Structural Monitoring with Fiber Optic Technology
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Structural Monitoring with Fiber Optic Technology
Raymond M. Measures
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# . . " / " . .% 7--$ " " 7 - #- - " - / - " - > # "/ - ##- . "% 1 ." $ *" #- - . "" -/ "/ C1 -. (::9D% - " # #- " * - +"-- " " "/ % " "/ *> (:59 (:5: ! - (::; < # 6 (::9 " " . / - " > . # % " - . # F " #- . - - -- " #/ " % " - .. . " ! - "/ (::; " - .H . -
- % #
- . " " -% .- #-. " > - " 7 - (::& C % &%3D% " "
- " #- " - #
- " > " - . " ". % " #- " # /
" F#
. . . . . " . . F#
. " " - - -#- ." " # #- / - . " > "" " #-G - " # . .% " F- - - # " > - " " . -> % 7" " . -- F#
. #- . # #- - "
- " - # " - # % " . # - - - " - -- #- C( . ""D
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. -
F " - H " "#- " > % " ,+ . - ." / -- F - " " - " - C % &%(:D% 7" -.
" # . # "/ # H - . " " . - #- . # " # " - " % ,+ "#- "
&%3 ) ,1= "/ > - . " " . " > . C % &%&(D% " " - - - F
- " " " # - " - " " " .>.. .-- . " # % " " " # % ". .. " . . #- " F#
- . . # % &%&&%
FIGURE 2.21.
- - . F#
. ,+
"%
40
1 +), &
- *
FIGURE 2.22.
- - F#
. " # %
2.8 OTHER STRUCTURAL MONITORING APPLICATIONS #
. # " .- -- ."- . % " . " / #-
F# # " " " "- . . . # # - .
- -"% " # - --
- F#
- " #- -- .H - - - C et al. (::3D F . C % &%&4D " > . - - . #- . . " - % # " - # " - " - " " " -% - #- -
- F# " " " -
. " - % " " - - " F F- - " . - H
..?%
&%5 1), ,, ! * , A ++!
41
FIGURE 2.23. #
- . - - - -%
* " -- . - . $ - - -
"- > " " . - - . "
- / .% " " . . . - . "" . . " " " " "- C-" (::4D% #
#- . # " " . " - " "
. . " % - . # " " "
" - " " " - .%
- # " - - " % - - #- # " #/ % ).# F#
- . " # # " . " . - # - "
- " #- > - " " C*R? et al. (:5:D% " "" # . F " " - ." . (''''' . #- C - (::'D% " F B $ . " " " G H "
- F#
" - % --
$""
" # - " ""% " .$ . " " # " " " " "" " " % 7 " " - # # . # " F#
- .
42
1 +), &
- *
. " - . " # - " # -#- - . F " - % " - . " - - " - # # % 7" - / . " . - - # #- " # " " " > " - -. " # % " - " -
F#
" - - . % *!"- C(::9D -
" . F#
KK %GG -"
- F# "- " # # " >
" . .- " # . % " # - "
- F# - "- " " # C % &%&;D% " " " -- "
- F# . ." . -"% " " " G " . -# " " - % - #- .# " -
- F# optical time domain re¯ectometry C,D . B" "" " #- . "
B - - -" C % &%&9D% " 1 C(::5D " # -
F#
" " ".- " . -
FIGURE 2.24. + - #" " F#
%
&%: 7 +7), ,, ! * , A
43
FIGURE 2.25. - . . B .
- " F#
%
# % " - -- - ..? - . # . .$ "-% " " # "/ . * " #- "" -
F# " . - " " - > - - % " - " # # . " -" - " " "
- F# " . " - -
" . # % " 1 C(::5D " " - / - " "/%
2.9 WIND POWER AND STRUCTURAL MONITORING 7" " " - #- . " . " -
. " - - - - - # . "" % 7
" . # #- -" " - - -- . % - G . " " > (9'' *7 "" $ # (%9O " G - # (::4 C*A (::4D% # (::3 . -" " F " -
# "- - . # " &'4'%
44
1 +), &
- *
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9'' - # 39' *7 "-- - # " &''5 CNew Scientist (::3D% .
$ -# (:55 " " KK.-- + , " -
. GG
% " - .- - # #- " " - (5O " -# . C-- (::;D% " .? F " #- $
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% > " #- -. ,+ # #-
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- F# " - $ . " -
. " #- / - C % &%&2D% " $ - " - F#
- %
&%(' * A ) !)L , * , A
45
FIGURE 2.26. - . - - %
2.10 MAGNETIC LEVITATION TRAIN MONITORING 1"$ . ""- #- " .-- . # " - - . $ F . % * - C.-D - . ""$ " .
- "- 9'' . " ( % " ! )> "" # -
-- - # " 6 - .-- - # electrodynamic suspension C)D # . " - # . C # " "-D " $ -.. - . - " C)". (::9D% " . " " " "" " "- . " - " - " "- / "- - C9' ('' . " ( D% " ) . " ? # - ('' .. "" # .-- #-% " A . '3 - " # " A . . " A . - ,- ! " - .# - - . " * ".
46
1 +), &
- *
- - ". C HF (::2D% " .- ;'' 9'' . " ( #- -.# ('O .-- - # . # " "-$# $ - . . -. " % " electromagnetic suspension C)*D . " - #- . # .-- #-? # # - " . > " " % " ('
(9 .. . .-- " " " - ) # - "- / - C)". (::9D% " ) )* "- " . " # - - -. " " % " - $ - .
- # " % -. #- # " . " % -" " " > > " (:5' . -? # - #- " "" " . " - - . " .H " ;'' . " ( .-- - " - " "
-- - # " / . " CPopular Science (::3D% - #- " .- " # " .-- - " . % " - - . F- . F#
- " . " - #- " .- # " .. - . %
2.11 AEROSPACE ENGINEERING PROBLEMS " " - " - 343 1- 1 " ". - . " ".% * " " - - " $ . # " 6-meter " -
" B" % " - 2( " :9 H % " (:55 - .- " KK GG .% " 343 " # #- (:2: -" " " # - - .-- " .- # C (::2D% . - # (:5: "
- " "
&%(( ),+ ) ) A )), A +, !)*
47
" - "
" " - 3;3 . > .- # " +F % " " - . "" F> - " .H " "-" . .% " $ " -
" - - F
- " # " " - " $ . - " . " # " # " . -- -.% - # " - -% 7" "
" health and usage monitoring C1*D " # . - % " #
.0
1 - . )- = +
- .
1* "
- . ""- $B" - . # . - . % .. - "
- .- # # . % - $B" - . " # . " # -- - ""- - "-
C -- - (::&D% " %% - Aircraft Structural Integrity Program C +D "
- $ -% " - - " #- .- . . #- B" . B # " # .
"% ,-$. - . $ - . . . " - . " . . " " " "
#- . # >- - % . . - . - > - -% " " #- .- " . . . - $ - #
" . - " - . % 7" " . -- ""$
. % 7" # - -
. . - % - " .-- - " . - C - (::&D% "
48
1 +), &
- *
FIGURE 2.27. ". -- " - . - . B" - . %
. -$. "-" . -- -- "" . - .H - . .- # . " C - (::&D% . . $ --
% " " " "" - # - . " #-$ - $ #- C % &%&3N ". -- (::&D% .- . .
"" -- B
%
2.12 NEW MATERIALS FOR THE AEROSPACE INDUSTRY * " . -- - ,+ . - . ". -#- " % " -- "-
" % , " # # F# . > % 1 -# "/ " " . "
- # " - . . " "G % #- " F#
"/ - # -$
&%(& )7 * ), ! , 1) ),+ ) ,
49
" - " . " "
C (&%('%&D% " # "" " $ $" ,+ . - - - - # . - #- " - "" % " " " ,+ . . . ""- #-% " " . ,+ "
-- " " . . - " .-% ,+ . - - - - - " " .- . - - -$# % " - - " - .
-- " " " " % . . . # " -. #- ,+ . - "
. -> " . -G " .
% " . " " - " - - % ,+ # - C- F-.$ D . -- .#
- F# . % " "
- F# -- " . ? " " ,+ - C % &%&5D . .#. #-
" >-- "
. .% - .#. - - " " - C (::9N 6 (::9D / - " " "
- F# - " - >
% =
- - # - %
FIGURE 2.28. ).#. F#
- " .-$ - ,+ %
50
1 +), &
- *
2.13 FIBER OPTIC MONITORING OF AIRCRAFT " - $. - -
- . # " . % 1 - # " . .. - .- - > .- . -> - " " % - - " " -- - # . % " "- ?#- .# ""- - - " - #F . ,% " -- " "-
-- $ "" #H #- # - - % $ F#
- . - - . . - . ..- . % " . . - - -- ""$ "
- - . . " - " > % - " , - #-- - $- -
" . " / - -- . # "
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" .#- "-- -- " " / $ . " # .% " " - # . .. - " # " " . -- # -#- " - " " . " # -% - - " " " .
FIGURE 2.29. ". -- " #-
- F#
- . .%
&%(4 ), + * , A ,,
51
. . " . -G -
/ . > " -% * " . -. # . "$ . # - > "-- "% " -- " # -? # . -F . " # " " . " -$. " - . . % - - - - . - # > .-
- -- . -#- - " # % #- " > . # - - # . . - "-" % , - " - . # . . F- "" - # . " "-" F - % " . - - .- " . % " . - # " -
. " B" " % " #- " - #- . " " . " #
? - . " # -- .% " > " -- . -- -- . - . - # . . % " " -- " - " " - . - # # " -. #-% -- . -. . " " " - # - "" " C7 et al. (::&D% " %% #. " .# - " .- " - (:3' "
" KK. GG " " + H % . " . " - F " " - .- - . - C*? et al. (:55N * (:5:N 7 (::'D% (::9 . - # , " -#. #- .-- - . - -- KK* " %GG - . - " - B " - " " " - - # . # ? - C % (%4D% " ." . B" - " - " . " ." . - ."- -. " . " - . " - . %
1 +),
4
!"
3.1 BACKGROUND AND OVERVIEW ..# " - - " - - " . % )- - . M .
# " # M . " " $ . % " - S
" F ? " -- . # # . "" ".- # " % " " " . > .- .-- C(' (9 .D - " -% " - . ::O " . " .% - " - -- - C(' (' .D H " " .# - " - . " .
- -- C % 4%(D% Electronics " . - - %% - " " # F- ? " . . " # . " B
- - F-% .- " . photonics " . - " " .-- -"% " . # - " " . $ ?% )- > " . # . % +" > - 0 - " -"E " . light -- . - $ . " -" C - D " " # " ". % " . - - . . . .. " -" " - -"% " #
KK-"GG " # . - .$ % " " ". -" - # " > " -
% >. - " , . .. .. - " "-
-" . C % 4%&D% " 52
4%(
- - -" " " "
F# . - " - " "
" . - " . - . " % " F laser (:2' # " *. .-- - # " - # -" . "-- B" -. #. -" " " " . C % 4%4D% -" " " - -" -
- F# ? " - (:2' C? (:2(D " - $- -$- F# C .- .
- F# - " . .# "- "
% " " " - "- " > - " . . $# $ . -- . " $ " " " . "" #"
- F# % . # . -
- F# .# C % 4%9D% " . - - " " . -" " .% 7 -- " analog modulation% digital modulation . -" - . # " # - " /% " "
- - - .. % Spectral modulation " . " -" " -"% " -- - " " -" - " - . " " " . % " -" - . - / C-- " - " ? " ?D " .$ # " / " " " /% " . frequency modulation% -- " - $ C# " > "
- F# D " - " - F- " " -" # . " . polarization modulation% -" "
- F# $ .. .. " # . " .% " -- ". # " -. " .
- -% " #
"-- "
- F# KK - . GG " . . . % " - # " " F#
4%(
" -"
FIGURE 3.3. CD ". # - % C#D - ,# - % *.% . " " 6 % ,% % L A%% - % % KKAtomic Light LasersGG - +#-" (:23% %
56
1 +), 4 !"
FIGURE 3.4. --. - $-
- F# - .. %
" #/ "
- F# % " - . / " # "
-"$ % 7 " " - ? -" > - . % -- -
" - -" #
- F# " " .
B %
3.2 ELECTROMAGNETIC RADIATION )- . . "
$ " " . - .
" . % 7 " -- > " - - # . # " % " # # " G - . " - " . -" .$ - . % " 6. - *>-- " .$(55' # - . # / " . " .- / " # " . C-" " (::(D% " / # -- - . " . . - F- CED . F- CBD% " /
4%& )!),* A ) ,
57
FIGURE 3.5. ." . . # -" -
- F# %
. % 7" - " " # . #H - F- E; " - -> "
C# " - - " D " F-% " > " - W; # " - F- . " - . s( s& C % 4%2D #
s& W
eEds:
4:( s(
58
1 +), 4 !"
FIGURE 3.6. )- F- # - # - " - - %
1 " " - V(& ; # s( s& # " - " F- " %%
s& Eds:
4:& V(& s(
" W
eV(& :
4:4
" " " - " # > . electron volts C eVD " ( L " / # - -- " " - - ( -% - " . # " - /. ." " " # # # . % " #
. " /? . - " . " /? - . C % 4%3D% $ /. ." " .-- - . frequency n hn; " h Planck's constant " " - 2:2&2 (' 4; 6 % " . " - - > -- " . CU( ; U& ; U4 ; . . .D % 4%3% - # # . - . " . / . n " F " - n DU=h;
4:;
" DU " # . " .%
4%& )!),* A ) ,
59
FIGURE 3.7. ) -- " . . >. - " - %
" - - " - # # > " "" # .# - " # "
. - . C % 4%5D% " > - -- " - " ground C- D U( ; # " " .- .
" - . / n C % 4%('D # .
" -> " - # " . -% .- . -- # ;%&% " . .. -" " # " " F-. " -" #-# % " - > "" # -- . - . . " - . $ % "
" -" # " electromagnetic wave equation C-" " (::(D "" C%% .D " . H& F
( @& F ; c& @t&
4:9
" c " - -" F
E B " " - " . F- # " "
60
1 +), 4 !"
FIGURE 3.8. )> # - # " # -" "
-" " #/ " . -> %
/ % -" " E B " .0 CEx ; Ey ; Ez D CBx ; By ; Bz D -
" " . $ - F C4%9D "-- E -- " " . % . " . C%% - /D - - . - " z$ " E$®eld - )/% C4%9D " .
E; x; y; z; t E
x; yei
kz
ot
E
x; ye
i
kz ot
;
4:2
" E
x; y; " amplitude " " -
" E$F- " - " x@y - k &p=l " " free-space propagation constant o &pn; " angular frequency
4%& )!),* A ) ,
61
l " free- space wavelength " % " . " " )/% C4%2D " complex conjugate Cc.cD " F .% " - " . " E
x; y zN % 4%:% " . F- B; " " . . - > " *>--G / / # - "
" E$®eld
.. C-" " (::(D% "
" E$®eld . F> "
" " linearly polarized wave C % 4%('D% 7 "-- - " -"
-
- F# > . . ->
- ? %
FIGURE 3.9. - . " . - . - " z$ 0 CD " E$F- - "
C#D " " E$ B$F- " - %
62
1 +), 4 !"
FIGURE 3.10. > E$F- - - - ? -"%
" - " # " -" / -$ . # # # # " - - )/% C4%2D " / % " - k& o& =c& :
4:3
" " .
- . - " - " general propagation constant b; "" " . -
% " " - " " )/% C4%2D # " "- - " E$®eld% " "
- - " . E
x; y; z; t Re : E
x; yei
bz
ot
E
x; y fbz
otg;
4:5
" electromagnetic wave equation . - "" " velocity of light u " . H& F
( @& F : u& @t&
4::
# C4%5D C4%:D - b& o& =u& ;
4:('
"" " index of refraction " . - n c=u;
4:((
.# C4%3D " C4%('D " b nk:
4:(&
"-- - b . / " "
-" -
- F# % b # " " " "
% " z; " phase " . - z ' # f bz: " " &p; .- - " " E$®eld
63
4%& )!),* A ) ,
- z ' C % 4%((D %% E
f &mp E
f " m '; (; &; . . . : - " - . . > . " " -" C- " '%( .D gamma rays " " " - -" C ('' m.D " % . - " -"
- F# "-- # " M F-- (%4 (%9 m. " $ -" ""
- F# " " # . " C " 9 F-- % 9%(9D% " "" / -" -- " #- - " . - " E$ F-% " " . " -"$ -- " % -"
- " / E$F- C 7 - (:39D " . intensity I C D F " -" B - "
" % " # " # # " - I e' chE Ei
7. & :
4:(4
" hE Ei . " " E$F- " . -> H . - ." - " " " # -- ." " " . > .% " . $ - - . " )/% C4%2D h &
oti h&
oti (& ; "- h
ot
oti ': " " / C4%5D - C4%(4D " . I (& e' cE&'
7. & ;
4:(;
" " E' " .$ . -$ " % . .- / -" " radiance J
w; j C # "D "" F " B - $ . - - H %% J
w; j
( d& + w dSdO
7.
&
( ;
4:(9
" P " C7D # " w " - . " .- " j " - " .- d " -. - - "" "
-
64
1 +), 4 !"
FIGURE 3.11. , . -" %
% 4%((% " " - " # " " " " -" " .
p=&
&p J
w; j wdO
7. & :
4:(2 I w' j'
J
w; j J; I pJ: 7 - " spectral radiance J
n
dJ dn
7.
&
(
1? ( ;
4:(3
" spectral irradiance I
n
dI dn
7.
&
1? ( :
4:(3#
" . # " - # " -" . / #" CHzD% " )/% C4%3D - " $ -" l; " / n; -" " " " / nl c
. ( :
4:(5
3.3 BIREFRINGENCE AND POLARIZATION 7" - . " . " . - .
$ " z$ " "
.. C
"
D # # # )/% C4%2D% " -"
" z$ "
4%4
65
,) , A) ) +! ,T
birefringent medium " " > > # " #/- "
- " " E$F-% " -- % 4%(& " nx 6 ny ; " - " Ex Ey . " -" % " " -" # # / " # " "
" " E$F- . % " # > " . matrix equation i
bx z otdx ~ t Re Ex
z; t Re Exo e i
b z td ;
4:(: E
z; y Ey
z; t Eyo e y " " . - " -" Eo
Exo; eidx ; Eyo; eidy ; o;
4:&'
d x ; dy bx ; by Exo ; Eyo
" phases " E$field z ' t '; " propagation constants ::; bj nj k
"
j x; y; " positive field amplitudes:
7 . - C4%(:D # " total phase retardation CKK "GG " f
z; t bx z
ot dx ;
"" -- Exo f
z; t Ex
z; t ; Eyo f
z; t d
z Ey
z; t
4:&(
4:&&
FIGURE 3.12. .. . " x$ y$ . " E$F-%
66
1 +), 4 !"
" d
z
by
bx z dy
dx
4:&4
" . " differential phase% " KK
GG .. by bx b
4:&;
Exo ff
z; tg Ex
z; t ; Ey
z; t Eyo ff
z; t dg
4:&9
" " differential phase " - d dy
dx
4:&2
ot dx :
4:&3
" phase f
z; t bz
" polarization angle y F " " y$ x$ .
" E$F- C % 4%(4D Ey
z; t ( ;
4:&5 y
z; t Re Ex
z; t "" # C4%&&D " . Eyo ff
z; t dg ( : y
z; t Exo ff
z; tg
FIGURE 3.13. ! - - ? -" # # " - ? - y%
4:&:
4%4
,) , A) ) +! ,T
67
)/ C4%&:D " . " state of polarization C+D %% " - # " - ? - y " " f: fy
z; tg g d
d ff
z; tg;
4:4'
" " g Eyo =Exo :
4:4(
" . .. . - ? -" . linearly polarized light C!+!D% " " d mp
m '; (; &; . . .:
4:4&
y g
mp
(m g;
4:44
" .
" - ? - y; # z t "
- " E$F- F>% " " - - ? " " . C % 4%:D% linear polarizer .
- F- " . - " . -" " E$F- --- " . > " # F- .N % 4%(;% "
- - ? - - - ? -" " - " . > " - ? " -" .% " % 4%(9 " " - - ? - . " Ex . $ " -" "- " " ? - - ? #- " .$ " . % " .# polarizer . . - dichroic sheet " -- " # # " . E$F- - . > C-" " (::(D -" - - ?
- F# " - E$F- . - " - . % - . " . " E$F- " # " - " E$F- # # "
% " - ? . circularly polarized light C+!D " &m ( d p
m '; (; &; . . .
4:4; & g (;
::;
Eyo Exo :
68
1 +), 4 !"
FIGURE 3.14. !"$#- - ? %
FIGURE 3.15. , " E$F- " . - - - - ? -"%
69
4%; +),+ 1),) ) ), ),) )
" C4%4'D # . fy
z; tg (:''
f
z; t;
"" " . y
z; t
f
z; t
4:49
" +! " E$F- C F # yD "
" - f
z; t: " d
&m (p=& " y
z; t f
z; t " left$+! "" - E # # " -" C % 4%(9D% - $ - d
&m (p=& " y
z; t f
z; t; " right$+! "" - E; # # %
3.4 SUPERPOSITION, COHERENCE, AND INTERFERENCE 7" . " . -" - "
% " principle of superposition -- . " - " - . / C4%9D " " E$F- C B$ F-D # .. " C -D % " -"
- " / " E$ F- )/% C4%(4D - " " " . # " . " . " " - % " " . " E$F- " " " - -- " .% " . interference% - - - ? -" " " . - ?$ - y; . . " . -
" " " - " A B % 4%(2% " E$F- . " " .
z; t # > " . E(
z; t E(' E&
z; t E&'
b( ds b& ds
ot d( ot d& ;
4:42
4:43
70
1 +), 4 !"
" . .. angular frequency o; " E(' ; E&' b( ; b&
" E$field amplitudes; " propagation constants
.. . :
7 " " spatial phase retardation
ba ds da ; fa
4:45
"
> # " " - " " C
N % 4%(2% )/% C4%45D a ( &% 7 - " temporal phase retardation ot " " . t
. " . # " -" - # " "
" % 7 - d( d& " initial phases " " - # - z ' t ': " " # . . C4%(4D %% I e' chjE( E& j& i:
4:4:
" # > " . I e' chfE('
f(
ot E&'
f&
otg& i;
4:;'
"" > # . I e' chE&(' &
f( ot E&&' &
f& ot &E(' E&'
f( ot
f& oti:
FIGURE 3.16. . . " # -" - " .
" %
4%; +),+ 1),) ) ), ),) )
71
7 " - . - . " " . - . - I e' chE&(' f f( ot f( otg& i
4:;(
6 " KK# - .GG " - KK# - "%GG - " " # " " . #
# # " " .% 7 " F " - " "
b( ds
4:;& f(
b& ds d;
4:;4
d d(
d& ;
4:;;
f&
"
" # " - " " -"% " -" coherent " . - " - " # " % " d "
. "" f( f& . # . . " . )/% C4%;(D %% I e' cE&(' & f( h & oti E&(' & f( h& oti :
4:;9
- " . h & oti h& oti (& h ot oti ':
4:;2
"" . " . )/% C4%;9D ? " . - " " # interference equation p
4:;3 I I( I& & I( I& f;
" I( I& " " - # # C % 4%(3D " " -" - #
" %% Ia (& e' E&ao
a (; &:
4:;5
72
1 +), 4 !"
FIGURE 3.17. /- %
7 " " # " -" " H " . " - % " > - interference term "
- f; " f
b( ds
b& ds d
4:;:
" differential phase # " -"% - " " . " - . -% " " /- . - C%% E(' E&' D coherent " " - ? " f p; % 4%(3% " . " KK . -GG destructive interference% " - # #- " . " " " f ': 1 . - constructive interference % " . KK " GG
# " " d .% " " C . " " " D " " " - " " %
3.5 PARTIAL COHERENCE AND COHERENCE LENGTH " KK " GG d " - " - " . . > " "
4%9 + , ! 1),) ) 1),) ) !) A1
73
%% I I( I& : " > . incoherence coherence - " .-
partial coherence% # "
" - -$ / -" # # E E' fkzg % 4%(5 " k &p=l; l " $ -"% " - " - / . n; " % 4%(5# " nl c; " c # " $ - " % " " " z; " - - -" . " % -" . " " #
. " -- " " .- > - " . -- " " . -" -- - .# " . - % " ".-- -- % 4%(:% - . - " " . . -> " . - #" " # . C-" " (::(N % 4%&'D% #-" " - " # " #" -" . - " Fourier transform theory% -"
FIGURE 3.18. CD * " . -" C#D - .%
74
1 +), 4 !"
FIGURE 3.19. -- " " E$F- -" # . %
" . - . # # f
t " / .
( 1 f
teiot dt;
4:9' s
o p &p 1
# " Fourier transform f
t; " " inverse Fourier transform s
o f
t C - (:39D0
( 1 s
oe iot do:
4:9( f
t p &p 1
FIGURE 3.20. ". -- " E$F- - " . ->
" . - #" " -"% " . . -> " . - " " .%
75
4%9 + , ! 1),) ) 1),) ) !) A1
" f
t # -" . . - - / oc ; F tc C % 4%&(D% " f
t e
ioc t
f
t '
t=& < t < t=&;
4:9&
-- " .:
" . f
t - " frequency distribution0 ( s
o p &p
tc =&
e
i
o oc t
tc =&
r &
o oc tc =& : dt p
o oc
4:94
" . " / # " " % 4%&(#% " power spectrum S
o; " F # - . " / " . C - (:39D %% S
o js
oj&
& &
o p
o
oc tc =&
oc &
;
4:9;
FIGURE 3.21. CD -" F . - C#D . CD .% . - A%,% C(:39D KKIntroduction to Modern OpticsGG & % 3&%
76
1 +), 4 !"
" % 4%&(% 7 " " . " .>.. - o oc
? o oc &p=tc : *
" " # " F ..
-. " " effective width " . Do &p=tc :
4:99
-" " " " - " F >. - --
" . - . " " coherence time -" /- " #" %% tc (=Dn:
4:92
7 " . " -" Dl; " C4%(5D0 tc
l& : cDl
4:93
" coherence length " # ctc ; " " . `c
l& ; Dl
4:95
7 " - " # " . " " -- # " -"% -"$.
-" (%99 m. " -" 9' . `c ;5 m.% -$. -
(%99 m. " #" (' *1? " " -" # #-N `c 4' .%
3.6 HIGH-COHERENCE INTERFEROMETERS * . - " . - -" . $ " . - " % " . - # . -" >. - " #. - " - .# " " " > " % " -- "
#-
Michelson interferometer % 4%&&% --. #. -" . . # #- - # " " #. - C D #. " % 4%&4% #. - . *( "- " #.
" - . *&% " # $ B -" " .$ # " #. - " # . B :' : " ""$ " . - . " . -" - / o: " E$F- "
4%2 1A1$1),) ) ), ),*)),
77
FIGURE 3.22. -
*"- . % - " -" " " " . --- -%
B . *( # " #. - # E( E(' fbL(
ot d( g;
4:9:
" E$F- " B . *& # " #. - # E& E&' fbL&
ot d& g:
4:2'
L( L& " - # " F #. . " #. - " . # -% " " . " " .. # " #. C " " #. - D " % " " - " L( L& ; d& d( " .# " " .. . -% " # >. -
" . # - # " .-- . C " " -" " -"D " % 4%&&% L& 6 L( " d& 6 d( ; " . -" . % . " -" # " " " E "" L& L( DL; " DL d& d ( t : c
78
1 +), 4 !"
FIGURE 3.23. CD L " " . - " " L% C#D -
#- " L%
" " - C D " " B . *& " . " - " " B . *( " retarded time DL=c: " -- - DL=c " " coherence time t ; " " d
d& d( . $ % -- " " " . " DL # *"- . " 9'=9' #. - % 4%&;% " # # " )/ C4%;3D . F " - " %% I
I' ( u~ f; &
4:2(
" I' " intensity " #. # E$F- "- # " #. - f " phase difference # C4%;:D% " KK#-GG " " . F # " - u~
I.> I. ; I.> I.
4:2&
4%3 *!+ ,
79
" I.> I. " .>.. ... - " % " - # " " . C4%2(D # " 9'=9' " E$F- " " # " #. - % - " .. . .. b( b& b;
f bDL: *"- . " 9'=9' #. - # . " " -" ct ; -" # . $ " visibility " DL C % 4%&;#D% $ F coherence length KK" - " . " "" " #-
'%&9%GG " / . KK7" "
" -" " f p; " ""$ " u~ (; " . " . - I ' $ C4%2&DSGG " . - " " - # " "
" -" " " " B " . % -- " " - " -" - - # # " " #. - # " " % " " " " - " " destructive interference
-" - " " C " " -"D " constructive interference " -" - # " C -- " -" # " D% " F " # - " " -" # - absorbing medium - "% -" " " " - #
" " " " -" B% " " " " . "" " > %
3.7 MULTIPASS FABRY±PEROT INTERFEROMETER . . " - --. # . L - " " .- "
- -" C % 4%&;D% - - " . B F (''O " . -" -- # . " " " Fabry±Perot interferometer C +D% " . .- B #- . " -" - # " " " " . # " . % " $ . - " " . - F# $
- # % 7 . " - . " . -" - / o . - E'
. " " F
80
1 +), 4 !"
FIGURE 3.24. -- " .- - B " - . # @+ . %
. " . % " amplitude re¯ection coef®cients " . # r( r& ; -% " E$®eld >- z; . t; # > " . E
z; t E' ei
bz
ot
;
4:24
" " propagation constant b nk
&pn : l
4:2;
" z$> " " " .- " " F . % . - " C4%24D . -F # . " .. . - " " E$®eld " " . z L; # " > E
L E' eibL :
4:29
t& " transmission coef®cient " . " " " E$F- . B t& E' eibL r& E' eibL ; -% " - -" E$F- . " " " . " . " E$F- . . " ; . . . " " " %% E E' t& eibL ( r( r& e&ibL r&( r&& e;ibL :
4:22
" F " # " - . E
E' t& eibL : ( r( r& e&ibL
4:23
81
4%3 *!+ ,
" . I ; # . )/% C4%23D C4%(4D -- -# 0 I (& e' cjET j& I'
& R&
(
a
R; bL:
4:25
1 " Airy function a
R; bL
( ; ( f &
bL
4:2:
" coef®cient of ®nesse f
;R
(
R&
:
4:3'
> C4%25D I' " total intensity " + N T&
jt& j& R
r( r& " transmission re¯ection coef®cients $ -% " " .#- . $ . ".-- -- % 4%&9 " + .- F- -" " " % " #" # @+ -- # . - " 9 " - % " " a
R; bL (:' " bL mp: " - -- F " FPI resonant frequencies mc ;
4:3( nm &nL " m % !" . " " " + . " - " " > B F # " " " % " -
FIGURE 3.25. " - $ .-? . . # @+ . b -
- l%
82
1 +), 4 !"
FIGURE 3.26. . " " - $ .-? B . # @+ . %
.#- . . C1" TH (:3;D " . % 4%&2% + / " " .-? B . # # . " .-? B . " -- - .".% . " " % 4%&2%
3.8 LOW-COHERENCE INTERFEROMETRY -" " . .
" "" " " - " . " " - " -" " light-emitting diode C!)D% .. " - !) - > " - % " . " - " . . ." # - " . - - " " - " -" " " -"N 4%9% " # . "" " . " " coherence length " -" " " ? " . % " " *"- . 4%2 . " " -" B . *( *& - -- " " " .#% " - / . "
#- " DL < `c ;
4:3&
" L( L& "
- " - B *( *& -N DL L( L& N `c " source coherence length% " " F- - KK " #-. " - GG - $ " .$ %
4%5 !7$1),) ) ), ),*),
83
" - " "
" --. #-
Michelson interferometer " # # C- " D C % 4%&3D% " L( L& `c ; "
# " " " . *& .-- C -" " -"D% " " " # 4%2 " " . # # " % 1
- *& " " L( L& ; " -- # " " - " " " -" " C % 4%&5D% " " -" 9' m. " ##- . " " " ." " 9 m. # # -
" *& " " % L( " . C " 9 m.D "
" L( - .% L( ( . " /- strain resolution 9 me C. D% 7 "-- - " low-coherence interferometry - # . . -> F " .# F#
# @ + *"- . % 7 $
FIGURE 3.27. ". -- " -. " -
*"- . > # - $ " -" %
84
1 +), 4 !"
FIGURE 3.28. )> - - $ " . . -
" $ %
- $ " . % - -" -? coherence wavepacket -" `c " " - - " % " " #-
*"- . - " " p; H
" -" # # " #. - % " #. " # B . " . .# # " #. - " " p( p& ; "
" C % 4%&5D% " "
- C " `c D " -- # # "
" % - - " -- - - " " - " . %% L( L& : " " . *( C%% L( D " . - *& " " - L& "" .>.. # % . . L& /
/ % #- " - $ " . " . . % " # . -" # Fizeau interferometer - " charge coupled detector CD " " " .# #.% 7 " " . # " " % 4%&:% 1 " " " " p p# ; " - " " " *"- . % 7 " " " - .
. - -- ".%
" " " " . DL; > " " -" " -" `c : " " # p( p& ; #
4%5 !7$1),) ) ), ),*),
85
p#( p#& ; "" DL; ." " " " " " ` ; "" - #
# " # " ? . % % 4%&:# " " " " " " " ? . " % ? . .- # @+ . > " " - " " . - " % % 4%&:# " " ? . - H " . " " DL; # *& *( " *"- . % /-
# # " " " p#& "
FIGURE 3.29. CD ! " . ? - -$. . .% C#D -- ? . " $
%
86
1 +), 4 !"
B . " " ? . #/- . #- " " " H - " p#( " - .% " " . "
- " ? . - " - " " " *"- . " # > .- - " - - " " - . / " " %
3.9 RADIATION COUPLING BETWEEN OPTICAL FIBERS "-- " 9 -" - - -
- F# " -- # . " - - # " "
- F# % " " "" > " " - . - " -" # " " # F # - B " # # " ""$ - $> C % 4%4'D% -" " " " -" F " " "
- F# . .". / " > $-- evanescent E$®eld
> # " " - % - "
F# - " E$F- - - -" . " % "
KK -GG " "
- F# # " - "
- # >" # " " -
- % " -- #
# . " 9 " >" -" #
F# - " " .# - direction couplers% 7" . " #- " " # " E$F- " -" # " " "
- F#
FIGURE 3.30. F. -" # - B " @- $ %
4%: , +! A )7)) + ! ),
87
C % 4%4(D% 7 # " - -" #
F# - / % 7 "
- . " . -" " z$ F " "
- F# % 7 " )/% C4%2D " " E$F- " -" # > " . E
z; t E
'; 'ei
bz
ot
::
4:34
" # " . E aeibz ;
4:3;
. % 7 - ? " " / # " " " - " . - - / " # " >- " E$F- - -
- F# %% dE ibE: dz
4:39
" / " -
- F# " - " > # " E$F- z " "%
FIGURE 3.31. E$F- # " - -
- F# " " F# # " F- " -" # " " F
- F# %
88
1 +), 4 !"
# - " " "
- F# # " F- - " " >"
- % 7 " " . - -- # coupling term )/% C4%39D "
- F# "
- " E$F- " "#
- F# %% dE( ib( E( iC(& E& dz dE& iC&( E( ib& E& ; dz
4:32
4:33
" C(& C&( " coupling coef®cients% " F " " " " " E$F- .
- F# " " "
- F# C! (:52D% 7 . " > " E$F- " F
- F# # " > E( a( eib( z
4:35
E& a& eib& z ;
4:3:
" " " amplitude coef®cients a( a&
z: # )/% C4%35D C4%3:D " )/% C4%32D C4%33D - - F $ - / " amplitude coef®cients " . da(
z iC(& a&
zeiDbz dz da&
z iC&( a(
ze iDbz ; dz
4:5'
4:5(
" " " phase mismatch Db b&
b( ;
4:5&
" " " a(
- a& % . " " . - " -" " F
- F# a(
' " -" "
- F# " - a&
' '; " " )/% C4%5'D C4%5(D # - # . - " . a(
z p( eig( z
4:54
89
4%: , +! A )7)) + ! ),
a&
z p& eig& z :
4:5;
" - )/% C4%5'D C4%5(D - " - ig( p( eig( z iC(& p& ei
g& Dbz
4:59
ig& p& eig& z iC&( p( ei
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4:52
Dbz
:
p( p& # z; " g& g(
Db:
4:53
" . )/% C4%59D # C4%52D # " - g& g( C(& C&( :
4:55
.# )/% C4%53D " C4%55D - / / g( ; " - s & Db Db C& ;
4:5: g( & & " C& C(& C&( :
4::'
s & Db C& ; g &
4::(
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" " amplitude coef®cients " -" "
- F# " . a&
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4::&
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z &ip& e
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4::4
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- F# 0 &p iDb gz :
4::; a(
z & eiDbz=& g gz C&( &
90
1 +), 4 !"
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4::9
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- F# 0 iDb iDbz=& gz gz
4::2 a(
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-
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4::5 P(
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phase-matched b( b& b;
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4:('(
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4:('4
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- >" # " F# S 7" "
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- F# " .SU " - " :'
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- F# % " :' " . " " F- "
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91
FIGURE 3.32. !" >" # -
- F# % ! " $ " # " E$F- "
- F# " >"%
F
- F# # " F- #- "
- F# -- # (5' " " " - F- C:' - :' D " - % " " "$." F- # " F
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3.10 BRAGG GRATING REFLECTION " >. - . - " -" . " > % " Bragg gratings # " $ " - # " -" "
92
1 +), 4 !"
. " .- " # # " . ! "
V$ . - - -% 7 "-- " ; " - - . # - . " 2 " .
- F# . - . % " " # # B -" " " C " ."D F% " B - . $ # " "
-" " - . " -" # " % 7" " . - . " . -"
" z$ " " "" " > " - % 4%44 # # " - n
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4:(';
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4:('9
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4:('2
" o " - / C4%('2D " - . / " .. C4%:D " $. . " Helmholtz wave equation0 d& E
z dz&
o& E
z: u&
4:('3
FIGURE 3.33. >- " > " F# %
4%('
93
, AA A, A ,) !)
" C4%('D C4%(&D # C4%(';D n; " / d& E
z dz&
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7 . - - C4%(('D " . E
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94
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4:((3
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4:((5
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:
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:
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95
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FIGURE 3.34. # -" E$F- . - - F# %
" C4%(;D " # -. b( . "
- P' ; "
- " # " " 0 P#
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b&
P' x& "& fkLA g
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:
4:(&;
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kLA P#
'=P' ;
4:(&9
# " . R
kLA "
b&
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p& &
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" fkLA g
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&
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#:
4:(&2
. C4%((:D " k - x&
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4:(&3
96
1 +), 4 !"
" - .-- -" -. . " Bragg wavelength l ; " -" " phase-matched condition F b p;
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4:(&5
7 " " phase-matched condition - " . > " Bragg wavelength %% l &n' L:
4:(&:
" "$."
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4:(4'
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4:(4(
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kLA "& fkLA g;
4:(4&
" kLA . " grating strength% " " B " " . % 4%49 " B . % 4%42% " B . # . . C4%(&2D% - " " B . # C4%(4&D " -"% .-- -$
FIGURE 3.35. L " B F# " " " " %
4%('
97
, AA A, A ,) !)
FIGURE 3.36. # B - " "% . ) % KK # A GG J. Lightwave Technology 15 (&33@(&53 # )))%
. . " -" > C4%(&2D " k - # " .% - -. . " -" x&
b& p& & ; C4%((:D k # . . % 7 " $ s
b& p& & x& ; kW ik ;p& ;p&
4:(44
" B . " -" # # " > R
kWLA "
b&
x&
p& &
& fkWLA g &
fkWLA g
;p& kW& x&
&
fkWLA g
#:
4:(4;
B . C. -$ -D ($..$- . " " kLA (:2; C) (::3D % 4%43% / " - " B - " -" " -- " " B % " F -- R
kWLA " kLA p:
4:(49
98
1 +), 4 !"
FIGURE 3.37. . " - > .- B % . ) % KK # A GG J. Lightwave Technology 15 (&33@(&53 # )))%
C4%('9D C4%((&D " C4%(44D ? " " $ -" " F -- b
&pn' ; l Dl
4:(42
" Dl " -" -. . " -" " -- C % 4%45D )/% C4%(49D
>. # " > s & & pLA Dl Dn p;
4:(43 L l &n' . Dl l ; " . #- HF % " - # " half-spectral width " B . s & & L Dn :
4:(45 Dl l LA &n' 7 " " " " - " .-- . - " > . >% C4%(4(D C4%(4&D - " > Dn LA :
4:(4: R.>
kLA "& p L &n'
4%('
, AA A, A ,) !)
99
FIGURE 3.38. # B . " - . . " " . %
7 # " - B / " # - . " # " > . - " - # - . " . >% 7 " $ . # #- " # " -- ""$ B % . . " - " B C #- et al. (::9D LA & :
4:(;' R.>
l ; LA " ':5pDn l >. - "-- . "
- F# "" " -- . #-0 n' (:9; Dn (' ; ; L ':9(3 m. LA 9 ..% " l &n' L (:99 m. Dn LA 95:5% R.> "& p &n' L s & & L Dn ':(25 .: Dl l LA &n'
1 +),
;
!"
4.1 INTRODUCTION " " # " -" " -" " . #- F#
- . % - -" # " " broadband and incoherent " " narrowband and coherent% -" #-# -- " F $ "- . - # # " % 7 "- . "0 .-- / --
# "
- - .# % " # " . " $ "" - " #- # #- .-- ? "" - % " .
. > #- . - C D .%
4.2 LIGHT GENERATION AND GAIN MEDIA )- . -" " F . # " - . > . - " .% " - > # " .- -- - " " % " " -- - . " - .
" .% " " . - C- -D % " .- # "-.@ - - - # - #-" # - " % 7" F - .# " - " ? - . - . - % * 100
101
;%& !A1 A) ), A *)
" - -- # " / F
? . > " # - " . "
" . "" " " " . C % ;%(D% " " - - " -" " KK . %GG 7 " 4 " -" " " -" # # # - . # " . " " . C % 4%5D% " . . # . # -# ) " /. " . " " /-# . / " > " # -" .% " " . KK.- . GG " " . #- " - % " . laser " .0 KK-" . -F # .- . %GG Stimulated emission " > . .. F- "
/ " % " induces " . " > -- # " - " " . " " - " .- " C % ;%&D% . " - . " " " .- " " " . frequency direction, phase " " % 7" . .- . . " -
. -F " -" . . > " "" " " - " C % ;%4D% "
- "
- # Np Nq - " " " > " population inversion n Np
Nq > ';
;:(
" " n " inverted population density " % . - . C%% . - --D% - -
- / " . -F " F-% .. "" -" " " . KKGG KKGG .. ""- $/-# . " F % " ./-# . " .- . - " " . " - C % ;%4D% " .- /-# . " "
- " "" - " # # " Boltzmann distribution Np Nq e
DU=kT
;
;:&
102
1 +), ; !"
FIGURE 4.1. CD . -" . " . - "
% C#D )- " - $ . - - "
- - F- -- " . " > ". " - / F ? ".%
;%& !A1 A) ), A *)
103
FIGURE 4.2. " . 0 CD # C#D . CD .- . %
" DU Up Uq " # " "" - k (:45'3 (' &4 6< ( " Boltzmann constant T " . g
nz;
;:((
" % ;%;% gain medium # . - . -- " "" " ""
-
# % " "
- C % ;%;D% " " # - *. # -" . B" -.
- " # - % 4%4% " -- % -- # # -
" B" -. # # # - " $ 4 " # - "" . " - " # # C % ;%9D% # " High Reflectivity End Mirror
Output Mirror
Laser Beam
Ruby Crystal Laser Medium
Helical Flashlamp
Ruby Crystal Excited by Flashlamp
Rapid Lattice Relaxation
Flashlamp Light
Band of Transitions Pumped by Flashlamp
Laser State Laser Beam
Ground State
Flashlamp Photons
FIGURE 4.5. ". -- # - . F %
;%4 , @+), L ! ),
107
" " - " # - # . " > " -
- # " " - % -- -" " " " . ". " F - " . F- # ?#- " $
- " # > "
- % * - " - " ." - " " "-
- " - " - C. (:52D% " > population inversion %% Cn > 'D " .$ " F- # F
- % " # -- -" "
/
. " - -- # . -F " - >" " . -F # #- " # "% " - gain medium - " . " --- " "
- "
" - -" #. C % ;%2D% -- " . - - " " .. Fabry±Perot cavity $ . " 4% " -" " .. "
. - - -" " % " -"
" " " .. " -- # . -F " B # " " " .. . -F % " . . " -" #-- F " - % 7 "-- " " " > % " - # " " " . . -> . . - " . - " " Fabry±Perot cavity C +D F % " " -
-- # - ;%3%
4.3 FABRY±PEROT CAVITY LASERS - # . " " " - -- "
" - . " > # " -" - " " " .. . " - " B . " - % " -B " + . " - G threshold condition " -
" #. " . - . - " . .. " + C % ;%2D% ""- B
- . " . - B F r(
" .. " z ' - B -
108
1 +), ; !"
FIGURE 4.6. # @+ - ". -- .- - B %
. " . - B F r& " " " .. z L% 7 . monochromatic plane wave " " x y
" z$ % " " " " -" - E$F-% . " . - " 4%& " I e' cE& ;
;:(&
"" . " " " E$F- > . F c . " E$®eld gain coef®cient " . )/% C;%((D C;%(&D - " c
n g
n=&:
;:(4
109
;%4 , @+), L ! ),
7 " complex propagation constanta # " " " "
- > # " E$F- / n
" " " .. a
n b
n ic
n:
;:(;
. " " E$F- . - " - z ' E' e iot " z L E
n; L E' ei
aL
ot
:
;:(9
" . - e iot .. " - F - % " -" " " " .. -- B -- .% " " -" E$F- / CnD " . " " " . # r& E' eiaL ;
E
n; Lt(
(
;:(2
. - " # " . % ;%2% "
" -" E$F- / CnD " B E
n; Lr( r& E' eiaL :
;:(3
" " - . " " " " .. B " " . " " " " .. " . % " " " " . # E
n; Lt&
(
r& r( r& E' e4iaL :
;:(5
" -- - . . . -- " . E$F- . " . E$F- / n " . E
n; L
(
r& E' eiaL r( r& E' e4iaL r( r& & E' e9iaL . . . :
;:(:
" F " # " . - . E
n; L
(
r( r& E' e&iaL < (%
r&
(
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nL ; r( r& E' e&ia
nL
;:&'
110
1 +), ; !"
" " - -- " . " " " -- B output mirror% - . )/% C;%&'D )/% C;%(&D " . -# " . I
n I' T
z
n f( G
ng&
( ; ;G
n & fb
nLg ( f( G
ng&
;:&(
" I
n " spectral intensity C - D 7. & 1? ( I' " - -- T " . F " -- B . z
n " line pro®le function " - G
n " double pass gain # G
n r( r& > &g
nL;
;:&&
b
n "
F # )/% C4%('D %% b
n &pnn=c:
;:&4
- " line pro®le function z
n > " ##-
.- . / n - " " - / n' ; % ;%3 z
ndn " ##- . # " / -
n; dn% " " .. " " # @+ - " # .-$ . " % ;%5% " - F- " -
" .# - . # " # @+ % " " - -
"
FIGURE 4.7. ! F- " - %
111
;%4 , @+), L ! ),
FIGURE 4.8. . -F . . A . - - H #- " - " " -% " - .
# . . . " -
" " " - - --
"% " " KK GG - C#D CD " " - -" C#D ." - " CD% . KKLasersGG % )% .
(:52 % ;;2%
> # " gain-modi®ed line pro®le " " " > C;%&(D% " zW n; G
n
z
n ; f( G
ng&
;:&;
" gain curve " .. " " . - - n
" " line center frequency n' ; " - G
n " - " - zW n; G
n % - " "-.@ - " # / ." - " ':( .% . " . - # > 9' .% " " C;%&(D ( O
n; G ; ;G
n & fb
nLg ( f( G
ng&
;:&9
. " gain-modi®ed Airy function
" # @+ .# - - % ;%5% 7 " 4 % 4%&3 " normalized Airy function B . # + " KK#GG ..%
112
1 +), ; !"
" # .. " frequency separation " # @ + . " % 4%&3 # " - Dn
c : &nL
;:&2
" " -"- " .. # F
" - " - $- B " . " % ! . - - " - $- / > - " . -> - . " -
% " .. . . - " " . "
- " double pass gain
" % /
. C;%&(D " " output intensity " - # . - " .- - F
(
G
n ';
& b
nL ':
;:&3
;:&5
" C;%&3D C;%&5D # " .
G r( r& e&gL (;
;:&:
b
nm L mp;
;:4'
" m " F " Fabry±Perot cavity resonance mode% " cavity loss per pass ( ( ;
;:4( g - & r( r& > " F . - " " - population inversion density nc # / " " gain per pass " - / n' )/% C;%:D . H /- " loss per pass %%
gc L nc bhncLz
n' g; "" - # > " . g nc s
n' L
;:4&
;:44
" " stimulated emission cross-section " - / s
n' bhnz
n' c:
;:4;
113
;%4 , @+), L ! ),
)/ C;%4&D -- " - # #- " -$ " " - g L . # - /- " -$ - " " " . g% )/ C;%44D " / . . " critical value " inverted population density nc % " C;%4'D " Fabry±Perot mode frequencies nm
mc ; &nL
;:49
. " 4 )/% C4%3(D% .. - / " " .. . " " - " " " - - "
- % 7" " " -
" / " " " - $- # @+ . % " ".-- -- % ;%: " " - - " / " " - ." " - - . C D " + % " B " -" " " -
" " .. -" ." " L " "- -" " ..% "
- " .- " / " " F- "" / . - " " / " " F- % . " -. " . "
FIGURE 4.9. " - - F- " # @+ - - " - - " . "" " > " - %
114
1 +), ; !"
- " - " # " - % " . " # . " . " - -- - # @+ . -- " . - " " % " # % ;%(' semiconductor laser injection current . (99 (32 . % " H " ." . " " - " - # " " - " . (
('' # " " (32 . ('' . " (99 . % " - - #
FIGURE 4.10. -$. - . " .-. . -F $ . A - #H H % " " " - - " % . . %)% KKLasersGG C(:52D%
% ;2;%
;%4 , @+), L ! ),
115
FIGURE 4.11. * "
- - - . " - " - # .-- B " - %
#% - " # - B ""
- . - " # .-- B$ #- - . H % " " KK. "
GG -- . " . - . ." # " - . % ;%((% " -- # . . " - . - F#
% - gain saturation " -. " " - . " " - F - # )/% C;%&(D% "- " C;%&:D C;%4'D " necessary suf®cient - % A - $
. " -. . -#- " - " . "
- % )" . " " #
. " "" " - -#- " - #. " " " .- . % " " " . " # > " . " -. - " # -. # "
. %
116
1 +), ; !"
4.4 SEMICONDUCTOR RADIATION SOURCES .# " F#
% # -F .# " / . " " # # " . #- # F% " - / . " " . . "
% !" " broadband narrowband
pulsed continuous . % "-- " - "
"
- F# -. " -" " "- " .. " ." . - C D " . " " - # # # # - % " " # . > " " " F "
- F# - # F
/ signal-to-noise ratio " " % !- " # F # coherent incoherent% 7 "-- - " . " " " F
" " # -- --% - semiconductor -" " F#
- # " .-- " - / . "" . . ""- #- . $ - . # % . # -F -- 0 (% !" . C!)D &% -. C!D 4% ! C!D # " - . " # " . . -% semiconductor -- . " - " electrical conductivity " - # " - metals insulators% " $ . - - # F- " # - .
" - . % )- " . .. " . . - " - CD "-
- " - . # / . C@LD -. " #-% - - -" -- .-- $" ? " # # > . ." > .- -
. - " - #-- -- % > .-
# . . # . - gallium arsenide CA D indium phosphide C+D " . "" /- "
;%; )* , , ,)
117
% " C " - D . . > .- " - . - - A + " #
" # C % ;%(&D% #
- " energy bandgaps p±n junctions electron±hole recombination% 7 - " " - " - . > /? " F -- % 4%3% 7" - .# " . > - " -- . # C % ;%(4D% " . - # - F #% " . " valence conduction #% - . # - - > " -- F
" .. " .% " " /. # - ""- - -? % 4%3% " " " conduction CD # - " " - . " " " - "
- - F-% )- " - " - # " $ L$#% " forbidden energy zone . . " bandgap energy CEg D% . # " .-- quanta of radiation C"nD > - . " L$#
" $#% - - - . " . -
% Insulator . - - - " - # C>4 LD
-- - - - # " .-- > . " L$# " $# " . - >"# > .- - - -
FIGURE 4.12. - " . - " %
118
1 +), ; !"
C % ;%(;D% 7 ." " " - " L$#
. " B
- - F- #
" - - " . -% " " / . . " /? . -% - " Pauli exclusion principle " KK - " . /. %GG - . "
. " . /. % " " - -- " .G . F-- " "- " - . " L$ #% -- " " L$# C%% F-- " - D " - . % 7" " L$# - > " .-- " $ # " # . . " . " KK" -GG - #" " L$# - . % " #
. - % F-- # > " - . #- " " . #- . " " -- " . #- #H " % " .-- . " . #- " - " - " " . #- # - -- " " - # - " " - " "
" . #- C - D% # ." " " " - - . #- " . . % .- . " C" -D " L$# " - " .
- - F- "
" " -
FIGURE 4.13. # " . -- - . " KK GG KK-GG # - . . " .%
;%; )* , , ,)
119
- % " / # " > - " - " " - . -- # " -% 7" . " > - #- " " -
# " L$# electron±hole recombination " > - " . C % ;%(9D% " / " - n . - . # " bandgap energy CEg D %% hn Eg ;
;:42
. "" " -" l " - $" - .# $ # l hc=E :
;:43
FIGURE 4.14. . " . F . - -
.- - . . -%
120
1 +), ; !"
metal " # .-- . - " .-- # > - " " $# " #- . " B
- - F- " " "" - " " .- % ;%(;% Semiconductor . - C- ..D -- # " > . .- - - > " $# - -- - - % " " # - # #-
. . -%
" donor -. # - " $# . ntype . - " .H % " # " . " - electron af®nity " " " . #- . " - " " $#%
" acceptor -. C . " "" electron af®nity " " " .D . - . " L$# " - C % ;%(2D . p$ . " .H % " . #- - " p$ . - " " - " n$ . - minority carriers%
- . .# p$ n$ . - % " -" " - @" - .# -
- " bandgap energy )/% C;%43D F -" / . .$ . - " "
" % " -" . " " - @" - .#
" .
" -
FIGURE 4.15. )- " - .# - - " . " hn /- " # E%
121
;%9 !A1$)* A ) TABLE 4.1 +
- !) ! * - * A+ - A + -A = A +
CLD
7-" Cm.D
&%&; &%': (%;& (%44 '%4;
'%99 '%9: '%53 '%:4 4%2'
A--.@+" " -..@ A--.@ .@+" " .@
(%;@(%2
'%33@'%53
-..@A--.@
'%3@(%(
(%('@(%23
.@A--.@ $+" $
"
- # % . . . - . . L -. " #- # " " -" -" F / .% " .
$ - . . - -" . " " #- ;%(%
4.5 LIGHT-EMITTING DIODES - -" " . # . -" # p±n junction " p$ n$ . - H " " % " p±n H . #
" . # homojunction% p±n H . " . . - . heterojunction% -" " " - . - -" F " . - . . -" # . . " H$ %
p±n H . . " - . " n$ . - . " "" -
p$ . - "- . " - . " p$ . - " n$ . -% " " - -? CD " p$ . - -? C $ D " n$ . -% " depletion layer "
- C# D # " p$ n$ . - " H F . " " B " .H
122
1 +), ; !"
" p±n H C % ;%(3D% - # " " H -- " KK - - GG # . -. -- -
. #- .H " .
" #- . -
% forward bias voltage C -
- " p$ " H D "
.
- " H " # - ? " - " - . " n$ p$ . - . " H .# -" . C % ;%(5D% " " # " light-emitting diode C!)D "
. -" . "" - H % "" H - .# - " - " . C" p±n H D " " .# " " . C % ;%(5D% " !)
- P' # > " . C-" " (::(D P' ZhnJ=e;
;:45
" J " !) H n " . / -" e " - " % Z " - F - " F -" " F " "" " -" . " " " %
!) -- .-- H > ('' . % 1 "-- - - "
- " -$.
- F# %
FIGURE 4.16. ". -- n$ p$ . . -% . $ . -
- " # " - " . " - p$ . -%
;%9 !A1$)* A )
123
FIGURE 4.17. ". " . p n H 0 CD p$ n$ . -N C#D # # " H .N CD " " - ? . . " " - 7N CD " # " H % . KKOptoelectronics, An IntroductionGG & ) 6% 7- Q 6% % % 1 + 1-- - (:5: % 2&%
" - # . . # !) " " . " % - " spectral width Dl 7 C -" "- .>.. ""D !) " # C-" " (::(D% " . )/% C;%43D " " - " -" " . . !) " .% " -- " A + !) . % ;%(: CA (:5;D% - " # ('' . #- !)
# (:9 m.% " " !) " - " - # B % Low coherence -- # " -- . " . - . C " ('D "- - #- # B " >
- - C " 9D% - )/% C;%43D "
124
1 +), ; !"
FIGURE 4.18. "
- # - p H "
- C " #D " " - C " - #D " " " p n H % " " - " -"$. %
. -" !) " # " . . - . " p±n H N %% lm.
(:&; : Eg L
;:4:
!) surface-emitting edge-emitting C % ;%&'D% )>. - - #- !) " " % ;%(:% " surface-emitting !) !) . -"
. . " " --- " - " p±n H % " .
- $. " Burrus diode C -" (:55@:3D ".-- -- % ;%&(% " " - .-.
- F# - # butt coupled " " F# "- - " > % ;%&(% " " -- " . -" # -- - . " H - # - .- " -" C( &OD - "
- F# % " $F- . $. !) .- " Lambertian source " " -" y " y " - . " . - .-% Microlenses " - . " F -" -
- F# C -" (:55@:3N A (:5;D% ) " " . - F- - ." -" . !) " .-- -$.
- F# C (:59D%
;%9 !A1$)* A )
125
FIGURE 4.19. )>. - . !) . 0 CD - . $
A N C#D . A + !) " " - . % . 7 % C(:5&D KK+ . ,-#- 1" , A +=+ 1 !) " (%(9@(9 m. 7-" , GG ))) J. Quantum Electronics, QE 18 425@43;%
edge-emitting !) )!) " " -"$ - " # - . - " # - > % " double heterojunction F C-" " (::(D % ;%&& F # " " B " -" . " . F #- - .
- - .
- F# " !)% " H - - > .# " " stripegeometry " -"$ - . optical waveguide " F " -" " total internal re¯ection " # " % ;%&&% . - light guiding "
- F# -- # " 9%
126
1 +), ; !"
FIGURE 4.20. ". -- CD C#D . -"$. % . ! )%6% C(::5D KK ! !" .. + GG Laser World 34C(D% # +-- " . %
- )!) - - - - . " ""$/- # - .
" B ---
" )!)% " . " #- B C4'OD " "" > " . . - Cn 4:2 A n 4:9 +D%
- " -" )!) . -- " . " - # ('' m. . 4'' m. " B "
" " "
- $ B % " -
" -" " #H " H
;%9 !A1$)* A )
127
FIGURE 4.21. ""$ $. % . %*% % KKOptical SourcesKK , " . . KKOptical Fiber Sensors, Principles and ComponentsGG (:55 -" C) D% " 1 %
* % "" % .%
% ;%&4% " -- " # - " "- "- " -"$ ?
" - " "" . % - F. " -" " - " H # " H - - > % " "- " - " #. " C - " H -D # 4' % " - " #. " H - # - (&' % ;%&4% " - - - .# " " .-- . " . " )!) -- F - - -$.
- F# % superluminescent diode C!D . - # # " )!) # ampli®ed spontaneous emission C )D% " # " " frustrated laser " H #
" "
- .- . F " . #- " H % 1 - #
" B . # " % " . -" " " " "
- B # .
128
1 +), ; !"
FIGURE 4.22. + - F # $. #- " $ H %
" -"$ .-- - " % / -
- F# ! " / #- # B % " . - ! - "
- - B #-" % ,- "/ " " # C -.D --$
- " -- # -. " #-. C % ;%&;D% " " - -" " - . !G " - !)
;%2 )* , ! ), )
129
FIGURE 4.23. ". $. !) # " - %
- " % " - " . ! -- . -
- -$ .
- F# % " ! # ; 9 . " . )!)% % ;%&;
- 5 .7 - " " " %
4.6 SEMICONDUCTOR LASER DIODES ! . . . . - .- !) " " - diode junction devices " " surface$ edge-emitting% " - # !) ! " " -" . .
FIGURE 4.24. !" " "
- . -. . - !$42' % + . # -. !%
130
1 +), ; !"
" . -- . spontaneous emission "- " " - stimulated emission " #- " % L -- -- - F#
- . . "-- " !% " - # " " vertical cavity surface-emitting lasers CL)!D > - -
. " - (::' . " " . -- - F#
- . C6-- et al. (::& #D% . " " - ! > .- .-- F - . - . # " - - / .% " . " ""
- . . # .- - "" # " "- " (4% " / " # " -
" . - - # " peak gain coef®cient Cg D " injection carrier concentration CDnD C-" " (::(D g z
Dn Dn
( ;
;:;'
" z Dn . " " -- -.0 7" Dn '; g z " z " absorption coef®cient " . . - " absence of carrier injection% 7" Dn Dn ; g 'N " Dn " transparency injected carrier concentration " " - Dn "" . H #- # % " . - % ;%&9 "
" - Dn " " H " .. " . absorber " - -" ampli®er " % " (''O " H J " " " " J
ewdLDn ; t
;:;(
" t " lifetime C- D e " charge " w; L; d " width length thickness " % ;%&2% )/ C;%;(D . -- "
;%2 )* , ! ), )
131
FIGURE 4.25. ! "
- g
Dn - " > H " Dn " .# n %
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173
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- " " " . % " F . % 3%9' " " # # " . &5 % - - $ # - - " > - F- " # " . . $ C " et al. (::3#D% " -"@. $ -"@ F !+A " L (22 m. -" L 4:29 . . # &:9 . ( &:3 . me ( -N % 3%9(% " thermal cross-sensitivity " !+A " . &9 (&9 " % " - % 3%9& " " - " . B % -" " !+A # " -- > . -$ . CL et al. (::2D " - . % " - " ""- #- -$ " - "
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321
FIGURE 7.50. )> .- . A -" C " % 3%;:D
- . % . V *%$A% ".#- 6%$!% , !% 6%+% KK - # A $ GG Proc. SPIE 2292 ;'3@;(40 # ! V +- ,%+% C)%D%
"
- F# . % " -. - - " #-. "
" / % 1 " .- " . . !+A . F- -" .- -> - " % "
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. $ " " - # . . #- F#
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% ---- et al. C(::9D . " " - " .-
" - " > # @+ - # -. ( me ( % " . -" # - " B F# " " .- F# " " .- > F " - " " " #- C % 3%94D% $ - " " $. -$ F "" . ". > " " # - $. " " % " . " - " ,+ . - " - " " " .- > F " - F - " ,+%
322
1 +), 3 # .
FIGURE 7.51. CD .-- " -" " . " -- !+A " . % " " " . " . " 100 " . % C#D ! " -" " . " -- !+A " % " " " " . " .% . " et al% C(::3#D KK. $ ! $+ A , > GG SPIE 3042 &9%
3%5 , @)*+), ,) ,$) L
323
FIGURE 7.52. . " - . $ !+A " . " C&9 125 D " - X C' mED C9'' mED C('' mEDY% . " et al% C(::3#D KK. $ ! $+ A , > GG SPIE 3042 &9%
FIGURE 7.53. ". . $ ) + # " " " .- > F ." " " " % . ---- % - A% C(::4D KK7" !" . *. # $ GG Optics Letters 18 35@5'%
7.8 STRAIN±TEMPERATURE CROSS-SENSITIVITY . - . " " # . -- " # " " $
" . $
F "
- " . % " . - - . - " #
324
1 +), 3 # .
" - . - ." . F-% " - # )/% C3%;D # - -- # " - . " - - > % - - De DT " . - # #- "" $ . " > % " > . - - # " strain and temperature cross-sensitivity term # " " . cross-sensitivity coef®cient Ce;T " .- " De DT %% Dz! Se De ST DT Ce;T DeDT: z!
3:39
" et al. C(::'D L et al. C(::'D " " "
- F# " $ . -#- - - . $ > % 1 " - # " " $$ F
- " -" "
- F# " - $-" . - - # B # - . > " " % " et al. C(::'D " . " Ce;T (' 5 ( me ( m ( % . . - . $ " # # $
- F# 244 23' . # * et al. C(::3D% " C(::4D " " " . - ? $.
- F# -- $ F# . - #- $ " # $
- F# %
1 +),
5
-- * -
8.1 INTRODUCTION -#- - F#
- "
# --
- "" " " .# " % - " " # - " " # - " - - - % "
- F# " " " - % "
" " .H B " - - " -- " "
- F# " " " % - . # " # " - # .#
- F# " ,+ . $ " . -% " # stress concentration " .#
- F# " " " G . . . . " " G " - % 7"
- F# # " - " " - .# " - - " # % " " >. " " " " # F#
- F #
- - > - . " ..- B " " G " #-%
8.2 INSTALLATION OF FIBER OPTIC STRUCTURAL SENSORS -- F#
. -" - " " # " - " # 4 . "" 325
326
1 +), 5
-- * -
FIGURE 8.1. - F# " +B>* "$ #%
% "
- F# # . > # " " " # " +B>* C % 5%(D% 7 "-- " . ®ber optic cable . jacketed " --
- F# % *-- et al. C(::3D " -
- B F# - ## " 8$
- F# % " ®ber optic ribbon cable - F #
- " .# F#
/ - " . - . % "
- - " B ## "" - . . -> " - .% " - # - " " - " " % " - . F#
- % "
"" " -- 0 .- ,+ . . -% " F -- % #- " " " " # - # " " - " " # . -
#-%
5%& !! ), + ,, ! ) ,
327
8.2.1 Surface installation on metal structures " "/ # F#
.- " - -- " . - " " " - " % - " - " > .- . . -
- # . - " - " - " " " - . -
" .% #- " F#
" " - # . .-- .- - " # - - - C % 5%&D% " / # - A . ElectroPhotonics Corporation ) + . Roctest% 7" F#
# . - . " - - - " # -
FIGURE 8.2. 7-#- F#
% " . )- +" - %
328
1 +), 5
-- * -
# 5 cm A A % 5%4% B"# B B 2 mm "- - " # - C % 5%4#D% " -- - " " " > " # . - - % " " - # " > .-- # 4 6 mm - " H # - C % 5%4D% .
" " # - . " # 1 mm " "# A A . > > . " B"$ # C % 5%4D% " F#
" - " # - " > . - " " A A " "
FIGURE 8.3. ". -- " > # " > --
F#
% KK-- , # GG (::5% " . %
5%& !! ), + ,, ! ) ,
329
H F> " .-- " B"$ # C % 5%4D% " " # "
- F# " sensor should never be touched - " I H J " - # "-% -- " .
--
- " #- # . > # " H "
- F# " .-% " > - . " -- " > -- % " - - # > " - . " # " . #- ## " " # " " - ## - C % 5%4 D%
8.2.2 Installation on or within concrete structures " existing concrete structures # . .
" " -- "
- F# - " % " - >. - " . .- # ,+ " *#" , - + . - . - ,+ "#- " " C % 5%;D% " -# > . #- - . " F#
" C % 5%9D " " - #- - % " " " - # .
" " " " "- % $ .- " # # C -- % 5%4D " - " # -?% " .# " ,+ -. > . - " - F #
- " -
- # #% &; "
- --
% " -. " " F#
" # " " > -% . " . ###- " . - " > # " -.
" % "
- F# " - # - --- " " H
- " -. " . #. " % ! /
- F# #- . . " -. ? - " # -% " F#
#- " - - # #- " . . . - % " # # -- -- .-- F .. " .-- B " H - % >. - F#
- . " . " - C* et al. (::5D " % 5%2% " - - f 1 12g
- F# $
330
1 +), 5
-- * - Electrical Cables
Concrete Column
Optoelectronic Demodulation Boxes FBG Sensor Embedded within Protective Patch
Protected Optical Fiber Cable
FRP Rehabilitation and Strengthening Wrap
FBG Sensor Embedded within FRP Wrap
FIGURE 8.4. -- ." -- F#
> % C(D " .# " ,+ " # " % C&D " .# " "#- "$ ,+ %
- " " .% " # # "
- nitrile rubber sealant butyl rubber sheets % 5%4 % " . -- --
" -- - # . " - # .> " - % . - . - - # " " F#
C % 5%3D% #- #- #- " .
# -- . " " " " " " - # % # ,+ . - -- -- - -
" % " & : .# # " - # " +, - . " $
% " .
" " - - % &%9#
5%& !! ), + ,, ! ) ,
331
FIGURE 8.5. . F#
" -.%
-% * "
- F# # " ,+
/ .$ .
/ " - - . - "
"
> # " " " % " - ,+ " " #
% " . # . .
" . " % 1
" - . " # F# " - " % #- #- - " F#
" -
" " # .>.. - - % " -- " # .- . " . - " ." . #- " " - "" 9%2% # - " "
# " "- - # " ".
.- " # .- " - # -- #-% " F#
#- - -. " . "
332
1 +), 5
-- * -
FIGURE 8.6. #
. " - .
" - # # -- " %
C % 5%5D% " - metal housing - #
" > -"
- F# " " " # " % 5%: :%4: :%;'% "
- F# #- " " - "- . . / " . % 7" . . . " " "
- F# # . -- metal tube with two end ¯anges # " " C % 5%('D%
" ElectroPhotonics Corporation Roctest " " % " 0 # - " .> - # / "" " .>% " " instrumented briquettes
- - -#- " " - " - " $ .- % "-- " (' . . Smartec ? - " > " -
et al. C(::2D -
long gauge F#
.
5%& !! ), + ,, ! ) ,
333
FIGURE 8.7. - # . " # F#
-- " % - - " " #- ## " " "
- F# #- - " %
" . " .- . - % " . " # " " .
% " . . F#
-# " . #- ."
#- - -- - - # .
" - % . "
- - " F#
-- # -" #- " # " - #-. " " " % * - . -- -#- . $ " . "#
-0 KK-- , # GG% Prefabrication " ®ber optic structural monitoring . remote communications -- ##- # " " " - " . -- $ % " ,+ " $ . " - " : " % 5%(( #
334 1 +), 5 -- * -
FIGURE 8.8. - F#
. # " " ." - . % "
- F# #- - " ." " - " %
5%& !! ), + ,, ! ) ,
335
FIGURE 8.9. )>. - " - .- " " " F#
#- " % " " "
F# #- C D " % " . %
FIGURE 8.10. -- F#
.#$ " # % " . )- +" - %
# + * )*+ " F
" " . - - ) % )$ -- - " " . " F#
" - # -. "#- . . $ " %
336
1 +), 5
-- * -
FIGURE 8.11. ,+ " . # # + * . -" " . - % " . %
8.2.3 Installation within FRP laminated structures -- F#
- " FRP laminated structures
#
"" ..? " . "
. " " # % " .#
- F# " # #-" " " - . " - -$ ".% " > " "
- F# - " # . . " . . / .% " ingress=egress points - # #-" . . #- " " . " - -.% "
- F# > ,+ " " " " .. # " # " % .. "
- F# " " " . # " " - " ,+ - - "
- F# F-- . . " " "
- F# -% " ,+ . " > " optical ®ber pigtail . . strain relief . # % - # "
%
5%& !! ), + ,, ! ) ,
337
FIGURE 8.12. CD ! .#
- F# . " " . F# = > - " - 1$ % C#D # ,+ - - "
- " " .#
- F# . % , . ! - *% * ,%*% C(::&D KK. . . . * - " ).# # GG J Composite Engineering 2 934@9:2 " . . )- %
" . F# = > - " % 2%;# >. - ,+ " . " - 2D$ .#
- F# CA-
et al. (::'D% " "
- F# .# " - - " " % 5%(& . " " " " " -- " -" " $ # . " -" " % 5%(&# C! - * (::&D% * ,+ -. . .# - . . . - F " " " " . > . - # . -/$- . . " $-% "
- F# - " # .# - "
- " . " " " " " . - - "
338
1 +), 5
-- * -
% " F# /- -
- - . > . - -- # - " .# " F# . " - " > - F# # # %
8.3 FIBER OPTIC SENSOR INTEGRATION WITHIN FRP MATERIALS " " " -- - " F#
- " .# " ,+ . . - .#
/ 0 (i)
do embedded optical ®ber sensors degrade the performance and=or life of the host structure, (ii) can the far-®eld host strain be accurately determined from a measurement of the strain within the optical ®ber, (iii) how effective is the strain transfer from host to sensor, especially when steep strain pro®les are being measured.
"-- "
"
- F# - - " . % " F " # -0
- F# " " "
- " -
F# % " F / -- --% .#
- F# 0 CD microscopic stress concentrations . "" -- -- " " - " " -- " - CD macroscopic damage " -- - " G - %
" B "
.#
- F# " "
continuum mechanics% )- " " .-- " - - - - " " .. " " - # F # ." " C % 5%(4D% " -- stress concentration - " . -% 7 % &%4' "
- F# .# " ,+ . . - --- " H F# - - - " " " . -% " .." " " # " . - stress concentration -% " " .# F#
-- . - - F -" " # . " "
- F# # " . " . % C(::9D "
5%4 ), + ) , )A, 71 ,+ * ), !
339
FIGURE 8.13. ". F " " " - -$- -% . 6%% % KK - # [ . *"GG KKFiber Optic Smart StructuresGG ) 6% C)%D # (::9 7- % , # . 6 " 7- %
. obtrusivity " > " # " - #- f g " " .#
- F# % Obtrusivity - " -# " # . . " " >% " F . / # - ."- . -$ -
- F# " - $# # et al. C(:53D " # - " " -. . . - " .#
F# % ? et al. C(:5:D " # . " F Moire interferometric study " F- "
- F# .# "= > -. % " " - " > lenticular resin-rich " .
- F# .# . angle " indigenous reinforcing ®bers% " resin eyes " .. " - -- % 5%(; "" -
" notation # # " " / " - " ,+ " .#
- F# % ? et al. C(:5:D - " ? " " $ " ?
340
1 +), 5
-- * -
FIGURE 8.14. CD - F# .# --- - - - % C#D - F# .# ;9 - - - . % CD - F# .#
- " - - - - " . - %
5%4 ), + ) , )A, 71 ,+ * ), !
341
" " / H -. # F- " % " . " - -$ . # Moire interferometry
-
'& =:'& = f:'g=:'& ='& :'& ='& = f:'g='& =:'& >- $ . # " "
- F# ." - #$ f%% . g " - - F- " "
- F# 90 " F# " " - " ".% " # " .# - " F % " 902 . - 90 % ) " " * R /
" "
- F# " " - - F-% .- # -" et al. C(:5:D " $ . " - ? et al. C(:5:D . " % # -" et al. C(:5:D - " . > "" "
- " " "
- F# =" . :'; ='; = f:'g='; =:'; "$ > -.% "
. > . . " - " . -. . --
F# =-. . . .% -
F# ?$ " " strain perturbations
.#
- F# # . F . " 100 mm - 5%9% " > . F . # " " - . C(::2D%
8.3.1 Obtrusivity of embedded ®ber optic structural sensors " " obtrusivity " .# F#
-# # " basic opto-thermo-mechanical / C3%49D - ? -"% " # . " . " / " .-? " " sensor optical path length # 0 DzL eF( zL
n&' F e p ( fp p(& g
eF& eF4 ; & ( (& & ((
5:(
" eF( " axial strain eF& ; eF4 " transverse components of strain "
- F# % " " . " . " " strain in the optical ®ber is the same as that in the hostN %% H H
eF( ; eF& ; eF4
eH ( ; e& ; e4 ;
5:&
342
1 +), 5
-- * -
- " rarely " " # " "
- F# " . " - - " " / . $F- f #g -% C(::9D " #H " .# - "/ - " . . F0 KK" "
- F# / . " $ F- - " " GG% - " " " +! " " " host far-®eld strain " . ." # "
- F# " " # % " # " -
" " # " . - -- -$ . . " " "
- F# " C et al. (::'D% " " # #- . " #H C 1-" (::(N (::&N *" (::4N "" obtrusivity B " calibration .# F#
# > .-- . " "
*"$T" . " " F#
" . - % " phase sensitivity " F0 Sf
Df ; Le(
5:4
" Df " " " " . -" L >- e( % " >- " F#
# " . " " " " > . generalized plane strain " 1-direction . >% " - " > . " " " " - - # 1-" C(::(D % 5%(9% " .- 1 C(:35D . - " =" . " " zero coupling of host transverse strain "
- F# " " axial strain in the ®ber matches that of the host% /- " " - % 5%(9 " Butter and Hocker model # " " ? - -% " " " - " F " " . - 1 G . - # " " optical ®ber stiffness is 10-times greater than that of the host material "
- F# - -- " " . -% - " " "
-
5%; 1) !) ) ), + A
343
FIGURE 8.15. L " . " " " F# " > .- CnD 1 . - CsD 1- . - CuD%
F# .# " ,+ . . - -- " " H F# % -" " " - F F#
" " #
- /-- - intrinsic Fabry±Perot ®ber Bragg grating % 1 F#
$ . # $ " " ) + ! ) insensitive to transverse strain /- - # - - % " ." . " " 1 . - # # / C3%;(D%
8.4 THE INFLUENCE OF FIBER OPTIC COATINGS " " - " B optical ®ber coatings " =" " "
344
1 +), 5
-- * -
" .#
- F# % " - # # " - .. " - F# . # > . " - " -
.
surface microcracks . % " .
- - -. " -
- ." " - . "" . " " . % C " et al. (::3D # " thermoset polyimide coatings . 300 C . " 100 C -
- % + C(::&D C(::4D " " #H
.#
- F# . - ". - " F- - -
" . - C % 5%(2D% " "
- F# " - "
% % 5%(3 " " " "
- F# # " " " . - " optical ®ber coating - - " - % - " " " " " " "
- F# " " " . - " - " " " " . >% - " " " " . > " " " " C+ (::&D% " >- - " > "
- F# .>.. " " C % 5%(3#D C(::4D% C(::&D " "
- F#
- . "
"
" > ."-- KK
.-GG " .#
- F# % "
.? " # " . . ." fobtrusiveg - --
FIGURE 8.16. ". " . - >. " B . " .#
- F# % . 6%% % KK" , - ! - # . GG J. Intell. Mater. Syst. & Structures 4 &2'@&3( " . +#-" % % # (::4%
5%; 1) !) ) ), + A
345
FIGURE 8.17. CD L " F# " " " " F# C - F# D - " " " . -% C#D L " F# " " " F#
- - " " . - G . -% CD . + %)% C(::&D KK! - " # GG Smart Materials and Structures J 1 93@2& " . +" +#-" !% C#D . 6%% % KK - # = . *"GG Fiber Optic Smart Structures )% C)%D " . . " . +#-" % % # (::9%
. " . " " % . - - "" - "
- F# . -
$ > B # thermal expansion mismatches " . % C(::&D "
346
1 +), 5
-- * -
" ? -- . " .#
- F# #- "
- F# .# --- " F# - >- % >. - " -- C % 5%(5D "
.- coating radius to ®ber radius = " coating design space "$ > " " - - + G '%4% Design space F # " coating Young's modulus f .-? # G . -g - coating Poisson's ratio% " .- " % 5%(5D "
.# " - -. " " " . . - >- - % . , C(::&D " optimal coating concept -- .#
- F# # #- " - . et al. C(::( (::(#D% " optimal coating parameter curves ..? " " " - % 5%(:% " - > " " coating's Young modulus Yc " host's transverse modulus YtH % " " ? - > " " coating radius rc "
FIGURE 8.18. L "
- F# G . - C .-? # " - -D " G + - " " " "
- F# % . 6%% % KK - # = . *"GG% 0 Fiber Optic Smart Structures ) 6% # (::9 7- $ % , # . 6 " 7- %
5%; 1) !) ) ), + A
347
FIGURE 8.19. L "
- F# G . - .-? # " " G . - " " " "
- F# -
- F# " G . -%
" optical ®ber radius rF % )" "
- F# G * - YF " " " G . - YtH % " # . - " .
. " " - " % % 5%&' " " -- " maximum principal stress " . > . - angular position " .# ®ber=host interface " coating to matrix stiffness " " " #H transverse tensile loading% " " -
.. # " -
-- minimum .>.. - % . et al. C(::( (::(#D C(::'D C(::&D . -- C(::&D " #- .- - -- #- " . " $ - . % , # C(::(D - " # stress concentration " " weak optical ®ber coating materials weak optical ®ber=coating
coating=host interfaces - " formation of cracks -
348
1 +), 5
-- * -
FIGURE 8.20. L " .>.. - " " . > . - " - # " F# =" " " . > C G . -D% . . A% +% -- ,%% C(::&D KK -- * - * ."- L # $, . GG Proc IUMTAM Conf. &3@2( # L - A.#1%
--% " cracks - / - - - transverse cracking - ,+ . . - " % "
- micro-fractographic analysis " " .#
- F# % % 5%&( -- -
# " - -.
- F# % " .$ " " " " " . - -- " - ,+ . % 1 " ,+ -$ # " - % + et al. C(::( (::&D - " optical ®ber coatings transverse tensile longitudinal shear loading
" % " " " " thinner coating enhances strain transfer . " " " " " " " . >% " " " " " " " . > thicker coatings # shear strain transfer% " > .- F . " " - " " F- - " . " .#
F# . " # obtrusivity enhancing sensor performance C7 et al. (:55 (::&N + (::&N . et al. (::( (::(# (::4N " et al. (::( , # (::&D%
5%; 1) !) ) ), + A
349
FIGURE 8.21. ". -- - # - -.
- F# % . , # %%6% ,% C(::(D *"- +
. * - ).# # Fiber Optic Smart Structures and Skins IV SPIE 1588 4&2@4;(%
-" " " "" " " #
-- " acrylate coatings
# -
" " .- #- - composite curing temperatures% " .-- -- % 5%&&# "" " .F epoxy-acrylate coated 125 mm
- F# '=:' ,+ " -.% /
" " - " .- " - " resin-pocket " . "
F# G " - " H - % % 5%&& "
- F# .# --- " - - X:'='Y ,+ " -.% - - " - $ . " "
- F# " ..- B " . -%
8.4.1 Sensor=host bond and strain transfer # C .#D ? -- . >" " # - " F# -- % 5%&4%
350
1 +), 5
-- * -
FIGURE 8.22. * " .#
- F# % CD
- F# .# --- " - - # F# % C#D -$
- F# .# " - " - - # F# % , . ,%
%1% , # %6% KK . * - * " " ).# # GG International Journal of Optoelectronics 5 4:3@;'4 # (::'% , " .$ - Q +#-" % " 0[[% -$% .
5%; 1) !) ) ), + A
351
FIGURE 8.23. ". " " # .#
- F# - - . . " # " %
1" " - " " # -
. -" " .--. " " - . " " " F# % " #
. #- - shear stress ti
z " axial stress sFz
z "
- F# %% pr&F sFz
z &prF ti Dz pr&F fsFz
z DsFz
zg;
5:;
352
1 +), 5
-- * -
% 5%&4#% "" 0 ti
rF dsFz
z ; & dz
5:9
." " shear stress " # "
F# -
- " gradient of the axial stress " "
- F# % " creep bond degradation -. " ? -- " G " - " ? % 5%&4% #- " / # $-" " " . bond mechanics C* et al. (::3D% " bond # " sensor and its host " -. strain measurements% -
# " " " " "
- F# " -- . " - # -% et al. C(:5: (::(D " adhesion # optical ®bers and a FRP host # " --$ #
- F# .# " " " ,+ . . -% 7 C(:55D " -" " " # # - " " . - /
- F " . " " "
- F# - " -. " " " . - -
% " et al. C(::(D # " polyimide coatings # - # " "
- F# " " . - "- , # C(::(D " " # # " -
- F#
" # " - " " % # " ""- .F .--
.#
- F# % 5%&; " acrylate coating . # " " # " - - separated from the optical ®ber% " - - " - - $- . "
. " . - "
- F# - % " . " # , # C(::(D " " .. acrylate optical ®ber " 125 mm - . . 240 mm reduce the FRP composite strength # 13% f%% 57.0 MPa . 65.5 MPa 1% " # .#
- F# g% +- et al. C(::4D " " " bond strength # polyimidecoated optical ®bers graphite-epoxy host F " "" " "% . . silane coupling agent " " " # "
- F# polyimide coating # . " -- -.
5%; 1) !) ) ), + A
353
FIGURE 8.24. )- . "
- F# .# " ,+ . -. " " " - . # " " . > " " " # . . "
- F# % . , # %% ,% C(::(D KK*"- +
. * - ).# # GG Fiber Optic Smart Structures and Skins IV SPIE 1588 4&2@4;(%
- F# -- . " . . % . H C(::9D " " ." .#
- " " - - - # - # quantify the shear strength " interface # "
- F# # " " F " . -% " -- F#
. > - % #
#- -- - . . - H
"
- F# % *? et al. C(::4D . " --$ " # # "
- F# H . > .-
% " " " et al. C(::(D " " # # . " -
- F# F-
% ) # et al. C(::&D # " -?--
- F# . . .# # " - % "
" .. " #- 5%(%
354
1 +), 5
-- * -
Table 8.1 +
- # C1#- et al. (::;D
+ -. - -
)- * - C*+D
- " C*+D
,
". #-
&;'' 3'' &
(4'%' &2%' 9%9
M
" ".- #- " " optical ®ber polymer coatings " # C1#- et al. (::; 1#- 1--. (::9D # ". alkaline solutions #/- .# ". % " -. . - # " # . " " - " B $ " . - " .#. (9 % " - ." > " # F#
" - " # # / . " - .
- F# " " # " #- .# - . " " " - C* ?#" et al. (::2D " : ('%
8.5 INFLUENCE OF EMBEDDED OPTICAL FIBERS ON THE HOST STRUCTURE " & . F#
- . . . % #- #- " . # - . -. "
- F# " - -- # ". " / " % " . " -- " " " " - -- . . " . -
" . % F-- -- # -
" embedded optical ®ber sensors "0 stiffness, strength and fatigue characteristics of their host structure% - " #H " # # . H C(::9D% - # "
- F# " " . " " exception of aerodynamic surfaces -- "
F % - "
- F# .# " # -. -
5%9 !) ) )* )) + ! ),
355
FIGURE 8.25. ". -- " --- .- -> - " #"
- F# " %
" " -- " -#- B% "
. - " .#
- F# " ,+ . . -% " .# .# sensor con®guration #- FRP arrangement - " " B .# F#
" -#- . - " "
$ " " % #- " # . " - " % - " .#
- F# " -. - - # .-- . % " > " - # " .#
- F# # " " . .. = "
- . $ " " -- " . --- .- -> C % 5%&9D%
8.5.1 Optical ®ber resin-pockets " interlaminar lenticular resin-rich pockets .
- F# .# " ,+ . "
" " --- " H
356
1 +), 5
-- * -
FIGURE 8.26. +" . " C D .
F# " .# " - " - - - % . % 7 % 6%% C(::&D KK+ . -
- F# .# -. . %GG Smart Materials & Structures 1 ('(@('3 "
. +" +#-" !%
F# % " H " B " resin-pockets " " -. " - " " C et al. (::' et al. (::&D . " " obtrusivity "
" -# .# % % 5%&2 - " >. - resin-pocket " "
- F# .# $ - " H F# % % 5%(; " ?
" resin-pockets " .-- " - # "
F# " F# % " - .-- " .-- " " " -.% ! $ interlaminar discontinuities potential reliability hazard # " " "
- - " - % Finite element analysis " #
- ." " stress concentration .#
- F# % " - # "- #-" - " # " optical ®ber strain " far-®eld host strain . -> . % " " resin-pocket geometry " -- - - -. / - " " # - # - " $ . C-" et al. (:5: et al. (::'D% " . " " > . # $
5%9 !) ) )* )) + ! ),
357
FIGURE 8.27. , - " ,+ - "" - - " - # "
- F# " - - - D # " " . - > .% . % 7 % 6% % C(::&D KK+ . -
- F# .# -. . $ %GG Smart Materials & Structures 1 ('(@('3 " . +" +#-" !%
- . "% - . " # # # . - . - " # $ . "$ > . % 5%&3% " F " " . # . resin-pocket aspect ratios > -. /% " " > $ .- - . . " . " " $
% " . . " " C6 et al. (::& 1 -- (::4D " " .#
- F# " -- f\5%g " stiffness ,+ 0 " optical ®ber volume fraction - " . "
- F# - " 250 mm% " # 1 -- " " polyimide coated optical ®bers - 250 mm . "
. #- " " tensile compressive stiffness # " - /$
,+ -.% " . F
- F# .# " - " - " F# %
358
1 +), 5
-- * -
8.5.2 Effect on tensile strength .# " C* et al. (:5: , # (::( . et al. (::4 1 -- (::4 +- "
(::4D " " B .#
- F# 0 spacing size orientation " tensile strength ,+ . . - " % " - " " " . #-
- F# .# --- " " F# % - - % 5%&5 .- " - > "
- F# " F % 7" "
- F# .# -
" F# .-- - . " - F# " # " . "
- F# % " " " - - F .--
- F# . f\&'' m.g "
#- " " tensile strength " " %
FIGURE 8.28. 1"- .F
- F# .# --- " - - F# " " ,+ . -% . , # %6% ,% C(::&D KK" . " . * - ).# # GG ('" )
. * - A- SPIE 1777 &99@&2&%
5%9 !) ) )* )) + ! ),
359
8.5.3 Effect on transverse strength " transverse strength - ,+ .
- F# .# --- " . "
. "
- F# % !- " #
# static loading " . - " 100 mm C . H (::9D% - , # C(::(D - " =" =
- F# - transverse crack formation - % 5%&(% . , C(::&D --- " " coated optical ®ber .# ,+ . . - #H transverse strains% " " a coating with the appropriate compliance may avoid any premature failure " . . -% "= > -. "
.. . - - polyimide coating f%% 3.45 GPag%
8.5.4 Effect on compressive strength -" " " .#
- F#
" -#- " tensile strength ,+ . " " . # " " compressive strength%
- " C(:5:D 6 et al. C(::& (::&#D " 250 mm -$
- F# " compression strength
,+ -.% 7" "
- F# .#
--- " F# " compression strength # % / F f 70%g " compression strength . " "
- F# embedded perpendicular " H F# % " "
" - > . - " -
- F# ,+ . " "=#.-. C6 et al. (::&D / -- "" . " - .- #- % 5%&&% , # C(::(D . et al. C(::&D - " - $.
- F# " compression strength ,+ . . - .# -- " " - F# % " B .--
- F# .#. - compression strength " # -- % - - " / . - " .#
- F# . "%
360
1 +), 5
-- * -
" . C(::;D -
compression strength model # " " " lenticular region # et al. C(::'D " - . . - # 1" C(:5'D% 7" " . - " - " degradation in compression strength 0 optical ®ber size laminate stiffness properties laminate lay-up and processing parameters% " . " $ " . "
- F# .# - - " 15 degrees " " - % " - " " " " . " . " % " . - "- > - " - " " . "
compression strength%
8.5.5 Effect on shear strength " C(:5:D . 3O " interlaminar shear strength
- ,+ . -. " .# 250 mm -$
- F# % #/- , # C(::(D
. interlaminar shear test " $ # . "$ > . 100 mm -.M -$ F# % " - .- " # # +- "
C(::4D no degradation in the shear strength
" " .#
- F# %
8.5.6 Effect on fatigue " " # -- " B .#
F# " fatigue life ,+ . % , # C(::&D - ,+ . . - .#
- F# - - -- #- 80% -. - - " 20,000 - . " .# F#
- $ - - % " - .# 140 mm -.$
- F# cross-ply laminate --- " 90 . F# " X'=:'Y - ". - "
- F# . " $ - F % " *- et al. C(::&D " -.$
- F# " - .- " fatigue life ,+ -. " - F# "- > > . ! C(::'D " " - $
5%9 !) ) )* )) + ! ),
361
,+ -. # .#
- F# " . - " 150 mm%
8.5.7 Effect on fracture toughness - H" et al. C(::'D " .#
- F#
" interlaminar fracture toughness -.% #- - #. " " Mode I delamination
" -.% " " "
.#
- F# " critical energy release rate # " # # 15% - -.% "
- F# stiffener " - - . > " "
%
8.5.8 End-Effects of optical ®bers terminating within host - F#
- " termination of the optical ®ber " " " % " ,+ . " " . "
- F# " . - - " .
resin-cone at the tip of the optical ®ber% " " interfacial failure " - - " " . -% " - #- F . . -
. % - " . debonding material yielding " # # # ! - C(::5D% 1 " " G . - " " "
- F# F " " "
coating with the same modulus of elasticity " " " G . > -- # eliminates this stress intensi®cation% ! - C(::5D " " #-.
- F# . " ,+ . . - 0 (% " " "
- F# " - # .# # -- - " " H F# % &% " "
.# . - . - " - # -. " - % . , C(::&D " " .# G . - " ..? " " %
362
1 +), 5
-- * -
4% " " F . , G / . -- - " F " " # . "
- F# % " " " . " " " G . > " " " stiffness discontinuity " "
F# eliminated% " softer coating f F . - " thicker " g -- # " . " % - - - longer strain transfer length% 7" " # " " interfacial shear stress -- " stress energy " " . - % " . " .
" yielding " . - debonding -% " failure onset strain% ! - C(::5D -
. . - " -- . -
"" - -- F % " . - - # - "" " .-- "" . - F % ! - C(::5D -
- > . " . $ - . " # @+ # "
- F# % 1 " " . . " - . " - #
" A - # - # - " (&%('%4% 1 - " singleended embedded optical ®ber sensors # - - "
#- - $? . ?% Polyimide "" #- .# -
- # satisfactory for the end-zone problems% *"- " " " " " polyimide coating " - # ." thicker " - 0 60 mm . " 10 15 m.% ) > " . - " ."-
.- "
-.% " radial compression "
- F# . # " F - . ef®cient strain transfer . " " "
- F# "
# - % + -. " residual stresses " "- - " %
8.5.9 Minimization of adverse effects . # " 6 C(::9D " - " minimization adverse in¯uence .#
- F# " - " " . - / "0
5%2 +!,) ), + ,, ! ) ,
363
CD
"
- F# . f- " g # # ('' m. - - . " $ - " % CD "
- F# " - # . . - " " " . >% " -- # " . " " # -- " -"% CD "
- F# " - # .# --- " - F# C%% --- " H - D% CD #- "
- F# " - - # --- " - %
8.6 PULTRUDED FIBER OPTIC STRUCTURAL SENSORS . . F# -. . . -
# .# . "/ -0 prepreg lay-upN pultrusion ®lament winding% " >-- ,+ -$ # % " - " "
- F# - " ,+ . . - . - C #- et al. (::; (::9D% " & FRP rebar and prestressing tendons F
- - ) - -. - . % " " " " " -
. F#
- " # . " - .
. " . - " : (( C* et al. (::9 -- et al. (::3D% . " F#
" # # " " ,+ % " " - F # . -. -- # " . " " - -. . % . " ,+ . # pultrusion # " F#
" - -. " -
F " " - . % . - "
- F# . ,+ . " ? " . C --. ! (::9D % 5%4&%
FIGURE 8.31. ".
- F#
- F# .# " ,+ . . - % . --. 7% % 6 % ! 6%,% KK*"
# [) . GG 0 KKFiber Optic Smart StructuresGG )% ) 6% # (::9 7- % , # . 6 " 7- %
5%3 ), + ,, ! ) , ),T
367
FIGURE 8.32. - F# ,+ . .#
- F# % . --. 7% % 6 % ! 6%,% KK*" # [) . GG 0 KKFiber Optic Smart StructuresGG )% ) 6% # (::9 7- % , # . 6 " 7- %
" " " . " ,+ " "#- " " . - / % )>. - "
" # " : ('% pultruded FRP host structures " . continuous feedstock - .#
- F# B" " " >. - % 5%4'% * -#- #
- "
- F# "-- -- " " # > -% " "
- F# # -- " " # - - # . .% "
- " " .# $
- % " . . " % 1
- " - - . - > - % -" " # .#
- -- # . "
" # "
- % " . F
- -- # # . - " " " #- # # % " .# .H
- F#
$ - . - " - " F# " F " : -- " " -
- A % " - -- -
# @+ " -
- % " :%& " "/ . - A -- # % " " A " " / "/ ". " -% " - "/ # - . -% " -- - " " F " - " "
- :%4% " . . $ - . -
" $ # @+ -- # :%; . " .
-
:%& ), , AA A, A ) , )*!
371
" " - -- . " # :%9% -" " . -- # . . " - $ #- #- " -- " - # - " - " - - " 4 ; 9%
9.2 FIBER BRAGG GRATING SENSOR DEMODULATION " " 9 " " 3 " A " " . "" #H " C D -"N % 2%&4% " . - "/ A # - F- - passive ratiometric
"% - " ". -- # #% " -
"/ # - #- # F- " " " .% - "" " # . " .
" $ -- " .# " - - "" " - - " -" " > - % !-
" # #- - " # . # ..# . -# " . . -- " . - "" A # # " " . .%
9.2.1 Passive spectral ratiometric demodulation " - - ." . " -" F# - " " . . " . % " . - > / . - F- " .% " " ."
. . >
- " A " - % .H # " " . " " " " -" - # . # . . - - F- C* et al. (::&#D% ". -- " . . % 2%&;% !" . # # " A 4 - "" #/- . "- " -" B . " A 4 - " " % - F-
- " " " " " . " -" - # " " -" "
- -% " " . . B$
372
1 +), : " A
-
-. . # - "
F# % -- " . F " - F- " - # - -" % 2%&;% " F- " - . F
l " F
l A
l
l' ;
::(
" A " -
" F- l' " -" "" F
l ' *-- et al. C(::&D . " " # -" # $ B . " A " A . " - " Dl -" l % " " " " " F- CF- D -" - I: A l I,
Dl l' p ; p
::&
- -
- " -" l % " > .- . - "
" . - superluminescent diode
# 54' . > " A % >. - " - " - " " . " C54& .D A " # -.. - #. % :%(% " " " . " ,A54' , "" # F- . - " > . C*-- et al. (::4#D% 1"-" " -- - . " - " % . - # "- # electronic lookup table " "
.% " - " " - " -" " # " . > # " A % >. - " . " $ . wavelength determination system C7D - % :%&% - - " " -
" . A " "" " - #-% 1 " . " > " -- % :%4% - " . - " . 70 CD . " F- G . .N CD $ - F- CD - ? " - .# " $ # " A% )> # )- +" C)+D . " " #-. -- ". .. - . # " % :%; - " " )+ $ "- ®ber optic grating strain indicator C AD % " F
:%& ), , AA A, A ) , )*!
373
FIGURE 9.1. CD L " " - - . A . - .% C#D )> " - F- "
- . A . - .% " - ""$ -"% . *-- %*% ! .- . % 2%&; - " " wavelength-dependent coupler " -- # " - #-$ F- % " # " "
- - " " # # - F- " " - -
% " > .- F ".-- -- % :%2 " - . " A -
FIGURE 9.4. +" " " )- +" $"- F#
. - !$49''% " . )- +" - $ %
376
1 +), : " A
-
FIGURE 9.5. +" " - --- $"- F#
. - !$4(''% " . )- +" - %
Single Mode Optical Fiber 3 dB Coupler
Broadband Source or Laser
Fiber Bragg Grating
Isolator P1
Light Dumps
Photodetectors P2
Wavelength Division Coupler
(P1 + P2 ) FilterP1Transmission
S
P1 Spectral Response FBG-Signals FBG-Signals
λΒ
Wavelength
P2 (P1 + P2 )
P2 Spectral Response FBG-Signals
λΒ
Wavelength
FIGURE 9.6. + - . . - . A -"$ - - - F- %
:%& ), , AA A, A ) , )*!
377
FIGURE 9.7. - . " -" - > .- . -- % :%2% . *% % .- $ . -- % :%2% . *% % .. # $ B -" . " A% .
"
" - . " effective derivative " - " + -"
" A - #% " . -" # .-- " " + F- . - . - " + F- # -"
':'( .% " " - .> - -- " " " / - $ F- > " . " " /% " + F- "
380
1 +), : " A
-
FIGURE 9.10. . - . # " - . . -- % :%:% . + 1%6% 9''' me - # " " .% AOTF Filter. " 9 9%5 " acousto-optic tunable ®lter C D " . #- # F- C % 9%;4D% . " . -"
. -- # " / radiofrequency C, D$ -
- " % " . - . # .- - # # "
, /% . . " "/ - . A # 7* . F A # /$- #- CV et al. (::4#D% "
- C - " - *$, D " -" (:& m. &:9 m. - - C 71*D ; .% " # # " . /$ .- -> A .% ". " . # A et al% C(::9D % :%(9% # # )!) (4'' . --. " A " 4%4 . . # " "
" % " . # " . -" " " . $ , -$ -- -- CLD% "
384
1 +), : " A
-
. - " - A - -- " # $ B -" . A # "
-" % " #" " . " " A C4%4 . % '%& .D . "
" . - " - - # /% " -" A # . " #- # " " , /
- " # " .- - / " A -" C%% < "/D " " - . - . - C *D - . " " ? % :%(9%
RF Dither
AOTF profile dithers about λ B
AOTF profile dithers about Offset from λ B
Photodetector Signal
Photodetector Signal
RF Dither
Time Small amplitude signal when λ AOTF λ B
~
Time Large amplitude signal when λ AOTF = λ B
FIGURE 9.15. $
#- F- . - . - A % - " ."- . " . # . . B - #. " " " # " #.% " " , " " . . . " -"% . A 1% V *%A% 6%+% C(::9D KK*- -> * . " ! A !" GG SPIE 2507 &9@4;%
:%& ), , AA A, A ) , )*!
385
" . " # . - $ . - # V et al. C(::2D # " /$ . - - #. - -- " "" -- - N % :%(2% " /$-- - -.. - #. -# " .% " $ .-- - - #. . ,+ - " $ .# . -% " - - " .% :%(3 - " - " . / "
- % " - . " " .
" - " . ;4'' me " . . . . 9 1? " . . & me CA et al. (::9D% " frequency±strain sensitivity . " % :%(3 :2:3 1? me ( % " C(::2D
FIGURE 9.16. . A . - # " . # % :%(9% . A 1% V *%A% 6%+% C(::9D KK*- -> * . " ! A !" GG SPIE 2507 &9@4;%
386
1 +), : " A
-
FIGURE 9.17. ! / " A " > .- -- % :%(9% . A 1% V *%A% 6%+% C(::9D KK*- -> * . " ! A !" GG SPIE 2507 &9@4;%
" " -
.
. " $.- . - - . - . . . . $$ -"$.- -> A " & e 1z ':9 % Matched FBGs. " "-- . " -" A - # # " - .>. KK " " " %GG 6 et al. C(::4D " F " " A # # matching demodulation FBG% " . " reading grating B . F -" -- # . piezoelectric stretcher C % :%(5D% " . #
" " . " . % " . - .
- " ? - " " -- - " A B . " # -" - - " A .% 7" " " " .>.. " -" " " - " -
- " A " " # > # " A # .% " - . closed-loop servo - " A $ -" " " A "
? - - - " -"% " "/ - # -$.- -> A N " ((% - ; me # - # . " $#" A%
:%& ), , AA A, A ) , )*!
387
Single Mode Optical Fiber Broadband Source or Laser
Sensing Fiber Bragg Grating
S
Interrogating Fiber Bragg Grating 3 dB Coupler
Light Dump Photodetector
Scan Servo FIGURE 9.18. ". " ." A "/ . - A%
" " ". " - - "
B - . # #- "
" A C" -" (99(%5 . (993%& .D . -.. - " "" #H " $ #% " $ ." A . - . - ? - " % " A --. # # # B #.$
F# " -- - -" .- -> .# A% " " - " " .% " - . " "
- $ . -F " " " -
- " F- A% " " - $ .. " " " - # " A% " # -
-- " F- - $ -" " > # " A " " - $
388
1 +), : " A
-
- - -
- " . C % :%(:D% " " F " " - / " # " - .
- " A%
" A #- " /
- " % -" " #- - " (' e 1z ':9 " -. # " ? - " % "
" - " - " . $ $ -" > . - # - " " $
FIGURE 9.19. . - . A # - $-
" ." A% " - " " -
- ? - -. -- " A B .% . *% % " " 0 f
l f
l, "" #
. " . " A " .
- - % - ':2 e 1? ':9 - $ / # ( 1? . " " .%
9.2.4 Laser sensor demodulation -- " . - "/ # # " # A% " F " # - N " -
-$ $ -. " . .% -
" . " - " A " . - C* et al. (::&D% " #
#
" ". % :%&&% " -"
" - . # " " B " A% "" B A F- - " .. " - -" -- " " -" " % " " . " A " " - -" " $ $ - % " . . " H -" " are encoded into the laser wavelength% - - " > - " - % -" " " -
- C* et al. (::&D " " A " -" . - " F . " - A -- " -" #.$
F# - C*-- et al. (::4D% " > .- . % :%&4% - - 1st Laser Mirror
Single Mode Optical Fiber
λB
λB
Gain Medium Laser Cavity Sensing Fiber Bragg Grating Also Serves as 2nd Laser Mirror Ideally Laser Operates at the Bragg Wavelength,
λB
FIGURE 9.22. . -F " - " # F F# - %
393
:%& ), , AA A, A ) , )*!
:5' . . -" #.$
- F# # . :5'=(99'$-" .- -> % "
F# . "- " " A . - #.% " B -- F " F# - % " -" " F# - . # . " - . "/ C*-- et al. (::&#D% " . " " - " B
F# . #
- . -? " . - - - % :%&;% - -- . - C\ &%& .7D -" " -" " A # " " " B .% " .
&%2 .7 " " - # .-- . -F -" " -"% "
. - - " . F# - - " -"% " - " F# - -" " . % :%&9 C" et al% (::4D% #-. " " F " " - -" - C ( .D " - + . .-- " - - -- " " A B -"% " . $-" F-% "- " - . " "
" - # # " . . . " - 9 me #" (4 1?% - et al. C(::4D . "
Erbium Doped Single Mode Optical Fiber 980 nm Pump Laser Diode
Endface Laser Mirror 980 nm
980 nm Wavelength Demodulation System
1550 nm 1550 nm Wavelength Division Coupler 1550 nm
3 dB Coupler
Photodetectors Fiber Bragg Grating and 2nd Laser Mirror
Light Dump Cantilever Beam Test Structure
Spectral Filter
FIGURE 9.23. " > .- F A F# - % " -" " #.$
F# - . # " - . "/%
394
1 +), : " A
-
FIGURE 9.24. - " A F# - -- % :%&4% - - H " :5' . . - " .
B " # " " A # " .% " " " - - > " - " - # " - -%
- " F# - C A!D - # -- .- ->% " . A! F# F " - C N - # $ % " " " universal demodulation system - # > .- -" - - " # " " (' . # ( .% - " # F . " C* et al. (::5D% ". -- " - > . . . "
" " % :%&3% - gain-coupled distributed feedback CA$ D #- - C. -#- # - D (94& . A C et al. (::5D% " A$ - . $ #-? &( .
" . (949%9 (9;;%9 . " - # # '%9 2%&9 .7 " % " A # - #. " " # F- - " -" " % - # > " F#
. .% " B - . " A -- # " % " " - " - H "" " - -" - . . . " / % " A$ - - -"
>.- &%9 . " -"
397
:%& ), , AA A, A ) , )*! Single Mode Optical Fiber Gain Coupled DFB Laser
3 dB Coupler
Cantilever Beam
S
λΒ
t
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(b) FIGURE 9.29. CD ". . " . /.$-- - $# F- C=7) D . " -" A % C#D $-
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Optical Fiber Illuminating the The Quantum-Well Electro-Absorption Device in Waveguide Configuration
Optical Fiber Illuminating the The Quantum-Well Electro-Absorption Device in Mesa Configuration
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418
TABLE 9.1.
Speci®cations for Several Types of FBG Sensors Strain
Embeddable
Bondable
Weldable
Weldable high temperature
Temperature
Bolt
Probe
Gauge length 150 mm 10 mm 25 mm 25 mm >10 mm Ð Gauge material Stainless steel Fused silica glass Stainless steel Stainless steel Bolt material Metallic=nonmetallic Cable length 1 m to 1 km 1 m to 1 km 1 m to 1 km 1 m to 1 km 1 m to 1 km 1 m to 1 km Cable diameter 3 mm 1 to 3 mm 1 to 3 mm 1 to 3 mm 3 mm 1 mm to 3 mm Connector type FC, ST, SC FC, ST, SC FC, ST, SC FC, ST, SC FC, ST, SC FC, ST, SC Strain range 0.6% 1% 1% 1% 1% Ð Temperature ÿ50 C to 80 C ÿ50 C to 80 C ÿ50 C to 80 C 0 C to 325 C ÿ50 C to 80 C ÿ70 C to 350 C range
ÿ58 F to 176 F
ÿ58 F to 176 F)
ÿ58 F to 176 F)
32 F to 617 F)
ÿ58 F to 176 F)
ÿ90 F to 660 F)
CHAPTER 9 Short Gauge Sensor and Applications
Sensor type
Load
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FIGURE 9.99. ". -- - $ " . - ) + ? . -
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- F# # " $-" " A C % &%((D% " . . " . . quasi-distributed sensing% - " " # ." .-- " " - -" " " #- " " . /$ # ." . # .% #- " " " - - # . " /$ # .% >. - " # # . ,. C (::9D% " - - " "/ ( . "- - #- " ." F - " $-" % "- " #
" . " # # /$ # " " " . % 7 -. - " KKF#
" - - -%GG " " 595
596
1 +), (&
# .
-. # " - # " - # . # " " " Bragg intragrating C AD . . C1 et al. (::5D% " -- - # # . C et al. (::5D # " - - -- " " "/ " # -. ( .% " -. .# " " - "- ? "" " . . . - . - .
- % # " # " . $ . " - - ( .. C1 et al. (::9N &'''D% " - . " # A " -" " -. # ( .% - -" > (' . / > " . . # #- "
" % #- " .# > A -
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# " F#
" - % . - -. " " # " ( .. - - . " - #- " KK - -
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" #- .# #-. "" - " - " % . " #-. " " - % #- " " . .
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- --
#- - % F- . . ." . " ,+ #- " . # " " " " - " #
-- # H % " -- # " - # A . " -#-
- " . .
- % #- " " - . #- ." # . - > " " " high-resolution strain mapping% -- - " " F - - #- " -
- F# A - . . - # .%
(&%& ), , ) ) A )+
597
12.2 FIBER BRAGG INTRAGRATING DISTRIBUTED SENSING CONCEPT " "-- > - " Bragg intragrating C AD . . . # % 7" $ . . . within - % A # " " . " - - # -.% 7" .
F- . " " # > " . -" " " " . . % /- -- " .--
- - . " " # -. " B " $ -"
" % " " " " . - " A " " # > -"- B -" -" " " B . # . -- # .- - C % (&%(D% 7" " " . - " > - " A " # KK" %GG
$ . F- - strain-chirped FBG% -- " " " " % (&%& " " B . A
FIGURE 12.1. $ " A - B B .% " " " " -" . B . - " %
598
1 +), (&
# .
FIGURE 12.2. ". -- " " " " B . " F- . . .%
- " " "" > " . # . " - F-% " " B . " F- # - " -- .% " . " " . " optical period CF nLD " A > . - % -" " # " KK#-$ " GG - " " . > " > . - "-- # . - " A " " - . " . . F-% " " chirp A " # " " - . "" B -" # . " -"% uniform FBG " B . . primary peak C 4%('D " -" l &n' L' ;
(&:(
. > . "" " A . *"- . " B
. " midpoint of the grating%
599
(&%4 $* ,V ,* !* , ,* A
" A " " "
- # . >- z l
z &n
zL
z &n' L' DfnLg;
(&:&
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# B " local strain e
z strain-gauge factor Ge C 3%4DN %% l
z &n' L' f( Ge
zg;
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(&:;
1 et al. C(::9D . " F# " $ .
- > . - " . # -? # " T-matrix .-. C1 (:5;D%
12.3 T-MATRIX FORMALISM FOR NONUNIFORM FIBER BRAGG GRATINGS " #" F# # # .
- F " "
- F# " A% -- . " " .
- nL " > . - Dn' " . " " " % " - F- " # " . # # # " > E
z; t a
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bzg
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z dz
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600
1 +), (&
# .
da#
z ika
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DL aD! - " - $ E$F- . -> . - " # " " "$N % (&%4 %% T(( T(& a
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' ;
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T(& TW&(
pDn' "fkDLg ipDL e : ikl
(&:(9
" T$. > - # # "
-" " " " A # " " N # $
601
(&%4 $* ,V ,* !* , ,* Uniform Short Fiber Bragg Grating af(∆L)
af(0)
ab(∆L)
ab(0) T(∆L) z=0
z = ∆L
(a) N - Fiber Bragg Sub-Gratings af(L G)
af(0) ab(0) z=0
ab(L G) T(∆Lj ) jth Sub-Grating
z = LG
(b) FIGURE 12.3. CD . " -" F# # % C#D , F# # # -.%
" # . -. " T$. > -"- - L Dn' . " "# % (&%4#% " a
L a
' T
DL( T
DL& T
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l
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l jr
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602
1 +), (&
# .
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l - . # -" L
z " $> . - " Dn'
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FIGURE 12.4. >- F- " " > . - Dn
z " - B R
l % (&%; " " -- R
l " " - . - " -" "
" # -" . > % 7" "
- " . B . # . . " B% A " #H - " - B R
l # . .- - " % (&%9% A #H # " A$ # > . - " - " "
- " - - B -- .
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604
1 +), (&
# .
FIGURE 12.6. " B - " B . A " A$" # " " > . - % . 1 % ! - *% " *%*% * ,%*% C(::9D KK $A GG Applied Optics 34 9''4@9'':%
12.4 INTENSITY REFLECTION SPECTRUM FOR DISTRIBUTED STRAIN SENSING " / " . . " B -" " F- " A % " F
" -- . . - . - " % . A " > # # # % " A # " " . # -. " " B . - - " -- A . - . - # " . " . -- " #$ % . . " A " " # #H "- " . -- # " . % " # > "" - " -- # " . "
- " . -% 7 . . - . - $" A # . " " F- . " A . " " -"
B - - C
605
(&%; ) ,) !) +),*
. D " " " -" " AN % (&%3% 7 . " " # " B R
l . " mj C D # #H " B -" lj # " . " -" . . " ... - l. C. - F-D " -" ln # B . " zN %% jn P j(
R
lj a
jn P j(
mj Dz;
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l
l.
R
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l;
(&:&'
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l. l.
R
ldl
λ1
l.> l.
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λ4
FIGURE 12.7. . - . - - " " -" " A " - " -" .-? # " B%
606
1 +), (&
# .
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l .. " " -" l l R
ldl l :
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ldl l .
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l " -" -" l # B # . . " -- -" l .-? # " - B% " -" # - " " - )/% C(&%4D - " " F- - " A # - " " -- % " " ." -
-#- . F-% -" " " . -
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l . % ! - et al. C(::2D " " " > " F- . $" A " " " -
l
z p& z Dn&
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e
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# # / " - " - $ Cl$ D " " - " "$ Cz$ " ' z LA D % " et al. C(::2D . " " > . - " -- >- % " . . -F " . #- - - " >- - z - " A "" " -" l B
" - " - C(&%&4D %%
l &n z
l -( R
lWdlW f' z LA g:
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(&%; ) ,) !) +),*
607
z
l # . C(&%&;D " >- e " - C" " -" B lD . )/% C(&%4D " . e
l l' ; G e l'
(&:&9
" l' " - -" " A% " C(&%&;D B # " -" L # 1-- C(:3;D " - -" " A " # " B -" -" l " z - s L
z ;
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z Ge jde
z=dzj " jde
z=dzj " - - % - " - e
z . # " - "/ -- " L % ,- C(&%&2D
" - " - - " " C%% " " " -" " # D " # B $ -" -"% " " . - " . " B F -" " ... " # - - # " "/% - - "
- " . L > LA
>. . )/% C(&%&;D # . - - % " - - % . " - "/ A " $ #- , - 4$. "- " B
- - . " - A # " C" et al. (::2DN % (&%5% " $ -" " - . . " H % " " > . # " , " " -. " -" &' 9' ('' .. (' 4 % .. ( - " " C "D% " B " " A % (&%: "
- -- # )/% C(&%&;D " " - % (&%:#% - " " - F # " - " F " % /
" " - "/ #-
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608
1 +), (&
# . Single Mode Optical Fiber
Tunable DBR Laser Diode
Chirped Fiber Bragg Grating
Isolator S
3 dB Coupler
Mirror Tip
Photodetector
Intensity
DBR Laser Driver and Data Acquistion System
Wavelength FIGURE 12.8. )> .- . . " - " A # " B .% . " *%*% 1 % % ! - *% * ,% C(::2D KK # ! # A GG SPIE 2838 22@39%
# " " " % " #-. # -- . > # " " A (&%('%&% " /- - # " " - $ . - " % 7" F # #- .. . - " . . .
F- # - C % (&%('D% " . " - "/ # - # # " et al. C(::2D% " > . 9$.. - A C"" -- .D # "
-.. - - >. " - % (&%((% "
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(&%; ) ,) !) +),*
609
FIGURE 12.9. CD ,B " A -" # " . - " C10 3 %.. 12 D% C#D " " " -" . # " B . "/ " . - " % . " *%*% 1 % % ! - *% * ,% C(::2D KK # ! # A GG SPIE 2838 22@39%
" et al. C(::2D 1 et al. C(::5D # interferometric technique " # " spectral integration "/% 1 - -. . F-
" . -> " . . .# " " ." > " F- . #- .# " " "/ # " -. "" # " > %
610 Effective Strain Profile, ε(z)
1 +), (&
# .
file on Pro egi ain ient R r t d tS Ne w Gra e to g o L Du ratin n i No fG tra sS po Bia -Chir Pre Strain Profile Low Gradient Regions
Effective Strain Profile, ε(z)
Axial Position Along Grating, z
ile rof n P onic i a r not t St Ne w Mo No
o e t ing Du rat n G i a f Str irp o as Bi e-Ch Pr Strain Profile Including a Reversal
Axial Position Along Grating, z
FIGURE 12.10. ". -- " A #- -. "
#-. .-- . . F-
. %
FIGURE 12.11. )> .- . - . " $ A H " - - - - % . ! - *% 1 % " *% *% * ,%*% A. % " % C(::2D KK # * . # A ,B . -GG Optics Letters 21 (;'9@(;'3%
(&%9 , ) , ) A
611
FIGURE 12.12. CD B . " A " - C % (&%((D - - % C#D )> .-- . F- C - D - " A " B . "/ . " " $ -- F- C# D%
12.5 DISTRIBUTED STRAIN SENSING BASED ON FOURIER TRANSFORMS F
# " et al. C(::3D #- KK -GG # # F- " - F# .# " . . .# " . -%
" " " . " " -$.
- F# " > 0 " . -> . - a
z # " . -> . - a#
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612
1 +), (&
# .
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. - " .. " " # -" %% Db
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- " - -
z
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613
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z " . f
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614
1 +), (&
# .
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l c
l - R
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12.6 EXPERIMENTAL FOURIER TRANSFORM DISTRIBUTED STRAIN SENSING " -. > . . # 1 et al. C(::5D
" . ." . " #
F- . F# " ".-- % (&%(4% #- , -
# (99& . " -" - C
>.- & .D F " B . C "D " F# % " - -" " " "
- F# " . # " " -"% " " . " -" B . " -"% " " - . " " -"
- " B $ . R
l% -# " . " $ .. - " - " " $ . R
l # .% " " F#
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-- " -.. - #. C % (&%(4#D% " #. -.
- " " % - C (&%;D "
"/ " " . # C! - et al. (::;D% .- - " " " #. - #" " " F# % (&%(; (&%(;# - " . " R
l c
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615
(&%2 )V+),*) ! ,), , ,* Reference Photodetector
Intensity Photodetector Tunable Laser Diode
Sensing Optical Fiber
Fiber Bragg Grating
86 mm
3 dB Couplers Phase Photodetector
Specially Shaped Aluminium Cantilever Beam
Mirrored Tip Reference Optical Fiber
(a) Applied Force
Beam Clamped
86 mm Fiber Bragg Grating in Groove
Specially Shaped Aluminium Cantilever Beam Resistive Foil Str ain Gauge on Underside of Beam
Slot Milled into Underside of the Beam
(b) FIGURE 12.13. CD )> .- . # " " - . . . 52$..$- A . -- - #.% C#D A -. "
" -- " - #. " " - " #.%
616
1 +), (&
# .
" F- . " " " . ." % -" " " > $ .- F " " - #- -- > . " #- " % . " . " .
" " - - # - #
FIGURE 12.14. #. - " A . # " #- - . -- (&%(4% C#D . " % CD - FG - F- - " A . . " . " " CD C#D% CD )> .- F- C - D . " . " " . " " -- F- C# D " #. # " - " #.%
(&%2 )V+),*) ! ,), , ,*
617
. " . " # " " % - . . " - - - "
" - " -.. - #. H #% - " - % (&%(4# "- # " " . - % (&%(9% " #. " -
" " > A #H - "
FIGURE 12.15. CD - " - #. " " - # . % C#D B " " #. - # " - . F- - " A % CD )> .-- .
F- " F- . F # " " - %
618
1 +), (&
# .
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" " H " " $ - -
Light
Light 4 cm Long Fiber Bragg Grating Circular Hole
Load
Aluminium Plate Under Axial Tension
(a) Load
(b)
FIGURE 12.16. CD " > .- . - ;$.$- A
H " - - - -% " - F- . . " . " " C " . #- - . " (&%(4D -" - # " - "
F# . " " " -- F-% . A% C&'''D KK # " # A GG +" "%
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619
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" #- . . " F- . " "/% - " >-- . # " > .- / #- . " " .. - . " " " --%
12.7 FOURIER TRANSFORM FOR SERIAL MULTIPLEXED FIBER GRATING SENSORS -
- F# # " " > A " ? B # .# -. #- " " .
" ." - # - " # . " - A % " - ." - .- -> - A " " - " / -" .- -> " -
- . .-$
->% " .
" . - A F . # % * et al. C(::5D " " " # " . .- ." . - > .- % " F- . . " A -
- F# % (&%(3% " " .- B . " " # % (&%(3# " . # " > " .- " # % (&%(3% 7 " " #- .
620
1 +), (&
# .
FIGURE 12.17. CD " - . " - A . - - #.% C#D T$. > -- B " " A #H " CD% CD " " " A # " . " T$. > .- B " % . * ,%*% " *%*% 1 % % 6% % % C(::5D KK#- ! . - L # A * -GG Smart Materials and Structures Journal 7 &43@&;3 " . . " +" +#-" !%
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B %% " >% -" . "
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- F# " " A -- " - #.% " - " . #- - " .
" . . . . " # - - . " - " . - .% (&%(5 - " -
. " " - " #.% " .
FIGURE 12.18. CD . -> B " $- A - - - #.% C#D " " . " A
- " #.% . * ,%*% " *%*% 1 % % 6% % % C(::5D KK#- ! . - L # A * -GG Smart Materials and Structures Journal 7 &43@&;3 " . . " +" +#-" !%
622
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623
12.8 LOW COHERENCE TECHNIQUES FOR DISTRIBUTED SENSING .# -
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