Abstract

A novel approach to distributed fiber-optic Brillouin sensing is presented and numerically analyzed. An integral equation that directly relates the Brillouin gain to the Brillouin signal is derived in the frequency domain, and from this result a new technique for the quantitative reconstruction of temperature–strain profiles along an optical fiber is developed. We achieve the reconstruction by minimizing a cost function that represents the error between the measured and the model data. We effectively perform such a minimization by representing the unknown (temperature–strain) profile with a finite number of parameters. Numerical results confirm the effectiveness of the proposed approach and its stability against noise in the data.

© 2002 Optical Society of America

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  1. T. Horiguchi and M. Tateda, J. Lightwave Technol. 7, 1170 (1989).
    [CrossRef]
  2. X. Bao, D. J. Webb, and D. A. Jackson, Opt. Lett. 19, 141 (1994).
    [CrossRef]
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    [CrossRef]
  4. X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, J. Lightwave Technol. 13, 1340 (1995).
    [CrossRef]
  5. D. Garus, K. Krebber, E. Schliep, and T. Gogolla, Opt. Lett. 21, 1402 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. E. Geinitz, S. Jetshke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, Meas. Sci. Technol. 10, 112 (1999).
    [CrossRef]
  8. T. Kurashima, T. Horiguchi, and M. Tateda, Appl. Opt. 29, 2219 (1990).
    [CrossRef] [PubMed]
  9. L. Zeni, R. Bernini, and R. Pierri, Solid-State Electron. 43, 761 (1999).
    [CrossRef]
  10. T. Isernia, F. Soldovieri, G. Leone, and R. Pierri, Radio Sci. 31, 1887 (1996).
    [CrossRef]

1999

E. Geinitz, S. Jetshke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, Meas. Sci. Technol. 10, 112 (1999).
[CrossRef]

L. Zeni, R. Bernini, and R. Pierri, Solid-State Electron. 43, 761 (1999).
[CrossRef]

1997

D. Garus, T. Gogolla, K. Krebber, and F. Schliep, J. Lightwave Technol. 15, 654 (1997).
[CrossRef]

1996

D. Garus, K. Krebber, E. Schliep, and T. Gogolla, Opt. Lett. 21, 1402 (1996).
[CrossRef] [PubMed]

T. Isernia, F. Soldovieri, G. Leone, and R. Pierri, Radio Sci. 31, 1887 (1996).
[CrossRef]

1995

M. Nikles, L. Thevenaz, and P. A. Robert, Opt. Lett. 21, 758 (1995).
[CrossRef]

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, J. Lightwave Technol. 13, 1340 (1995).
[CrossRef]

1994

1990

1989

T. Horiguchi and M. Tateda, J. Lightwave Technol. 7, 1170 (1989).
[CrossRef]

Bao, X.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, J. Lightwave Technol. 13, 1340 (1995).
[CrossRef]

X. Bao, D. J. Webb, and D. A. Jackson, Opt. Lett. 19, 141 (1994).
[CrossRef]

Bartelt, H.

E. Geinitz, S. Jetshke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, Meas. Sci. Technol. 10, 112 (1999).
[CrossRef]

Bernini, R.

L. Zeni, R. Bernini, and R. Pierri, Solid-State Electron. 43, 761 (1999).
[CrossRef]

Dhliwayo, J.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, J. Lightwave Technol. 13, 1340 (1995).
[CrossRef]

Garus, D.

D. Garus, T. Gogolla, K. Krebber, and F. Schliep, J. Lightwave Technol. 15, 654 (1997).
[CrossRef]

D. Garus, K. Krebber, E. Schliep, and T. Gogolla, Opt. Lett. 21, 1402 (1996).
[CrossRef] [PubMed]

Geinitz, E.

E. Geinitz, S. Jetshke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, Meas. Sci. Technol. 10, 112 (1999).
[CrossRef]

Gogolla, T.

D. Garus, T. Gogolla, K. Krebber, and F. Schliep, J. Lightwave Technol. 15, 654 (1997).
[CrossRef]

D. Garus, K. Krebber, E. Schliep, and T. Gogolla, Opt. Lett. 21, 1402 (1996).
[CrossRef] [PubMed]

Heron, N.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, J. Lightwave Technol. 13, 1340 (1995).
[CrossRef]

Horiguchi, T.

T. Kurashima, T. Horiguchi, and M. Tateda, Appl. Opt. 29, 2219 (1990).
[CrossRef] [PubMed]

T. Horiguchi and M. Tateda, J. Lightwave Technol. 7, 1170 (1989).
[CrossRef]

Isernia, T.

T. Isernia, F. Soldovieri, G. Leone, and R. Pierri, Radio Sci. 31, 1887 (1996).
[CrossRef]

Jackson, D. A.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, J. Lightwave Technol. 13, 1340 (1995).
[CrossRef]

X. Bao, D. J. Webb, and D. A. Jackson, Opt. Lett. 19, 141 (1994).
[CrossRef]

Jetshke, S.

E. Geinitz, S. Jetshke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, Meas. Sci. Technol. 10, 112 (1999).
[CrossRef]

Krebber, K.

D. Garus, T. Gogolla, K. Krebber, and F. Schliep, J. Lightwave Technol. 15, 654 (1997).
[CrossRef]

D. Garus, K. Krebber, E. Schliep, and T. Gogolla, Opt. Lett. 21, 1402 (1996).
[CrossRef] [PubMed]

Kurashima, T.

Leone, G.

T. Isernia, F. Soldovieri, G. Leone, and R. Pierri, Radio Sci. 31, 1887 (1996).
[CrossRef]

Nikles, M.

Pierri, R.

L. Zeni, R. Bernini, and R. Pierri, Solid-State Electron. 43, 761 (1999).
[CrossRef]

T. Isernia, F. Soldovieri, G. Leone, and R. Pierri, Radio Sci. 31, 1887 (1996).
[CrossRef]

Robert, P. A.

Röpke, U.

E. Geinitz, S. Jetshke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, Meas. Sci. Technol. 10, 112 (1999).
[CrossRef]

Schliep, E.

Schliep, F.

D. Garus, T. Gogolla, K. Krebber, and F. Schliep, J. Lightwave Technol. 15, 654 (1997).
[CrossRef]

Schröter, S.

E. Geinitz, S. Jetshke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, Meas. Sci. Technol. 10, 112 (1999).
[CrossRef]

Soldovieri, F.

T. Isernia, F. Soldovieri, G. Leone, and R. Pierri, Radio Sci. 31, 1887 (1996).
[CrossRef]

Tateda, M.

T. Kurashima, T. Horiguchi, and M. Tateda, Appl. Opt. 29, 2219 (1990).
[CrossRef] [PubMed]

T. Horiguchi and M. Tateda, J. Lightwave Technol. 7, 1170 (1989).
[CrossRef]

Thevenaz, L.

Webb, D. J.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, J. Lightwave Technol. 13, 1340 (1995).
[CrossRef]

X. Bao, D. J. Webb, and D. A. Jackson, Opt. Lett. 19, 141 (1994).
[CrossRef]

Willsch, R.

E. Geinitz, S. Jetshke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, Meas. Sci. Technol. 10, 112 (1999).
[CrossRef]

Zeni, L.

L. Zeni, R. Bernini, and R. Pierri, Solid-State Electron. 43, 761 (1999).
[CrossRef]

Appl. Opt.

J. Lightwave Technol.

D. Garus, T. Gogolla, K. Krebber, and F. Schliep, J. Lightwave Technol. 15, 654 (1997).
[CrossRef]

T. Horiguchi and M. Tateda, J. Lightwave Technol. 7, 1170 (1989).
[CrossRef]

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, J. Lightwave Technol. 13, 1340 (1995).
[CrossRef]

Meas. Sci. Technol.

E. Geinitz, S. Jetshke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, Meas. Sci. Technol. 10, 112 (1999).
[CrossRef]

Opt. Lett.

Radio Sci.

T. Isernia, F. Soldovieri, G. Leone, and R. Pierri, Radio Sci. 31, 1887 (1996).
[CrossRef]

Solid-State Electron.

L. Zeni, R. Bernini, and R. Pierri, Solid-State Electron. 43, 761 (1999).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Temperature profile reconstructions, showing number of harmonics in our reconstruction.

Fig. 2
Fig. 2

Temperature profile reconstructions with noisy data, showing number of harmonics in our reconstruction.

Equations (10)

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

1vt+z+αIPu=-gIPuISt,
1vt-z+αISt=gIPuISt,
IPu0,t=Ic, IStL,t=Im0+Im1 cosωt.
IPuz,t=IP0z+ReIpzexpjωt, IStz,t=IS0z+ReISzexpjωt,
dIPdz=-jωv+αIP-gIPIS0+ISIP0,
dISdz=jωv+αIS-gIPIS0+ISIP0.
ISz,ω=Im1 exp-jωv+αL-z×expzLgzIP0zdz.
IpL,ω=-Im1 exp-2jωv+αL×0LgzIP0zexpzLgzIP0z-IS0zdz×exp2jωv+αzdz.
ΔTz=T0+2 Ren=1N-1Tnexpjn2πLz, 0zL,
FT=i=1MIPmodelT,νi-IPmeasνi2,

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