Abstract

A simple approach is proposed for quantifying the errors in measuring the Brillouin frequency shifts associated with stresses whose lengths are shorter than the pulse length. The smallest detectable Brillouin frequency shift is thus determined with respect to the size of the stressed sections and the frequency resolution. The lowest detectable frequency shift is found to be ~42% of the Brillouin gain natural linewidth. A worst-case iso-error curve that associates the minimum frequency shift to the length of the stressed region is derived. A minimum resolvable frequency shift and minimum detectable stress length are defined with an approach based on a Rayleigh equivalent criterion.

© 2005 Optical Society of America

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References

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  1. M. Niklès, L. Thévenaz, P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Light-wave Technol. 15, 1842–1851 (1997).
    [CrossRef]
  2. X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13, 1340–1348 (1995).
    [CrossRef]
  3. J. Smith, M. DeMerchant, A. Brown, X. Bao, “Simultaneous distributed strain and temperature measurement,” Appl. Opt. 38, 5372–5377 (1999).
    [CrossRef]
  4. H. Naruse, M. Tateda, H. Ohno, A. Shimada, “Deformation of the Brillouin gain spectrum caused by parabolic strain distribution and resulting measurement error in the BOTDR strain measurement system,” IEICE Trans. Electron. E86-C, 2111–2121 (2003).
  5. A. Brown, M. D. DeMerchant, X. Bao, W. Bremner, “Spatial resolution enhancement of a Brillouin-distributed sensor using a novel signal processing method,” J. Lightwave Technol. 17, 1179–1183 (1999).
    [CrossRef]
  6. T. Horigushi, K. Shimizu, T. Kurashima, M. Tateda, Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13, 1296–1302 (1995).
    [CrossRef]
  7. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).
  8. J. Smith, A. Brown, M. D. DeMerchant, X. Bao, “Pulse width dependence of the Brillouin loss spectrum,” Opt. Commun. 168, 393–398 (1999).
    [CrossRef]
  9. X. Bao, A. Brown, M. D. DeMerchant, J. Smith, “Characterization of the Brillouin-loss spectrum of single-mode fibers by use of very short (10 ns) pulses,” Opt. Lett. 24, 510–512 (1999).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics (Cambridge University, 1999).
    [CrossRef]
  11. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C, The Art of Scientific Computing, 1st ed. (Cambridge University, 1988).

2003

H. Naruse, M. Tateda, H. Ohno, A. Shimada, “Deformation of the Brillouin gain spectrum caused by parabolic strain distribution and resulting measurement error in the BOTDR strain measurement system,” IEICE Trans. Electron. E86-C, 2111–2121 (2003).

1999

1997

M. Niklès, L. Thévenaz, P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Light-wave Technol. 15, 1842–1851 (1997).
[CrossRef]

1995

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13, 1340–1348 (1995).
[CrossRef]

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

Agrawal, G. P.

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

Bao, X.

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge University, 1999).
[CrossRef]

Bremner, W.

Brown, A.

DeMerchant, M.

DeMerchant, M. D.

Dhliwayo, J.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13, 1340–1348 (1995).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C, The Art of Scientific Computing, 1st ed. (Cambridge University, 1988).

Heron, N.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13, 1340–1348 (1995).
[CrossRef]

Horigushi, T.

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

Jackson, D. A.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13, 1340–1348 (1995).
[CrossRef]

Koyamada, Y.

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

Kurashima, T.

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

Naruse, H.

H. Naruse, M. Tateda, H. Ohno, A. Shimada, “Deformation of the Brillouin gain spectrum caused by parabolic strain distribution and resulting measurement error in the BOTDR strain measurement system,” IEICE Trans. Electron. E86-C, 2111–2121 (2003).

Niklès, M.

M. Niklès, L. Thévenaz, P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Light-wave Technol. 15, 1842–1851 (1997).
[CrossRef]

Ohno, H.

H. Naruse, M. Tateda, H. Ohno, A. Shimada, “Deformation of the Brillouin gain spectrum caused by parabolic strain distribution and resulting measurement error in the BOTDR strain measurement system,” IEICE Trans. Electron. E86-C, 2111–2121 (2003).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C, The Art of Scientific Computing, 1st ed. (Cambridge University, 1988).

Robert, P. A.

M. Niklès, L. Thévenaz, P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Light-wave Technol. 15, 1842–1851 (1997).
[CrossRef]

Shimada, A.

H. Naruse, M. Tateda, H. Ohno, A. Shimada, “Deformation of the Brillouin gain spectrum caused by parabolic strain distribution and resulting measurement error in the BOTDR strain measurement system,” IEICE Trans. Electron. E86-C, 2111–2121 (2003).

Shimizu, K.

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

Smith, J.

Tateda, M.

H. Naruse, M. Tateda, H. Ohno, A. Shimada, “Deformation of the Brillouin gain spectrum caused by parabolic strain distribution and resulting measurement error in the BOTDR strain measurement system,” IEICE Trans. Electron. E86-C, 2111–2121 (2003).

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

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C, The Art of Scientific Computing, 1st ed. (Cambridge University, 1988).

Thévenaz, L.

M. Niklès, L. Thévenaz, P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Light-wave Technol. 15, 1842–1851 (1997).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C, The Art of Scientific Computing, 1st ed. (Cambridge University, 1988).

Webb, D. J.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13, 1340–1348 (1995).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge University, 1999).
[CrossRef]

Appl. Opt.

IEICE Trans. Electron.

H. Naruse, M. Tateda, H. Ohno, A. Shimada, “Deformation of the Brillouin gain spectrum caused by parabolic strain distribution and resulting measurement error in the BOTDR strain measurement system,” IEICE Trans. Electron. E86-C, 2111–2121 (2003).

J. Light-wave Technol.

M. Niklès, L. Thévenaz, P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Light-wave Technol. 15, 1842–1851 (1997).
[CrossRef]

J. Lightwave Technol.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13, 1340–1348 (1995).
[CrossRef]

A. Brown, M. D. DeMerchant, X. Bao, W. Bremner, “Spatial resolution enhancement of a Brillouin-distributed sensor using a novel signal processing method,” J. Lightwave Technol. 17, 1179–1183 (1999).
[CrossRef]

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

Opt. Commun.

J. Smith, A. Brown, M. D. DeMerchant, X. Bao, “Pulse width dependence of the Brillouin loss spectrum,” Opt. Commun. 168, 393–398 (1999).
[CrossRef]

Opt. Lett.

Other

M. Born, E. Wolf, Principles of Optics (Cambridge University, 1999).
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C, The Art of Scientific Computing, 1st ed. (Cambridge University, 1988).

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

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Figures (12)

Fig. 1
Fig. 1

Brillouin frequency distribution within the length of the spatial resolution. Both sections have the same Brillouin linewidth but a distinct Brillouin frequency.

Fig. 2
Fig. 2

Relative Brillouin loss amplitude as a function of the Brillouin frequency shift. Curves a, b, and c are associated with a Brillouin frequency of 12810, 12820, and 12860 MHz, respectively. The unstressed Brillouin frequency shift is 12800 MHz. The sensor settings are Pp = 30 mW, Pcw = 5 mW, L = 1000 m, z = 500 m, w = 20 m, δl = 5 m.

Fig. 3
Fig. 3

Metric definition on a relative Brillouin loss spectrum computed at z = 500 m for Pp = 30 mW, Pcw = 5 mW, L = 1000 m, w = 20 m, δl = 5 m, ΩBs = 0.67. RPP1 and RPP2 are the relative peak powers, ΩBs is the relative Brillouin frequency shift, and ΩBsobs is the observed Brillouin frequency shift.

Fig. 4
Fig. 4

Normalized Brillouin frequency shift at which two peaks start to be observed as a function of δl/w. Below the curve, only one peak can be seen. Above the curve, two peaks are present. The settings are Pp = 30 mW, Pcw = 5 mW, L = 1000 m, w = 20 m.

Fig. 5
Fig. 5

RPP measured for the following settings: Pp = 30 mW, Pcw = 5 mW, L = 1000 m, w = 20 m, z = 500 m, ΩBs = 0.64. Curves a and b correspond to stressed and unstressed peaks, respectively.

Fig. 6
Fig. 6

Correlation plot relating the observed Brillouin frequency shift to the expected Brillouin frequency shift: curve a, z = 0 fitted on averaged curve from various pulse size fiber lengths and pulse power; curve b, z = L, Pp = 30 mW, w = 20 m, L = 1000 m; curve c, z = L, Pp = 30 mW, w = 20 m, L = 5000 m.

Fig. 7
Fig. 7

Influence of position and fiber length on the Brillouin loss spectrum for, curve a, Pp = 30 mW, Pcw = 5 mW, z = 0, w = 20 m, L = 100 m and, curve b, Pp = 30 mW, Pcw = 5 mW, z = L, w = 20 m, L = 5000 m.

Fig. 8
Fig. 8

Influence of position and fiber length on the relative Brillouin loss spectrum Γ for, curve a, Pp = 30 mW, Pcw = 5 mW, z = 0, w = 20 m, L = 100 m and, curve b, Pp = 30 mW, Pcw = 5 mW, z = L, w = 20 m, L = 5000 m.

Fig. 9
Fig. 9

FWHM of the Brillouin loss spectrum as a function of the position in the sensing fiber, Pp = 30 mW, Pcw = 5 mW, w = 20 m; a, L = 100 m; b, L = 1000 m; c, L = 5000 m.

Fig. 10
Fig. 10

Normalized Brillouin loss spectrum dip Γmin for simulation settings corresponding to L = 1000 m, z = 0 m, Pp = 30 mW, Pcw = 5 mW, w = 20 m.

Fig. 11
Fig. 11

Average deviation of the relative error for L ≤ 5000 m and ΩBs < 1.33. The RE average deviation is calculated over a large ensemble of various sensing fiber lengths.

Fig. 12
Fig. 12

Two iso-error curves, a, RE = 2% and, b, RE = 5% relating ΩBs to δl/w. Curve c separates the two-peak regime (region above) from the single-peak regime (region below) as discussed in Fig. 5. The settings here are L = 1000 m, z = 0 m, Pp = 30 mW, Pcw = 5 mW, w = 20 m.

Equations (8)

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d d z I p = g I cw I p - α I p ,
d d z I cw = g I cw I p + α I cw ,
g ( ν B ,     Δ ν B ) = g 0 ( 2 ν B - ν Δ ν B ) 2 + 1 ,
G = I cw ( z ) I cw ( z + w ) = exp ( - α w ) exp ( κ 1 α exp ( β 1 ) { exp ( - β 1 x 2 ) x 2 - exp ( - β 1 x 1 ) x 1 + β 1 [ E 1 ( β 1 x 1 ) - E 1 ( β 1 x 2 ) ] } + κ 2 α exp ( β 2 ) { exp ( - β 2 x 3 ) x 3 - exp ( - β 2 x 2 ) x 2 + β 2 [ E 1 ( β 2 x 2 ) - E 1 ( β 2 x 3 ) ] } ) ,
β i = g i I cw ( L ) exp ( - α L ) α ,     i = 1 ,     2 ,
Ω Bs obs = { 2 Ω Bs [ ( Ω Bs ) 2 + 0.5382 ] 1 / 2 - [ ( Ω Bs ) 2 + 0.5382 ] } 1 / 2 .
RE = | ɛ - ɛ obs ɛ | = | T - T obs T | = | Ω Bs - Ω Bs obs Ω Bs | ,
WCRE = a 1 coth ( a 2 L ) exp [ - b 1 coth ( b 2 L ) Ω Bs ] × exp ( - δ l w ) - exp ( - 1 ) δ l / w .

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