° Ë
ÑV È ¥ß f Ä z ð ² â ì È8 ý ×Ì ¦ Rù p § Þ X ¢ Ç U ØÄ Z Ø º] k ù ì Å] k ù ï " eS y ð 8 ý X N ˽ Êy ¢ 4 Ò Å
»# Ü · * × << ) Ö < · Ù v: c ø ¶ B · »M Z Ì
z @ / < Æ § Ó ü t o < Æõ , F g Å Ò 500-757
(2011¸ 6 Z 4 2{ 9 ~ Ã Î6 £ §, 2011¸ 6 Z 4 27{ 9 Ã º& ñ : r ~ Ã Î6 £ §, 2011¸ 7 Z 4 25{ 9 > F S X & ñ )
© ì r ½ + É × æ o (WDM) ~ ½ Ód _ ï rì r í+ þ A F g$ 3 Ä » + þ AG ' p" fr Û ¼% 7 _ & ñ S X ¸ ¾ Ó © ` ¦ 0 A #
+ þ A ) a > hZ > G ' p" f_ ì ø Í Û ¼& 7 à Ô! 3 4 ¤" é ¶` ¦ : x ô Ç × æd © & ñ ~ ½ ÓZ O ` ¦ r + « > % i . 40> h_ + þ A G ' p" f r
Û ¼% 7 \ @ / # × æ o x 9 % i × æ o à ºu K $ 3 \ _ ô Ç ¸_ z ´+ « >\ " f 2.4 µε_ s : r& h & ñ S X ¸\ ¦ ] jr
% i . z ´+ « >\ _ ô Ç 7 £ x` ¦ 0 A # 4 © _ F g$ 3 Ä » Ð ½ ¨$ í ) a + þ A G ' p" f\ P ` ¦ ] j ¦ G ' p" f\
) a + þ A` ¦ or v 9 × æ o ) a ì ø Í Û ¼& 7 à Ô! 3 ` ¦ 8 £ ¤& ñ % i . 8 £ ¤& ñ Û ¼& 7 à Ô! 3 \ @ /ô Ç % i × æ o > í
ß ` ¦ : x # + þ As ) a G ' p" f\ ¦ d ¦ 6 x ô Ç Û ¼& 7 à Ô! 3 ì r$ 3 l _ & ñ S X ¸_ 1.4C 14 pm_
© s 1 l x ¢ ¸ H 17 µε s ? /_ ¸ Ð + þ A_ ß ¼l \ ¦ & ñ ½ + É Ã º e % 3 .
Ù þ
d # Q: © ì r ½ + É × æ o, F g$ 3 Ä » , ï rì r í+ þ A + þ AG ' p" fr Û ¼% 7 , Û ¼& 7 à Ô! 3 4 ¤" é ¶
Improved Accuracy of a Quasi-distributed Strain Sensor System by Using Fiber Bragg Grating Spectrum Restoration
Gyoung-A Kim · Jae-Soon Youn · Se-Jong Baik · Kiegon Im ∗
Department of Physics, Chonnam University, Gwangju 500-757 (Received 2 June 2011 : revised 27 June 2011 : accepted 25 July 2011)
The peak wavelength of a fiber Bragg grating (FBG) in quasi-distributed strain-sensor-systems based on the wavelength division multiplexing has been measured with improved accuracy by restor- ing the individual fiber grating reflectance spectrum. Computer calculations have been performed for demultiplexing of the multiplexed spectrum reflected from a 40 strain sensor system to test the restoration algorithm with its simulation code, and a theoretical prediction of 2.4 µε has been sug- gested for the strain measurement accuracy. We fabricated a strain sensor assembly with four pairs of FBGs and measured the reflection spectrum of the sensor train under various strains. Applied strains were measured within an error of 17 µε, corresponding to a 14-pm wavelength displacement, which is about 1.4 times larger than the accuracy of the optical spectrum analyzer employed in this experiment.
PACS numbers: 42.79.D, 42.81.P, 07.10.P
Keywords: Wavelength division multiplexing, Fiber Bragg grating, Quasi-distributed strain sensor system, Spectrum restoration
∗
E-mail: [email protected]
-750-
I. " e  ] Ø
F
g$ 3 Ä » (Fiber Bragg grating; FBG) H ½ ¨ ¸& h î
ß & ñ $ í õ © ï` ç : £ ¤$ í \ _ # ½ ¨ ¸Ó ü t _ î ß ¸ 1
p
x` ¦ 8 £ ¤& ñ H G ' p" f Ð B Ä º Ö ¸ µ 1 Ï > ½ ¨÷ & ¦ e [1].
F
g$ 3 Ä » G ' p" f H Â Òd s \ O ¦, ? /½ ¨$ í s Z } Ü ¼ 9, l
ç ß [ O \ Á º ' a ô Ç © & h ` ¦ t ¦ e l M :ë H \ ª ô Ç Ó ü t o
& h , o < Æ& h , Ò q tÓ ü t < Æ& h o\ ¦ & ñ S X > 8 £ ¤& ñ ½ + É Ã º e H y
t è Ð Å Ò3 l q` ¦ ~ Ã Î ¦ e . ¢ ¸ô Ç F g$ 3 Ä » _ l
- à Р¸ (self-referencing) 0 p x§ 4 õ f § > = ) a ´ ú § É r à º_ FBG G ' p" f ° ú H Z } É r × æ o l 0 p x É r Û ¼ à Ô ½ ¨ ¸Ó ü t _
+ þ A 8 £ ¤& ñ õ ° ú É r ï rì r í+ þ A > 8 £ ¤ ì r \ " f [ O u x 9 î r6 x q
6 x` ¦ ] X y < ÊÜ ¼ Ð+ FBG G ' p" f l > r _ l -% i < Æ& h G '
p" fü < â Ô q t½ + É Ã º e H B Ä º × æ כ ¹ô Ç : £ ¤$ í s . G ' p" f r Û
¼% 7 _ × æ o x 9 % i × æ o $ í 0 p x ¾ Ó © É r ï rì r í+ þ A F g$ 3 Ä
» G ' p" f r Û ¼% 7 _ © & h ` ¦ þ j@ / Ð Ö ¸6 x l 0 A #
ñ@ / ¸ ú 6 £ § q , crosstalk _ > h 1 p x õ 8Ô ¦ # Q © Ö ¸ µ 1 Ï ô
Ç ½ ¨ ì r ÷ & ¦ e .
F
g$ 3 Ä » G ' p" f_ × æ o H r ç ß ì r ½ + É × æ o (Time Division Multiplexing; TDM) ü < © ì r ½ + É × æ
o (Wavelength Division Multiplexing; WDM) x 9 / B N ç ß ì
r ½ + É × æ o (Spatial Division Multiplexing; SDM) Ð ½ ¨ ì
r ½ + É Ã º e [2–4]. r ç ß ì r ½ + É × æ o_ â Ä º F g$ 3 Ä »
_ ± ú É r ì ø Í ¸ü < ñ@ / ¸ ú 6 £ § q (SNR) : £ ¤$ í $ _
& h s e Ü ¼ 9 © ì r ½ + É × æ o ~ ½ Ód É r G ' p" f r Û ¼% 7 _
^ © ; ¤ õ y y _ F g$ 3 Ä » G ' p" f ° ú H z ´| 9
&
h Û ¼& 7 à Ô! 3 © ; ¤ \ _ K % ò ¾ Ó` ¦ ~ Ã Îl M :ë H \ × æ
o G ' p" f à º\ ¦ Z þ t o H X < ô Ç> e . @ /^ Ð TDM l Õ ü t s
WDM l Õ ü t` ¦ SDM ~ ½ Ód õ ½ + Ë # × æ o $ í 0 p x
`
¦ Z } s H ~ ½ ÓZ O s 6 x ÷ & ¦ e Ü ¼ , ` O Û ¼ Y Us $ ü < > s w
× ¼ Ø ¦ l (gated detector)_ 6 x É r r Û ¼% 7 _ q 6 x õ 4
¤ ¸ ú $ í ` ¦ ß ¼> Z } s H é ß & h s e .
+ þ A G ' p" f r Û ¼% 7 _ â Ä º, 10 nm_ © @ /% i \ 1-2 > h _
G ' p" f\ ¦ C u H l > r _ WDM ~ ½ Ód É r ô Ç& ñ ) a F g: x
© @ /% i ? /_ F g " é ¶ õ Ø ¦ l \ ¦ 6 x ½ + É â Ä º G ' p" f_
>
hà º\ ¦ Z þ t o H X < & ñ & h ô Ç> e . s Qô Ç ë H ] j& h
`
¦ K l 0 AK Ä ºo H 1 > h_ G ' p" f\ 2> h_ FBG Û ¼
&
7 à Ô! 3 ` ¦ @ /6 £ x r v H Û ¼& 7 à Ô! 3 I Õ ª ~ ½ ÓZ O (Spectral Tag Multiplexing; STM)` ¦ ] jî ß % i [5]. STM ~ ½ Ód É r F g
$
3 Ä » [ þ t s 1 l x{ 9 ô Ç Û ¼& 7 à Ô! 3 % ò % i ` ¦ / B N Ä » l M :ë H
\
F g: x © @ /% i ? /\ Ã º z > h_ G ' p" f\ ¦ C u ½ + É Ã º e
t ë ß , + þ A\ É r Û ¼& 7 à Ô! 3 _ s 1 l x Ü ¼ Ð × æ^ o ?s µ 1 ÏÒ q t
F g$ 3 Ä » _ × æd © 8 £ ¤& ñ _ & ñ S X ¸ ± ú
. s ½ ¨\ " f H 8 £ ¤& ñ ) a > hZ > _ Û ¼& 7 à Ô! 3 ` ¦ 4 ¤" é ¶
¦ + þ As ) a G ' p" f\ K { © H Û ¼& 7 à Ô! 3 _ × æd
© o\ ¦ Ð & ñ S X > ì r$ 3 H á Ô ÐÕ ªÏ þ ` ¦ > hµ 1 Ï
% i .
Fig. 1. The system configuration for a quasi-distributed fiber Bragg grating strain sensor system.
II. T Â ] Ø õ m Í 4 m
Û
¼& 7 à Ô! 3 I Õ ª ~ ½ Ód É r G ' p" f\ P ? /\ C u | ¨ c > hZ > G ' p" f
\
" f Ð É r Ú ÔA Õ ª © ` ¦ ° ú H ô Ç © _ \ ¦ C & ñ
¦ Ú ÔA Õ ª © _ s \ ¦ É r G ' p" fü < Ø Ô> # K { © G '
p" f_ d ³ ð Ð 6 x ô Ç . 1 p x ç ß _ Ú ÔA Õ ª © ` ¦ d
ï× ¼ Ð Ö ¸6 x H Û ¼& 7 à Ô! 3 I Õ ª ~ ½ Ód \ _ ô Ç + þ A G ' p
"
f r Û ¼% 7 _ [ O > Fig. 1\ e . F g " é ¶ \ " f
: r F g @ /% i y n C É r F g$ 3 Ä » \ P \ " f ì ø Í ÷ & ¦ ¦Ä » Û ¼& 7 à
Ô! 3 [ þ t s © × æ o ) a y n C É r ì rF g l \ " f 8 £ ¤& ñ ) a . 8 £ ¤
&
ñ ) a Û ¼& 7 à Ô! 3 É r © % i × æ o\ ¦ : x K ¦Ä » Û ¼& 7 à Ô! 3 [
þ
t _ ¸½ + ËÜ ¼ Ð ì r K ÷ & ¦ × æd © [ þ t` ¦ ì r$ 3 # + þ A s
) a G ' p" f[ þ t _ d Z > õ K { © + þ A° ú כ` ¦ ¸Ø ¦ > ) a
. y G ' p" f ¦Ä »ô Ç d ³ ð\ ¦ ° ú ¸2 ¤ Õ ªa Ë >\ " f Ð H ü
< ° ú s @ /g A& h Ü ¼ Ð Z ~ ¿ º Ú ÔA Õ ª © ` ¦ ° ú H ô Ç © _
F g$ 3 Ä » \ ¦ @ /6 £ x r .
+ þ As \ O H © I \ " f Ú ÔA Õ ª © λ
k1, λ
k2\ K { ©
H ¿ º > h_ Ð ½ ¨$ í ) a k P : G ' p" f_ ì ø Í Û ¼& 7 à Ô! 3
É
r 6 £ § õ ° ú s Å Ò# Q .
R
k(λ, ε = 0) =
2
X
i=1
r
ki· g(λ − λ
ki) (1)
d
(1)\ " f ¸ H F g$ 3 Ä » [ þ t É r Ú ÔA Õ ª © λ
ki\ " f ì
ø Í Ö ¦ s r
kis 9, g(λ) H F g$ 3 Ä » _ Û ¼& 7 à Ô! 3 Ü ¼ Ð
¸ H 1 l x{ 9 ô Ç + þ AI \ ¦ ° ú H ¦ & ñ Ù þ ¡ . ô Ç © _ Ú
ÔA Õ ª © É r 6 £ § õ ° ú s ³ ð & ³ ) a .
λ
k1= λ
11+(k−1)∆λ
p−p, λ
k2= λ
11+(2n−k−2)∆λ
p−p(2) d
(2)\ " f ∆λ
p−p É r Ú ÔA Õ ª © [ þ t _ 1 l x{ 9 ô Ç ç ß s 9
n É r G ' p" f_ Ì Ã ºs .
Fig. 2. (Color online) Calculated reference, perturbed, and difference spectrum.
+ þ A ε = {ε
k} s ÷ &% 3 ` ¦ M :, 8 £ ¤& ñ Û ¼& 7 à Ô! 3 É r d (3) õ ° ú s ³ ð & ³½ + É Ã º e .
R(λ, ε)
n
X
k=1 2
X
i=1
r
ki· g(λ − λ
ki(ε
k)) + N oise(λ) (3)
s
d \ " f λ
ki(ε
k) H Ú ÔA Õ ª © _ s 1 l x` ¦ ? / 9 N oise(λ) H G ' p" f r Û ¼% 7 s ° ú H ª ô Ç ¸ ú 6 £ §` ¦ ³ ð & ³ô Ç
.
Û
¼& 7 à Ô! 3 I Õ ª ~ ½ ÓZ O \ @ /ô Ç s : r& h 7 £ x` ¦ 0 A
#
Opti-Grating á Ô ÐÕ ªÏ þ ` ¦ s 6 x # 40> h G ' p" f (80> h F
g$ 3 Ä » )\ @ /ô Ç í ß ¸_ \ ¦ ô Ç > í ß õ Fig.
2 \ e . Ú ÔA Õ ª © ç ß ∆λ
p−p H 0.1 nm s 9 ì ø Í Ö ¦ É r r
ki H ¸¿ º 1 l x{ 9 > 10.5 %\ ¦ ° ú ¸2 ¤ [ O
>
% i . Ã ºu K $ 3 \ _ ô Ç Û ¼& 7 à Ô! 3 > í ß É r 1 pm _ ì r K
0 p x` ¦ ° ú ¸2 ¤ 10 nm _ # 3 0 A\ " f 10001 > h\ ¦ Ò re ¦a A
#
6 x % i . + þ As ÷ &t · ú § ¤` ¦ M :_ l ï r Û ¼
&
7 à Ô! 3 õ 1> h_ G ' p" f\ 10-1000 µε_ + þ As ÷ &% 3
`
¦ M :_ × æ o ) a Û ¼& 7 à Ô! 3 s ý a8 £ ¤ \ Õ ª 94 R e Ü ¼ 9 ¿ º Û
¼& 7 à Ô! 3 _ s Ä º8 £ ¤ \ Õ ª 94 R e . s Û ¼& 7 à Ô! 3
`
¦ R
+(λ, ε) Û ¼& 7 à Ô! 3 õ R
−(λ, ε) Û ¼& 7 à Ô! 3 Ü ¼ Ð ¾ º ¦, R
−(λ, ε) Û ¼& 7 à Ô! 3 ` ¦ s 6 x 1> h_ G ' p" f\ K { © H 2 > h_ FBG Û ¼& 7 à Ô! 3 _ × æd © ` ¦ d # s 1 l x ô Ç G '
p" f\ ¦ d Z > ½ + É Ã º e [5]. × æd © _ & ñ ` ¦ 0 A #
6 x ô Ç þ j& h o · ú ¦o 7 £ § É r simulated annealing ~ ½ ÓZ O s 9 þ j è o ÷ &# Q ½ + É 3 l q& h < ÊÃ º O(λ) H 6 £ § õ ° ú .
O(λ) = X
[R(λ, ε) − F (λ)]
2(4)
F (λ) =
n
X
k=1 2
X
i=1
