Abstract

An inverse approach based on an optimization technique is proposed to characterize a fiber Bragg grating (FBG) and the strain gauge factor (GF) when the FBG is bonded on a structure. By bonding an FBG on a substrate and simply straining this FBG into a chirped fiber Bragg grating with a predesignated strain, the proposed method, based on an optimization technique, can be used to reconstruct seven parameters of the FBG from the corresponding reflective spectrum. The parameters identified are the length of an FBG, the grating period, the average refractive index, the index modulation, the apodization coefficient, the starting point bonded on the plate, and the strain GF. The information from the predesignated strain, as well as the measured reflective spectrum, is used as the objective function during the optimal search. As a result, the design sensitivity for the optimal search is much improved compared with the design sensitivity when only the reflective spectrum is used. In particular, the strain GF, which depends on the adhesive, the bonding layer characteristics, etc., can be determined in order to provide a reference for an FBG used as a strain sensor. Results from numerical simulations and experiments show that seven parameters of an FBG can be obtained accurately and efficiently.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. P. A. Krug, R. Stolte, and R. Ulrich, "Measurement of index modulation along an optical fiber Bragg grating," Opt. Lett. 20, 1767-1769 (1995).
    [CrossRef] [PubMed]
  2. D. Ramecourt, P. Bernage, P. Niay, M. Douay, and I. Riant, "Improvement in the measurement of index modulation along an optical fiber grating by movement of the probe spot perpendicularly to the fiber axis," Appl. Opt. 40, 6166-6169 (2001).
    [CrossRef]
  3. N. Roussel, S. Magne, C. Martinez, and P. Ferdinand, "Measurement of index modulation along fiber Bragg gratings by side scattering and local heating technique," Opt. Fiber Technol. 5, 119-132 (1999).
    [CrossRef]
  4. D. W. Huang and C. C. Yang, "Reconstruction of fiber grating refractive-index profiles from complex Bragg reflection spectra," Appl. Opt. 38, 4494-4499 (1999).
    [CrossRef]
  5. G. Cormier, R. Boudreau, and S. Thériault, "Real-coded genetic algorithm for Bragg grating parameter synthesis," J. Opt. Soc. Am. B 18, 1771-1776 (2001).
    [CrossRef]
  6. K. A. Winick and J. E. Roman, "Design of corrugated waveguide filters by Fourier-transform techniques," IEEE J. Quantum Electron. 26, 1918-1929 (1990).
    [CrossRef]
  7. E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel'fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996).
    [CrossRef]
  8. H. C. Cheng and Y. L. Lo, "The synthesis of multiple parameters of arbitrary FBGs via a genetic algorithm and two thermally-modulated intensity spectra," J. Lightwave Technol. 23, 2158-2168 (2005).
    [CrossRef]
  9. J. Skaar and K. M. Risvik, "A genetic algorithm for the inverse problem in synthesis of fiber gratings," J. Lightwave Technol. 16, 1928-1998 (1998).
    [CrossRef]
  10. P. Dong, J. Azana, and A. G. Kirk, "Synthesis of fiber Bragg grating parameters from reflectivity by means of simulated annealing algorithm," Opt. Commun. 28, 303-308 (2003).
    [CrossRef]
  11. C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, and S. R. Lai, "Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing," Opt. Commun. 26, 167-173 (2003).
    [CrossRef]
  12. C. C. Cheng, Y. L. Lo, B. S. Pun, E. M. Chang, and W. Y. Li, "An investigation of bonding layer characteristics of a substrate-bonded fiber Bragg grating," J. Lightwave Technol. 23, 3907-3915 (2005).
    [CrossRef]
  13. D. S. Li, H. N. Li, L. Ren, and G. Song, "Strain transferring analysis of fiber Bragg grating sensors," Opt. Eng. 45, 024402 (2006).
    [CrossRef]
  14. K. W. Yang, A. G. Liu, C. C. Cheng, and Y. L. Lo, "Topology and shape optimization of substrate using for chirp fiber Bragg grating spectrum tuning," J. Lightwave Technol. 20, 1182-1187 (2002).
    [CrossRef]
  15. S. Huang, M. LeBlanc, M. M. Ohn, and R. M. Measures, "Bragg intragrating structural sensing," Appl. Opt. 34, 5003-5009 (1995).
    [CrossRef] [PubMed]
  16. M. Matsuhara, K. O. Hill, and A. Watanabe, "Optical-waveguide filters: synthesis," J. Opt. Soc. Am. 65, 804-809 (1975).
    [CrossRef]
  17. M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, "Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis," Opt. Lett. 21, 1405-1407 (1996).
    [CrossRef] [PubMed]
  18. C. D. Butter and G. B. Hocker, "Fiber optics strain gauge," Appl. Opt. 17, 2867-1869 (1978).
    [CrossRef] [PubMed]
  19. R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, "Fiber-optic Bragg grating sensors for bridge monitoring," Cem. Concr. Compos. 19, 21-33 (1997).
    [CrossRef]
  20. Y. B. Lin, K. C. Chang, J. C. Chern, and L. A. Wang, "Packaging methods of fiber-Bragg grating sensors in civil structure applications," IEEE Sens. J. 5, 419-424 (2005).
    [CrossRef]
  21. P. Ferraro and G. de Natale, "On the possible use of optical fiber Bragg gratings as strain sensors for geodynamical monitoring," Opt. Lasers Eng. 37, 115-130 (2002).
    [CrossRef]

2006

D. S. Li, H. N. Li, L. Ren, and G. Song, "Strain transferring analysis of fiber Bragg grating sensors," Opt. Eng. 45, 024402 (2006).
[CrossRef]

2005

2003

P. Dong, J. Azana, and A. G. Kirk, "Synthesis of fiber Bragg grating parameters from reflectivity by means of simulated annealing algorithm," Opt. Commun. 28, 303-308 (2003).
[CrossRef]

C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, and S. R. Lai, "Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing," Opt. Commun. 26, 167-173 (2003).
[CrossRef]

2002

P. Ferraro and G. de Natale, "On the possible use of optical fiber Bragg gratings as strain sensors for geodynamical monitoring," Opt. Lasers Eng. 37, 115-130 (2002).
[CrossRef]

K. W. Yang, A. G. Liu, C. C. Cheng, and Y. L. Lo, "Topology and shape optimization of substrate using for chirp fiber Bragg grating spectrum tuning," J. Lightwave Technol. 20, 1182-1187 (2002).
[CrossRef]

2001

1999

D. W. Huang and C. C. Yang, "Reconstruction of fiber grating refractive-index profiles from complex Bragg reflection spectra," Appl. Opt. 38, 4494-4499 (1999).
[CrossRef]

N. Roussel, S. Magne, C. Martinez, and P. Ferdinand, "Measurement of index modulation along fiber Bragg gratings by side scattering and local heating technique," Opt. Fiber Technol. 5, 119-132 (1999).
[CrossRef]

1998

1997

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, "Fiber-optic Bragg grating sensors for bridge monitoring," Cem. Concr. Compos. 19, 21-33 (1997).
[CrossRef]

1996

E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel'fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996).
[CrossRef]

M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, "Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis," Opt. Lett. 21, 1405-1407 (1996).
[CrossRef] [PubMed]

1995

1990

K. A. Winick and J. E. Roman, "Design of corrugated waveguide filters by Fourier-transform techniques," IEEE J. Quantum Electron. 26, 1918-1929 (1990).
[CrossRef]

1978

1975

Appl. Opt.

Cem. Concr. Compos.

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, "Fiber-optic Bragg grating sensors for bridge monitoring," Cem. Concr. Compos. 19, 21-33 (1997).
[CrossRef]

IEEE J. Quantum Electron.

K. A. Winick and J. E. Roman, "Design of corrugated waveguide filters by Fourier-transform techniques," IEEE J. Quantum Electron. 26, 1918-1929 (1990).
[CrossRef]

E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel'fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996).
[CrossRef]

IEEE Sens. J.

Y. B. Lin, K. C. Chang, J. C. Chern, and L. A. Wang, "Packaging methods of fiber-Bragg grating sensors in civil structure applications," IEEE Sens. J. 5, 419-424 (2005).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Commun.

P. Dong, J. Azana, and A. G. Kirk, "Synthesis of fiber Bragg grating parameters from reflectivity by means of simulated annealing algorithm," Opt. Commun. 28, 303-308 (2003).
[CrossRef]

C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, and S. R. Lai, "Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing," Opt. Commun. 26, 167-173 (2003).
[CrossRef]

Opt. Eng.

D. S. Li, H. N. Li, L. Ren, and G. Song, "Strain transferring analysis of fiber Bragg grating sensors," Opt. Eng. 45, 024402 (2006).
[CrossRef]

Opt. Fiber Technol.

N. Roussel, S. Magne, C. Martinez, and P. Ferdinand, "Measurement of index modulation along fiber Bragg gratings by side scattering and local heating technique," Opt. Fiber Technol. 5, 119-132 (1999).
[CrossRef]

Opt. Lasers Eng.

P. Ferraro and G. de Natale, "On the possible use of optical fiber Bragg gratings as strain sensors for geodynamical monitoring," Opt. Lasers Eng. 37, 115-130 (2002).
[CrossRef]

Opt. Lett.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Forward and inverse approaches of a strained FBG.

Fig. 2
Fig. 2

FBG parameter estimation method using combined spectrum and strain distribution information.

Fig. 3
Fig. 3

Flow chart for FBG parameter synthesis.

Fig. 4
Fig. 4

(a) Top and side views of an FBG being surface bonded on a cantilevered trapezoid substrate. (b) Strain distribution at the middle of the substrate (dotted curve) and the strain in the FBG (solid curve).

Fig. 5
Fig. 5

Wavelength spectrum corresponding to the strained FBG of Fig. 4.

Fig. 6
Fig. 6

(a) Comparison between the target and calculated spectra. (b) Comparison between the target and calculated strain distributions.

Fig. 7
Fig. 7

Experimental setup.

Fig. 8
Fig. 8

(a) Wavelength spectrum of the FBG after bonding on the substrate. (b) Wavelength spectrum of the strained FBG after the substrate tip is deflected 3 mm.

Fig. 9
Fig. 9

(a) Comparisons between the measured and calculated spectra. (b) Comparisons between the predesignated and calculated strain distributions.

Tables (5)

Tables Icon

Table 1 Target Values for Seven FBG Parameters

Tables Icon

Table 2 Bounds Used in FBG Parameter Reconstruction

Tables Icon

Table 3 Comparison between Reconstructed and Target Parameters

Tables Icon

Table 4 Bounds Used in FBG Parameter Reconstruction

Tables Icon

Table 5 Comparison between Reconstructed and Known Parameters

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

λ ( z ) = 2 n ¯ ( z ) Λ o ( z ) [ 1 + ε o p t ( z ) ] ,
ε o p t ( z ) = ( 1 ξ ) ε ( z ) + δ n p e r m ( z ) n ¯ ,
λ ( z = 0 ) λ ( z ) ln [ 1 R ( λ ) ] d λ = π 2 2 0 z Δ n 2 ( z ) n ¯ ( z ) d z ,
Δ λ λ = G ( 1 n 2 2 ( p 12 + p 11 ε r r ε z z + p 12 ε θ θ ε z z ) ) ε z z ,
Δ λ λ = GF ε z z ,
GF = G ( 1 n 2 2 ( p 12 + p 11 ε r r ε z z + p 12 ε θ θ ε z z ) )
F = n = 1 N | ε o p t ε o b j ε o b j | + n = 1 N | R ( λ ) o p t R ( λ ) o b j R ( λ ) o b j | ,

Metrics