical E.T.C., Inc. and Teledyne Brown........................................... 95 6.5.3 Wescam ............................................................................................. 99 6.5.4 Texas Instruments ........................................................................... 101 6.5.5 Raytheon .......................................................................................... 102 6.5.6 Raytheon .......................................................................................... 104 6.6 Focal Plane Arrays .................................................................................. 104 6.6.1 Agency for Defence Development ................................................... 104 6.6.2 Royal Institute of Technology .......................................................... 106 6.6.3 Royal Institute of Technology .......................................................... 106 6.7 References .............................................................................................. 108
ix
7. Reflective Infrared Zoom Systems ............................................................ 111 7.1 Obscured Systems .................................................................................. 111 7.1.1 Korea Advanced Institute of Science and Technology .................... 111 7.1.2 Center for Applied Optics, University of Alabama, Huntsville .......... 112 7.2 Unobscured Systems .............................................................................. 113 7.2.1 Hughes Aircraft Company ................................................................ 113 7.2.2 Optical E.T.C., Inc. ........................................................................... 113 7.2.3 Beijing Institute of Technology ......................................................... 116 7.2.4 Contraves Brashear ......................................................................... 117 7.3 Special Systems...................................................................................... 117 7.3.1 Lockheed Martin .............................................................................. 119 7.3.2 Industrial Research, Ltd. .................................................................. 119 7.3.3 Optical Research Associates ........................................................... 120 7.4 References .............................................................................................. 121 8. Future Trends .............................................................................................. 123 8.1 Athermalization ....................................................................................... 123 8.2 Diffractive Optical Elements .................................................................... 123 8.3 Conics and Aspherics ............................................................................. 123 8.4 Materials .................................................................................................. 123 8.5 Detector Technology ............................................................................... 124 8.6 Simulators ............................................................................................... 124 8.7 Mirror Systems ........................................................................................ 124 8.8 Wavelength Region ................................................................................. 125 8.9 Optomechanical Considerations ............................................................. 125 8.10 Computer Optimization ......................................................................... 125 8.11 References ............................................................................................ 125 9. Summary of Applications ........................................................................... 127 9.1 Scene Projection and Simulation ............................................................ 127 9.2 Wide and Narrow Field of View Scanning Telescopes for Target Search and Recognition ....................................................................................... 127 9.3 WFOV and NFOV FPA or CCD Surveillance, Tracking, and Target Recognition .............................................................................................. 127 9.4 Battlefield Detection of Enemy Soldiers and Armaments ....................... 127 9.5 Search and Rescue Operations .............................................................. 128 9.6 Mineral Resource Surveys and Forest Fire Detection ............................ 128 9.7 Laser Scanning Systems ........................................................................ 128 9.8 Cutting Sheet Metal with High-Power Lasers ......................................... 128 9.9 Observation of Solar Regions ................................................................. 128 9.10 Camera Cell Phones ............................................................................. 128 Appendix A. Miscellaneous Patents .............................................................. 129 Appendix B. Computer Analysis of Selected Patents ................................. 155 Appendix C. Answers to Problems from Chapter 2 ..................................... 159 Index ................................................................................................................. 161
x
Preface This tutorial is an outgrowth of my SPIE short course entitled “Infrared Optics and Zoom Lenses.” The title was selected to reflect the scope of the subject matter, and this has been carried over to the tutorial. The first three chapters present an introduction to the principles of optics and the unique aspects of the infrared region of the wavelength spectrum. This foundation makes it possible for those readers who are not optical engineers to acquire the background information needed for a treatise on infrared zoom lenses. Chapter 1 presents overall system considerations involved in establishing the requirements for an application that includes an optical system as one of its elements. Chapter 2 sets forth the basic fundamentals of optics involved in the design and analysis of optical systems. Chapter 3 presents the optics features that are unique to the infrared region of the spectrum. Chapter 4 discusses some of the optical design techniques that may be utilized in the optical design of infrared systems. These four chapters could serve as an introduction to any treatise on infrared optical systems. Further discussion of these topics may be found in the tutorial text on this subject by Max J. Riedl.1 Chapters 5 through 8 present the subject matter that is unique to the subject of zoom lenses in the infrared. Chapter 5 sets forth the basic types of zoom lenses and the establishing of specifications to meet the requirements of a particular application. Chapters 6 and 7 present numerous examples of refractive and reflective infrared zoom systems; the optical design techniques from Chapter 4 are employed in designing these representative infrared (IR) zoom lenses to illustrate the utilization of these techniques. Companies identified in Chapters 6 and 7 are the names in existence at the time the reference papers were published; some of them have since merged with other companies and lost their separate identity. Chapter 8 presents a brief discussion of future trends in this subject area. Chapter 9 presents a summary of infrared zoom lens applications. Appendix A contains three landmark IR zoom lens patents in their entirety as published. This appendix is included not only for the insights contained therein, but also to provide lens prescription data to serve as potential starting points for future design activity. Appendix B presents computer analysis that I have performed on these patents and on one additional patent described in Sec. 7.2.1. A definition of the analysis categories is to be found in Chapter 2. Appendix C gives the answers to self-test problems presented in Sec. 2.9. The infrared zoom lens literature consists primarily of patents and of papers presented at conferences or published in journals and proceedings. In 1993 SPIE published in its Milestone Series of Selected Reprints a volume on zoom lenses which included a number of infrared papers and patents.2 To my knowledge, this tutorial is the first publication to be devoted exclusively to IR zoom lenses. It xi
xii
Preface
should serve as an introduction to the subject for the uninitiated and as an aid to the engineer who has an infrared zoom lens application to pursue. It is not intended to be a step-by-step instruction manual for this complex optical design activity. Additions to Infrared Optics and Zoom Lenses are included in the second edition of this tutorial. The additions are based on an expanded short course that I recently presented. There are substantive additions to the topics in the table of contents. They are discussed below. Also, 18 new refractive and reflective systems have been added to the 23 zoom systems in the first edition, bringing the total to 41 optical systems. The 18 new systems were published in the reference literature since publication of the first edition, in the time interval from the year 2000 to 2007. These additional systems are in part the result of adding a new category—focal plane arrays—to the chapter on refractive infrared zoom lenses. In part these additions are a result of including dual field-of-view infrared optical systems in this tutorial. The 18 new zoom systems are intended to bring the technology and the list of refractive and reflective zoom infrared systems up to date. There are 24 additional references. One of the themes that will be presented is the gradual shift in recent years from the 8- to 12-micrometer (µm) region to the 3- to 5-µm region of the wavelength spectrum. This shift is discussed in Secs. 2.7, 3.1, 3.2, 6.5, and 6.6. The rationale for the substantive additions is presented below: 2.8 Principal planes: The location of the principal planes is important in order to calculate accurately the separation between lens elements when going from a thin-lens solution to a thick-lens solution. The location also affects the overall length of the zoom system. 2.9 Self-test problems: A problem set is included in order to ensure a clear understanding of optics fundamentals before discussing the infrared spectrum and infrared zoom systems. 3.5 Glass substitution: Glass substitution is a powerful technique for performing computer optimization and athermalization simultaneously by passive substitution of infrared optical materials. I have done this glass substitution successfully, and I present a detailed example with a reference to the paper I wrote on this subject. 4.14 Global search: Global search has been demonstrated in recent years to be a viable computer optimization tool. An example is presented of designing zoom lenses by means of global search without designer intervention. The computer program flowchart of the decision-making process is included in this discussion. 5.3 Extenders: Extenders are a practical means of extending the focal length range of zoom lens systems. It is important to understand the optical limitations of extenders. 6.6 Focal plane arrays: The use of focal plane arrays (FPA) to eliminate scanning is an important development in infrared optical systems. Techniques for
Infrared Optics and Zoom Lenses
xiii
overcoming the limitations of resolution of FPAs at higher spatial frequencies are discussed in this section. 7.3 Special reflective systems: Due to the increase in the number of reflective infrared zoom systems, it is important to understand techniques for dual-channel detector arrays and for designing compact reflective systems through the use of folding mirrors and the Mangin mirror. Chapter 9 Summary of applications: It is useful to summarize the scope and variety of infrared zoom lens applications. The discussion includes a reference to each of the zoom systems presented in this tutorial. This overview makes this chapter a fitting conclusion. I would like to thank the reviewers for their helpful comments and suggestions. Acknowledgment is also due to Gwen Weerts of SPIE for her editorial assistance in the publication of this second edition of Infrared Optics and Zoom Lenses. Allen Mann January 2009 1. Riedl, M. J., Optical Design Fundamentals for Infrared Systems, Second Edition, SPIE Press, Bellingham, WA (2001). 2. Mann, A., Ed., Selected Papers on Zoom Lenses, SPIE Press, Bellingham, WA (1993).
Chapter 1
System Considerations 1.1 Radiometry 1.1.1 Blackbody radiation Blackbody radiation is the emission of radiant energy which takes place from a blackbody at a fixed temperature.1 A blackbody is an ideal body which absorbs all incident radiation and reflects none. Its radiating and absorbing efficiency, called its emissivity factor, is unity. A graybody is an object with an emissivity factor less than unity. Although an ideal radiator, a blackbody should not be considered a meaningless abstraction. On a cosmological level, cosmic background radiation which came into being shortly after the creation of the universe has been observed to fit a blackbody curve with a high degree of precision. In the context of electro-optical system design, the ideal assumption of a blackbody is extremely useful because it represents a limiting case or may be an approximation to a real set of conditions, as for example in the calculation of stray radiation from an internal baffle. Blackbodies are used as calibrated sources in simulation and spectrometer applications. 1.1.2 Planck’s equation Blackbody radiation has a spectral energy distribution as a function of temperature which is described by Planck’s equation (see Fig. 1.1):
L (λ) =
2hc 2 1 W m −3sr −1 , 5 λ exp ( hc λkT ) − 1
where L is spectral radiance h is Planck’s constant, 6.6262 ×10-34 Joule (J) c is the velocity of light, 2.9979 × 108 m/s λ is the wavelength in meters k is the Boltzmann’s constant, 1.3806 × 10-23 J/K T is absolute temperature in degrees K.
1
(1.1)
2
Chapter 1
Figure 1.1 Blackbody radiation.
1.1.3 Stefan-Boltzmann law
The total power radiated per unit area of a blackbody is obtained by integrating Planck’s radiation law over all wavelengths and is known as the StefanBoltzmann law. Blackbody radiation takes place at a rate expressed by the Stefan-Boltzmann law as: M = εσT 4 ( W m 2 ) = total power radiated per unit area,
(1.2)
where ε is the emissivity factor and σ is Stefan-Boltzmann constant, 5.66961 × 10-8 (W m–2 K–4 ). 1.1.4 Wien displacement law
The wavelength at which maximum radiation occurs for a given temperature is described by the Wien displacement law: λ(max) = const/T = 2898/T (µm) .
(1.3)
This wavelength is significant for calibration purposes. It is desirable to use relatively hot blackbody calibration sources. However, this calibration ideal is often difficult to follow because of the problem of operating and maintaining high-temperature blackbodies (that is, blackbodies that operate above 1000° C, where the materials begin to glow red hot and suffer oxidation). Also, such hightemperature blackbody sources tend to overdrive or saturate sensitive electrooptical sensors.1 The radiant emittance of a blackbody as a function of temperature and wavelength is shown in Fig. 1.2.2
System Considerations
3
Figure 1.2 Blackbody curves as a function of temperature.2
1.2 Atmospheric Transmission 1.2.1 Scattering
Atmospheric attenuation of infrared radiation is caused by scattering and absorption. There are two types of scattering, Rayleigh and Mie. With Rayleigh scattering, the scattering particle diameter is smaller than the wavelength of transmission. Rayleigh scattering is wavelength dependent. With Mie scattering, the particle diameter is equal to or greater than the wavelength of transmission. Mie scattering is independent of wavelength and predominates in the infrared region of the spectrum. Since water droplets in clouds and fog have sizes between 5 and 100 µm, Mie scattering in haze or fog is just as bad in the infrared as it is in the visible. The attenuation τs resulting from scattering by particles suspended in the atmosphere may be calculated according to τs = e– βx,
(1.4)
4
Chapter 1
where x is the path length and β is a function of wavelength, concentration of particles and their diameters, refractive index, and absorption coefficient. 1.2.2 Absorption
Absorption in the atmosphere is influenced primarily by the amount of ozone and absorbing gases present, in particular water vapor, and by the wavelength of transmission, which helps determine whether infrared radiation will encounter absorbing gases or go through a window in the atmosphere. Atmospheric transmission due to absorption as a function of wavelength is shown in Fig. 1.3.2 1.2.3 Infrared windows
The most important windows for infrared zoom lens systems are the 3- to 5-µm and 8- to 12-µm regions because of the relatively low amount of atmospheric absorption in those regions. The choice of the particular window to be used is determined by the temperature of the source and by the spectral sensitivity of the detector. Atmospheric transmission τa attenuated by absorption can be expressed as τa = e–αx , (1.5) where x is the path length and α is the absorption coefficient. When both absorption and scattering are present, the effective transmittance can be expressed by the product τeff = τa ⋅ τ s = e − ( α+β ) x . (1.6) 1.2.4 Computer calculation
Detailed computer models exist for the calculation of transmission through the atmosphere. The best known of these models is the LOWTRAN from the Geophysics Directorate at Hanscom Air Force Base in Massachusetts.3
Figure 1.3 Atmospheric transmission due to absorption as a function of wavelength through 1.8 km at sea level.2
System Considerations
5
1.3 Lens Transmission Lens transmission can be expressed by r + t + a = 1,
(1.7)
where r = reflectance t = transmittance a = absorptance
r = 1 for an ideal reflector, t = 1 for an ideal transmitter, a = 1 for an ideal absorber (blackbody).
Additionally, according to conservation of energy, if no energy is lost through absorption, r + t = 1. (1.8) 1.3.1 Transmittance
The transmission Ta through an optical element after absorption losses is expressed by Ta = e–δx , (1.9) where δ = absorption coefficient and x = distance traveled through optical element. 1.3.2 Reflectance
The uncoated reflection loss per surface r (see Fig. 1.4) is expressed by
( n − 1) r= , 2 ( n + 1) 2
Figure 1.4 Uncoated reflection loss per surface.
(1.10)
6
Chapter 1
where r = uncoated reflection loss per surface and n = index of refraction of optical material. Table 1.1 shows the uncoated reflection loss per surface as a function of index of refraction. The total transmission Tr through an optical system after reflection losses is Tr = (1 – r)m,
(1.11)
where m = number of surfaces. Figure 1.5 shows the uncoated transmittance of common IR materials.2 Table 1.1 Uncoated reflection loss per surface in air as a function of index of refraction.
Index of refraction n 1.5 2.0 2.5 3.0 3.5 4.0
Reflection loss per surface (uncoated) 4% 11% 18% 25% 31% 36%
Figure 1.5 Transmittance of common IR materials (uncoated).2
System Considerations
7
Figure 1.6 Snell’s law of refraction.
1.4 Coatings 1.4.1 Single-layer coatings
As an introduction to a discussion of coatings, Snell’s law is the law of refraction at an interface between two media, such as air-glass (shown in Fig. 1.6) or glassair. It can be stated as n ⋅ sin i = n '⋅ sin i ',
(1.12)
where n and n′ are the two media, i is the angle of incidence, and i′ is the angle of refraction. Antireflection coatings play a significant role in increasing the throughput of an optical system. This is particularly true in the infrared region where high index materials like germanium and silicon are so commonly used. As noted in the previous section, reflection losses increase dramatically with higher index materials. Also, zoom lens systems may require additional elements in order to minimize the aberration residuals, which also increases the transmission losses through the optical system. According to coating theory, the index of refraction for a thin-film single-layer coating should be equal to the square root of the index of refraction of the substrate at one particular wavelength. According to the principle of the interactions at surface boundaries, there is a half-wave phase change when light travels through a low-index medium and is reflected from a high-index medium. There is no phase change when light travels through a high-index medium and is reflected from a low-index medium. When the thin-film layer thickness is a quarter wave, reflection losses are minimized and transmission is maximized.
8
Chapter 1
Figure 1.7 Infrared multilayer antireflection coating.4
1.4.2 Multilayer coatings
For broad spectral bands such as from 3 to 5 and from 8 to 12 µm, a single layer is not sufficient and a multilayer coating must be used. Most infrared materials can be antireflection coated to reflectivities of 0.5% or less. An example of an infrared multilayer antireflection coating is shown in Fig. 1.7.4 A layer of zinc sulfide is used as an antireflection coating for a germanium substrate. However, zinc sulfide has a relatively bad adhesion to the substrate. Thus, there is a potential problem in that the layer of zinc sulfide could be easily stripped and removed. This is solved by having a layer of silicon dioxide formed contiguously to the germanium substrate. Silicon dioxide has good adherence to the substrate, but will absorb a certain percentage of infrared light in the 3- to 5-µm range. However, in this case the predetermined thickness of the silicon dioxide layer is so slight that its absorption is negligible. Referring to Fig. 1.7, the first layer is made of fluoride, the second layer of zinc sulfide, the third of germanium, and from the fourth layer, zinc sulfide and germanium layers are formed alternately. The (n–1) layer is made of germanium, and the n’th layer is made of silicon dioxide.
System Considerations
9
1.5 Infrared Detectors 1.5.1 Basic relations
The signal-to-noise ratio (SNR) is a useful means of measuring the performance of a complete system. In its simplest form the signal-to-noise ratio is stated by SNR =
P , NEP
(1.13)
where P is the collected radiant power in watts received by the detector, and NEP is the noise-equivalent power (the radiant power that produces a signal-to-noise ratio of one at the output of the detector). The NEP is a function of the detector size d’, the electrical bandwidth Δf used in the measurement, and the detector figure of merit D*. D* is a relative sensitivity parameter used to compare performance of different detector types. D* is the signal-to-noise ratio at a particular electrical frequency and in a 1-Hz bandwidth when 1 W of radiant power is incident on a 1-cm2 active area detector. The higher the D*, the better the detector.
active area ( cm 2 ) W )= 12 NEP ( W Hz )
12
D ( cm Hz *
12
−1
.
(1.14)
Responsitivity is the detector photocurrent output per unit incident radiant power at a particular wavelength. 1.5.2 Types
An infrared detector is a converter that absorbs infrared energy and converts it into an electrical signal. There are two principal types of infrared detectors. Thermal detectors measure the rate at which energy is absorbed; their response is independent of wavelength. They tend to have a slow response time. The most common types of thermal detectors are thermocouple, thermopile, bolometer, and pyroelectric. The most important type of detector for infrared zoom lens applications, however, is the photon detector. Photon detectors respond only to incident photons that possess more than a certain minimum energy; their response at any wavelength is proportional to the rate at which photons of that wavelength are absorbed. All photon detectors are composed of semiconductor material. They have a fast response time but require cooling for optimum sensitivity. Typically, liquid nitrogen is used in a Joule-Thomson cooler to achieve an operating temperature of 77 K. A detector dewar assembly diagram is shown in Fig. 1.8. HgCdTe is a photoconductor detector with a spectral range from 2 to 25 µm. InSb is a photovoltaic detector with a spectral range from 1 to 5.5 µm.
10
Chapter 1
Figure 1.8 Detector dewar assembly diagram.
A charge-coupled device (CCD) may be used in the near-infrared region from 0.65 to 1.05 µm for imaging applications. A CCD chip is an array of photoelectric detectors built on a silicon base using layers of electrical components printed on the surface. This structure divides the base into a grid of separate compartments, called pixels, that hold electrical charges; the size of a pixel may vary from about 6 to 25 µm. The CCD chip provides a 2D array that converts incoming photons into electrical signals. These signals are then sent to a display where they are reconverted into an image or to a storage device for future reconversion. Sensitivity of the CCD array may be improved by cooling using either circulating water, liquid gases, or by means of a thermoelectric cooler that can be integrated into the CCD camera package. The idealized relative spatial response of a CCD to long-wavelength photons is shown in Fig. 1.9. 5
Figure 1.9 Idealized relative spatial response of a CCD to long-wavelength photons.
5
System Considerations
11
Figure 1.10 Linear-detector arrays, large-square rectangular arrays, and staring arrays.2
1.5.3 Arrays
Infrared systems have evolved over the years through the development of lineardetector arrays, large-square rectangular arrays, and staring arrays. They are defined below and illustrated in Fig. 1.10.2 (1) Serial scan: A small detector array with only a few elements is scanned in a serial form. Two scan mirrors are required, one for azimuth and the other for elevation. (2) Parallel scan: A long detector array covering the full extent of the field of view (FOV) in one dimension is swept out across the object space, creating the full format image. Only a single-scan mirror is required. (3) Staring array: No moving parts are required, and a full-format image is created directly. The advent of staring arrays has eliminated scanning and the corresponding need for pupil control. 1.5.4 Matching the detector with the optics
In an imaging system, the optics, detector, electronics, and display all have inherent resolutions (Fig. 1.11). The overall system resolution is a composite of these subsystem resolutions. Generally, in well-designed systems, the electronics and display do not adversely affect the perceived image quality; therefore, it has become commonplace to infer image quality from the optics and detector performance. System resolution depends on the optical blur diameter and the detector size. When the system is detector limited, small changes in the blur diameter have little effect on the system resolution. The detector size limits the smallest size that can be discerned. With a large blur diameter, the resolution is limited by the optics; most infrared imaging systems fall into this category. A commonly used measure of optical resolution is the Airy disk size. It is the bright center of the diffraction pattern produced by an ideal optical system. In the focal plane of the lens, the Airy disk diameter β is β = 2.44 λF, where λ is the wavelength and F is the lens f/#.
(1.15)
12
Chapter 1
Figure 1.11 Imaging system.
Detector arrays are specified by the detector size and the number of pixels. Again, the smallest target that can be discerned is limited by the detector size. For example, a 256 × 256 one-half-inch detector array would have a pixel width of 50 µm. The optical designer can select both the aperture size D and the focal length f (i.e., the f/#, where F = f/D). As the detector size decreases, the f/# must also decrease to match the detector. For a system with a pixel width of 40 µm operating at a central wavelength of 10 µm, the system will be optics limited above an f/# of 1.64.6 The lower the f/# for a diffraction-limited system, the higher the resolution and the smaller the optical blur diameter. The challenge for the optical designer is to minimize image aberrations while decreasing the f/#. CCD arrays operate in the visual and near-infrared regions of the wavelength spectrum. A typical one-half-inch CCD array may have pixels that are about 10 µm in size. For most CCD camera applications, the camera will be operating in the detector-limited region when the f/# is less than about 6 due primarily to the relatively short operating wavelength. Refer to Sec. 6.3 for an example of an infrared zoom lens using a CCD camera.
1.6 References 1. Wyatt, C.L., Radiometric System Design, Macmillan Co., New York (1987). 2. Fischer, R.E., “Lens design for the infrared,” in Infrared Optical Design and Fabrication, R. Hartmann and W. J. Smith, Eds., SPIE Press, Bellingham, WA (1991). 3. Riedl, M.J., Optical Design Fundamentals for Infrared Systems, SPIE Press, Bellingham, WA (1995). 4. Hatano, T., “Antireflection coating for infrared light,” U.S. Patent No. 5,243,458, (September 1993). 5. Holst, G.C., CCD Arrays, Cameras, and Displays, 2nd Ed., SPIE Press, Bellingham, WA (1998). 6. Holst, G.C., “Image quality: does your detector match your optics?” Photonics Spectra 33(1), 144–146 (1999).
Chapter 2
Optics Fundamentals 2.1 Lens Equation The basic lens equation is illustrated in Fig. 2.1 and can be stated as
1 1 1 = − , f l′ l
(2.1)
where f is the effective focal length, l is the object distance, and l′ is the image distance. In Fig. 2.1, l is negative and l′ is positive, in accordance with the sign convention. The focal length f = 1/P, where P is the power of the lens. For example, if l = –1 and l′ = +1, then P = 2 and f = 0.5. An important special case of the lens equation is illustrated in Fig. 2.2. This is when the object is assumed to be at infinity, as is the case in most infrared zoom lens applications. In accordance with Eq. (2.1), 1/l = 0, f = l′, and the image plane lies in the focal plane of the lens. In the above example, f = l′ = 0.5.
2.2 Stops and Pupils The aperture stop is the limiting aperture of the optical system. The aperture stop for a simple lens is shown in Fig. 2.3.1 The entrance pupil is the image of the aperture stop in object space and is coincident with it. The exit pupil is the image of the aperture stop in image space and is also coincident with the aperture stop in the figure.1 The field stop limits the size of the detector at the image plane.
Figure 2.1 Basic lens equation.
13
14
Chapter 2
Figure 2.2 Lens equation with object at infinity.
The chief ray is the central ray of an off-axis bundle of rays. Figure 2.41 illustrates the entrance and exit pupils and chief ray of an optical system. The entrance pupil is located where the projection of the chief ray at the first lens surface crosses the optical axis. The aperture stop is located where the chief ray crosses the optical axis. If the aperture stop is in front of the optical system, it is coincident with the entrance pupil; if it is behind the optical system, it is coincident with the exit pupil. The location of the aperture stop has a strong influence on such first-order properties as pupil location, lens diameters, chromatic aberration, and illumination at the image plane. Achieving the desired solution for all of these properties is further complicated in a zoom lens system because the relationships that relate to the aperture stop location have to hold for all magnifications all the way from one end of the zoom range to the other. Placement of the aperture stop has particular importance for infrared systems.
Figure 2.3 Aperture stop for a simple lens.1 (From Wyatt, Radiometric System Design, Macmillan, 1987, with permission of The McGraw-Hill Co.)
Optics Fundamentals
15
Figure 2.4 Entrance and exit pupils and chief ray of an optical system.1 (From Wyatt, Radiometric System Design, Macmillan, 1987, with permission of The McGraw-Hill Co.)
2.3 Optical Formulas The following are some basic formulas used in the design and analysis of optical systems; the nomenclature definitions follow. These equations are utilized in formulating the first-order parameters and in analyzing the theoretical and actual performance of the optical system (refer to Figs. 2.3 and 2.4).
and
NA = n ⋅ sin u′,
(2.2)
F = f / D = 1/ ( 2n ⋅ sin u′ ) = 1/ ( 2 NA ) ,
(2.3)
Vo = 2 NA / λ (mm),
(2.4)
α = 2.44 λ / D,
(2.5)
α′ = spot size / f,
(2.6)
IFOV = d′ / f,
(2.7)
tanθ′ = (d/2) / f,
(2.8)
depth of focus (Rayleigh limit) = 4λF2 ,
(2.9)
2π 2 2 −( 2 πφ)2 Strehl ratio ≈ 1 − ⋅ Φ ≈ e λ β = 2.44λF,
(2.10) (2.11)
16
Chapter 2
where λ = wavelength Ф = rms wave error F = f/# f = effective focal length D = entrance pupil diameter u′ = half-angle of the limiting axial ray θ = half-angle field of view in image space d′ = pixel width d = image diameter IFOV = instantaneous field of view n = index of refraction NA = numerical aperture α = limiting angular resolution (diffraction) α′ = angular resolution (geometrical) Vo = diffraction limit (line pairs/mm) β = diffraction limited blur size (Airy disk).
2.4 Optical Performance Criteria The following are various performance criteria utilized in evaluating the image quality of an optical system: Angular resolution: image spot size divided by the lens focal length. Modulation transfer function (MTF): percent reduction in object contrast in the image at a given spatial frequency. Strehl definition: the ratio of the light intensity at the peak of the diffraction pattern of an aberrated image to that at the peak of an aberration-free image. Seidel aberrations: the five terms in the fourth degree in the expansion of the wavefront aberration in the image plane.2 They can be expressed for each surface and can be summed up for the entire optical system. Examples can be found in Appendix B. Zernike polynomials: mathematical decomposition of the aberrations present in an optical system, which provides an evaluation of the effects of each order of the aberration set on the image. This set of terms provides a useful method for determining the most appropriate balance for the various Seidel aberrations against higher-order residuals.3 Rayleigh limit: An optical system is considered essentially perfect if the wavefront can be included between two concentric spherical surfaces λ/4 apart. If the peak-to-valley optical path difference is λ/4, the system just meets the Rayleigh criterion. For the 3- to 5-µm and 8- to 12-µm spectral bands, the longitudinal depth of focus that meets the Rayleigh criterion is shown in Table 2.1. This is a very useful value for infrared zoom lens systems because it indicates the extent to which the image plane may vary longitudinally from one end of the zoom range to the other.
Optics Fundamentals
17
Table 2.1 Longitudinal depth of focus at 4 µm and 10 µm.
f/# 1 2 3 4 5
4 µm (in mm) 0.016 0.064 0.144 0.256 0.400
10 µm (in mm) 0.04 0.16 0.36 0.64 1.00
2.5 Telescopes The basic formulas for telescope magnification m and overall length L are expressed as f D tan θ′ (2.12) . m = − o = o = f e De tan θ
L = fo + fe .
(2.13)
There are two types of telescopes, astronomical and Galilean (refer to Fig. 2.5).4 For each case, the object and the image are at infinity. In the astronomical telescope, both the objective and the eyepiece have positive focal lengths. Therefore, the overall length is the sum of the two focal lengths. An intermediate image is formed at the common focal point of the objective and eyepiece. In the Galilean telescope, the objective is positive and the eyepiece is negative. The image point of the object and the object point of the eyepiece are coincident. Therefore, applying the above formula, the overall length between the objective and the eyepiece is the difference between the absolute focal lengths. For example, if fo = 100 and fe = 10, L = 110; but, if fo = 100 and fe = –10, then L = 90.
Figure 2.5 (a) Astronomical telescope and (b) Galilean telescopes.4 (Reproduced from W. J. Smith, Modern Optical Engineering, 2nd Ed. with permission of The McGraw-Hill Companies, Inc.)
18
Chapter 2
4
Figure 2.6 Primary aberrations: spherical, coma, distortion, astigmatism, and chromatic. (a) A simple converging lens with undercorrected spherical aberration; (b) graphical representation of spherical aberration: longitudinal spherical aberration (LA′) is plotted against ray height (Y), and transverse aberration, in which the ray intercept height (H′) at the paraxial reference plane is plotted against the final ray slope (TAN H′); (c) coma, where the rays through the outer portions of the lens focus at a different height than the rays through the center of the lens; (d) the coma patch, where the image of a point source is spread out into a comet-shaped flare; (e) distortion, where dotted lines denote the undistorted image; (f) astigmatism; (g) the primary astigmatism of a simple lens, where the tangential image is three times as far from the Petzval surface as the sagittal image; (h) undercorrected longitudinal chromatic aberration of a simple lens due to blue rays undergoing greater refraction than red rays; and (i) lateral color, which results in different sized images for different wavelengths. (Adapted from W. Smith, Modern Optical nd Engineering, 2 Ed., with permission of The McGraw-Hill Co.)
Optics Fundamentals
19
These are important considerations in the design of infrared zoom lenses. In some applications, a zoom telescope serves as an afocal attachment in front of a fixed imager; if it is of the Galilean type, it tends to have a shorter overall length than would otherwise be the case (for an example, refer to Fig. 6.16).
2.6 Primary Aberrations 2.6.1 Definition of the Seidel aberrations
The primary aberrations, also known as the Seidel or third-order aberrations, are shown in Fig. 2.6.4 Strictly speaking, the Seidels do not include longitudinal and lateral chromatic aberration. They may be defined as follows: (1) Spherical aberration: the variation of focus with aperture. (2) Coma: the variation of magnification with aperture. (3) Astigmatism: tangential and sagittal images from a point source do not coincide. The tangential image is three times as far from the Petzval surface as the sagittal image. (4) Field curvature: image is formed on the Petzval surface in the absence of astigmatism, or the variation of magnification with field angle. (5) Distortion: displacement of an off-axis image point from the paraxial image position. An increase in the FOV produces pincushion distortion; a decrease in FOV results in barrel distortion. (6) Longitudinal color: variation of focus with wavelength. (7) Lateral color: variation of image height with wavelength. 2.6.2 Variation of primary aberrations with aperture and field height
Table 2.2 shows how the primary aberrations vary as a function of aperture and field height.4 For example, since longitudinal spherical aberration varies with y2, a 1.5× increase in aperture will cause this aberration to be 2.25× as large. Table 2.2 Variation of primary aberrations as a function of aperture and field height.
Aberration Spherical (longitudinal) Spherical (transverse) Coma Astigmatism Astigmatic line length Field curvature Distortion (linear) Distortion (percentage) Chromatic (longitudinal) Chromatic (lateral)
Versus semiaperture y2 y3 y2 -y2 ------
Versus field height --h h2 h h2 h3 h2 -h
20
Chapter 2
2.6.3 Stop shift equations
Thin-lens approximations provide a useful tool for calculating the third-order aberrations of an optical system.4 For a lens element not at the stop, the aberration contributions may be determined from the following formulas: spherical
≡ SC* = SC,
(2.14)
≡ CC* = CC + SC . Q u′k, 2Q + SC ⋅ Q 2 , astigmatism ≡ AC * = AC + CC u′k Petzval sum ≡ PC* = PC,
coma
distortion
(2.15) (2.16) (2.17)
≡ DC * = ( PC + 3 AC )Q u′k + CC ⋅ 3 ⋅ Q 2 + SC ⋅ Q 3 u′k . (2.18)
These “stop shift” equations may be applied to the surface contributions to determine the third-order aberrations for a different stop position by setting
Q=
y *p − y p y
,
(2.19)
where y is the axial paraxial marginal ray height at a surface, yp is the principal paraxial ray height at a surface, y *p is the principal paraxial ray height at a surface after the stop is shifted, and u′k is the angular slope of the axial paraxial marginal ray in image space. Since Q is an invariant, the values for y, yp, and y*p may be taken at any convenient surface. When the equations are used in this way, the unstarred terms refer to the aberrations with the stop in the original position, and the starred terms refer to the aberrations with the stop in the new position. Another consequence of the invariant nature of this definition of Q is the fact that the stop shift may be applied either to the individual surface contributions or to the sum of the contributions of the entire system. Some obvious conclusions can be drawn from an examination of the above formulas. Third-order spherical aberration and the Petzval sum, also known as the field curvature, are unaffected by a shift of the aperture stop to a new location. If third-order spherical aberration is zero, coma is unaffected by a shift of the aperture stop. Additionally, if third-order spherical and coma are both zero, which is the aplanatic condition, astigmatism is unaffected by a stop shift. It should be kept in mind that the effect on higher-order aberrations due to a shift of the aperture stop cannot be determined from these formulas.
Optics Fundamentals
21
2.7 Achromatism Since achromatism is a first-order property, achromatic balance can be determined through the application of thin-lens equations. 2.7.1 Primary achromatism For a series of thin lenses in close contact, the longitudinal chromatic aberration is given by
Φ Φ Δl = − f 2 1 + 2 V1 V2
(2.20)
for a thin-lens doublet where
V=
( nM − 1) , ( nS − nL )
Ф = 1 / f,
(2.21) (2.22)
and nM, nS, and nL are the mid-, short-, and long-wavelength indices of refraction. For a thin-lens achromatic doublet, two wavelengths will come to focus when V − Vb fa = f a Va
and V − Va fb = b Vb
.
(2.23)
To make a positive achromat, combine a positive low-dispersion element with a negative high-dispersion element: 3 to 5 µm: silicon is low dispersion (V = 250) germanium is high dispersion (V = 107) f = 100: fa = 57.2, fb = –133.6 8 to 12 µm: germanium is low dispersion (V = 1073) zinc selenide is high dispersion (V = 58) f = 100: fa = 94.6, fb = –1750.
22
Chapter 2
2.7.2 Secondary spectrum
The secondary spectrum is the variation in focus of the third wavelength with respect to the other two wavelengths:
(P − P ) Δls = − f 1 2 , (V1 − V2 ) where
P=
( ns − nM ) . ( nS − nL )
(2.24)
(2.25)
2.8 Principal Planes In a thin-lens first-order solution the principal planes are located coincident with the thin lens. In the basic lens imaging Eq. (2.1), l and l′ are measured from the principal planes. In a thick-lens starting point solution the optical train object-toimage distance is set according to the location and separation of the principal planes of each lens element. A complex lens system has only two principal planes which move about as the lens system is zoomed. In Fig. 2.7(a), diverging rays from the primary focal point F emerge parallel to the axis. In 2.7(b), parallel incident rays are brought to a focus at the secondary focal point F". In each case the incident and refracted rays have been extended to their point of intersection between the surfaces. Transverse planes through these intersections constitute primary and secondary principal planes. The ray height on the first principal plane is the same on the second principal plane, i.e., unit lateral magnification.
Figure 2.7 Ray diagrams showing the primary and secondary principal planes of a thick 5 lens. (Reproduced from Jenkins and White, Fundamentals of Optics, copyright of The McGraw-Hill Co., Inc.)
Optics Fundamentals
23
Figure 2.8 Illustrating the significance of the nodal points and nodal planes of a thick lens.5 (Reproduced from Jenkins and White, Fundamentals of Optics, copyright of The McGraw-Hill Co., Inc.)
Of all the rays that pass through a lens from an off-axis object point to its corresponding image point, there will always be one ray for which the direction of the ray in the image space is the same as in the object space, i.e., the segments of the ray before reaching the lens and after leaving it are parallel. The two points at which these segments, if projected, intersect the axis are called the nodal points. This third pair of points and their associated planes are shown in Fig. 2.8, which also shows the optical center of the lens at C. Since the incident and emergent rays make equal angles with the axis, the nodal points are called conjugate points of unit angular magnification. This concept is discussed further in Ref. 6. In general, the focal points and principal points are not symmetrically located with respect to the lens but are at different distances from the vertices. The positions of the principal planes for a given lens focal length can be changed by bending the lens shape, as shown in Fig. 2.9. Moving the principal planes to the right decreases the overall object-to-image distance. This can be a useful technique in designing compact zoom lens systems. Moving the principal planes to the left increases the overall object-to-image distance.
Figure 2.9 Illustrating the variation of the positions of the primary and secondary principal 5 planes as a thick lens of fixed focal length is subject to bending. (Reproduced from Jenkins and White, Fundamentals of Optics, copyright of The McGraw-Hill Co., Inc.)
24
Chapter 2
2.9 Problems 1. An f/2.5 zoom lens system is to be used in the 8- to 12-µm wavelength region. What is the Rayleigh limit at the central wavelength? 2. A Galilean telescope has a positive thin lens with 120-mm focal length and a negative thin lens with 12-mm focal length. (a) What is the magnification? (b) What is the overall length? (c) If the exit pupil diameter is 10 mm, what is the entrance pupil diameter? 3. A 150-mm focal length doublet consists of two singlets with V values of 200 and 100, respectively. (a) Which singlet has the higher dispersion, the one with the higher or lower V value? (b) What is the focal length of each singlet in an achromatic doublet? 4. An f/2 singlet has a clear aperture of 50 mm with a refractive index of 3.5 and dn/dt = 0.000150 per degree C. The operating temperature range is 40° C. The wavelength region is from 8 to 12 µm. (a) What is the change in focal length with temperature? (b) Is this change within the depth of focus for this wavelength region? 5. A 1× to 5× zoom lens is to be used as part of a forward-looking infrared (FLIR) scanning system. It will operate at f/2 in the 8- to 12-µm wavelength region. It has a 12-mm exit pupil and an eyepiece focal length of 20 mm. (a) What is the entrance pupil diameter at each end of the zoom range? (b) What is the objective lens focal length at each end of the zoom range?
2.10 References 1. Wyatt, C.L., Radiometric System Design, Macmillan Co., New York (1987). 2. Welford, W.T., Aberrations of the Symmetrical Optical System, Academic Press (1974). 3. Kim, C.J. and Shannon, R.R., “Catalog of Zernike Polynomials,” in Applied Optics and Optical Engineering, Vol. X, R.R. Shannon and J. Wyant, Eds., pp. 193–221, Academic Press, New York (1987). 4. Smith, W.J., Modern Optical Engineering, Second Ed., McGraw-Hill, New York (1990). 5. Jenkins, F.A. and White, H.E, Fundamentals of Optics, McGraw-Hill, New York (1957). 6. Johnson, R.B., “Correctly making panoramic imagery and the meaning of optical center,” Proc. SPIE, 7060, 70600F (2008).
Chapter 3
Unique Features of the Infrared Region 3.1 Optical Materials 3.1.1 Materials for the infrared A large number of optical materials transmit in the infrared region of the spectrum. However, the list of materials is quite limited when one considers physical characteristics, workability, and cost. Table 3.11 indicates the materials most commonly used in infrared zoom-lens systems for the 3- to 5-µm and 8- to 12-µm regions. It is apparent that indices of refraction are higher than they are for optical materials in the visible spectrum. This is an advantage in the correction of third-order and higher-order aberrations. For example, with a lens shaped for minimum spherical aberration, the angular spherical aberration βSPH for an object at infinity can be expressed by β SPH =
n ( 4n − 1)
128 ( n − 1) ( n + 2 ) ( F 3 ) 2
,
(3.1)
where n = index of refraction and f focal length F = , or . d diameter
The variation with a refractive index can readily be seen by tabulating β for an f/1 lens as an example in Table 3.1. The advantage of using a high-index material like silicon or germanium is quite apparent from these calculations. Table 3.1 Variation of spherical aberration with a refractive index.
f/# 1.0 1.0 1.0
n 4.0 3.0 2.0
β 0.008681 0.012891 0.027344 25
26
Chapter 3
Figure 3.1 V value versus index of refraction for several of the more commonly used 2 infrared materials.
Also, infrared materials tend to have low dispersion, which corresponds to a high V number. Figure 3.1 presents the V value versus the index of refraction for several of the more commonly used infrared materials.2 The hatched area indicates the more limited range of V values and refractive indices as compared with visible materials. However, one should keep in mind that the Schott catalog alone contains some 200 optical glasses within the hatched area;3 in fact, the number of available glasses in the visual region is more than one order of magnitude greater than in the infrared. Germanium is less expensive than zinc selenide or zinc sulfide. Since silicon has become an order of magnitude less expensive than germanium, its use in infrared zoom lens systems has greatly increased in recent years. This development, in turn, has helped caused a shift from the 8- to 12-µm to the 3- to 5-µm region. Another factor is the availability of detectors such as InSb which work well in the 3- to 5-µm waveband. In Table 3.2, V is defined as:
V3−5 μm =
n4 μm −1 n3 μm − n5 μm
, V8−12 μm =
n10 μm −1 n8 μm − n12 μm
.
(3.2)
Unique Features of the Infrared Region
27
Table 3.2 Refractive index data for infrared materials.
Material 3 µm 4 µm 5 µm V
Zinc sulfide 2.2570 2.2520 2.2460 114
Zinc selenide 2.4376 2.4331 2.4295 177
Silicon 3.4320 3.4255 3.4223 250
Germanium 4.0452 4.0243 4.0161 107
Calcium fluoride 1.4179 1.4097 1.3990 22
8 µm 10 µm 12 µm V
2.2229 2.2005 2.1704 23
2.4173 2.4065 2.3930 58
3.4184 3.4179 3.4157 896
4.0051 4.0032 4.0023 1073
-----
dn/dt density
0.000043 4.09
0.000060 5.27
0.00015 0.000396 2.33 5.33
0.000011 3.18
Since many infrared components require aspheric or diffractive surfaces, diamond turning is often the method of choice for the fabrication of these surfaces that are so difficult to fabricate by traditional methods. Among other methods, reactive ion etching has been successfully utilized to transfer a binary optic diffractive pattern into the substrate.4 3.1.2 Calculation of index of refraction
The calculation of refractive index data may be accomplished through the use of general polynomials to provide interpolation at infrared wavelengths of interest for purposes of optical design and analysis. Several forms of general polynomials are available for use with infrared materials. For their optical glasses Schott uses: n2 = A0 + A1λ2 + A2λ–2 + A3λ–4 + A4λ–6 + A5λ–8,
(3.3)
which provides a worst-case fit of the refractive index to within ±0.000005. For infrared materials, Barr & Stroud5 used a modified version of the Schott formula. The data for infrared materials require additional positive terms. The full expansion is: n2 = C–8λ–8 + C–6λ–6 + C–4λ–4 + C–2λ–2 + C0 + C2λ2 + C4λ4 + C6λ6.
(3.4)
A least-squares technique is applied to form a set of linear equations to solve to obtain the required coefficients. The least-squares fit process allows an estimation of error by computing the fit error. This process is dependent on using more data points than polynomial coefficients. The rms refractive index error
28
Chapter 3
ranges from 0.00008 for germanium in the 8- to 13-µm range to 0.00002 for zinc sulfide. Another commonly used formula in the infrared is the Sellmeier equation, m
n −1 = 2
k =1
(λ
Ak λ 2 2
− Bk2 )
.
(3.5)
For example, the Optical Research Associates CODE V optics program uses this equation in its special materials catalog for infrared materials. The number of terms varies from two to five, depending on the material. Most materials use three terms.6 The acceptable level of fit accuracy for inclusion in the CODE V special catalog is based on the optical path difference (OPD) errors that can be expected due to departures from measured data. The criterion chosen is that the induced chromatic effect, ΔOPD, be less than λ /10 for a f/1.5 singlet of 200-mm diameter in any one of three spectral bands: 8 to 12, 3 to 5, and 0.4 to 0.7 µm. The result of imposing these criteria is that in certain cases, the same material is fitted for two spectral ranges and both fits are included in the special catalog using different names.7 Some infrared zoom lens applications may require tighter criteria. For example, the Pilkington "Dezir" compact infrared zoom telescope has an entrance lens that has a diameter somewhat in excess of 200 mm and operates at approximately f/1.0.8
3.2 Thermal Compensation 3.2.1 Focus shift with temperature
Focus shift with temperature is a significant problem in the infrared region. The change in refractive index with temperature, dn/dt, is presented in Table 3.1 for the listed materials. Germanium, in particular, has a very high dn/dt. For a thin lens the change in focal length with temperature can be expressed as1
f dn df = dt. ( n − 1) dt
(3.6)
For a system with a 100-mm focal length and a 40o C temperature range, the focal shift is 0.527 mm for germanium. This would exceed the Rayleigh limit for acceptable performance of 0.400 mm for an f/5 system in the 3- to 5-µm spectral region and of 0.490 for f/3.5 systems in the 8- to 12-µm region. 3.2.2 Athermalization
Athermalization is the correction of this effect of focus shift with temperature. There are several mechanical and optical methods, active and passive, available to accomplish athermalization. It is possible to solve for achromatism and
Unique Features of the Infrared Region
29
athermalization at the same time with three infrared materials by solving the following simultaneous equations:9 J
Total power
k
i
= k.
(3.7)
= 0.
(3.8)
i =1
Achromatism
J
ki
V i =1
i
1 + dl J dk dl Athermalization + ⋅ k = 0, dt ⋅ Δt i =1 dt i dt
(3.9)
where dl/dt is the coefficient of expansion of the mounting material. The above equations can be used to derive an achromatic, athermal hybrid doublet with only two materials if a diffractive surface is considered to be the third material. 3.2.3 Athermalization methods
There are several mechanical and optical methods available to accomplish athermalization: (1) Mechanical passive: The basic principle behind this approach is to passively modify the axial position of a lens or lens group in order to compensate for the image shift caused by temperature change. This movement is achieved by natural expansion or contraction of mechanical components. (However, for germanium this type of correction by such metals as aluminum does not provide sufficient movement.) (2) Mechanical active: A lens or lenses are moved axially either manually or, preferably, by electromechanical means. Typically, temperature sensors feed information to actuate motors which drive the athermalizing elements to the required positions. This is particularly useful in zoom lenses where the required athermalization movements differ with magnification change. (3) Optical passive: It is possible to select a combination of optical materials that will minimize focus shift over a limited temperature range. For simultaneous correction of achromatism and athermalization at least three optical materials are required (refer to Sec. 3.2.2). By solving the basic equations for power, achromatism and athermalization, the relative power for each material can be derived. The use of zinc selenide, zinc sulfide, and germanium is one such combination. (4) Optomechanical: Optics with reduced temperature sensitivity can be compensated by small passive or active mechanical movements. (5) Passive-active mechanical: Passive mechanical means are combined with small active movements to minimize temperature effects.
30
Chapter 3
(6) Reflective optics: A single spherical mirror, if fabricated from the same material that separates the mirror from the focal plane, is in effect selfathermalized. A uniform temperature soak will cause a uniform expansion or contraction without any induced defocus. Illustrations of the use of these techniques may be found in Figs. 6.17, 6.23, and 6.30. The use of materials such as zinc sulfide and zinc selenide in combination with germanium makes it possible to provide some passive optical athermalization. Hybrid passive/active mechanical athermalization techniques are also being utilized. The most common arrangement involves the additional movement of lens elements which move for other reasons, such as zooming. These movements are either real time computed or calculated from look-up tables, and the whole process involves carefully selected temperature sensors as part of a closed-loop system.
3.3 Cold Stop and Cold Shield The cold stop is an aperture or baffle which prevents the detector from looking at any extraneous stray radiation. If it is not the aperture stop of the system, it is a cold shield.
3.4 Narcissus Narcissus is a change through scan or across the format resulting from radiation reflected from lens surfaces back into the detector/dewar assembly. The large temperature differential between the 300 K ambient temperature and the 77 K cooled detector temperature provides the potential for a large spurious signal. 3.4.1 Types of retroreflections
Narcissus consists of two components: (1) pedestal level at the center of scan, and (2) variation of the pedestal level with scan. Mechanisms which create large pedestal levels are as follows: (3) A refractive surface is at or near an intermediate image plane (y = 0), where y is the paraxial marginal ray height at the offending surface. (4) The marginal axial ray is normal or nearly normal to a refractive surface (ni = 0), where n is the refractive index and i is the angle of incidence of the marginal ray following this surface. These two types of retroreflections are shown in Fig. 3.2.10 3.4.2 Reduction techniques
Narcissus reduction techniques include improved multilayer antireflection coatings on the offending lens surfaces and optical designer-controlled methods.
Unique Features of the Infrared Region
Figure 3.2 Two types of retroreflections.
31
10
In the latter technique, the optical designer introduces baffles into the design in order to reduce the solid angular subtense of the cold signal and/or controls the position and shape of offending surfaces during the optical design process. Controls based on paraxial quantities at each surface can be highly effective in reducing total narcissus and/or variation with scan. The paraxial quantity yni is one measure of narcissus that can be controlled. In general, increasing yni at a surface reduces the overall pedestal signal by defocusing the reflected bundle so that it can be clipped by existing apertures or the cold stop itself. Unfortunately, lens curvature changes which increase ni at a surface usually increase third-order spherical aberration and coma contributions at that surface. These aberrations may be balanced by contributions of opposite sign from other lens elements in the system or may require the introduction of an aspheric surface.
3.5 Glass Substitution Optimization of glasses is handled differently than other lens data because there does not exist a continuum of glasses on the glass map. This is particularly true in the infrared region of the wavelength spectrum where the number of available glasses is very limited. Glass substitution is a very effective method for choosing glasses in the infrared. The glass types are directly altered from a previously stored substitute list, and then the optical system is reoptimized while seeking a better solution. By selecting substitute glasses with a similar refractive index, the first-order characteristics of the optical system are maintained before reoptimization. This means that the principal planes of each altered lens are spatially maintained when bending the lens or when shifting the lenses proximate to the altered lens to maintain the proper distance between principal planes, or when bending and shifting simultaneously in combination. For further discussion of computer optimization, refer to Sec. 4.13.
32
Chapter 3
This substitution feature was used by the author to achieve passive athermalization of the all-germanium 3:1 zoom lens solution described in detail in Sec. 6.1.2.11 Optical materials were selected during optimization with a lower dn/dt than germanium. Various optical materials such as GaAs and AMTIR-1 were inserted with similar refractive index as germanium. Table 3.3 shows the optical materials selected during the design process. Table 3.4 presents the optical properties of these materials. Table 3.3 Optical materials selected during the design process.
System #1
System #2
System #3
System #4
Lens 1 Lens 2
Ge Ge
Ge Ge
Ge Ge
Ge Ge
Lens 3
Ge
GaAs
GaAs
GaAs
Lens 4 Lens 5 Lens 6
Ge Ge Ge
CdSe Ge ZnGeP2
CdSe Ge GaAs
AMTIR-1 Ge GaAs
Table 3.4 Optical properties of materials selected during the design process.
N(10.0 µm)
V(8 to 12 µm)
dn/dt
CTE(×10E-6)
Ge
4.0031
1007
.000396
5.9
GaAs
3.2781
106
.000150
5.0
ZnGeP2
3.0791
49
.000003
--
AMTIR1
2.4975
113
.000076
12.0
CdSe
2.4292
84
.000135
4.9
The final passive solution contains one conic and one diffractice surface. It is about 20% longer than the starting solution. Performance over the zoom range and temperature range from 0 to 40° C is comparable to performance achieved by active compensation.
3.6 References 1. Fischer, R.E., “Lens design for the infrared,” in Infrared Optical Design and Fabrication, R. Hartmann and W. J. Smith, Eds., SPIE Press, Bellingham, WA (1991). 2. Robert E. Parks, “Fabrication of infrared optics,” Optical Engineering 33(3), 685–691 (1994).
Unique Features of the Infrared Region
33
3. Schott Optical Glass Catalog, Schott Glass Technologies Inc., Duryea, PA (2006). 4. Kathman, A., and Johnson, E., “Binary optics: new diffractive elements for the designer’s tool kit,” Photonics Spectra 26(9), 125–132 (1992). 5. Lidwell, M., ODSA Technical Manual, Barr & Stroud Ltd. (1991). 6. John Isenberg, Optical Research Associates, Private Communication (1994). 7. CODE V Reference Manual, Optical Research Associates, Inc. (1994). 8. Roberts, M. “Compact infrared continuous zoom telescope,” Optical Engineering 23(2), 117–121 (1984). 9. Rogers, P.J., “Athermalization of IR optical systems,” in Infrared Optical Design and Fabrication, R. Hartmann and W. J. Smith, Eds., SPIE Press, Bellingham, WA (1991). 10. Ford, E.H. and Hasenauer, D.M., “Narcissus in current generation FLIR systems,” in Infrared Optical Design and Fabrication, R. Hartmann and W. J. Smith, Eds., SPIE Press, Bellingham, WA (1991). 11. Mann, A. “Athermalization of an infrared zoom lens system for target detection,” Proc. SPIE 4487, 118–129 (2001).
Chapter 4
Optical Design Techniques A number of techniques are available to assist the optical designer in the process of designing infrared systems. This chapter describes some of them and they are further illustrated in the detailed descriptions of infrared zoom lenses in Chapters 6 and 7.
4.1 Optical Design Starting Point The starting point for the design of an infrared optical system may be one of the following, in order of increasing difficulty: (1) commercially available zoom lens systems (Sec. 6.1.1) (2) zoom lenses described in patents or other reference literature (Sec. 6.5.2) (3) a thin lens solution (Sec. 6.1.2). Selection of the starting point is a very important decision to be made by the optical designer since it will strongly influence the direction in which the design activity will proceed and the likelihood of achieving the desired solution. Since zoom lenses in general are more complicated and time consuming to design than fixed focal length lenses, selection of the best starting point is more crucial to the duration and cost of the design task.
4.2 Scaling Scaling a lens is a simple but powerful tool for assisting in selecting a starting point. When a previously designed optical system is chosen as a candidate for the starting point, it is more than likely that the first-order parameters are somewhat different from the requirements for the new design. Scaling by the appropriate factor makes it possible to match the required focal length with that of the candidate starting point (Secs. 6.1.2 and 7.2.2). It is important to keep in mind what does and does not scale along with the focal length. What do scale are the longitudinal distances along the optical axis and the lateral dimensions perpendicular to that axis; thus, lens thicknesses and separations will scale along with total track length. Lens diameters and pupil diameters will also scale. The image size at the focal plane will scale. What do not scale are the f/#s and the 35
36
Chapter 4
Table 4.1 Scaling a lens by a factor of two with an object at infinity.
Focal length Track length Entrance pupil diameter Image semidiameter f/# Field of view (deg) Wavelength (µm)
Candidate lens
Required lens
5 5 1 0.262 5 3 3–5
10 10 2 0.524 5 3 3–5
angular fields of view; they remain constant regardless of the scale factor. Wavelength also remains unchanged. An example to illustrate some of these scaling relationships is presented in Table 4.1. It may be that some adjustments will still have to be made before and/or during the detail design. For example, if an f/4 lens is needed, the entrance pupil diameter would have to be increased from 2.0 to 2.5 since F = f/D, and D = f/F = 10/4 = 2.5. A related concept that should be mentioned is the Lagrange invariant,1 which can be expressed as nuη=n'u'η' , (4.1) where n and n′ are the indices of refraction before and after refraction, u and u′ are the entrance and exit angles of the axial ray, and η and η′ are the object height and image height (Fig. 4.1). This quantity is an invariant from object space through all intermediate spaces of any symmetrical optical system. Scaling a lens as shown in Table 4.1 does not change the Lagrange invariant, but changing the f/# or the field of view would, in which case the optical system would go into another design region.
Figure 4.1 Lagrange invariant.
Optical Design Techniques
37
4.3 Optical Materials Selection A large number of optical materials transmit in the infrared region of the spectrum. However, the list of materials is quite limited when one considers physical characteristics, workability, and cost. Refer to Sec. 3.1 for the list of materials most commonly used for infrared zoom lenses. It is essential to select combinations of glasses that provide a solution for first-order longitudinal and lateral chromatic aberration (Secs. 6.5.1 and 6.5.2).
4.4 Techniques for Compactness Several techniques for compactness of infrared zoom lens systems are illustrated in Fig. 4.2.2 High powers in the front objective tend to shorten the travel of moving components. Also, minimizing eyepiece focal length decreases the overall length of the system, and good control of pupil aberrations minimizes beam wander and reduces the diameter of the front element. There also is space available around the smaller elements that can be utilized for packaging of electronic and mechanical components (Sec. 6.2.2).
4.5 Symmetry Principle The symmetry principle states that if an optical system has complete symmetry about a central plane perpendicular to the axis, and if the magnification is unity, then all aberrations depending on odd powers of the field vanish identically.1 That is, coma, distortion, and transverse chromatic aberration of all orders are zero. Departure from symmetry will have some effect on the aberration residuals (Sec. 6.1.2).
2
Figure 4.2 Several techniques for compactness of infrared zoom lens systems.
38
Chapter 4
Figure 4.3 Spherical aberration as a function of lens shape.3 (Reproduced from W. J. Smith, Modern Optical Engineering, 2nd Ed. with permission of The McGraw-Hill Companies, Inc.)
4.6 Bending As long as the net curvature of a singlet lens is kept constant, the surface curvatures can vary without changing the power P of the lens, where P = (n – 1)(c1 – c2) = (n – 1)c, where n is the index of refraction. This changing of the lens shape, called bending, is a powerful design tool because the shape of the lens affects spherical aberration and coma without changing the Petzval sum and the power (i.e., focal length, since P = 1/f). Figure 4.3 shows spherical aberration minimized as a function of lens shape.3
4.7 Aplanatic Condition A condition may be imposed upon the design that the system continually satisfy the aplanatic condition while it is zooming. In an aplanatic system spherical aberration and coma are zero. During design, use can be made of the concept in third-order aberration theory that for an aplanatic system the shift of the aperture
Optical Design Techniques
39
stop does not affect the aberration coefficients for spherical aberration, coma, and astigmatism (Sec. 7.1.1).
4.8 Adding an Element It is always an optical designer’s goal to minimize the number of lenses utilized to meet the overall requirements. However, during the course of designing an infrared zoom lens, it may become desirable or necessary to add an element in order to reduce the residual aberrations to an acceptable minimum. If one of the elements in the starting first-order solution has a very low f/#, it will introduce a significant amount of aberration. By splitting it into two elements with a very small separation between them, the focal length of each will be doubled and the f/# of each will be correspondingly increased without affecting the first-order parameters. The curvatures can then be allowed to vary to optimize their values while maintaining the required focal length. Adding an element can also be done by introducing a plane-parallel plate at a suitable location in the optical train. By allowing the curvatures to vary during optimization, the new element can become a lens with either positive or negative power without upsetting the first-order parameters of the optical system (Sec. 6.1.2).
4.9 Field Lens Utilization According to aberration theory, a thin lens placed at an image plane introduces no aberrations but field curvature. This field-flattening feature can be utilized when it becomes desirable to make the sagittal and tangential astigmatic field curves more inward curving or more outward curving (Sec. 6.1.2). The field curvature of this lens can be calculated by the thin-lens formula
( n '− n ) , 1 = − ρ nn ' R
(4.2)
where R is the radius of curvature of the lens surface and ρ is the radius of curvature of the Petzval surface. A field lens placed at or near an intermediate focal plane may be used to reduce the needed detector image size for a given field coverage. In this case, the power of the field lens is chosen to image the aperture stop of the objective lens onto the exit pupil, as shown in Fig. 4.4.3 It should also be noted that a thin lens placed at an image plane will have no effect on the focal length of the system. In practice, the field lens has finite thickness and is usually located a few millimeters away from the image plane. Thus, some aberrations and some power may be introduced into the system by the field lens. Also, introduction of a field lens will change pupil conjugates and aberrations.
40
Chapter 4
Figure 4.4 Field lens.3 (Reproduced with permission of The McGraw-Hill Co.)
4.10 Conics and Aspheres Conics and aspheres present the designer with additional degrees of freedom in defining the prescription data for an infrared zoom lens system. With the advent of precise single-point diamond turning techniques, it adds little to the cost and time of fabrication to specify conics and up to tenth- or twelfth-order aspherics in the refractive or reflective surface description. These additional variables can be very useful in minimizing aberration residuals during optimization (Secs. 6.5.2 and 7.2.2). The general equation for an aspheric surface can be stated as
z=
cy 2 1 + 1 − (1 + k ) c y 2
2
+ α1 y 2 + α 2 y 4 + α3 y 6 + α 4 y 8 + α 5 y10 + ... ,
where e is the eccentricity, k is the conic constant equal to –e2, and k = 0 for a sphere, k = –1 for a parabola, k < –1 for a hyperbola, k > 0 for an ellipse with foci on a line normal to the optical axis, –1 < k < 0 for an ellipse with foci on the optical axis, and α1 . . . n are the aspheric coefficient terms.
(4.3)
Optical Design Techniques
41
4.11 Diffractive Surfaces A diffractive optical element (DOE) can improve optical system performance while lowering the cost and weight by reducing the number of lens elements and desensitizing misalignment tolerances (Sec. 6.5). A DOE in combination with a refractive component and with the appropriate power distribution produces an achromatic system. It may also be possible to use the available DOE parameters to correct for temperature. A new class of optical element consisting of an aspheric surface and a DOE can be efficiently fabricated by diamond turning the aspheric at the same time as the DOE. However, scattering may be a concern in infrared systems. Many computer programs now include the capability of modeling diffractive optical elements.
4.12 Aperture Stop Location In forward-looking infrared (FLIR) systems, the detector responds to temperature differentials across the field of view. Vignetting is the blocking of some bundles of light from within the field of view before they reach the image plane. Therefore, vignetting at the edge of the field of view cannot be tolerated because vignetting will be sensed by the detector as a false temperature differential. This means that clear aperture diameters must be large enough to transmit an unvignetted beam from all points in the field of view. These diameters will vary as a function of aperture stop location. Therefore, placement of the aperture stop may be a critical parameter in applications where packaging constraints place limitations on lens diameters (Secs. 6.1.2 and 6.5.2). This constraint on vignetting is in contrast to visual photographic systems, where some falloff at the edge of the field can be accommodated by the eye of the observer of an image on film. Lateral chromatic aberration is influenced by the aperture stop location. This is an important consideration for infrared systems because the choice of optical materials is so limited. Therefore, in the initial layout of the system the lens powers, optical materials, and aperture stop location have to be selected so as to provide for correction of both longitudinal and lateral color. It should be noted that longitudinal chromatic aberration is unaffected by shifting the location of the aperture stop.
4.13 Computer Optimization Several software optics programs are available with zoom lens capability. The first step is to find a suitable preliminary design starting point. One should select infrared materials that provide longitudinal and lateral chromatic correction, since these are first-order properties. Then one needs to define the merit function, a single number representing the quality of the lens, in terms of target values and weightings. The merit function considers the boundary conditions as well as the image defects; boundary conditions include first-order properties such as focal
42
Chapter 4
length, and also physical parameters such as overall length and center and edge thickness (Sec. 6.5.2). The variable parameters have to be defined, starting with curvatures and spacings. An essential step is to be certain that all of the rays will trace trigonometrically over the full aperture and field of view or the program may not be able to start optimizing. It may be necessary to start with a reduced aperture or field and then increase them during optimization. It is important to review the boundary violations after each optimization run and adjust the configuration as is deemed appropriate. Analysis should be performed after each run as required to evaluate optical performance and tolerance sensitivity.
4.14 Global Search Several computer optimization programs utilize a global search technique without designer intervention to find one or more solutions to optical design problems. One successful approach is to set one radius to get a reasonable effective focal length (EFL) and let the optimization program take over. Starting at a local minimum tends to work more effectively in finding a good solution. Starting from a set of plane parallel plates with a merit function that contains important constructional considerations has been found to converge to a satisfactory solution.4 Numerous examples of global search may be found in the literature, particularly at the quadrennial International Lens Design Conference that is held every four years. Among these programs there is an expert system for the automatic generation of real solutions of zoom lens systems.5 Two databases are established for analyzing nearly 2000 zoom lens patents and 7,124 lens groups. The first database is for the Gaussian optics of finished designs, and the second is for individual lens groups. The expert system searches the first database for Gaussian
Figure 4.5 Examples of video camera real solutions.4
Optical Design Techniques
43
Figure 4.6 Flowchart of the expert system program for the selection of a single layout.4
layouts with specifications (zoom ratio, field of view, f/#, pupil position) close to the design requirements. The goal is to achieve the required zoom ratio with smooth cam curves and reasonable lens group f/#. The structure of each lens group is selected from the lens group database according to the range of zoom ratio, field of view, and f/#. A thick-lens system is selected for each lens group with the simplest possible structure. The program computes the Gaussian parameters and prints out satisfactory preliminary solutions. Further optimization is needed to achieve the system focal length when real lens groups are assembled into a complete system. Examples of real solutions include a 2.5×, 8.9- to 22.5-mm-focal-length video camera shown in Fig. 4.5. A flowchart of the decision making process for the selection of a single layout is presented in Fig. 4.6.
44
Chapter 4
4.15 Tolerances Tolerancing an optical system is a complex subject that deserves a treatise of its own. This is particularly true for zoom lens systems because the effects of tolerances on performance have to be considered throughout the zoom range. Computer programs can be very helpful by performing a statistical analysis of the cumulative effect of all of the individual variable parameters such as radius of curvature, surface accuracy, thicknesses, spacings, refractive index variations, centering, and a host of other parameters. Compensators, usually spacings, are utilized to relax tolerances as much as possible while maintaining the required system performance. A rule of thumb frequently used to form a basis for establishing tolerances can be stated as3 T=
n
t
2 i
.
(4.4)
i =1
This states that the expected total variation in performance T in an optical assembly is given by the square root of the sum of the squares of the individual tolerances ti. This is a conservative estimate by as much as a factor of two, but it is a handy tool for predicting the cumulative effect of tolerances on performance at one position.
4.16 References 1. Welford, W.T., Aberrations of the Symmetrical Optical System, Academic Press, London (1974). 2. Roberts, M., “Thermal zoom optics for R.P.V. sensors,” in Fifth Int. Conf. Remotely Piloted Vehicles, Univ. Bristol, 15.1–15.8 (1985). 3. Smith, W.J., Modern Optical Engineering, Second Ed., McGraw-Hill, New York, (1990). 4. Mouroulis, P., “Optical design and engineering: lessons learned,” Proc. SPIE 5865, 586502 (2005). 5. Cheng, X., Wang, Y., Hao, Q., and Sasian, J.M., “Expert system for generating initial layouts of zoom systems with multiple moving lens groups,” Optical Engineering 44(1), 013001 (2005).
Chapter 5
Zoom Lenses 5.1 Types of Zoom Lenses There are two types of zoom lenses, optically compensated and mechanically compensated. 5.1.1 Optically compensated zoom lens In an optically compensated zoom lens, two or more alternate lenses are linked and move together with respect to the lenses between them (refer to Fig. 5.1).1 This arrangement simplifies the mechanical construction and helps to maintain good control of boresight and alignment. The image motion produced by this type of system is a cubic curve, with the image in focus at a specific number of positions during zoom. The maximum number of positions where the longitudinal image motion is zero is equal to the number of moving air spaces. If the object is at infinity and the first lens group moves during zoom, the space between this lens group and the object is not considered a variable air space. A. D. Clark has developed one form of the calculations used to evaluate the image shift movements in an optically compensated zoom lens.2 Figure 5.2 represents a general three-lens zoom unit, with the zoom elements in their midzoom positions2 and also displaced from the midpoint. Small letters indicate
Figure 5.1 Optically compensated zoom lens.1 (Reproduced from W. J. Smith, Modern Optical Engineering, 2nd Ed. with permission of The McGraw-Hill Companies, Inc.) 45
46
Chapter 5
Figure 5.2 General three-lens zoom system.2 (Reproduced with permission from Elsevier Science.)
the midzoom values and capital letters the values at some other general zoom position. Thin-lens theory is used to investigate the zooming properties. The Newtonian image equation is utilized, whereby x′ = –f 2/x. Using Newton’s equation,
X 'B =
− f b2 XB
(5.1)
X 'C =
− f c2 , XC
(5.2)
and
but X C = X 'B − D =
− f B2 − D, XB
(5.3)
and using this in Eq. (4.2) gives X 'C =
f C2 X B . f B2 + DX B
(5.4)
As previously defined, Z is the axial distance moved by elements A and C from the midzoom position, and Δ is the axial distance moved by the image plane at zoom setting Z from the midzoom position. Thus,
Zoom Lenses
47
X B = xB + Z ,
(5.5)
X 'C = x 'C + Δ − Z ,
(5.6)
D = d + Z,
(5.7)
and Eq. (5.4) becomes x 'C = Δ − Z =
f C2 ( xB + Z )
f B2 + ( d + Z )( xB + Z )
.
(5.8)
But, as with Eq. (5.4), x 'C =
f C2 xB , f B2 + dxB
(5.9)
and this alters Eq. (5.8) after rearrangement to Δ=
fC2 ( xB + Z )
f B2 + ( d + Z )( xB + Z )
or Δ=
−
fC2 xB + Z, f B2 + dxB
Z 3 + aZ 2 + bZ , Z 2 + eZ + g
where a = d + xB −
(5.10)
(5.11)
f C2 xB f B2 + dxB
2 B
b = f + dxB +
fC2 ( f B2 − xB2 ) f B2 + dxB
e = d + xB g = f B2 + dxB . It is interesting to note that only the square of the focal lengths appears in Eq. (5.11), so the image deviation is independent of the sign of the power of the lenses.
48
Chapter 5
Figure 5.3 Mechanically compensated zoom lens.1 (Reproduced from W. J. Smith, Modern Optical Engineering, 2nd Ed. with permission of The McGraw-Hill Companies, Inc.)
5.1.2 Mechanically compensated zoom lens In a mechanically compensated zoom lens, typically one movable component provides the change in magnification (or focal length), and defocusing is eliminated by a shift of one of the other elements of the zoom system (refer to Fig. 5.3).1 It is usually found that one or more of the components has to be driven by some form of cam. Although this arrangement is more complex mechanically, the image stays in focus throughout the zoom range, and this type of system tends to have a shorter overall length than the optically compensated type. Almost all infrared zoom lenses are mechanically compensated.
Figure 5.4 General two-component zoom unit, with the zoom elements in their midzoom 2 positions. (Reproduced with permission from Elsevier Science.)
Zoom Lenses
49
Clark has also developed a form of the calculations used to evaluate the zoom element movements in a mechanically compensated zoom lens. Figure 5.4 represents a general two-component zoom unit,2 with the zoom elements in their midzoom positions. Small letters indicate the midzoom values and capital letters the values at some other general zoom position. Thin-lens theory is used to investigate the zooming properties. For the first lens,
1 1 − = P1 , l '1 l1
(5.12)
where P1 is the power of the lens and equal to the inverse of the focal length of the lens. This becomes l l '1 = 1 . (5.13) 1 + Pl 11 Likewise for the second lens: l '2 =
l1 . 1 + P2l2
(5.14)
But, l2 = l'1 – d.
(5.15)
Therefore, using Eqs. (5.15) and (5.13) in (5.14),
l1 −d 1 + Pl 11 l '2 = . l1 1 + P2 −d 1 + Pl 11
(5.16)
Since the power of the combined system P is given by P = P1 + P2 – dP1 P2,
(5.17)
d dP1 l1 l '2 = . 1 − dP2 ) ( P+ l1
(5.18)
the above simplifies to 1−
As the two components move, the following conditions must hold:
50
and
Chapter 5
Z2 – Z1 = D – d ,
(5.19)
–L1 + L′2 + D = K ,
(5.20)
where K is the object-to-image distance, K = –l1 + l′2 + d. Equation (5.20) specifies that the final image plane remains fixed. By using Eqs. (5.17) through (5.20), the movements of the zoom elements can be calculated, given the midzoom or any other starting position and the selected values of P, the power of the complete system. Equation (5.17) gives D=
P1 + P2 − P , P2 P2
(5.21)
and by combining Eqs. (5.18) and (5.20), where
L12 a + L1 b + c = 0, a = –P, b = D (P2 – P1 + P) – KP, c = KP2D – K – P2D2.
D is calculated using Eq. (5.21), and the above values of a, b, and c can then be evaluated. Finally, −b ± ( b 2 − 4ac )
12
L1 =
2a
.
(5.22)
Since L1 = Z1 + l1, the motion of the first zoom element Z1 may be evaluated, and using Eq. (5.19), the motion of the second element Z2 may also be found.
5.2 Infrared Zoom Lens Specifications Infrared zoom lens specifications may be stated in terms of any of the following categories.
Zoom Lenses
51
5.2.1 Spectral region
The spectral region may be from 0.65 to 1.05, 3 to 5, or 8 to 12 µm. The region selected will depend upon the application, the detector, and the optical materials utilized. 5.2.2 Optical system performance
Optical system performance may be stated in terms of spot size, angular resolution, or MTF. Using MTF allows one to multiply the optics MTF by the detector MTF in order to compute the system MTF. Performance may be stated differently for various zoom positions. 5.2.3 Aperture
The aperture requirement may be stated in terms of f/#, numerical aperture, entrance pupil diameter, or exit pupil diameter. If the aperture stop is located behind the zooming elements, the f/# will remain constant throughout the zoom range. 5.2.4 Effective focal length
Establishment of the EFL range will determine the required fields of view for a given detector size at the image plane. It will also determine the required entrance pupil diameter for a given f/# at each zoom position. 5.2.5 Magnification range
The magnification range is the zoom ratio from the lowest to the highest magnification. It may vary anywhere from 2:1 up to 20:1 or even greater, depending upon the system requirements. It is important to recognize that a singularity may occur at a magnification of unity for the zoom groups. In the case where such a condition exists, mathematical asymptotes in zoom group loci will probably be observed. The result will be a discontinuity at this unique location, with a loss of focus constancy. Therefore, continuous zooming with constant focus may not be available throughout the zoom range.3 5.2.6 Size constraints
Size constraints will be a function of the physical location of the zoom lens system. Size constraints may be tighter for an operational system than for a laboratory experimental unit. There may also be weight limitations for an operational system. 5.2.7 Operating environment
The most common requirement in the operating environment is the temperature range in which the system will function. This in turn will influence the selection of optical and structural materials needed in order to achieve athermalization.
52
Chapter 5
Several representative temperature ranges are presented in Chapter 6. Other possible environmental requirements are vibration and pressure, shown in Sec. 6.3.1. 5.2.8 Distortion
A certain amount of distortion at the edge of the field of view can be tolerated at each zoom position. Typically, 5% is an acceptable outer limit. 5.2.9 Transmission
The required transmission will depend on the needed system throughput. Typically, transmission through the optics should be 50% to 75% or more. 5.2.10 Narcissus
Narcissus can be a significant problem in infrared zoom lens systems. Less than 0.25° C temperature differential at each zoom position may be an acceptable requirement. 5.2.11 Vignetting
Any vignetting is unacceptable in an infrared application because it will lead to a false indication of a temperature differential at the image plane.
5.3 Extenders An extender can be installed between the zoom lens and the sensor as a magnifier to increase focal length. The focal length range increases in accordance with the extender magnification. The f/# also increases in accordance with the extender magnification because the focal length increases while the entrance aperture remains the same. The zoom ratio remains unchanged while the decrease in field of view is inversely proportional to the magnification. The spectral waveband remains the same with proper extender glass selection. These attributes are illustrated in Table 5.1. Navitar, Inc. of Rochester, New York is one of the leading suppliers of extender lenses. Table 5.1 Example of use of zoom lens extender.
Focal length f/# Zoom ratio Field of view Spectral band
Zoom lens without extender 50 to 200 f/2 4 to 1 20 to 5 deg 3 to 5 µm
Zoom lens with 2× SiGe extender 100 to 400 f/4 4 to 1 10 to 2.5 deg 3 to 5 µm
Zoom Lenses
53
5.4 References 1. Smith, W.J., Modern Optical Engineering, Second Ed., McGraw-Hill, New York (1990). 2. Clark, A.D., Zoom Lenses, Elsevier, New York (1973). 3. Neil, I.A., “Optimization glitches in zoom lens design,” Proc. SPIE 3129, 158–180 (1997).
Chapter 6
Refractive Infrared Zoom Lenses 6.1 Target Simulators Considerable progress has been made in the development of infrared target simulators with zoom optics. One important application is in the realistic testing of advanced missiles. This can be achieved with an electro-optical system that operates in the 3- to 5-µm or 8- to 12-µm waveband and reproduces an object moving with respect to a sky background, as it is seen by an approaching missile with a FLIR. The radiance texture of both object and background are achieved by an infrared transparency, whose pixel level can be chosen from as many as 256 gray levels. An infrared zoom lens simulates the closing distance between the missile and the target. The block diagram of an example of a target simulator is presented in Fig. 6.1.1 The target scene generator, background scene generator, and flare scene generator combine to present a varying image of the target at the entrance aperture of the unit under test. 6.1.1 CI Systems CI Systems of Agoura Hills, California, has been a leader in the realistic simulation of infrared scenes for testing of advanced missiles. This has been achieved by building a completely automatic PC-controlled electro-optical system which operates in the 3- to 5-µm waveband and reproduces an object moving with respect to a background. The radiance texture of both the object and background are achieved by an infrared transparency, whose pixel radiance can be chosen from 256 gray levels. In one implementation with a 10:1 magnification ratio, a modulated infrared image passes through an array of nine lens elements that make up the zoom optics. The focal length range is from 150 to 1500 mm. The beam that exits the zoom optics is a collimated image of the simulator target. An optical schematic of the zoom lens is presented in Fig. 6.2.2 Although depicted going left-to-right toward the focal plane, in reality the light proceeds in the reverse direction. In order to match the 75-mm entrance aperture of the rest of the simulator system, the zoom lens exit pupil is by design positioned 200 mm in front of the first lens of Group I. Group I forms a fixed intermediate image. This 55
56
Chapter 6
Figure 6.1 Block diagram of an example of a target simulator. 1
image introduces field curvature at the short focal length but also allows a relaxation of the coaxiality tolerance between Group I and Groups II, III, and IV. The zoom lens is mechanically compensated, with two moving groups which are driven by computer-controlled electromechanical drivers. The optical materials are calcium fluoride, silicon, and germanium. There is one aspheric surface in Group II. In addition, CI Systems in collaboration with Sturlesi Computational Engineering has designed an advanced simulator system with a number of unique features.2 It can provide simultaneous projection with two different zoom lenses of the 3- to 5-µm and 8- to 12-µm wavebands. The focal length range is from 150 to 900 mm. An 8-deg field of view focal plane is projected at all focal lengths. A unique feature of this dynamic zoom system is the very high velocity-to-range and acceleration-to-range ratios which can be achieved. The zoom lens construction is similar to the one described above, but there are important differences. The number of lens elements has been reduced from nine to six, with Group IV eliminated entirely. One or two additional aspheric surfaces are utilized in order to achieve the desired optical performance. The moving Groups II and III travel only in one direction. 6.1.2 Hughes Aircraft Company While at Hughes Aircraft Company, I designed an infrared zoom lens system to operate in the 8- to 13-µm wavelength region for the detection of missile signatures.3 The requirement is for diffraction-limited, high resolution (1 mrad) imaging optics at f/2 with transmission greater than 50%. Three different lens modes operating over a 3:1 magnification range are needed to cover a 9.525-mm diameter detector for three different sets of target range and FOV. The focal length range is 37.76 to 113.28 mm and the corresponding FOV is ±7.19 to ±2.41 deg.
Refractive Infrared Zoom Lenses
57
Figure 6.2 Optical schematic of the target simulator zoom lens. 2
Schematics of the final lens system are shown at three zoom positions in Fig. 6.3.3 The lens system consists of an afocal attachment in front of a fixed imaging lens and a field flattener. The afocal attachment is made up of a positive singlet, a negative air-spaced doublet, and another positive singlet. The first singlet and the air-spaced doublet are the two moving lens components linked together with a cam to provide mechanical compensation. Germanium was selected for all of the lens elements because its high refractive index was essential to minimize the aberrations at the lens working apertures. Its low dispersion made it possible to achieve the desired color correction. The symmetry principle was utilized in the afocal attachment to further reduce lens aberrations. Therefore, only spherical surfaces were utilized in the zoom lens system, and the 1 mrad resolution requirement has been met for all conditions of use without any aspheric surfaces. The total glass weight has been
58
Chapter 6
Figure 6.3 Schematic of three zoom positions of final 3:1 lens consisting of an afocal attachment in front of a fixed imaging lens and a field flattener. 3
calculated to be only 172.4 g, and the total length is 161.79 mm from the first lens vertex to the image plane in the midposition. Some of the design techniques discussed in Chapter 5 can be illustrated using this zoom lens system as an example. A symmetrical afocal telescope of unit power can be constructed by placing a negative lens midway between two identical positive lenses so that the lens system is working at unit magnification. If the middle lens is moved along the axis from the midposition in either direction, the magnification will change rapidly. Such an afocal system is shown schematically in Fig. 6.4.3 An afocal attachment in front of a fixed imaging lens was used as the starting point for this design. A 3:1 zoom ratio is achieved in this manner. By placing the aperture stop behind the moving elements it is possible to maintain a constant f/# at the image plane without a variable iris. The symmetrical construction of the afocal telescope in the midposition makes it possible to take advantage of the symmetry principle in minimizing the lens aberrations.
Refractive Infrared Zoom Lenses
59
Figure 6.4 Afocal system in which the middle lens is moved along the axis from the midposition in either direction.3
The afocal attachment was scaled up five times and placed in front of a 70mm fixed imaging lens. This thin-lens solution was used as the starting point for the design activity. The first-order analysis of limiting rays shown in Table 6.1 indicated that nearly all of the lens apertures appear reasonable for a high-index material like germanium. However, the middle negative element “B” operated at f/0.50 at the high end of the zoom range and was split into an air-spaced doublet to minimize aberration residuals. A quick calculation of spherical aberration β as a function of f/#, as shown in Table 6.2 for refractive index n = 4.0, demonstrated the desirability of splitting the negative element into two air-spaced doublets, with a corresponding doubling of the f/# for each singlet. The aperture stop was placed in front of the rear fixed element of the afocal portion to minimize the aperture diameter of the large front element while maintaining a constant f/# at the image plane.
60
Chapter 6 Table 6.1 First-order analysis of limiting rays.
Magnification diameter (D)
1.73 1.0 0.58
Lens A EFL = 46 60 40 20
f/D=f/#
1.73 1.0 0.58
0.77 1.15 2.30
Lens B EFL = –15 30 25 20
Lens C EFL = 46 35 35 35
Lens D EFL = 70 35 35 35
0.50 0.60 0.75
1.31 1.31 1.31
2.0 2.0 2.0
Table 6.2 Spherical aberration as a function of f/#.
F 1.0 0.75 0.50
n 4.0 4.0 4.0
β 0.008681 0.020409 0.069448
A field flattener was added during the course of the design to reduce field curvature and astigmatism within acceptable limits. Review of the aberration data and astigmatism field plots indicated a need to make the field curvature more outward curving by introducing a field-flattening lens into the system. Since the field flattener is a lens with finite thickness placed 6.76 mm away from the image plane to provide mechanical clearance for the lens housing and the detector, there is some deviation from thin-lens theory in the design solution. The design technique utilized was to place a parallel plate of finite thickness at the appropriate location and let the optimization program vary the curvature of the plate as needed to obtain the desired performance improvement. As can be seen by examination of the sagittal and tangential field plots in Fig. 6.5,3 the desired results have been obtained. Field curvature has been shifted outward by adding the field flattener, and the corresponding shift of the S and T curves has reduced astigmatism to an acceptable magnitude. This system is close to diffraction limited, as evidenced by the axial and 0.9 FOV MTF plots in Fig. 6.6.3 Residual chromatic aberration has some effect on the broadband MTF at the longer focal lengths. 6.1.3 Lockheed Martin T. H. Jamieson designed a 10:1, 2- to 5-µm, diffraction-limited infrared zoom collimator4 to be used as a variable magnification scene generator to test infrared imaging and seeker systems. It simulates the approach of a moving
Refractive Infrared Zoom Lenses
Figure 6.5 Sagittal and tangential field plots before and after inserting a field flattener.
61
3
target, which requires that a fixed size radiation source be projected into the entrance pupil of the test optical system at varying magnifications, such that it always fills the entrance aperture and field of view of the test optics. The range of focal lengths required was from 300 to 3000 mm, with a maximum test aperture of 60-mm diameter, so that the relative aperture range was from f/5 to f/50. The field of view is a modest 2 deg. The zoom system consists of fixed foreoptics of 1000-mm focal length and a relay with magnification varying from 0.316 to 3.16 to achieve the 10:1 zoom ratio. The zoom system schematic is shown in Fig. 6.7.4 It consists of four doublets, for a total of eight elements, made from silicon and germanium to achieve achromatization. The foreoptics is of a telephoto construction. The two mechanically compensated doublets in the zoom relay are controlled by high-performance stepper motors. Computer optimization was initiated at three zoom positions and was expanded to five and eventually to eleven zoom positions. Diffraction-limited performance was achieved over the entire zoom range. The components of the system were mounted on a laboratory table, and this arrangement is shown in Fig. 6.8.4
62
Chapter 6
Figure 6.6 Axial and 0.9 FOV MTF plots for the final 3:1 zoom system. 3
Figure 6.7 (a) Telephoto foreoptics and (b) zoom relay at extreme and midposition.4
Refractive Infrared Zoom Lenses
63
Figure 6.8 View of zoom projector optics, motion control, and blackbody.
6.1.4 Optics 1 Optics 1 developed a long-wave 5:1 infrared zoom projector to project simulated infrared scenes to FLIRs and missile seekers while mounted in an aircraft.5 The optical schematic of this zoom scene projector is shown in Fig. 6.9. The projector optomechanical assembly is presented in Fig. 6.10. Object space for the projector is to the left of the zoom lens projector. Image space for the projector is to the right of the zoom lens projector and coincides with object space for the common module imager. It is designed to operate over the 8- to 12-µm spectral waveband. The zoom ratio is 5:1 from 220- to 1100-mm focal length. It operates with a 512 × 512 emitter array having 0.05-mm pitch size. The system consists of eight lens elements with three +, –, + moving groups. The fixed 150-mm-diameter zoom lens entrance pupil is located 300 mm in front of the assembly. The aperture stop of the zoom lens is situated so as to match the zoom lens exit pupil with the entrance pupil of the common module imager. This entire optical train is shown in Fig. 6.9. The field of view varies from 6.65 to 1.33 deg. Performance is near diffraction limited over the entire zoom range. The object space f/# is f/1.4 at the 220-mm-focal-length position where the limiting aberrations are spherical and coma. At the long-focal-length position the limiting aberration is secondary color. The convex surface of the front lens is diffractive. The lens materials are germanium and zinc selenide. Thermal compensation from 0 to 40° C is achieved through choice of materials used in mechanical assembly and by means of zoom group motion adjustments. This zoom projector has been manufactured and successfully tested.
64
Chapter 6
Figure 6.9 Long-wave infrared (LWIR) 5× zoom scene projector optical layout.5
Figure 6.10 LWIR projector optomechanical assembly.5
Refractive Infrared Zoom Lenses
65
Figure 6.11 FLIR system schematic.6 (Reproduced with permission of Marcel Dekker, Inc.)
6.2 Scanning Systems One of the most important applications of infrared zoom lenses has been with forward-looking infrared scanning systems. Figure 6.116 indicates how a FLIR system operates. The objective forms an image onto a linear array of infrared detectors. The amplified output of each detector drives a corresponding lightemitting diode (LED). This array of LEDs is imaged, after reflection from the back side of the scanning mirror, onto an image tube (vidicon). This, in turn, drives a conventional cathode ray tube display. In this manner, a scanned infrared image is converted into a visual image on a television screen. The infrared zoom lens serves as the afocal attachment in front of the FLIR objective lens. This can be an astronomical zoom telescope with an intermediate image between the objective and the eyepiece. It is usually mechanically compensated with two zooming groups, one negative and one positive. The magnification ratio is often on the order of 4:1 or 5:1 or higher. Another arrangement is to use the Galilean telescope, with which there is no intermediate image, as the afocal zoom attachment to reduce the overall length of the system. 6.2.1 Barr & Stroud Barr & Stroud developed a series of infrared zoom lenses for use in scanning applications. They are intended to operate in the 8- to 13-µm waveband over a continuous zoom range of at least 3:1 and preferably up to 10:1. They are mechanically compensated so as to minimize overall length. As shown in Fig.
66
Chapter 6
Figure 6.12 Barr & Stroud zoom telescope divided into five component groups. 7
6.12,7 the zoom telescope is divided into five component groups comprising a stationary primary objective component, front and rear zoom components, a compensator component, and an eyepiece component. The final 2× to 10× zoom telescope configuration is shown in Fig. 6.13,7 with the zoom objective forming one subsystem and the eyepiece coupled to the compensator component to form another subsystem. The latter subsystem is interchangeable to match the given scanner system, and to minimize complexity it has no moving parts. This is in keeping with the Barr & Stroud philosophy of a modular design concept to utilize a versatile zoom objective lens with a series of interchangeable compensator/eyepiece lenses to accommodate different scanner systems. Color correction is achieved through the use of one zinc selenide element in the front zooming component. All of the other lens elements are made of germanium. All of the lens elements have high-efficiency antireflection coatings except the external surface of the primary objective element, which has an ultrahard coating. Focusing from the minimum object distance to infinity and athermalization are achieved by movement of at least one zoom component. The athermalization method is based upon an electromechanical servo loop system which includes carefully located temperature probes during assembly. As part of its design philosophy, Barr & Stroud emphasized paying particular attention to tolerances at an early design stage so as to minimize or eliminate tolerancing problems during production. In the area of general manufacturing and assembly, for example, compensation for center thickness errors is accomplished by specifying medium to small center thickness tolerances on the auxiliary and eyepiece lens elements and medium to large thickness tolerances on the zoom objective optics. In addition, zoom components may be repositioned away from their nominal design positions through the use of a variable-thickness spacer placed between the primary objective element and the rest of the optics. Boresight error may be minimized or eliminated by tilting or decentering at least one lens element. It has been found that tilt or decenter of the zooming components may be more effective in reducing boresight error without degrading resolution. Judicious choice of carriage mechanisms may reduce boresight error to an acceptable level and remove the need to provide additional compensation.
Refractive Infrared Zoom Lenses
67
Figure 6.13 Final Barr & Stroud 2× to 10× zoom telescope configuration.7
6.2.2 Pilkington P.E. A compact 20× to 5× infrared continuous zoom telescope named “Dezir” was designed and manufactured for production by Pilkington P.E. (PPE) Ltd. It was intended to satisfy the requirements listed in Table 6.3. Table 6.3 Requirements for a Dezir zoom telescope.
8 to 12 µm ± 36-deg FOV in exit pupil space 10-mm exit pupil diameter focus range 100 m to ∞ overall length 350 mm operating range –10 to +20° C transmission > 60%
68
Chapter 6
Figure 6.14 Dezir first-order solution for the objective zooming groups.8 (Reproduced with permission of Philip Rogers and Qioptiq, Ltd.)
The system consists of a continuous-zoom objective and a fixed focal length eyepiece. The Dezir has a +, –, +, + mechanically compensated power construction; its fixed entrance lens is followed by internal negative and positive zoom elements, and a fixed doublet is in front of the eyepiece. The first-order solution for the zoom objective in the midposition is shown in Fig. 6.14,8 and the final zoom telescope design is shown in Fig. 6.15.9 The prime refracting medium is germanium with a zinc selenide negative element in the negative moving group to ensure good chromatic correction at all magnifications. The fixed internal power group was made into an air-spaced doublet to make the group slightly telephoto so as to reduce the back focal length of the complete zoom objective. The eyepiece focal length was minimized, which reduced the objective focal length and the overall physical length as well. The overall length of the zoom telescope is 380 mm. Measured performance of the Dezir largely meets the stringent target specification. Narcissus effect due to retroreflections from lens surfaces was minimized by use of low reflection coatings and through the correct choice of lens shapes. A relatively large narcissus contribution caused by a surface in the negative zoom group at low magnifications was eliminated by reconfiguring the negative group optical power balance. The entrance lens diameter was controlled mainly by reduction of pupil spherical aberration. Focusing from ∞ to 100 m and athermalization are achieved by an axial movement of the entrance lens. The total optics mass is 3.6 kg, and the total transmission is typically on the order of 65%. Another compact infrared continuous-zoom telescope with the code name Zulu has been designed and manufactured by PPE to be used in the optics sensor package for remotely piloted vehicles. It is intended to satisfy almost identical requirements as those listed in Table 6.3 and is of a similar mechanically compensated construction as the Dezir. The Zulu MK.I goes from 10× to 3.8× and has an overall length of 200 mm. The techniques used for compactness are shown in Fig. 4.2 of Sec. 4.4. To ensure compactness of the complete telescope, the space available adjacent to the
Refractive Infrared Zoom Lenses
69
Figure 6.15 Final Dezir zoom telescope design.9
waisted section of the optics is utilized by zoom mechanisms and motors. The zoom motions are provided by an arrangement of concentric cylinders; each zoom group is mounted within cylinders connected by means of a cam follower to a cam cylinder, which is rotated by an electric motor via a gearhead. The MK.I was superseded by an MK.II version in which mechanical modifications were incorporated and by a MK.III design which increased the zoom ratio from 2.6:1 to 4:1 with a small increase in overall length. The zoom lens configuration chosen by PPE has a number of important advantages in production, including inherent self-centering and ease of assembly resulting from axial symmetry. Centration tolerance is achieved mechanically without optical alignment of individual lens elements. For the PPE zoom lens design to be suitable for production, the individual component tolerances must be achieved using conventional machining methods and without the need to match components. By concentrating on and finding solutions in the mechanical tolerancing problem areas, PPE has achieved a zoom lens design suitable for volume production while meeting the performance specifications.
70
Chapter 6
6.2.3 Optics 1 Optics 1, Inc., in Westlake Village, California, designed an afocal zoom attachment for the common module FLIR to be used on the U.S. Navy P-3 Orion aircraft.10 The system is an 8- to 12-µm long-wave IR imaging system using a linear HgCdTe detector array. This system must be fully interchangeable with the present dual field of view switching afocal lens assembly. The designed zoom attachment has a 5:1 magnification range from 0.9× to 4.5×. The required MTF at ambient temperature is 85% on axis 0 to 12 line pairs per millimeter (lp/mm). Transmission needs to be at least 75% on axis. Focusing is required from 500 ft to ∞. An optical schematic of the system, including the common module FLIR, is presented in Fig. 6.16.10 The zoom attachment is a Galilean form of afocal zoom lens, which provides an acceptable level of performance while still meeting the demanding packaging and other requirements. The zoom attachment has two moving groups with a –, + power distribution. The design employs all germanium elements with the exception of one weak zinc selenide element for color correction. There are four aspheric surfaces utilized for compactness in order to achieve the desired optical performance. The aperture stop is located toward the aft end of the zoom attachment so as to properly match the zoom lens exit pupil to the entrance pupil of the common module imager. Narcissus is tightly controlled through the judicious use of high-efficiency antireflection coatings. The final design for this system provides an excellent level of performance throughout the entire zoom range and is fully producible. Athermalization over a temperature range of ±25° C is required for this system; the methodology is shown in concept in Fig. 6.17.10 Each moving group is controlled by one stepper motor that is microprocessor controlled and has an associated look-up table programmed into erasable programmable read-only
Figure 6.16 5:1 afocal attachment for the common module FLIR. 10
Refractive Infrared Zoom Lenses
71
Figure 6.17 Athermalization methodology for the 5:1 system. 10
memory (EPROM). The microprocessor controls the motions of the two zooming groups so as to allow the user to proceed to any desired magnification. Two sets of look-up tables are employed which are programmed into the EPROM; one set is for the motion of the groups as a function of temperature and the other is for changes to group motions as a function of range. Two thermistors bonded to the housing in the vicinity of the first element instruct the microprocessor as to which look-up table to access for thermal compensation. The approach taken to achieve the required tight tolerances in manufacturing and assembly is to utilize linear bearings for the zooming group motions, with three separate bearings per group. The mechanical housing and all associated components are manufactured of stress-relieved aluminum in order to avoid any bimetallic effects. The lens elements are bonded into their respective housings using a compliant bond material. 6.2.4 Precision-Optical Engineering Precision-Optical Engineering in Hertfordshire, England, has been active in this field for a number of years and developed a compact 3.5× to 20× zoom telescope with an overall length of 300 mm for use in the 8- to 12-µm waveband at four specific zoom positions.11 It has a +, –, +, + mechanically compensated construction illustrated in Fig. 6.18;11 the scroll cam configuration for the two zooming groups is shown in Fig. 6.19.12 The telescope is designed to interface with a UK TICM2 scanner, although it is capable of adaptation to other scanner types. The telescope operates with a 10-mm pupil over a total field of view of 60 deg horizontal by 40 deg vertical. There is an internal turret which permits the high magnification to be switched to 40× operating at half aperture. The
72
Chapter 6
Figure 6.18 Compact 3.5× to 20× zoom telescope.11
manufactured telescope demonstrates near-diffraction-limited performance over a substantial portion of the field of view together with a very high level of narcissus control. The high MTF levels are due in large part to the lens accuracies achieved using the potting techniques developed by the company. The prime refracting medium is germanium with a zinc selenide negative element in the negative moving group to ensure good chromatic correction at all magnifications. The zoom drive is achieved via the scroll cam, which comprises a cylinder with a pair of slots in which followers are located. It selects specific magnifications within the zoom range and is also responsible for athermalization compensation, rotating itself according to the focal length requirement and the
Figure 6.19 Scroll cam configuration.12 (Reproduced with permission of Richard Simmons, BAE Systems).
Refractive Infrared Zoom Lenses
73
temperature. For athermalization, the aberration balance is maintained by adjusting the air space between the fixed front lens and the zooming groups, and the position of the focusing lens is adjusted to ensure that the overall length of the system is maintained. At the long focal length setting, an additional degree of freedom is introduced to allow the zoom groups to be moved differentially. At the short focal length setting, only the focusing lens position is adjusted while the zoom groups remain stationary. The profiles of the slots in the regions between athermalization zones have been configured to provide the smoothest mechanical motions possible, with minimum variations in torque; this makes it possible to minimize power requirements for the cam drive. 6.2.5 Zhejiang University, Department of Optical Engineering The Deptartment of Optical Engineering at Zhejiang University in Hangzhou, China, has designed a compact afocal infrared zoom telescope with a 3:1 magnification ratio from 2× to 6× which operates in the 8- to 12-µm spectral region.13 The focal length and object field are 32 to 96 mm and 20.6 to 6.94 deg, respectively. The overall length is 159 mm with an entrance lens diameter of 94 mm. The system operates at a constant relative aperture of f/2 over this zoom range. The position and diameter of the exit pupil remain constant during zooming. It has a 20 m to ∞ object distance. An optical schematic of the system is shown in Fig. 6.20.13 The five groups have a +, –, +, +, + power distribution, with Groups I, IV, and V stationary, while II and III are the mechanically compensated moving groups. The zooming groups are fixed into two lens mountings that slide the main concentric cylinder on which there is an outer cylinder for the adjustment of zooming. Two sets of three roller followers distributed equiangularly on each lens mounting are inserted into six cam slots on the main cylinder and into six linear slots on the outer cylinder. The high concentricity of these cylinders and the accurate match in machining ensure that the concentric deviations of zooming and compensating lenses are in tolerance during zooming. Athermalization has been achieved in an infrared zoom telescope of similar construction with a magnification range from 3.87× to 12×;13 the temperature range is from –10 to +40° C. The lens elements are all made of germanium, and the lens mount is made of aluminum alloy. The system is athermalized by means of a combination of manual adjustment of the front lens and mechanical passive athermalization of the rear collimating lens group.14 The front lens is placed into its lens cell for focus adjustment by manually turning until the needed distance mark on the outer cylinder is aligned to a temperature mark on a stationary sleeve. The temperature lines are marked at the proper position to obtain the appropriate compensation displacement of the separation between Groups I and II due to variation of ambient temperature during focusing. During focusing, the front lens is rotated according to the ambient temperature. In the rear group, three nylon 1010 bars and two invar bars are connected in series. The nylon bar end of the part is attached to the fixed cylinder, and the other end is connected to the
74
Chapter 6
Figure 6.20 Compact afocal infrared zoom telescope with 3:1 magnification from 2× to 6×.13
collimating lens cell. The summarized expansion or contraction of the series bar due to the ambient temperature is utilized to compensate displacement of the separation between Groups IV and V by moving the collimating lens cell, which can slide smoothly inside the fixed cylinder. 6.2.6 Electrooptical Industries, Ltd. Electrooptical Industries in Rehovot, Israel, designed a compact highperformance IR zoom telescope with a 15:1 magnification range from 0.5× to 7.5×.15 It is characterized by three optical element groups which are moved in a predetermined manner to change magnification and compensate for temperature effects. An optical schematic of the system is presented in Fig. 6.21.15 The five groups have a +, –, +, +, + power distribution. Groups A and D are stationary, while B, C, and E are the movable groups. The unfolded length of the telescope from the front lens to the exit pupil is 275 mm, and the entrance pupil diameter is
Refractive Infrared Zoom Lenses
75
Figure 6.21 Compact high-performance IR zoom telescope with 15:1 magnification range 0.5× to 7.5×.15
76
Chapter 6
150 mm. The telescope operates in the 8- to 12-µm region of the infrared spectrum. The lens elements are of germanium except for a zinc selenide negative singlet in the negative moving group. This group has an undercorrected spherical aberration that compensates for the overcorrected spherical aberration in the front fixed lens element. High optical transmission is achieved due to using only seven lenses in the overall system. Magnification change and athermalization are achieved at the instant of actual use by computer-controlled positioning of the movable groups in accordance with data precomputed for each magnification and temperature of the system. The computer receives three inputs: the instantaneous required magnification, provided by manual input from the controller; the actual temperature of the system, which is monitored by a sensor; and the required focusing factor for the collimator. Static and dynamic tolerance requirements are achieved primarily through proper control of the negative pair of lenses. Boresight stability is accomplished through high lateral accuracy of the linear bearings provided for the lens groups, and the simplicity of the mechanical design and production is due to the use of standard high-accuracy assemblies such as translators, linear bearings, and lead screw mechanisms. 6.2.7 Scotoptix 6.2.7.1 Boresighted zoom lens
I. A. Neil of Scotoptix designed a boresighted zoom lens with a 2:1 zoom range from 10× to 20×.16 It consists of all spherical surfaces and has all germanium elements except for one zinc selenide element for color correction in the 8- to 12µm region. There are two movable components (–, +) in the zoom assembly. An auxiliary lens system minimizes variation in boresight accuracy by offsetting at least one component from its nominal position by a fixed amount of decentration or tilt; in this way, differences in angular errors at various zoom settings can be reduced to near zero without significant degradation of other performance criteria. The zoom lens schematic at three zoom positions is shown in Fig. 6.22;16 the optical prescription data are presented in Table 6.4. 6.2.7.2 Athermalized zoom lens
Neil also designed an athermalized zoom lens with a 3.3:1 magnification range from 6× to 20×.17 It too consists of all germanium elements except for one zinc selenide element for color correction in the 8- to 12-µm region, and again there are two movable components (–, +) in the zoom assembly. Athermalization is achieved with movable carriages which are independently axially positioned according to position signals generated by preprogrammed computing means that correlate lens position with focusing distance, magnification, and automatically measured temperature. The mechanical mechanisms are driven by electric motors arranged in a servo loop. The zoom lens schematic at three zoom positions is shown in Fig. 6.23.17 The optical prescription data are presented in Table 6.5.
Refractive Infrared Zoom Lenses
Figure 6.22 Boresighted zoom lens.16
77
78
Chapter 6 Table 6.4 Optical prescription data of a boresighted zoom lens.
Lens
Surface
Pupil
--
Separation 0
Magnification
Radius of Curvature
Material
all
flat
air
A1
22.30
all
–36.32
air
A2
4.58
all
–34.19
Ge
B
B1 B2
0.48 4.81
all all
–233.38 –114.30
air Ge
C
C1 C2
0.48 4.58
all all
50.80 61.47
air Ge
D1
61.62
all
–69.09
air
D2
2.70
all
–122.78
Ge
E1
23.84
all
–94.79
air
E2
5.58
all
–67.16
Ge
F1
22.68 43.93 62.75
10× 15× 20×
2976.88 ---
air ---
F2
4.80
all
–308.71
Ge
G′1
53.50 28.08 7.16
10× 15× 20×
–177.80 ---
air ---
G′2 G″1
2.91 7.20
all all
321.46 –123.70
Ge air
G″2
3.20
all
–216.48
ZnSe
H1
107.82 111.99 114.09
10× 15× 20×
–239.78 ---
air ---
H2
19.70
all
–176.00
Ge
A
D
E
F
G′
G″
H
Refractive Infrared Zoom Lenses
Figure 6.23 Athermalized zoom lens.17
79
80
Chapter 6 Table 6.5 Optical prescription data of an athermalized zoom lens.
Radius of Curvature flat –44.32 –36.37
Lens
Surface
Separation
Magnification
Pupil A
--A1 A2
0 22.29 4.50
all all all
B
B1 B2
0.50 4.25
all all
193.01 –1724.73
air Ge
C
C1 C2
0.50 16.83
all all
35.33 21.85
air Ge
D
D1 D2
69.21 5.00
all all
–95.37* –77.52
air Ge
E
E1
15.75 49.59 73.62
6× 13× 20×
–34722.22* ---
air ---
E2
5.50
all
–243.31
Ge
F′1
78.45 35.83 8.59
6× 13× 20×
–331.31 ---
air ---
F′2 F″1 F″2 F″′1 F″′2
2.75 6.00 2.75 9.75 3.00
all all all all all
556.48 –407.05 585.41 –112.81 –157.93
Ge air Ge air ZnSe
G1
82.47 91.25 94.46
6× 13× 20×
–263.19 ---
air ---
G2 22.50 all *Surfaces D1 and E1 have aspheric profiles.
–182.97
Ge
F′
F″ F″′
G
Material air air Ge
Refractive Infrared Zoom Lenses
81
Surfaces D1 and E1 are aspherics having profiles governed by the well-known aspheric equation: ZC = 1 – [1 – C (CH2 + BH4 + GH6 + DH8 + …)]1/2, (6.1) where Z = distance parallel to the optical axis, C = inverse of the radius of curvature of spherical surface, and H = radial distance perpendicular to the optical axis. In the case of surface D1, H has a maximum value of 18.54 mm for the axial field and C = 1/(–95.37 mm), B = –2.79 × 10–8, G = 0, and D = 0. In the case of surface E1, H has a maximum value of 29.03 mm for the axial field and C = 1/(–34722.22 mm), B = –7.54 × 10–8, G = 0, and D = 0. 6.2.7.3 Optically compensated zoom lens
A patent issued to Neil describes a compact optically compensated infrared zoom lens system for the 8- to 12-µm wavelength region.18 The first and third components are single positive lens elements which remain stationary while the second and fourth components, mounted on a common carriage, are selectively positionable along the optical axis. These components consist of a negative airspaced doublet and a negative singlet, respectively. This zoom lens system is shown in Fig. 6.2418 in front of a one-component collecting system which forms a real image of the object space radiation. The rear surface of the first lens element is aspheric to help reduce system length. All of the lens elements are of germanium except for one zinc selenide element in the air-spaced doublet. The collecting system is movable to a limited extent to enable refocusing of the image to compensate for the limited defocusing throughout the zoom range and for defocusing due to effects of temperature variations. The telescope is athermalized over the range from –10 to +50° C. The magnification range is from 1× to 9×, and performance is nearly diffraction limited over 75% of the field of view. An alternative arrangement described in the patent goes from 4× to 20×. 6.2.8 Optimum Optical Systems A modern infrared zoom lens has been designed and fabricated by E. Ford of Optimum Optical Systems of Calabasas, California.19 It has a 3.5:1 zoom range, operates at f/3.0 in the midwave infrared (MWIR) from 3.8 to 5.0 µm and is a reimaging system with all spherical surfaces. The focal length range is from 85 to 300 mm, the overall length is 280 mm, and the maximum aperture diameter is 100 mm. The image format diagonal is 12 mm. The stop location is 25 mm from the image plane. The focus range is from ∞ to 30 m, but at the near focus the narrow field suffers some spherical aberration due to the conjugate shift. The operating temperature range is from –35 to +60° C and the wavefront remains diffraction limited over most of this temperature range. The lens schematic is shown in Fig. 6.25.19 One of the unique features of this lens is that it was designed to be microprocessor controlled and driven by stepper motors. Two motors are
82
Chapter 6
required for the two independent group motions, and the range and thermal compensation are accomplished by these motors. The zoom look-up table, stored in nonvolatile computer memory, is a list of allowable positions and the
Figure 6.24 Compact optically compensated infrared zoom lens system.18
Figure 6.25 Modern infrared zoom lens.19
Refractive Infrared Zoom Lenses
83
Figure 6.26 Step-zoom dual-field-of-view telescope, NFOV.20
corresponding number of the motor step to reach that position. The number of table positions determines the speed and smoothness of the motion. Active temperature compensation is accomplished in software. 6.2.9 Royal Institute of Technology The Royal Institute of Technology in Stockholm, Sweden designed a step-zoom dual-field-of-view infrared telescope to operate in the 8- to 12-µm waveband.20 The zoom ratio from narrow field of view to wide field of view is 3.75:1. The optical schematic is presented in Fig. 6.26. The system consists of six lenses with one conic surface. The zoom system has three +, –, + groups. The axial motion of a single lens group is used to switch field of view and for focus and athermalization. The narrow field of view is 2.56 deg horizontal with a 4 to 3 aspect ratio. The narrow field of view has a 150-mm entrance pupil diameter. The front objective is a germanium singlet bent to minimize spherical aberration. The second lens group is a zinc selenide/germanium doublet. The third lens group is a germanium singlet with one conic surface. The eyepiece consists of two simple germanium lenses. Wide field-of-view performance is limited by lateral color at the corners. The system operates at f/1.2, where the f/# is defined as the objective lens focal length divided by the objective lens entrance pupil diameter. The zoom ratio can be increased to 10:1 in a variation of this design. This variation is presented in Fig. 6.27. 6.2.10 Fuji Photo Optical Company An infrared zoom lens has been designed by Fuji Photo Optical Company with a 4:1 zoom ratio. The optical schematic is presented in Fig. 6.28.21 The f/# is f/1. There are two operating modes. This infrared zoom lens operates in the 3- to 5µm waveband using silicon and germanium as the optical materials. It also has an operating mode in the 8- to 12-µm waveband using zinc selenide and germanium as the optical materials.
84
Chapter 6
Figure 6.27 10× step zoom telescope.20
6.2.11 Carl Zeiss, Inc. Carl Zeiss, Inc. has designed a modular infrared Kepler telescope (U.S. patent No. 6,057,960). This optical system is presented in Fig. 6.29.22 The objective has a positive front group and a negative rear group. The objective includes an interchangeable optic W to change field of view. An intermediate image is located at position 27 in the schematic. This intermediate image is important as it is placed at the common focal point of the objective-eyepiece combination to make this subsystem afocal as an essential ingredient of a scanning system. The spectral waveband is from 7.5 to 10.5 µm. The optical materials are germanium with zinc selenide for color correction.
6.3 Charge-Coupled Device Imaging Systems 6.3.1 Angenieux A zoom lens compensated for temperature, vibration, and pressure (Fig. 6.3023) has been developed by Angenieux, Inc., for volume production,23 with over 600 units produced. Operating in the near infrared from 0.65 to 1.05 µm, it was developed for use with CCD sensors and is compatible with many airborne, tank, and missile applications. This lens has a 10:1 zoom ratio, a 20- to 200-mm-focallength range, and operates at an aperture of f/6 or better. Its environmental specifications are as follows: temperature: –40 to +70° C vibration: 5 Grms (50 – 500 Hz) pressure: 850 – 1050 mbar. These specifications are met through the use of (1) passive optical and mechanical athermalization to keep the MTF constant at all temperatures, (2)
Refractive Infrared Zoom Lenses
85
resonance damping of Group 1 to reject resonance frequencies above 500 Hz, and (3) reduction of the power of the air lenses so as to minimize the effect of air index variation with pressure. Note: The power of the air lenses refers to the steepness of the radii of curvature of the surfaces adjacent to the airspaces.
Figure 6.28 Infrared zoom lens system consisting of five groups.21
86
Chapter 6
Figure 6.29 Modular infrared Kepler telescope.22
Figure 6.30 The 20–200-mm zoom lens compensated for temperature, vibration, and pressure.23
Refractive Infrared Zoom Lenses
87
Figure 6.31 Multiwavelength zoom lens for the Advanced Technology Solar Telescope.24 (a) Layout of zoom position 1 and (b) layout of zoom position 9.
6.3.2 University of Alabama, Huntsville A multiwavelength zoom lens for the Advanced Technology Solar Telescope (ATST) has been designed by the University of Alabama, Huntsville.24 The zoom lens is an integral part of the ATST for observing radiation zones of the sun at nine discrete wavelengths from 388.3 nm in the UV range to 854.2 nm in the near IR. The optical schematic at the extreme positions is shown in Fig. 6.31. This system requires constant resolution for identical image sampling at each wavelength. An eight-element zoom lens meets the performance requirement over the field of view. Each zoom position has a different focal length and f/# for constant CCD sampling. The CCD camera has format size of 37 × 37 mm with 4096 × 4096 pixels corresponding to 9-µm pixel size. The CCD sampling size is 18 µm (two pixels) on the CCD detector. The design starting point is Japan patent No. 58-34810 scaled to a 3000-mm focal length and adjusted to f/27 at 550 nm. The glass materials are FKN5 crown index 1.48914 and NLASF44 flint index 1.80832. The optimization program utilized lens splitting, adding lenses, bending, and one aspheric surface. The final design has two moving groups: a singlet for zooming and a doublet/singlet for compensation. The Strehl ratio is greater than 90% at all zoom positions. 6.3.3 National First University of Science and Technology A compact 2:1 mobile phone zoom lens has been designed by the National First University of Science and Technology in Taiwan.25 The overall length has been reduced to 18.9 mm. The optical schematic is presented in Fig. 6.32. The front diameter has been minimized with the aperture stop at the first element. The f/# varies from f/2.8 in the wide field of view to f/3.8 in the narrow field of view. The focal length varies from 5.5 mm to 11.0 mm. The system is designed for a two-million pixel complimentary oxide semiconductor (CMOS) or CCD. There are three +, –, + moving groups with a motion distance for each group of less than 10 mm. The optical materials are glass with one or more aspherical surfaces. Distortion is less than 1% at all field and zoom positions.
88
Chapter 6
Figure 6.32 Compact 2:1 mobile phone zoom lens.25
6.3.4 Industrial Technology Research Institute A compact 2.5:1 zoom lens has been designed for cell phone applications and inexpensive mass production by the Industrial Technology Research Institute of Taiwan.26 Injection-molded plastic aspheres improve performance and compactness and decrease the cost due to the reduced number of lens elements. There are only five lens elements. The first lens is negative with the concave surface facing the object. Its rear principal plane is moved forward to shorten the total length of the lens system. Control of optical power of the variator second lens group shortens the zooming distance. The third lens group zooms to adjust focus. Distortion is 3.5% in the wide field of view (WFOV) and 1.7% in the narrow field of view (NFOV). The overall length is only 5.9× the image height. The optical schematic can be seen in Fig. 6.33.
6.4 Laser Beam Expanders 6.4.1 Carl Zeiss, Inc. Carl Zeiss, Inc. designed a beam expander telescope with variable magnification for use with a 33:1 zoom ratio CO2 laser scanning system.27 The entrance pupil varies from 1.5 to 50 mm, and the exit pupil is fixed at 1.5 mm; the latter pupil serves as the entrance pupil for the scanner assembly. The scan angle is ±12.5
Refractive Infrared Zoom Lenses
89
Figure 6.33 Compact 2.5:1 cell phone zoom lens.26
deg, and the overall length is 200 mm. To fulfill these requirements, a threeelement mechanically compensated lens system was chosen for the zoom objective. It consists of a positive first-element focator, a negative secondelement variator, and a positive third-element compensator. Optimization of the optical design was facilitated by splitting the compensator into two lenses with powers of opposite sign. The change of magnification is accomplished by a large axial movement of the variator and a relatively small axial movement of the compensator. The lens schematic is shown in Fig. 6.34.27 Since the optical system was to be used with a monochromatic light source, no color correction was required; therefore, all of the lenses were made of zinc selenide because of its low absorption at 10.6 µm. The telescope has since been achromatized and athermalized. In all positions the telescope is diffraction limited both on axis and for a field of view of ±5 deg. The Seidel aberrations and astigmatic field curves are presented in Fig. 6.35.27 6.4.2 University of Twente The University of Twente designed a zoom lens for use with CO2 lasers. It is used by high-power lasers in the 1- to 2-kW range for cutting sheet metal.28 It must match the numerical aperture of the focused beam to the material thickness. The Rayleigh range should be about half of the material thickness. This zoom lens has near-diffraction-limited performance from f/3 to f/8. The back focus is in excess of the focal length, also known as a retrofocus telescope. The moving lens
90
Chapter 6
Figure 6.34 Beam expander telescope with variable magnification for use with a CO2 laser scanning system.27
group is mechanically compensated. The focal length varies from 60 to 200 mm for a fixed 20-mm entrance pupil diameter. Zinc selenide is utilized as the optical material for low absorption at 10 µm. The field of view is 0.5 deg at the 60-mmfocal-length position. Other considerations in the design include focusing of reflected radiation, thermal gradients, and power density. The three-element system with all spherical surfaces shown in Fig. 6.36 has been built and tested.
Refractive Infrared Zoom Lenses
91
Figure 6.35 Seidel aberrations and astigmatic field curves for a beam expander telescope.27
92
Chapter 6
Figure 6.36 Three-element zoom system with all spherical surfaces.
28
Refractive Infrared Zoom Lenses
93
6.5 Diffractive Optics A diffractive optical element (DOE) is produced by replicating multilevel phase patterns into an optical material, creating a stepwise approximation to an optical phase profile (Fig. 6.37).29 DOEs, sometimes known as “binary optics” due to their multilevel structure, are being utilized with increasing frequency in visible and infrared systems. Their use can improve optical system performance while lowering the cost and weight by reducing the number of lens elements and desensitizing misalignment tolerances. A DOE in combination with a refractive component and with the appropriate power distribution produces an achromatic system; it will also be possible to use the available DOE parameters to correct for temperature. A new class of optical element consisting of an aspheric surface and a DOE can be efficiently fabricated by diamond turning the aspheric surface at the same time as the DOE. With its very high V number in the 8- to 12-µm region, germanium is a superior material for diamond turning compared with other available infrared materials. However, scattering may be a concern in infrared systems; 5% or more of the radiation will be diffracted into higher orders, and stray radiation will raise the background signal level and lower the contrast. Many computer programs now include the capability of modeling DOEs. Diffractive optics provide a strong negative dispersion which can be combined with conventional lenses to reduce chromatic aberrations. The color of a simple lens can be corrected without the usual method of adding another lens of
Figure 6.37 Hybrid refractive/diffractive lens element produced by replicating multilevel phase patterns into an optical material, creating a stepwise approximation to an optical phase profile.29 (Reprinted from the May 1993 issue of Photonics Spectra, copyright of Laurin Publishing Co., Inc.)
94
Chapter 6
a different glass type; this provides a degree of freedom that allows the designer to reduce the number of elements. In addition, diffractive optics may be used in infrared systems to reduce or eliminate the need for aspheric surfaces or for a color-correcting element in the optical design. They may also allow a reduction of alignment tolerances. At the same time, increased scattering and higher-order diffraction are concerns that need to be addressed when considering diffractive optics in the infrared. In any event, there is no doubt that infrared zoom lens systems will benefit from the use of diffractive optics in the years ahead. The dispersion of a DOE is negative and is independent of the substrate. Therefore, a refractive/diffractive singlet can replace a conventional achromatic doublet. For example, let us consider a silicon hybrid refractive singlet in the MWIR 3- to 5-µm region with focal length f = 100. For the diffractive surface, V = (λM)/(λS – λL) = –2. Using the primary achromatism Eq. (2.20) from Sec. 2.7.1, fR = 100.85 and fD = 11,850. The optothermal coefficient of expansion of a DOE is independent of the change in refractive index of the substrate with temperature. An achromatic and athermal solution can be achieved with three optical materials that have different powers, optothermal expansion coefficients, and dispersions. A thin-lens solution in which the individual components are in contact can be derived by solving the three simultaneous equations for system power, achromatism, and athermalization. These equations can also be used to derive an achromatic, athermal hybrid doublet by considering the diffractive surface to be the third material or lens. 6.5.1 Optics 1 A 4:1 zoom lens with one diffractive element was designed by R. Hudyma for the 3- to 5-µm spectral band.30 Table 6.6 presents the lens specifications. Table 6.6 Diffractive zoom lens specifications.
Parameter focal length (f) f/# Encircled energy Focal plane array format Spectral region
Specification 50–200 mm (4×) f/2.8
