Abstract

In this paper, a technique to estimate the deformation profile of a Sampled Fiber Bragg Grating (SFBG) is proposed and experimentally verified. From the SFBG intensity reflection spectrum, any arbitrary longitudinal axis deformation profile applied to a SFBG is estimated. The synthesis algorithm combines a custom defined error metric to compare the measured and the synthetic spectra and the Particle Swarm Optimization technique to get the deformation profile. Using controlled deformation profiles, the proposed method has been successfully checked by means of simulated and experimental tests. The results obtained under different controlled cases show a remarkable repetitiveness (< 50 με) and good spatial accuracy (< 1 mm).

© 2012 OSA

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  1. K. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
    [CrossRef]
  2. J. Lopez-Higuera, Handbook of Optical Fibre Sensing Technology (John Wiley and Sons Inc, 2002).
  3. Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2011).
    [CrossRef]
  4. Z. Zang and Y. Zhang, “Low-switching power (< 45 mw) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
    [CrossRef]
  5. M. LeBlanc, S. Huang, M. Ohn, A. Guemes, and A. Othonos, “Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis,” Opt. Lett. 21, 1405–1407 (1996).
    [CrossRef] [PubMed]
  6. S. Huang, M. M. Ohn, M. LeBlanc, and R. M. Measures, “Continuous arbitrary strain profile measurements with fiber Bragg gratings,” Smart Mater. Sruct. 7, 248–256 (1998).
    [CrossRef]
  7. J. Azaa and M. Muriel, “Reconstructing arbitrary strain distributions within fiber gratings by timefrequency signal analysis,” Opt. Lett. 25, 698–700 (2000).
    [CrossRef]
  8. X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
    [CrossRef]
  9. F. Casagrande, P. Crespi, A. Grassi, A. Lulli, R. Kenny, and M. Whelan, “From the reflected spectrum to the properties of a fiber Bragg grating: a genetic algorithm approach with application to distributed strain sensing,” Appl. Opt. 41, 5238–5244 (2002).
    [CrossRef] [PubMed]
  10. C. Cheng, Y. Lo, W. Li, C. Kuo, and H. Cheng, “Estimations of fiber Bragg grating parameters and strain gauge factor using optical spectrum and strain distribution information,” Appl. Opt. 46, 4555–4562 (2007).
    [CrossRef] [PubMed]
  11. F. Teng, W. Yin, F. Wu, Z. Li, and T. Wu, “Analysis of a fiber Bragg grating sensing system with transverse uniform press by using genetic algorithm,” Opto-electron. Lett. 4, 121–125 (2008).
  12. Z. Wu, Q. Qiao, F. Wu, and L. Cai, “Research on fiber Bragg grating spectral optimization with particle swarm optimization algorithm,” Appl. Mech. Mater. 128, 690–693 (2012).
    [CrossRef]
  13. B. Eggleton, P. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
    [CrossRef]
  14. J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of International Conference on Neural Networks, ed. (IEEE, 1995), vol. 4, pp. 1942–1948.
  15. M. Muriel and A. Carballar, “Internal field distributions in fiber Bragg gratings,” Phot. Tech. Lett. IEEE 9, 955–957 (1997).
    [CrossRef]

2012 (2)

Z. Zang and Y. Zhang, “Low-switching power (< 45 mw) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

Z. Wu, Q. Qiao, F. Wu, and L. Cai, “Research on fiber Bragg grating spectral optimization with particle swarm optimization algorithm,” Appl. Mech. Mater. 128, 690–693 (2012).
[CrossRef]

2011 (1)

Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2011).
[CrossRef]

2008 (1)

F. Teng, W. Yin, F. Wu, Z. Li, and T. Wu, “Analysis of a fiber Bragg grating sensing system with transverse uniform press by using genetic algorithm,” Opto-electron. Lett. 4, 121–125 (2008).

2007 (1)

2006 (1)

X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
[CrossRef]

2002 (1)

2000 (1)

1998 (1)

S. Huang, M. M. Ohn, M. LeBlanc, and R. M. Measures, “Continuous arbitrary strain profile measurements with fiber Bragg gratings,” Smart Mater. Sruct. 7, 248–256 (1998).
[CrossRef]

1997 (2)

K. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
[CrossRef]

M. Muriel and A. Carballar, “Internal field distributions in fiber Bragg gratings,” Phot. Tech. Lett. IEEE 9, 955–957 (1997).
[CrossRef]

1996 (1)

1994 (1)

B. Eggleton, P. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

Azaa, J.

Boisrobert, C.

X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
[CrossRef]

Cai, L.

Z. Wu, Q. Qiao, F. Wu, and L. Cai, “Research on fiber Bragg grating spectral optimization with particle swarm optimization algorithm,” Appl. Mech. Mater. 128, 690–693 (2012).
[CrossRef]

Carballar, A.

M. Muriel and A. Carballar, “Internal field distributions in fiber Bragg gratings,” Phot. Tech. Lett. IEEE 9, 955–957 (1997).
[CrossRef]

Casagrande, F.

Casari, P.

X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
[CrossRef]

Chapeleau, X.

X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
[CrossRef]

Cheng, C.

Cheng, H.

Crespi, P.

Eberhart, R.

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of International Conference on Neural Networks, ed. (IEEE, 1995), vol. 4, pp. 1942–1948.

Eggleton, B.

B. Eggleton, P. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

Grassi, A.

Guemes, A.

Hill, K.

K. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
[CrossRef]

Huang, S.

S. Huang, M. M. Ohn, M. LeBlanc, and R. M. Measures, “Continuous arbitrary strain profile measurements with fiber Bragg gratings,” Smart Mater. Sruct. 7, 248–256 (1998).
[CrossRef]

M. LeBlanc, S. Huang, M. Ohn, A. Guemes, and A. Othonos, “Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis,” Opt. Lett. 21, 1405–1407 (1996).
[CrossRef] [PubMed]

Kennedy, J.

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of International Conference on Neural Networks, ed. (IEEE, 1995), vol. 4, pp. 1942–1948.

Kenny, R.

Krug, P.

B. Eggleton, P. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

Kuo, C.

LeBlanc, M.

S. Huang, M. M. Ohn, M. LeBlanc, and R. M. Measures, “Continuous arbitrary strain profile measurements with fiber Bragg gratings,” Smart Mater. Sruct. 7, 248–256 (1998).
[CrossRef]

M. LeBlanc, S. Huang, M. Ohn, A. Guemes, and A. Othonos, “Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis,” Opt. Lett. 21, 1405–1407 (1996).
[CrossRef] [PubMed]

Leduc, D.

X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
[CrossRef]

Li, W.

Li, Z.

F. Teng, W. Yin, F. Wu, Z. Li, and T. Wu, “Analysis of a fiber Bragg grating sensing system with transverse uniform press by using genetic algorithm,” Opto-electron. Lett. 4, 121–125 (2008).

Lo, Y.

Lopez-Higuera, J.

J. Lopez-Higuera, Handbook of Optical Fibre Sensing Technology (John Wiley and Sons Inc, 2002).

Lulli, A.

Lupi, C.

X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
[CrossRef]

Measures, R. M.

S. Huang, M. M. Ohn, M. LeBlanc, and R. M. Measures, “Continuous arbitrary strain profile measurements with fiber Bragg gratings,” Smart Mater. Sruct. 7, 248–256 (1998).
[CrossRef]

Meltz, G.

K. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
[CrossRef]

Muriel, M.

J. Azaa and M. Muriel, “Reconstructing arbitrary strain distributions within fiber gratings by timefrequency signal analysis,” Opt. Lett. 25, 698–700 (2000).
[CrossRef]

M. Muriel and A. Carballar, “Internal field distributions in fiber Bragg gratings,” Phot. Tech. Lett. IEEE 9, 955–957 (1997).
[CrossRef]

Ny, R.

X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
[CrossRef]

Ohn, M.

Ohn, M. M.

S. Huang, M. M. Ohn, M. LeBlanc, and R. M. Measures, “Continuous arbitrary strain profile measurements with fiber Bragg gratings,” Smart Mater. Sruct. 7, 248–256 (1998).
[CrossRef]

Othonos, A.

Ouellette, F.

B. Eggleton, P. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

Poladian, L.

B. Eggleton, P. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

Qiao, Q.

Z. Wu, Q. Qiao, F. Wu, and L. Cai, “Research on fiber Bragg grating spectral optimization with particle swarm optimization algorithm,” Appl. Mech. Mater. 128, 690–693 (2012).
[CrossRef]

Scudeller, Y.

X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
[CrossRef]

Teng, F.

F. Teng, W. Yin, F. Wu, Z. Li, and T. Wu, “Analysis of a fiber Bragg grating sensing system with transverse uniform press by using genetic algorithm,” Opto-electron. Lett. 4, 121–125 (2008).

Whelan, M.

Wu, F.

Z. Wu, Q. Qiao, F. Wu, and L. Cai, “Research on fiber Bragg grating spectral optimization with particle swarm optimization algorithm,” Appl. Mech. Mater. 128, 690–693 (2012).
[CrossRef]

F. Teng, W. Yin, F. Wu, Z. Li, and T. Wu, “Analysis of a fiber Bragg grating sensing system with transverse uniform press by using genetic algorithm,” Opto-electron. Lett. 4, 121–125 (2008).

Wu, T.

F. Teng, W. Yin, F. Wu, Z. Li, and T. Wu, “Analysis of a fiber Bragg grating sensing system with transverse uniform press by using genetic algorithm,” Opto-electron. Lett. 4, 121–125 (2008).

Wu, Z.

Z. Wu, Q. Qiao, F. Wu, and L. Cai, “Research on fiber Bragg grating spectral optimization with particle swarm optimization algorithm,” Appl. Mech. Mater. 128, 690–693 (2012).
[CrossRef]

Yin, W.

F. Teng, W. Yin, F. Wu, Z. Li, and T. Wu, “Analysis of a fiber Bragg grating sensing system with transverse uniform press by using genetic algorithm,” Opto-electron. Lett. 4, 121–125 (2008).

Zang, Z.

Z. Zang and Y. Zhang, “Low-switching power (< 45 mw) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2011).
[CrossRef]

Zhang, Y.

Z. Zang and Y. Zhang, “Low-switching power (< 45 mw) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

Appl. Mech. Mater. (1)

Z. Wu, Q. Qiao, F. Wu, and L. Cai, “Research on fiber Bragg grating spectral optimization with particle swarm optimization algorithm,” Appl. Mech. Mater. 128, 690–693 (2012).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (1)

B. Eggleton, P. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[CrossRef]

J. Lightwave Technol. (1)

K. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
[CrossRef]

J. Mod. Opt. (1)

Z. Zang and Y. Zhang, “Low-switching power (< 45 mw) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

J. Opt. A-Pure Appl. Op. (1)

X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R. Ny, and C. Boisrobert, “Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fiber Bragg gratings,” J. Opt. A-Pure Appl. Op. 8, 775 (2006).
[CrossRef]

Opt. Commun. (1)

Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2011).
[CrossRef]

Opt. Lett. (2)

Opto-electron. Lett. (1)

F. Teng, W. Yin, F. Wu, Z. Li, and T. Wu, “Analysis of a fiber Bragg grating sensing system with transverse uniform press by using genetic algorithm,” Opto-electron. Lett. 4, 121–125 (2008).

Phot. Tech. Lett. IEEE (1)

M. Muriel and A. Carballar, “Internal field distributions in fiber Bragg gratings,” Phot. Tech. Lett. IEEE 9, 955–957 (1997).
[CrossRef]

Smart Mater. Sruct. (1)

S. Huang, M. M. Ohn, M. LeBlanc, and R. M. Measures, “Continuous arbitrary strain profile measurements with fiber Bragg gratings,” Smart Mater. Sruct. 7, 248–256 (1998).
[CrossRef]

Other (2)

J. Lopez-Higuera, Handbook of Optical Fibre Sensing Technology (John Wiley and Sons Inc, 2002).

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of International Conference on Neural Networks, ed. (IEEE, 1995), vol. 4, pp. 1942–1948.

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Figures (9)

Fig. 1
Fig. 1

No apodized (a(z) = 1) Sampled FBG illustration. A periodic sampling function (s(z)) is applied to the FBG structure creating extra reflection peaks on the reflection spectrum.

Fig. 2
Fig. 2

Some parameters of the employed error metric are applied to two different spectra. The main peak from both spectra are just considered for drawing clarity.

Fig. 3
Fig. 3

Five solutions obtained by the proposed optimization algorithm compared to the reference deformation values used to generate the artificial spectrum (left) and a synthetic spectrum generated with the PSO solution compared to the artificial (desired) one (right).

Fig. 4
Fig. 4

Continuous strain profile used to compute the artificial spectrum compared to five PSO solutions (left) and a synthetic spectrum compared to the artificial one (right).

Fig. 5
Fig. 5

Illustration of the sampled apodized SFBG profile(left) and its characteristic spectrum (right) used in the experimental demonstration.

Fig. 6
Fig. 6

Right: spectrum of the written SFBG before being embedded into the resin block (solid line) and after the embodiment (dashed line) against their synthetic spectra (thin lines). On the left: the obtained deformation profile of the residual strain and its interpolation (dotted line).

Fig. 7
Fig. 7

Resin block dimensions and SFBG location (left). Simulated deformation profile applied to the SFBG (right)

Fig. 8
Fig. 8

Experimental setup employed for loading the resin block. The block is glued to two aluminum pieces which are slightly separated using a ball screw positioner.

Fig. 9
Fig. 9

Deformation profile of the measured spectrum (compensated and not) against the simulated normalized deformation (left). Measured spectrum of the SFBG under load condition compared with its synthetic one (right).

Equations (4)

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Δ n ( z ) = s ( z ) a ( z ) A ( z ) e ( j 2 π Λ z + j ϕ ( z ) ) + c . c .
s ( z ) = m F m e ( j 2 m π P z ) ) .
{ v i d ( t + 1 ) = w v i d ( t ) + c 1 r 1 ( p i d ( t ) x i d ( t ) ) + c 1 r 1 ( p g d ( t ) x i d ( t ) ) x i d ( t + 1 ) = x i d ( t ) + v i d ( t + 1 )
{ X i = ( x i 1 , x i 2 , , x i N ) V i = ( v i 1 , v i 2 , , v i N )

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