Abstract

The performance of post-processing techniques carried out on the Brillouin gain spectrum to estimate the Brillouin frequency shift (BFS) in standard Brillouin distributed sensors is evaluated. Curve fitting methods with standard functions such as polynomial and Lorentzian, as well as correlation techniques such as Lorentzian Cross-correlation and Cross Reference Plot Analysis (CRPA), are considered for the analysis. The fitting procedures and key parameters for each technique are optimized, and the performance in terms of BFS uncertainty, BFS offset error and processing time is compared by numerical simulations and through controlled experiments. Such a quantitative comparison is performed in varying conditions including signal-to-noise ratio (SNR), frequency measurement step, and BGS truncation. It is demonstrated that the Lorentzian cross-correlation technique results in the largest BFS offset error due to truncation, while exhibiting the smallest BFS uncertainty and the shortest processing time. A novel approach is proposed to compensate such a BFS offset error, which enables the Lorentzian cross-correlation technique to completely outperform other fitting methods.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. T. Kurashima, T. Horiguchi, and M. Tateda, “Distributed-temperature sensing using stimulated Brillouin scattering in optical silica fibers,” Opt. Lett. 15(18), 1038–1040 (1990).
    [Crossref] [PubMed]
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    [Crossref]
  3. M. Nikles, L. Thévenaz, and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
    [Crossref]
  4. A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, Part A, 81–103 (2016).
    [Crossref]
  5. M. A. Soto and L. Thévenaz, “Modeling and evaluating the performance of Brillouin distributed optical fiber sensors,” Opt. Express 21(25), 31347–31366 (2013).
    [Crossref]
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  7. A. W. Brown, M. D. DeMerchant, X. Bao, and T. W. Bremner,“Spatial resolution enhancement of a Brillouin-distributed sensor using a novel signal processing method,” J. Lightwave Technol. 17(7), 1179 (1999).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  13. Y. Zhang, D. Li, X. Fu, and W. Bi, “An improved Levenberg–Marquardt algorithm for extracting the Features of Brillouin scattering spectrum,” Meas. Sci. Technol. 2(1), 015204 (2013).
    [Crossref]
  14. L. Zhao, Y. Li, and Z. Xu, “A fast and high accurate initial values obtainment method for Brillouin scattering spectrum parameter estimation,” Sensor. Actuat. A-Phys. 210, 141–146 (2014).
    [Crossref]
  15. Y. Zhang, G. Fu, Y. Liu, W. Bi, and L. Weihong, “A novel fitting algorithm for Brillouin scattering spectrum of distributed sensing systems based on RBFN networks,” Optik 124(8), 718–721 (2013).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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  20. O. L. Bot, J. I. Mars, and C. Gervaise, “Similarity matrix analysis and divergence measures for statistical detection of unknown deterministic signals hidden in additive noise,” Phys. Lett. A 379(40), 2597–2609 (2015).
    [Crossref]
  21. F. Wang, W. Zhan, Y. Lu, Z. Yan, and X. Zhang, “Determining the Change of Brillouin Frequency Shift by Using the Similarity Matching Method,” J. Lightwave Technol. 33(19), 4101–4108 (2015).
    [Crossref]
  22. M. Alem, M. A. Soto, M. Tur, and L. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” in 25th International Conference on Optical Fiber Sensors, 103239J (2017).
  23. M. Alem, M. A. Soto, and L. Thévenaz, “Analytical model and experimental verification of the critical power for modulation instability in optical fibers,” Opt. Express 23(23), 29514–2532 (2015).
    [Crossref] [PubMed]
  24. S. Kanakambaran, R. Sarathi, and B. Srinivasan, “Identification and localization of partial discharge in transformer insulation adopting cross recurrence plot analysis of acoustic signals detected using fiber Bragg gratings,” IEEE T. Dielect. El. In. 24(3), 1773–1780 (2017).
    [Crossref]
  25. A. Dominguez-Lopez, Z. Yang, M. A. Soto, X. Angulo-Vinuesa, S. Martín-López, L. Thévenaz, and M. González-Herráez, “Novel scanning method for distortion-free BOTDA measurements,” Opt. Express 24(10), 10188–10204 (2016).
    [Crossref] [PubMed]
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    [Crossref]

2017 (1)

S. Kanakambaran, R. Sarathi, and B. Srinivasan, “Identification and localization of partial discharge in transformer insulation adopting cross recurrence plot analysis of acoustic signals detected using fiber Bragg gratings,” IEEE T. Dielect. El. In. 24(3), 1773–1780 (2017).
[Crossref]

2016 (3)

2015 (3)

2014 (1)

L. Zhao, Y. Li, and Z. Xu, “A fast and high accurate initial values obtainment method for Brillouin scattering spectrum parameter estimation,” Sensor. Actuat. A-Phys. 210, 141–146 (2014).
[Crossref]

2013 (4)

Y. Zhang, G. Fu, Y. Liu, W. Bi, and L. Weihong, “A novel fitting algorithm for Brillouin scattering spectrum of distributed sensing systems based on RBFN networks,” Optik 124(8), 718–721 (2013).
[Crossref]

Y. Zhang, D. Li, X. Fu, and W. Bi, “An improved Levenberg–Marquardt algorithm for extracting the Features of Brillouin scattering spectrum,” Meas. Sci. Technol. 2(1), 015204 (2013).
[Crossref]

M. A. Farahani, E. Castillo-Guerra, and B.G. Colpitts, “A detailed evaluation of the correlation-based method used for estimation of the brillouin frequency shift in BOTDA sensors,” IEEE Sens. J. 13(12), 4589–4598 (2013).
[Crossref]

M. A. Soto and L. Thévenaz, “Modeling and evaluating the performance of Brillouin distributed optical fiber sensors,” Opt. Express 21(25), 31347–31366 (2013).
[Crossref]

2011 (1)

2008 (1)

C. Zhang, Y. Yang, and A. Li, “Application of Levenberg-Marquardt algorithm in the Brillouin spectrum fitting,” Proc. SPIE 7129, 71291Y (2008).
[Crossref]

2007 (1)

N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, “Recurrence plots for the analysis of complex systems,” Phys. Rep. 438(5), 237–329 (2007).
[Crossref]

2005 (1)

2004 (1)

C. Kanzow, N. Yamashita, and M. Fukushima, “Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints,” Comput. Appl. Math. 172, 375–397 (2004).
[Crossref]

1999 (1)

1997 (1)

M. Nikles, L. Thévenaz, and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
[Crossref]

1995 (1)

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

1990 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

Alem, M.

M. Alem, M. A. Soto, and L. Thévenaz, “Analytical model and experimental verification of the critical power for modulation instability in optical fibers,” Opt. Express 23(23), 29514–2532 (2015).
[Crossref] [PubMed]

M. Alem, M. A. Soto, M. Tur, and L. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” in 25th International Conference on Optical Fiber Sensors, 103239J (2017).

Angulo-Vinuesa, X.

Bao, X.

Bergman, A.

A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, Part A, 81–103 (2016).
[Crossref]

Bi, W.

Y. Zhang, D. Li, X. Fu, and W. Bi, “An improved Levenberg–Marquardt algorithm for extracting the Features of Brillouin scattering spectrum,” Meas. Sci. Technol. 2(1), 015204 (2013).
[Crossref]

Y. Zhang, G. Fu, Y. Liu, W. Bi, and L. Weihong, “A novel fitting algorithm for Brillouin scattering spectrum of distributed sensing systems based on RBFN networks,” Optik 124(8), 718–721 (2013).
[Crossref]

Bot, O. L.

O. L. Bot, J. I. Mars, C. Gervaise, and Y. Simard,“Cross recurrence plot analysis based method for tdoa estimation of underwater acoustic signals,” in Proceedings of 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (IEEE, 2015)

Bremner, T. W.

Brown, A. W.

Castillo-Guerra, E.

M. A. Farahani, E. Castillo-Guerra, and B.G. Colpitts, “A detailed evaluation of the correlation-based method used for estimation of the brillouin frequency shift in BOTDA sensors,” IEEE Sens. J. 13(12), 4589–4598 (2013).
[Crossref]

M. A. Farahani, E. Castillo-Guerra, and B. G. Colpitts, “Accurate estimation of Brillouin frequency shift in Brillouin optical time domain analysis sensors using cross correlation,” Opt. Lett. 36(21), 4275–4277 (2011).
[Crossref] [PubMed]

Colpitts, B. G.

Colpitts, B.G.

M. A. Farahani, E. Castillo-Guerra, and B.G. Colpitts, “A detailed evaluation of the correlation-based method used for estimation of the brillouin frequency shift in BOTDA sensors,” IEEE Sens. J. 13(12), 4589–4598 (2013).
[Crossref]

DeMerchant, M. D.

Dominguez-Lopez, A.

Farahani, M. A.

M. A. Farahani, E. Castillo-Guerra, and B.G. Colpitts, “A detailed evaluation of the correlation-based method used for estimation of the brillouin frequency shift in BOTDA sensors,” IEEE Sens. J. 13(12), 4589–4598 (2013).
[Crossref]

M. A. Farahani, E. Castillo-Guerra, and B. G. Colpitts, “Accurate estimation of Brillouin frequency shift in Brillouin optical time domain analysis sensors using cross correlation,” Opt. Lett. 36(21), 4275–4277 (2011).
[Crossref] [PubMed]

Fu, G.

Y. Zhang, G. Fu, Y. Liu, W. Bi, and L. Weihong, “A novel fitting algorithm for Brillouin scattering spectrum of distributed sensing systems based on RBFN networks,” Optik 124(8), 718–721 (2013).
[Crossref]

Fu, X.

Y. Zhang, D. Li, X. Fu, and W. Bi, “An improved Levenberg–Marquardt algorithm for extracting the Features of Brillouin scattering spectrum,” Meas. Sci. Technol. 2(1), 015204 (2013).
[Crossref]

Fukushima, M.

C. Kanzow, N. Yamashita, and M. Fukushima, “Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints,” Comput. Appl. Math. 172, 375–397 (2004).
[Crossref]

Garcés, I.

Gervaise, C.

O. L. Bot, J. I. Mars, and C. Gervaise, “Similarity matrix analysis and divergence measures for statistical detection of unknown deterministic signals hidden in additive noise,” Phys. Lett. A 379(40), 2597–2609 (2015).
[Crossref]

O. L. Bot, J. I. Mars, C. Gervaise, and Y. Simard,“Cross recurrence plot analysis based method for tdoa estimation of underwater acoustic signals,” in Proceedings of 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (IEEE, 2015)

González-Herráez, M.

Haneef, S. M.

S. M. Haneef, K. Srijith, D. Venkitesh, and B. Srinivasan, “Accurate determination of Brillouin frequency based on cross recurrence plot analysis in Brillouin distributed fiber sensor,” in 25th International Conference on Optical Fiber Sensors, 103239M (2017).

Horiguchi, T.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

T. Kurashima, T. Horiguchi, and M. Tateda, “Distributed-temperature sensing using stimulated Brillouin scattering in optical silica fibers,” Opt. Lett. 15(18), 1038–1040 (1990).
[Crossref] [PubMed]

Kanakambaran, S.

S. Kanakambaran, R. Sarathi, and B. Srinivasan, “Identification and localization of partial discharge in transformer insulation adopting cross recurrence plot analysis of acoustic signals detected using fiber Bragg gratings,” IEEE T. Dielect. El. In. 24(3), 1773–1780 (2017).
[Crossref]

Kanzow, C.

C. Kanzow, N. Yamashita, and M. Fukushima, “Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints,” Comput. Appl. Math. 172, 375–397 (2004).
[Crossref]

Koyamada, Y.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

Kurashima, T.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

T. Kurashima, T. Horiguchi, and M. Tateda, “Distributed-temperature sensing using stimulated Brillouin scattering in optical silica fibers,” Opt. Lett. 15(18), 1038–1040 (1990).
[Crossref] [PubMed]

Kurths, J.

N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, “Recurrence plots for the analysis of complex systems,” Phys. Rep. 438(5), 237–329 (2007).
[Crossref]

L. Bot, O.

O. L. Bot, J. I. Mars, and C. Gervaise, “Similarity matrix analysis and divergence measures for statistical detection of unknown deterministic signals hidden in additive noise,” Phys. Lett. A 379(40), 2597–2609 (2015).
[Crossref]

Lázaro, J. A.

Li, A.

C. Zhang, Y. Yang, and A. Li, “Application of Levenberg-Marquardt algorithm in the Brillouin spectrum fitting,” Proc. SPIE 7129, 71291Y (2008).
[Crossref]

Li, C.

C. Li and Y. Li, “Fitting of Brillouin spectrum based on LabVIEW,” in 5th International Conference on Wireless Communications, Networking and Mobile Computing (IEEE, 2009) 1–4.

Li, D.

Y. Zhang, D. Li, X. Fu, and W. Bi, “An improved Levenberg–Marquardt algorithm for extracting the Features of Brillouin scattering spectrum,” Meas. Sci. Technol. 2(1), 015204 (2013).
[Crossref]

Li, Y.

L. Zhao, Y. Li, and Z. Xu, “A fast and high accurate initial values obtainment method for Brillouin scattering spectrum parameter estimation,” Sensor. Actuat. A-Phys. 210, 141–146 (2014).
[Crossref]

C. Li and Y. Li, “Fitting of Brillouin spectrum based on LabVIEW,” in 5th International Conference on Wireless Communications, Networking and Mobile Computing (IEEE, 2009) 1–4.

Liu, Y.

Y. Zhang, G. Fu, Y. Liu, W. Bi, and L. Weihong, “A novel fitting algorithm for Brillouin scattering spectrum of distributed sensing systems based on RBFN networks,” Optik 124(8), 718–721 (2013).
[Crossref]

López-Gil, A.

Lu, Y.

Mars, J. I.

O. L. Bot, J. I. Mars, and C. Gervaise, “Similarity matrix analysis and divergence measures for statistical detection of unknown deterministic signals hidden in additive noise,” Phys. Lett. A 379(40), 2597–2609 (2015).
[Crossref]

O. L. Bot, J. I. Mars, C. Gervaise, and Y. Simard,“Cross recurrence plot analysis based method for tdoa estimation of underwater acoustic signals,” in Proceedings of 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (IEEE, 2015)

Martín-López, S.

Marwan, N.

N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, “Recurrence plots for the analysis of complex systems,” Phys. Rep. 438(5), 237–329 (2007).
[Crossref]

Motil, A.

A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, Part A, 81–103 (2016).
[Crossref]

Nikles, M.

M. Nikles, L. Thévenaz, and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
[Crossref]

Robert, P.

M. Nikles, L. Thévenaz, and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
[Crossref]

Romano, M. C.

N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, “Recurrence plots for the analysis of complex systems,” Phys. Rep. 438(5), 237–329 (2007).
[Crossref]

Salinas, I.

Sarathi, R.

S. Kanakambaran, R. Sarathi, and B. Srinivasan, “Identification and localization of partial discharge in transformer insulation adopting cross recurrence plot analysis of acoustic signals detected using fiber Bragg gratings,” IEEE T. Dielect. El. In. 24(3), 1773–1780 (2017).
[Crossref]

Shimizu, K.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

Simard, Y.

O. L. Bot, J. I. Mars, C. Gervaise, and Y. Simard,“Cross recurrence plot analysis based method for tdoa estimation of underwater acoustic signals,” in Proceedings of 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (IEEE, 2015)

Soto, M.

Soto, M. A.

Srijith, K.

S. M. Haneef, K. Srijith, D. Venkitesh, and B. Srinivasan, “Accurate determination of Brillouin frequency based on cross recurrence plot analysis in Brillouin distributed fiber sensor,” in 25th International Conference on Optical Fiber Sensors, 103239M (2017).

Srinivasan, B.

S. Kanakambaran, R. Sarathi, and B. Srinivasan, “Identification and localization of partial discharge in transformer insulation adopting cross recurrence plot analysis of acoustic signals detected using fiber Bragg gratings,” IEEE T. Dielect. El. In. 24(3), 1773–1780 (2017).
[Crossref]

S. M. Haneef, K. Srijith, D. Venkitesh, and B. Srinivasan, “Accurate determination of Brillouin frequency based on cross recurrence plot analysis in Brillouin distributed fiber sensor,” in 25th International Conference on Optical Fiber Sensors, 103239M (2017).

Tateda, M.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

T. Kurashima, T. Horiguchi, and M. Tateda, “Distributed-temperature sensing using stimulated Brillouin scattering in optical silica fibers,” Opt. Lett. 15(18), 1038–1040 (1990).
[Crossref] [PubMed]

Thévenaz, L.

Thiel, M.

N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, “Recurrence plots for the analysis of complex systems,” Phys. Rep. 438(5), 237–329 (2007).
[Crossref]

Tur, M.

A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, Part A, 81–103 (2016).
[Crossref]

M. Alem, M. A. Soto, M. Tur, and L. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” in 25th International Conference on Optical Fiber Sensors, 103239J (2017).

Venkitesh, D.

S. M. Haneef, K. Srijith, D. Venkitesh, and B. Srinivasan, “Accurate determination of Brillouin frequency based on cross recurrence plot analysis in Brillouin distributed fiber sensor,” in 25th International Conference on Optical Fiber Sensors, 103239M (2017).

Villafranca, A.

Wang, F.

Weihong, L.

Y. Zhang, G. Fu, Y. Liu, W. Bi, and L. Weihong, “A novel fitting algorithm for Brillouin scattering spectrum of distributed sensing systems based on RBFN networks,” Optik 124(8), 718–721 (2013).
[Crossref]

Xu, Z.

L. Zhao, Y. Li, and Z. Xu, “A fast and high accurate initial values obtainment method for Brillouin scattering spectrum parameter estimation,” Sensor. Actuat. A-Phys. 210, 141–146 (2014).
[Crossref]

Yamashita, N.

C. Kanzow, N. Yamashita, and M. Fukushima, “Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints,” Comput. Appl. Math. 172, 375–397 (2004).
[Crossref]

Yan, Z.

Yang, Y.

C. Zhang, Y. Yang, and A. Li, “Application of Levenberg-Marquardt algorithm in the Brillouin spectrum fitting,” Proc. SPIE 7129, 71291Y (2008).
[Crossref]

Yang, Z.

Zhan, W.

Zhang, C.

C. Zhang, Y. Yang, and A. Li, “Application of Levenberg-Marquardt algorithm in the Brillouin spectrum fitting,” Proc. SPIE 7129, 71291Y (2008).
[Crossref]

Zhang, X.

Zhang, Y.

Y. Zhang, D. Li, X. Fu, and W. Bi, “An improved Levenberg–Marquardt algorithm for extracting the Features of Brillouin scattering spectrum,” Meas. Sci. Technol. 2(1), 015204 (2013).
[Crossref]

Y. Zhang, G. Fu, Y. Liu, W. Bi, and L. Weihong, “A novel fitting algorithm for Brillouin scattering spectrum of distributed sensing systems based on RBFN networks,” Optik 124(8), 718–721 (2013).
[Crossref]

Zhao, L.

L. Zhao, Y. Li, and Z. Xu, “A fast and high accurate initial values obtainment method for Brillouin scattering spectrum parameter estimation,” Sensor. Actuat. A-Phys. 210, 141–146 (2014).
[Crossref]

Comput. Appl. Math. (1)

C. Kanzow, N. Yamashita, and M. Fukushima, “Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints,” Comput. Appl. Math. 172, 375–397 (2004).
[Crossref]

IEEE Sens. J. (1)

M. A. Farahani, E. Castillo-Guerra, and B.G. Colpitts, “A detailed evaluation of the correlation-based method used for estimation of the brillouin frequency shift in BOTDA sensors,” IEEE Sens. J. 13(12), 4589–4598 (2013).
[Crossref]

IEEE T. Dielect. El. In. (1)

S. Kanakambaran, R. Sarathi, and B. Srinivasan, “Identification and localization of partial discharge in transformer insulation adopting cross recurrence plot analysis of acoustic signals detected using fiber Bragg gratings,” IEEE T. Dielect. El. In. 24(3), 1773–1780 (2017).
[Crossref]

J. Lightwave Technol. (4)

F. Wang, W. Zhan, Y. Lu, Z. Yan, and X. Zhang, “Determining the Change of Brillouin Frequency Shift by Using the Similarity Matching Method,” J. Lightwave Technol. 33(19), 4101–4108 (2015).
[Crossref]

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

M. Nikles, L. Thévenaz, and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1 BGS measured using standard BOTDA setup with 20 ns pump pulses (red trace) and the fit with a Lorentzian profile with a linewidth of 57 MHz.
Fig. 2
Fig. 2 (a) Simulation results showing a quadratic fit over a sample Lorentzian with SNR = 5 dB, represented by the noisy spectra points (in black circles). The obtained fit curve over FWHM (shaded region) is also shown as black. (b) Comparison of the BFS uncertainty obtained from quadratic fitting using direct peak search and the moving averaging technique with different window size for initial BFS value
Fig. 3
Fig. 3 BFS estimation using quadratic fitting technique for noisy BGS with (a) SNR = 5 dB and (b) SNR = 3 dB. Fitting window selected for each SNR condition is shown for reference and the green dot represents the measured BFS
Fig. 4
Fig. 4 (a) A noisy BGS with SNR =5 dB (red line) and the corresponding Lorentzian fit (blue line). Green dot represents the actual BFS and the black dot represents the BFS estimated using Lorentzian fitting. (b) BFS uncertainty estimated in different cases of initial BFS estimation. (c) BFS uncertainty estimated using different spectral fitting window size
Fig. 5
Fig. 5 A sample noisy spectrum with SNR of 5 dB (red line) and the (normalized) correlated output (black line)
Fig. 6
Fig. 6 (a) Reference Lorentzian spectrum and measured Brillouin spectrum from a hotspot with SNR of 5 dB and (b) The cross-recurrence plot corresponding to the similarity of the two delay-embedded spectra.
Fig. 7
Fig. 7 Experimental setup of a conventional BOTDA sensor scheme using a pump-probe configuration. SOA: Semiconductor Optical Amplifier, PPG: Programmable Pulse Generator, EDFA: Erbium Doped Fiber Amplifier, TA: Tunable Attenuator, EOM: Electro-Optic Modulator, FUT: Fiber Under Test, PS: Polarization Switch, PD: Photodetector, FBG: Fiber Bragg Grating
Fig. 8
Fig. 8 (a) 3D plot of measured BGS and (b) the SNR values obtained from the measured BGS along the 50 km standard single mode test fiber
Fig. 9
Fig. 9 BFS uncertainty based on simulations as well as experimental data for different BFS estimation techniques considered in our work
Fig. 10
Fig. 10 (a-c) Lorentzian spectrum with SNR = 5 dB, measured with a frequency scanning step of 1 MHz over a range from 10.605 GHz to 10.805 GHz (red line) along with the spectrum measured at larger frequency steps of 3 MHz, 5MHz and 7 MHz (blue line) respectively. BFS uncertainty as a function of different frequency scanning step, measured for different schemes for (d) SNR= 5 dB and (e) SNR= 3 dB
Fig. 11
Fig. 11 (a-d) Demonstration of performance of different BFS estimation techniques for a truncated BGS and (e) the BFS estimated using the these techniques for BGS truncated at a fixed position
Fig. 12
Fig. 12 (a) Offset error and (b)BFS uncertainty with BGS spectrum truncated at different positions for SNR = 5 dB
Fig. 13
Fig. 13 (a) Estimated offset error in the cross correlation technique for a truncated BGS. Estimated offset error for different truncation as a function of SNR of measured BGS is shown in inset. (b) The estimated offset error is shown as a function of difference between estimated BFS and the end frequency of scanning range plotted along with the corresponding exponential fit, (c) offset error as a function of the number of points after the actual BFS with and without compensation procedure is shown as a function of the number of points after the actual BFS.
Fig. 14
Fig. 14 (a) Estimated offset error in the cross correlation technique for a truncated BGS with (a) different linewidth and (b) different frequency scanning step are shown as a function of difference between estimated BFS and the end frequency of scanning range.

Tables (1)

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Table 1 Comparison of performance of BFS estimation techniques for different measurement conditions

Equations (12)

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g ( ν ) = g B 1 + 4 ( ν ν B Δ ν B ) 2
g r ( ν ) = 1 1 + 4 ( ν ν B Δ ν B r ) 2 ,
g n ( ν ) = g ( ν + ν s ) + n ( ν ) ,
G r n ( ν ) = g r ( ν ) g ( ν + ν s ) + g r ( ν ) n ( ν ) = G c ( ν ) + N c ( ν ) ,
C R P A ( i , j ) = S i m ( g n   ( ν ) , g n   ( ν ) ) ϵ
B F S = f p A exp ( c 1 ( f 2 f p ) ) ,
g ( ν ) = ( g ( f 1 ) , g ( f 2 ) ) , .. g ( f N g ) )
g n m ( ν ) = [ g n ( i ) , g n ( i + δ ) , g n ( + ( m 1 ) δ ) ] = [ g ( f 1 ) g ( f 2 ) g ( f 3 ) . . g ( f m ) g ( f 2 ) g ( f 3 ) g ( f 4 ) . . g ( f m + 1 ) . . . . . . . . . . . . g ( f N ) g ( f N + 1 ) g ( f N + 2 ) . . g ( f N g ) ]
g r m ( ν ) = [ g r ( j ) , g r ( j + δ ) , g r ( j + ( m 1 ) δ ) ]
d ( i , j ) = S i m ( g n   ( ν ) , g r   ( ν ) )
C R P A ( i , j ) = S i m ( g n   ( ν ) , g r   ( ν ) ) ϵ
S S ( ν ) = { i = 1 C R P A ( i ν , i ) d ( i ν , i ) i = 1 C R P A ( i + ν , i ) d ( i + ν , i )

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