Abstract

It has been recently shown that in stimulated Brillouin amplification (pulsed pump & CW probe) the line-shape of the normalized logarithmic Brillouin Gain Spectrum (BGS) broadens with increasing gain. Most pronounced for short pump pulses, a linewidth increase of ~3 MHz (~1.5 MHz) per dB of additional gain was observed for a pump pulse width of 15 ns (30 ns), respectively. This gain-dependency of the shape of the BGS compromises the accuracy of the otherwise attractive, highly dynamic and distributed slope-assisted BOTDA techniques, where measurand-induced gain variations of a single probe, are converted to strain/temperature values through a calibration factor that depends on the line-shape of the BGS. A previously developed technique with built-in compensation for Brillouin gain variations, namely: the Ratio Double Slope-Assisted BOTDA (RDSA-BOTDA) method, where both slopes of the BGS are interrogated, fails to meet this new challenge of the gain-induced shape dependence of the BGS, resulting, for instance, in significant measurement errors of ~5% per dB of gain change for a 15 ns pump pulse. Here, we propose and demonstrate an extension of the RDSA-BOTDA method, which now offers immunity also to Brillouin gain-dependent line-shape variations. Requiring a prior characterization of the gain-induced line-shape dependency of the fiber and pump-pulse-width in use, this mitigation technique takes advantage of the fact that the sum of the measured logarithmic gains at judiciously chosen two fixed frequency points of the BGS can be used to determine the local peak gain, via a pre-established calibration curve. Based on the deduced correct peak gain, its associated BGS shape can now be used in the application of the previously introduced RDSA-BOTDA technique to obtain error-free results, independent of the gain dependence of the line-shape. The proposed technique has been successfully put to test in an experiment, involving a RDSA-BOTDA measurement of a fiber segment, vibrating at 50 Hz with a constant, peak-to-peak amplitude of 640 microstrain. As the Brillouin gain was manually varied from 1 to 3.5 dB, classical data processing, based on a single gain value, predicted amplitudes which varied by as much as 90 microstrain, while the proposed mitigation technique produced the correct constant amplitude, regardless of the gain changes. This restored accuracy of the RDSA-BOTDA technique is of importance, especially for monitoring real-world dynamic scenarios, where high Brillouin gains, which often locally vary due to dynamically introduced losses, can successfully achieve fast gain-independent double-slope-assisted Brillouin measurements (many kHz’s of sampling rates over hundreds of meters), with enhanced spatial resolution and signal to noise ratio.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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  1. A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, 1–23 (2015).
  2. L. Thévenaz, Advanced Fiber Optics - Concepts and Technology (EPFL University, 2011).
  3. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  4. A. Motil, R. Hadar, I. Sovran, and M. Tur, “Gain dependence of the linewidth of Brillouin amplification in optical fibers,” Opt. Express 22(22), 27535–27541 (2014).
    [Crossref] [PubMed]
  5. J. Marinelarena, J. Urricelqui, and A. Loayssa, “Gain dependence of the phase-shift spectra measured in coherent Brillouin optical time-domain analysis sensors,” J. Lightwave Technol. 34(17), 3972–3980 (2016).
    [Crossref]
  6. Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
    [Crossref] [PubMed]
  7. A. Motil, O. Danon, Y. Peled, and M. Tur, “Fast pump-power-independent brillouin fiber optic sensor,” in Optical Fiber Communication Conference (OFC, 2014), pp. 1–3.
  8. Y. Peled, A. Motil, and M. Tur, “Fast Brillouin optical time domain analysis for dynamic sensing,” Opt. Express 20(8), 8584–8591 (2012).
    [Crossref] [PubMed]
  9. I. Sovran, A. Motil, and M. Tur, “Frequency-scanning BOTDA with ultimately fast acquisition speed,” IEEE Photonics Technol. Lett. 27(13), 1426–1429 (2015).
    [Crossref]
  10. A. Voskoboinik, O. F. Yilmaz, A. W. Willner, and M. Tur, “Sweep-free distributed Brillouin time-domain analyzer (SF-BOTDA),” Opt. Express 19(26), B842–B847 (2011).
    [Crossref] [PubMed]
  11. A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
    [Crossref]
  12. R. Bernini, A. Minardo, and L. Zeni, “Dynamic strain measurement in optical fibers by stimulated Brillouin scattering,” Opt. Lett. 34(17), 2613–2615 (2009).
    [Crossref] [PubMed]
  13. J. Urricelqui, A. Zornoza, M. Sagues, and A. Loayssa, “Dynamic BOTDA measurements based on Brillouin phase-shift and RF demodulation,” Opt. Express 20(24), 26942–26949 (2012).
    [Crossref] [PubMed]
  14. A. Motil, I. Sovran, R. Hadar, and M. Tur, “Ramifications of the gain dependence of the Brillouin linewidth on the shape and slopes of the Brillouin gain spectrum,” in Fifth Asia-Pacific Optical Sensors Conference, (2015).
  15. I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
    [Crossref]
  16. Y. Peled, A. Motil, I. Kressel, and M. Tur, “Monitoring the propagation of mechanical waves using an optical fiber distributed and dynamic strain sensor based on BOTDA,” Opt. Express 21(9), 10697–10705 (2013).
    [Crossref] [PubMed]
  17. M. Alem, M. A. Soto, M. Tur, and J. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” Proc. SPIE 10323, 103239J (2017).
    [Crossref]
  18. X. Angulo-Vinuesa, S. Martin-Lopez, J. Nuño, P. Corredera, J. D. Ania-Castañon, L. Thévenaz, and M. González-Herráez, “Raman-assisted Brillouin distributed temperature sensor over 100 km featuring 2 m resolution and 1.2 C uncertainty,” J. Lightwave Technol. 30(8), 1060–1065 (2012).
    [Crossref]

2017 (1)

M. Alem, M. A. Soto, M. Tur, and J. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” Proc. SPIE 10323, 103239J (2017).
[Crossref]

2016 (1)

2015 (3)

A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, 1–23 (2015).

I. Sovran, A. Motil, and M. Tur, “Frequency-scanning BOTDA with ultimately fast acquisition speed,” IEEE Photonics Technol. Lett. 27(13), 1426–1429 (2015).
[Crossref]

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

2014 (2)

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

A. Motil, R. Hadar, I. Sovran, and M. Tur, “Gain dependence of the linewidth of Brillouin amplification in optical fibers,” Opt. Express 22(22), 27535–27541 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (3)

2011 (2)

2009 (1)

Alem, M.

M. Alem, M. A. Soto, M. Tur, and J. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” Proc. SPIE 10323, 103239J (2017).
[Crossref]

Angulo-Vinuesa, X.

Ania-Castañon, J. D.

Balter, J.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Bergman, A.

A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, 1–23 (2015).

Bernini, R.

Botsev, Y.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Corredera, P.

Danon, O.

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

A. Motil, O. Danon, Y. Peled, and M. Tur, “Fast pump-power-independent brillouin fiber optic sensor,” in Optical Fiber Communication Conference (OFC, 2014), pp. 1–3.

Dorfman, B.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

González-Herráez, M.

Gupta, N.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Hadar, R.

A. Motil, R. Hadar, I. Sovran, and M. Tur, “Gain dependence of the linewidth of Brillouin amplification in optical fibers,” Opt. Express 22(22), 27535–27541 (2014).
[Crossref] [PubMed]

A. Motil, I. Sovran, R. Hadar, and M. Tur, “Ramifications of the gain dependence of the Brillouin linewidth on the shape and slopes of the Brillouin gain spectrum,” in Fifth Asia-Pacific Optical Sensors Conference, (2015).

Handelman, A.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Joseph, A. M.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Kressel, I.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Y. Peled, A. Motil, I. Kressel, and M. Tur, “Monitoring the propagation of mechanical waves using an optical fiber distributed and dynamic strain sensor based on BOTDA,” Opt. Express 21(9), 10697–10705 (2013).
[Crossref] [PubMed]

Loayssa, A.

Marinelarena, J.

Martin-Lopez, S.

Minardo, A.

Motil, A.

I. Sovran, A. Motil, and M. Tur, “Frequency-scanning BOTDA with ultimately fast acquisition speed,” IEEE Photonics Technol. Lett. 27(13), 1426–1429 (2015).
[Crossref]

A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, 1–23 (2015).

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

A. Motil, R. Hadar, I. Sovran, and M. Tur, “Gain dependence of the linewidth of Brillouin amplification in optical fibers,” Opt. Express 22(22), 27535–27541 (2014).
[Crossref] [PubMed]

Y. Peled, A. Motil, I. Kressel, and M. Tur, “Monitoring the propagation of mechanical waves using an optical fiber distributed and dynamic strain sensor based on BOTDA,” Opt. Express 21(9), 10697–10705 (2013).
[Crossref] [PubMed]

Y. Peled, A. Motil, and M. Tur, “Fast Brillouin optical time domain analysis for dynamic sensing,” Opt. Express 20(8), 8584–8591 (2012).
[Crossref] [PubMed]

Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
[Crossref] [PubMed]

A. Motil, O. Danon, Y. Peled, and M. Tur, “Fast pump-power-independent brillouin fiber optic sensor,” in Optical Fiber Communication Conference (OFC, 2014), pp. 1–3.

A. Motil, I. Sovran, R. Hadar, and M. Tur, “Ramifications of the gain dependence of the Brillouin linewidth on the shape and slopes of the Brillouin gain spectrum,” in Fifth Asia-Pacific Optical Sensors Conference, (2015).

Nuño, J.

Peled, Y.

Pillai, A. C. R.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Prasad, M. H.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Sagues, M.

Soto, M. A.

M. Alem, M. A. Soto, M. Tur, and J. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” Proc. SPIE 10323, 103239J (2017).
[Crossref]

Sovran, I.

I. Sovran, A. Motil, and M. Tur, “Frequency-scanning BOTDA with ultimately fast acquisition speed,” IEEE Photonics Technol. Lett. 27(13), 1426–1429 (2015).
[Crossref]

A. Motil, R. Hadar, I. Sovran, and M. Tur, “Gain dependence of the linewidth of Brillouin amplification in optical fibers,” Opt. Express 22(22), 27535–27541 (2014).
[Crossref] [PubMed]

A. Motil, I. Sovran, R. Hadar, and M. Tur, “Ramifications of the gain dependence of the Brillouin linewidth on the shape and slopes of the Brillouin gain spectrum,” in Fifth Asia-Pacific Optical Sensors Conference, (2015).

Sundaram, R.

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Thévenaz, J.

M. Alem, M. A. Soto, M. Tur, and J. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” Proc. SPIE 10323, 103239J (2017).
[Crossref]

Thévenaz, L.

Tur, M.

M. Alem, M. A. Soto, M. Tur, and J. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” Proc. SPIE 10323, 103239J (2017).
[Crossref]

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

I. Sovran, A. Motil, and M. Tur, “Frequency-scanning BOTDA with ultimately fast acquisition speed,” IEEE Photonics Technol. Lett. 27(13), 1426–1429 (2015).
[Crossref]

A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, 1–23 (2015).

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

A. Motil, R. Hadar, I. Sovran, and M. Tur, “Gain dependence of the linewidth of Brillouin amplification in optical fibers,” Opt. Express 22(22), 27535–27541 (2014).
[Crossref] [PubMed]

Y. Peled, A. Motil, I. Kressel, and M. Tur, “Monitoring the propagation of mechanical waves using an optical fiber distributed and dynamic strain sensor based on BOTDA,” Opt. Express 21(9), 10697–10705 (2013).
[Crossref] [PubMed]

Y. Peled, A. Motil, and M. Tur, “Fast Brillouin optical time domain analysis for dynamic sensing,” Opt. Express 20(8), 8584–8591 (2012).
[Crossref] [PubMed]

A. Voskoboinik, O. F. Yilmaz, A. W. Willner, and M. Tur, “Sweep-free distributed Brillouin time-domain analyzer (SF-BOTDA),” Opt. Express 19(26), B842–B847 (2011).
[Crossref] [PubMed]

Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
[Crossref] [PubMed]

A. Motil, O. Danon, Y. Peled, and M. Tur, “Fast pump-power-independent brillouin fiber optic sensor,” in Optical Fiber Communication Conference (OFC, 2014), pp. 1–3.

A. Motil, I. Sovran, R. Hadar, and M. Tur, “Ramifications of the gain dependence of the Brillouin linewidth on the shape and slopes of the Brillouin gain spectrum,” in Fifth Asia-Pacific Optical Sensors Conference, (2015).

Urricelqui, J.

Voskoboinik, A.

Willner, A. W.

Yaron, L.

Yilmaz, O. F.

Zeni, L.

Zornoza, A.

IEEE Photonics Technol. Lett. (2)

I. Sovran, A. Motil, and M. Tur, “Frequency-scanning BOTDA with ultimately fast acquisition speed,” IEEE Photonics Technol. Lett. 27(13), 1426–1429 (2015).
[Crossref]

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

J. Lightwave Technol. (2)

Opt. Express (6)

Opt. Laser Technol. (1)

A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, 1–23 (2015).

Opt. Lett. (1)

Proc. SPIE (1)

M. Alem, M. A. Soto, M. Tur, and J. Thévenaz, “Analytical expression and experimental validation of the Brillouin gain spectral broadening at any sensing spatial resolution,” Proc. SPIE 10323, 103239J (2017).
[Crossref]

Smart Mater. Struct. (1)

I. Kressel, B. Dorfman, Y. Botsev, A. Handelman, J. Balter, A. C. R. Pillai, M. H. Prasad, N. Gupta, A. M. Joseph, R. Sundaram, and M. Tur, “Flight validation of an embedded structural health monitoring system for an unmanned aerial vehicle,” Smart Mater. Struct. 24(7), 075022 (2015).
[Crossref]

Other (4)

A. Motil, O. Danon, Y. Peled, and M. Tur, “Fast pump-power-independent brillouin fiber optic sensor,” in Optical Fiber Communication Conference (OFC, 2014), pp. 1–3.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

L. Thévenaz, Advanced Fiber Optics - Concepts and Technology (EPFL University, 2011).

A. Motil, I. Sovran, R. Hadar, and M. Tur, “Ramifications of the gain dependence of the Brillouin linewidth on the shape and slopes of the Brillouin gain spectrum,” in Fifth Asia-Pacific Optical Sensors Conference, (2015).

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Figures (6)

Fig. 1
Fig. 1 Measured normalized (logarithmic) Brillouin gain spectra, BGSn(Gpeak,ν-νB) = BGS(Gpeak,ν-νB)/Gpeak, for a 15 ns wide pump pulse at different values of the pump-power dependent Brillouin peak gain, Gpeak (See Sec. 3 for the measurement setup. A similar family of BGS curves, showing the same gain-dependent broadening but for the case of a pump pulse width of 45 ns, appears in [4]). Also shown is another important consequence of the gain-dependent line shape effect: The −3dB frequencies, ν 3dB , that cut the BGS at half its peak for one value of G Peak (e.g., ν 3dB ( G Peak =1dB)in the figure), sample the BGSs of the other gains away from their respective −3 dB points (e.g., ν 3dB ( G Peak =3.55dB)), giving rise to errors in the application of slope-assisted BOTDA methods, which depend on the local slope of the BGS [6,7].
Fig. 2
Fig. 2 The Ratio Curves, R B (δ ν B (t,z))of Eq. (2) (in dB) calculated from the BGSs of Fig. 1 for the reference frequencies corresponding to a high gain of 3.55 dB: ν 3dB ± ( z, G Peak 0 (z)=3.55dB ).
Fig. 3
Fig. 3 The peak gain G Peak (z) as a function of the gain sum G SUM (z, ν 3dB ± (z, G Peak 0 (z), G Peak (z)), Eq. (5), evaluated at the reference points, ν 3dB ± (z, G Peak 0 (z)), which are the −3dB points for the BGS at another peak gain, G Peak 0 (z). The different curves, belonging to different choices of G Peak 0 (z), were numerically calculated from Eq. (5), using the shapes of the experimentally obtained BGSs of Fig. 1. Each curve refers to a different choice of the gain, G Peak 0 (z), whose corresponding interrogating (reference) frequencies, ν 3dB ± (z, G Peak 0 (z))were used to measure the gain sum G SUM (z, ν 3dB ± (z, G Peak 0 (z), G Peak (z)). Obviously, for each curve, G SUM equals G Peak 0 (z) if G Peak (z)= G Peak 0 (z)
Fig. 4
Fig. 4 Experimental setup: DFB-LD: narrow linewidth distributed feedback laser diode, AWG: arbitrary waveform generator, VSG: vector signal generator, whose {I,Q} inputs are fed by the AWG outputs, EOM1: electro-optic modulator used for the generation of the probe signal, SOA: A semiconductor optical amplifier, manufactured to act as a high extinction ratio (>50 dB) switch for the generation of the pump pulse, EDFA: Erbium-doped fiber amplifier, ATT: attenuator, CIR: circulator, FBG: fiber Bragg grating, PC: polarization controller, IS: isolator, Pol.: in-line polarizer, FUT: fiber under test, whose last 3m could be vibrated by a mechanical shaker, PD: photodiode, and A2D: analog to digital converter. The combined operation of the AWG + VSG allows this setup to implement two types of Brillouin interrogations: (1) A fast BOTDA [8-9], where the probe optical frequency (upper arm) is rapidly swept against that of a fixed frequency pump pulse (lower arm), thereby enabling full BGS characterization of the FUT; (2) RDSA-BOTDA operation, where the probe optical frequency rapidly alternates between two pre-determined values [11].
Fig. 5
Fig. 5 Two (raw) SA-BOTDA measured gain-variations induced by constant amplitude 50 Hz strain oscillations, taken at opposite slopes of the BGS, showing the evolution of the readings as the peak gain was increased from 1 to 3.55 dB. The black dashed curve is the sum of the two measured SA-BOTDA gains.
Fig. 6
Fig. 6 Extraction of the 50 Hz strain variations using the Ratio method of [11]. (a) Results of the conventional processing, where the ratio curve, R B (δ ν B ), Eq. (6), of peak gain of 3.55 dB is used throughout the whole duration of the experiment, despite the underlying change of the peak gain in the range [1-3.55 dB]. With this type of processing the method is immune to the linear dependence of the slope on the Brillouin gain but not to the gain-dependent line-shape variations. This results in incorrectly higher (peak-to-peak) strain readings at t = 0 (when the gain was only 1 dB): 730 με instead of the correct value of 640 με, representing a strain error of 90 με (13%). The side boxes in (a), showing the first and last 0.1 s of the measurement, clearly demonstrate how the error monotonically decreases as the gain approaches the reference gain of 3.55 dB. (b) Extraction using the proposed mitigation approach: at each instant the true peak gain is deduced from the measured GSUM, so that the correct Ratio Curve can be used, resulting in peak-gain-independent, as well as correct strain estimates, as expected.

Equations (6)

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δ(Δ ν B )| GainBroadening = 3 G peak [inneper] 4πT =0.055 G peak [indB] T ,
R B (δ ν B , ν 3dB + , ν 3dB )= Gain( ν 3dB + , ν avg +δ ν B ) Gain( ν 3dB , ν avg +δ ν B ) .
G SUM (z, ν 3dB ± (z, G Peak 0 (z)), G Peak (z)) BGS[δ ν B (t,z), ν 3dB (z, G Peak 0 (z)), G Peak (z)]+BGS[δ ν B (t,z), ν 3dB + (z, G Peak 0 (z)), G Peak (z)],
G SUM (z, ν 3dB ± (z, G Peak 0 (z)), G Peak (z))= BGS[δ ν B (t,z), ν 3dB (z, G Peak 0 (z)), G Peak (z)]+BGS[δ ν B (t,z), ν 3dB + (z, G Peak 0 (z)), G Peak (z)] ={ BGS[ ν 3dB (z, G Peak 0 (z)), G Peak (z)]BG S slope [ ν 3dB (z, G Peak 0 (z)), G Peak (z)]δ ν B (t,z) } +{ BGS[ ν 3dB + (z, G Peak 0 (z)), G Peak (z)]+BG S slope [ ν 3dB + (z, G Peak 0 (z)), G Peak (z)]δ ν B (t,z) }
G SUM (z, ν 3dB ± (z, G Peak 0 (z)), G Peak (z))=BGS[ ν 3dB (z, G Peak 0 (z)), G Peak (z)]+BGS[ ν 3dB + (z, G Peak 0 (z)), G Peak (z)]
R B (δ ν B , ν 3dB + ( G Peak 0 ), ν 3dB ( G Peak 0 ), G Peak )= Gain( ν 3dB + ( G Peak 0 ), ν avg +δ ν B , G Peak ) Gain( ν 3dB ( G Peak 0 ), ν avg +δ ν B , G Peak ) .

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