Abstract

Current methods of estimating the Brillouin frequency shift in Brillouin optical time domain analysis sensors are based on curve-fitting techniques. These techniques apply the same weight to all portions of the curve and dutifully fit into the peak and noisy ends of the curve. This makes them very sensitive to noise, initialization of fitting param eters, symmetry, and start and stop frequencies. We introduce a method based on the cross-correlation technique to estimate the central frequency of noisy Lorentzian curves, which is more robust to noise and free from initial settings of fitting parameters.

© 2011 Optical Society of America

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References

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  1. A. Yariv, Optical Electronics (CBS College Publishing, 1985).
  2. M. Nikles, L. Thevenaz, and P. A. Robert, J. Lightwave Technol. 15, 1842 (1997).
    [CrossRef]
  3. A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
    [CrossRef] [PubMed]
  4. X. Bao, A. Brown, M. DeMerchant, and J. Smith, Opt. Lett. 24, 510 (1999).
    [CrossRef]
  5. Z. Liu, G. Ferrier, X. Bao, X. Zeng, Q. Yu, and A. Kim, in 7th International Symposium on Fire Safety Conference (ISFPA, 2002), pp. 221–232.
  6. K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (Informatics and Mathematical Modeling Technical University of Denmark, 2004).
  7. G. Seber and C. J. Wild, Nonlinear Regression (Wiley-Interscience, 2003).
  8. M. DeMerchant, A. Brown, X. Bao, and T. Bremner, Proc. SPIE 3330, 315 (1998).
    [CrossRef]
  9. A. W. Brown, B. G. Colpitts, and K. Brown, J. Lightwave Technol. 25, 381 (2007).
    [CrossRef]
  10. F. Ravet, in Sensing Issues in Civil Structural Health Monitoring (Springer, 2005), pp. 515–524.
    [CrossRef]
  11. C. Li and Y. Li, “Fitting of Brillouin spectrum based on LabVIEW,” presented at the 5th International Conference on Wireless Communications, Networking and Mobile Computing, Beijing, China, September 24–26, 2009.
  12. L. Ngia, J. Sjöberg, and M. Viberg, in Conference Record of the 32nd Asilomar Conference on Signals, Systems, and Computers, 1998 (IEEE, 1998), pp. 697–701.

2007 (1)

1999 (1)

1998 (1)

M. DeMerchant, A. Brown, X. Bao, and T. Bremner, Proc. SPIE 3330, 315 (1998).
[CrossRef]

1997 (1)

M. Nikles, L. Thevenaz, and P. A. Robert, J. Lightwave Technol. 15, 1842 (1997).
[CrossRef]

1991 (1)

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Bao, X.

X. Bao, A. Brown, M. DeMerchant, and J. Smith, Opt. Lett. 24, 510 (1999).
[CrossRef]

M. DeMerchant, A. Brown, X. Bao, and T. Bremner, Proc. SPIE 3330, 315 (1998).
[CrossRef]

Z. Liu, G. Ferrier, X. Bao, X. Zeng, Q. Yu, and A. Kim, in 7th International Symposium on Fire Safety Conference (ISFPA, 2002), pp. 221–232.

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Bremner, T.

M. DeMerchant, A. Brown, X. Bao, and T. Bremner, Proc. SPIE 3330, 315 (1998).
[CrossRef]

Brown, A.

X. Bao, A. Brown, M. DeMerchant, and J. Smith, Opt. Lett. 24, 510 (1999).
[CrossRef]

M. DeMerchant, A. Brown, X. Bao, and T. Bremner, Proc. SPIE 3330, 315 (1998).
[CrossRef]

Brown, A. W.

Brown, K.

Colpitts, B. G.

DeMerchant, M.

X. Bao, A. Brown, M. DeMerchant, and J. Smith, Opt. Lett. 24, 510 (1999).
[CrossRef]

M. DeMerchant, A. Brown, X. Bao, and T. Bremner, Proc. SPIE 3330, 315 (1998).
[CrossRef]

Ferrier, G.

Z. Liu, G. Ferrier, X. Bao, X. Zeng, Q. Yu, and A. Kim, in 7th International Symposium on Fire Safety Conference (ISFPA, 2002), pp. 221–232.

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Kim, A.

Z. Liu, G. Ferrier, X. Bao, X. Zeng, Q. Yu, and A. Kim, in 7th International Symposium on Fire Safety Conference (ISFPA, 2002), pp. 221–232.

Li, C.

C. Li and Y. Li, “Fitting of Brillouin spectrum based on LabVIEW,” presented at the 5th International Conference on Wireless Communications, Networking and Mobile Computing, Beijing, China, September 24–26, 2009.

Li, Y.

C. Li and Y. Li, “Fitting of Brillouin spectrum based on LabVIEW,” presented at the 5th International Conference on Wireless Communications, Networking and Mobile Computing, Beijing, China, September 24–26, 2009.

Liu, Z.

Z. Liu, G. Ferrier, X. Bao, X. Zeng, Q. Yu, and A. Kim, in 7th International Symposium on Fire Safety Conference (ISFPA, 2002), pp. 221–232.

Madsen, K.

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (Informatics and Mathematical Modeling Technical University of Denmark, 2004).

Ngia, L.

L. Ngia, J. Sjöberg, and M. Viberg, in Conference Record of the 32nd Asilomar Conference on Signals, Systems, and Computers, 1998 (IEEE, 1998), pp. 697–701.

Nielsen, H. B.

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (Informatics and Mathematical Modeling Technical University of Denmark, 2004).

Nikles, M.

M. Nikles, L. Thevenaz, and P. A. Robert, J. Lightwave Technol. 15, 1842 (1997).
[CrossRef]

Ravet, F.

F. Ravet, in Sensing Issues in Civil Structural Health Monitoring (Springer, 2005), pp. 515–524.
[CrossRef]

Robert, P. A.

M. Nikles, L. Thevenaz, and P. A. Robert, J. Lightwave Technol. 15, 1842 (1997).
[CrossRef]

Seber, G.

G. Seber and C. J. Wild, Nonlinear Regression (Wiley-Interscience, 2003).

Sjöberg, J.

L. Ngia, J. Sjöberg, and M. Viberg, in Conference Record of the 32nd Asilomar Conference on Signals, Systems, and Computers, 1998 (IEEE, 1998), pp. 697–701.

Smith, J.

Thevenaz, L.

M. Nikles, L. Thevenaz, and P. A. Robert, J. Lightwave Technol. 15, 1842 (1997).
[CrossRef]

Tingleff, O.

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (Informatics and Mathematical Modeling Technical University of Denmark, 2004).

Viberg, M.

L. Ngia, J. Sjöberg, and M. Viberg, in Conference Record of the 32nd Asilomar Conference on Signals, Systems, and Computers, 1998 (IEEE, 1998), pp. 697–701.

Wild, C. J.

G. Seber and C. J. Wild, Nonlinear Regression (Wiley-Interscience, 2003).

Yariv, A.

A. Yariv, Optical Electronics (CBS College Publishing, 1985).

Yu, Q.

Z. Liu, G. Ferrier, X. Bao, X. Zeng, Q. Yu, and A. Kim, in 7th International Symposium on Fire Safety Conference (ISFPA, 2002), pp. 221–232.

Zeng, X.

Z. Liu, G. Ferrier, X. Bao, X. Zeng, Q. Yu, and A. Kim, in 7th International Symposium on Fire Safety Conference (ISFPA, 2002), pp. 221–232.

J. Lightwave Technol. (2)

M. Nikles, L. Thevenaz, and P. A. Robert, J. Lightwave Technol. 15, 1842 (1997).
[CrossRef]

A. W. Brown, B. G. Colpitts, and K. Brown, J. Lightwave Technol. 25, 381 (2007).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. DeMerchant, A. Brown, X. Bao, and T. Bremner, Proc. SPIE 3330, 315 (1998).
[CrossRef]

Other (7)

F. Ravet, in Sensing Issues in Civil Structural Health Monitoring (Springer, 2005), pp. 515–524.
[CrossRef]

C. Li and Y. Li, “Fitting of Brillouin spectrum based on LabVIEW,” presented at the 5th International Conference on Wireless Communications, Networking and Mobile Computing, Beijing, China, September 24–26, 2009.

L. Ngia, J. Sjöberg, and M. Viberg, in Conference Record of the 32nd Asilomar Conference on Signals, Systems, and Computers, 1998 (IEEE, 1998), pp. 697–701.

Z. Liu, G. Ferrier, X. Bao, X. Zeng, Q. Yu, and A. Kim, in 7th International Symposium on Fire Safety Conference (ISFPA, 2002), pp. 221–232.

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (Informatics and Mathematical Modeling Technical University of Denmark, 2004).

G. Seber and C. J. Wild, Nonlinear Regression (Wiley-Interscience, 2003).

A. Yariv, Optical Electronics (CBS College Publishing, 1985).

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Figures (4)

Fig. 1
Fig. 1

Ideal BGS.

Fig. 2
Fig. 2

Cross correlation between the reference and noisy Lorentzian curves.

Fig. 3
Fig. 3

Average of absolute error in the simulation. Inset, magnification of the correlation-based method.

Fig. 4
Fig. 4

Average of absolute error in the measurement.

Equations (5)

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

g ( ν ) = g B 1 + 4 ( ν ν B Δ ν B ) 2 .
ν B ( T , ε ) = C T Δ T + C ε ε + ν B 0 ,
g r ( ν ) = g B r 1 + 4 ( ν ν B r Δ ν B r ) 2 , g u ( ν ) = g B u 1 + 4 ( ν ν B u Δ ν B u ) 2 .
G c ( ν ) = G c 1 + 4 ( ν ν B c Δ ν B c ) 2 , { ν B c = ν B r + ν B u Δ ν B c = Δ ν B r + Δ ν B u .
G r n ( ν ) = g r ( ν ) * g n ( ν ) = g r ( ν ) * [ g u ( ν ) + n ( ν ) ] = g r ( ν ) * g u ( ν ) + g r ( ν ) * n ( ν ) = G c ( ν ) + N c ( ν ) .

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