Abstract

We show that, even when a polarization scrambler is switched off, PMF-based SA-BOCDR can operate with higher stability than that of standard silica-fiber-based systems. This leads to reduced cost and enables the use of the optimized state of polarization for higher sensitivity. After investigation of the strain/temperature dependencies of the Brillouin frequency shift and the Brillouin spectral power in the PMF, we show that the strain/temperature sensitivity of the PMF-based SA-BOCDR is 1.4 times the value of the standard silica-fiber-based configuration; we then demonstrate distributed temperature measurement with higher stability and sensitivity.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  3. H. Lee, Y. Mizuno, and K. Nakamura, “Detection of 2-mm-long strained section in silica fiber using slope-assisted Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 57(2), 020303 (2018).
    [Crossref]
  4. T. Horiguchi and M. Tateda, “BOTDA–nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
    [Crossref]
  5. Y. Dong, L. Chen, and X. Bao, “Time-division multiplexing-based BOTDA over 100 km sensing length,” Opt. Lett. 36(2), 277–279 (2011).
    [Crossref]
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    [Crossref]
  7. D. Garus, K. Krebber, and F. Schliep, “Distributed sensing technique based on Brillouin optical-fiber frequency-domain analysis,” Opt. Lett. 21(17), 1402–1404 (1996).
    [Crossref]
  8. R. Bernini, A. Minardo, and L. Zeni, “Distributed sensing at centimeter-scale spatial resolution by BOFDA: Measurements and signal processing,” IEEE Photon. J. 4(1), 48–56 (2012).
    [Crossref]
  9. A. Minardo, R. Bernini, and L. Zeni, “Distributed temperature sensing in polymer optical fiber by BOFDA,” IEEE Photon. Technol. Lett. 26(4), 387–390 (2014).
    [Crossref]
  10. K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique–Proposal, experiment and simulation–,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).
  11. K. Y. Song, M. Kishi, Z. He, and K. Hotate, “High-repetition-rate distributed Brillouin sensor based on optical correlation-domain analysis with differential frequency modulation,” Opt. Lett. 36(11), 2062–2064 (2011).
    [Crossref]
  12. A. López-Gil, S. Martin-Lopez, and M. Gonzalez-Herraez, “Phase-measuring time-gated BOCDA,” Opt. Lett. 42(19), 3924–3927 (2017).
    [Crossref]
  13. C. Zhang, M. Kishi, and K. Hotate, “5,000 points/s high-speed random accessibility for dynamic strain measurement at arbitrary multiple points along a fiber by Brillouin optical correlation domain analysis,” Appl. Phys. Express 8(4), 042501 (2015).
    [Crossref]
  14. W. Zou, C. Jin, and J. Chen, “Distributed strain sensing based on combination of Brillouin gain and loss effects in Brillouin optical correlation domain analysis,” Appl. Phys. Express 5(8), 082503 (2012).
    [Crossref]
  15. T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993).
  16. A. Masoudi, M. Belal, and T. P. Newson, “Distributed dynamic large strain optical fibre sensor based on the detection of spontaneous Brillouin scattering,” Opt. Lett. 38(17), 3312–3315 (2013).
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    [Crossref]
  18. A. Minardo, R. Bernini, R. Ruiz-Lombera, J. Mirapeix, J. M. Lopez-Higuera, and L. Zeni, “Proposal of Brillouin optical frequency-domain reflectometry (BOFDR),” Opt. Express 24(26), 29994–20001 (2016).
    [Crossref]
  19. Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR),” Opt. Express 16(16), 12148–12153 (2008).
    [Crossref]
  20. Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Operation of Brillouin optical correlation-domain reflectometry: theoretical analysis and experimental validation,” J. Lightwave Technol. 28(22), 3300–3306 (2010).
    [Crossref]
  21. N. Hayashi, Y. Mizuno, and K. Nakamura, “Distributed Brillouin sensing with centimeter-order spatial resolution in polymer optical fibers,” J. Lightwave Technol. 32(21), 3999–4003 (2014).
    [Crossref]
  22. R. Shimizu, M. Kishi, and K. Hotate, “Enlargement of measurement function in Brillouin optical correlation-domain reflectometry with combining four performance improvement schemes,” Proc. SPIE 10323, 1032390 (2017).
    [Crossref]
  23. Y. Mizuno, N. Hayashi, H. Fukuda, and K. Nakamura, “Single-end-access distributed strain sensing with wide dynamic range using higher-speed Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 56(7), 072501 (2017).
    [Crossref]
  24. Y. Yao, M. Kishi, and K. Hotate, “Brillouin optical correlation domain reflectometry with lock-in detection scheme,” Appl. Phys. Express 9(7), 072501 (2016).
    [Crossref]
  25. N. Hayashi, Y. Mizuno, and K. Nakamura, “Characterization of stimulated Brillouin scattering in polymer optical fibers based on lock-in-free pump-probe technique,” J. Lightwave Technol. 31(19), 3162–3166 (2013).
    [Crossref]
  26. Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5(12), e16184 (2016).
    [Crossref]
  27. H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Slope-assisted Brillouin optical correlation-domain reflectometry: proof of concept,” IEEE Photon. J. 8(3), 1–7 (2016).
    [Crossref]
  28. H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Operation of slope-assisted Brillouin optical correlation-domain reflectometry: comparison of system output with actual frequency shift distribution,” Opt. Express 24(25), 29190–29197 (2016).
    [Crossref]
  29. H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
    [Crossref]
  30. O. Furukawa, S. Tezuka, M. Tsukamoto, S. Matsuura, M. Kishi, and K. Hotate, “Beyond 21 km distributed strain measurement with Brillouin optical correlation-domain reflectometry using polarization diversity method and temporal gating scheme,” IEEJ Trans. Fund. Mater. 137(1), 52–57 (2017). [In Japanese]
    [Crossref]
  31. Y. Sasaki, K. Okamoto, T. Hosaka, and N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Optical Fiber Communication Conference, 1982 OSA Technical Digest Series (Optical Society of America, 1982), paper ThCC6.
  32. T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1(5), 107–108 (1989).
    [Crossref]
  33. T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects on the Brillouin frequency shift in jacketed optical silica fibers,” Appl. Opt. 29(15), 2219–2222 (1990).
    [Crossref]
  34. M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
    [Crossref]
  35. K. Y. Song, Z. He, and K. Hotate, “Optimization of Brillouin optical correlation domain analysis system based on intensity modulation scheme,” Opt. Express 14(10), 4256–4263 (2006).
    [Crossref]
  36. H. Lee, Y. Mizuno, and K. Nakamura, “Measurement sensitivity dependencies on incident power and spatial resolution in slope-assisted Brillouin optical correlation-domain reflectometry,” Sens. Actuators A 268, 68–71 (2017).
    [Crossref]

2018 (2)

H. Lee, Y. Mizuno, and K. Nakamura, “Detection of 2-mm-long strained section in silica fiber using slope-assisted Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 57(2), 020303 (2018).
[Crossref]

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

2017 (5)

O. Furukawa, S. Tezuka, M. Tsukamoto, S. Matsuura, M. Kishi, and K. Hotate, “Beyond 21 km distributed strain measurement with Brillouin optical correlation-domain reflectometry using polarization diversity method and temporal gating scheme,” IEEJ Trans. Fund. Mater. 137(1), 52–57 (2017). [In Japanese]
[Crossref]

R. Shimizu, M. Kishi, and K. Hotate, “Enlargement of measurement function in Brillouin optical correlation-domain reflectometry with combining four performance improvement schemes,” Proc. SPIE 10323, 1032390 (2017).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, and K. Nakamura, “Single-end-access distributed strain sensing with wide dynamic range using higher-speed Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 56(7), 072501 (2017).
[Crossref]

H. Lee, Y. Mizuno, and K. Nakamura, “Measurement sensitivity dependencies on incident power and spatial resolution in slope-assisted Brillouin optical correlation-domain reflectometry,” Sens. Actuators A 268, 68–71 (2017).
[Crossref]

A. López-Gil, S. Martin-Lopez, and M. Gonzalez-Herraez, “Phase-measuring time-gated BOCDA,” Opt. Lett. 42(19), 3924–3927 (2017).
[Crossref]

2016 (5)

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Operation of slope-assisted Brillouin optical correlation-domain reflectometry: comparison of system output with actual frequency shift distribution,” Opt. Express 24(25), 29190–29197 (2016).
[Crossref]

A. Minardo, R. Bernini, R. Ruiz-Lombera, J. Mirapeix, J. M. Lopez-Higuera, and L. Zeni, “Proposal of Brillouin optical frequency-domain reflectometry (BOFDR),” Opt. Express 24(26), 29994–20001 (2016).
[Crossref]

Y. Yao, M. Kishi, and K. Hotate, “Brillouin optical correlation domain reflectometry with lock-in detection scheme,” Appl. Phys. Express 9(7), 072501 (2016).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5(12), e16184 (2016).
[Crossref]

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Slope-assisted Brillouin optical correlation-domain reflectometry: proof of concept,” IEEE Photon. J. 8(3), 1–7 (2016).
[Crossref]

2015 (1)

C. Zhang, M. Kishi, and K. Hotate, “5,000 points/s high-speed random accessibility for dynamic strain measurement at arbitrary multiple points along a fiber by Brillouin optical correlation domain analysis,” Appl. Phys. Express 8(4), 042501 (2015).
[Crossref]

2014 (4)

G. Tu, X. Zhang, Y. Zhang, Z. Ying, and L. Lv, “Strain variation measurement with short time Fourier transform-based Brillouin optical time-domain reflectometry sensing system,” Electron. Lett. 50(22), 1624–1626 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Distributed Brillouin sensing with centimeter-order spatial resolution in polymer optical fibers,” J. Lightwave Technol. 32(21), 3999–4003 (2014).
[Crossref]

A. Minardo, R. Bernini, and L. Zeni, “Distributed temperature sensing in polymer optical fiber by BOFDA,” IEEE Photon. Technol. Lett. 26(4), 387–390 (2014).
[Crossref]

T. D. Vo, J. He, E. Magi, M. J. Collins, A. S. Clark, B. G. Ferguson, C. Xiong, and B. J. Eggleton, “Chalcogenide fiber-based distributed temperature sensor with sub-centimeter spatial resolution and enhanced accuracy,” Opt. Express 22(2), 1560–1568 (2014).
[Crossref]

2013 (2)

2012 (2)

W. Zou, C. Jin, and J. Chen, “Distributed strain sensing based on combination of Brillouin gain and loss effects in Brillouin optical correlation domain analysis,” Appl. Phys. Express 5(8), 082503 (2012).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Distributed sensing at centimeter-scale spatial resolution by BOFDA: Measurements and signal processing,” IEEE Photon. J. 4(1), 48–56 (2012).
[Crossref]

2011 (3)

2010 (1)

2008 (1)

2006 (1)

2000 (1)

K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique–Proposal, experiment and simulation–,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).

1996 (1)

1994 (1)

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[Crossref]

1993 (1)

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993).

1990 (1)

1989 (2)

T. Horiguchi and M. Tateda, “BOTDA–nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
[Crossref]

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).

Bao, X.

Belal, M.

Bernini, R.

A. Minardo, R. Bernini, R. Ruiz-Lombera, J. Mirapeix, J. M. Lopez-Higuera, and L. Zeni, “Proposal of Brillouin optical frequency-domain reflectometry (BOFDR),” Opt. Express 24(26), 29994–20001 (2016).
[Crossref]

A. Minardo, R. Bernini, and L. Zeni, “Distributed temperature sensing in polymer optical fiber by BOFDA,” IEEE Photon. Technol. Lett. 26(4), 387–390 (2014).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Distributed sensing at centimeter-scale spatial resolution by BOFDA: Measurements and signal processing,” IEEE Photon. J. 4(1), 48–56 (2012).
[Crossref]

Boot, A. J.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[Crossref]

Chen, J.

W. Zou, C. Jin, and J. Chen, “Distributed strain sensing based on combination of Brillouin gain and loss effects in Brillouin optical correlation domain analysis,” Appl. Phys. Express 5(8), 082503 (2012).
[Crossref]

Chen, L.

Clark, A. S.

Collins, M. J.

Dong, Y.

Eggleton, B. J.

Ferguson, B. G.

Fukuda, H.

Y. Mizuno, N. Hayashi, H. Fukuda, and K. Nakamura, “Single-end-access distributed strain sensing with wide dynamic range using higher-speed Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 56(7), 072501 (2017).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5(12), e16184 (2016).
[Crossref]

Furukawa, O.

O. Furukawa, S. Tezuka, M. Tsukamoto, S. Matsuura, M. Kishi, and K. Hotate, “Beyond 21 km distributed strain measurement with Brillouin optical correlation-domain reflectometry using polarization diversity method and temporal gating scheme,” IEEJ Trans. Fund. Mater. 137(1), 52–57 (2017). [In Japanese]
[Crossref]

Furukawa, S.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993).

Garus, D.

Gonzalez-Herraez, M.

Hasegawa, T.

K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique–Proposal, experiment and simulation–,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).

Hayashi, N.

Y. Mizuno, N. Hayashi, H. Fukuda, and K. Nakamura, “Single-end-access distributed strain sensing with wide dynamic range using higher-speed Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 56(7), 072501 (2017).
[Crossref]

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Slope-assisted Brillouin optical correlation-domain reflectometry: proof of concept,” IEEE Photon. J. 8(3), 1–7 (2016).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5(12), e16184 (2016).
[Crossref]

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Operation of slope-assisted Brillouin optical correlation-domain reflectometry: comparison of system output with actual frequency shift distribution,” Opt. Express 24(25), 29190–29197 (2016).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Distributed Brillouin sensing with centimeter-order spatial resolution in polymer optical fibers,” J. Lightwave Technol. 32(21), 3999–4003 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Characterization of stimulated Brillouin scattering in polymer optical fibers based on lock-in-free pump-probe technique,” J. Lightwave Technol. 31(19), 3162–3166 (2013).
[Crossref]

He, J.

He, Z.

Horiguchi, T.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993).

T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects on the Brillouin frequency shift in jacketed optical silica fibers,” Appl. Opt. 29(15), 2219–2222 (1990).
[Crossref]

T. Horiguchi and M. Tateda, “BOTDA–nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
[Crossref]

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

Hosaka, T.

Y. Sasaki, K. Okamoto, T. Hosaka, and N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Optical Fiber Communication Conference, 1982 OSA Technical Digest Series (Optical Society of America, 1982), paper ThCC6.

Hotate, K.

R. Shimizu, M. Kishi, and K. Hotate, “Enlargement of measurement function in Brillouin optical correlation-domain reflectometry with combining four performance improvement schemes,” Proc. SPIE 10323, 1032390 (2017).
[Crossref]

O. Furukawa, S. Tezuka, M. Tsukamoto, S. Matsuura, M. Kishi, and K. Hotate, “Beyond 21 km distributed strain measurement with Brillouin optical correlation-domain reflectometry using polarization diversity method and temporal gating scheme,” IEEJ Trans. Fund. Mater. 137(1), 52–57 (2017). [In Japanese]
[Crossref]

Y. Yao, M. Kishi, and K. Hotate, “Brillouin optical correlation domain reflectometry with lock-in detection scheme,” Appl. Phys. Express 9(7), 072501 (2016).
[Crossref]

C. Zhang, M. Kishi, and K. Hotate, “5,000 points/s high-speed random accessibility for dynamic strain measurement at arbitrary multiple points along a fiber by Brillouin optical correlation domain analysis,” Appl. Phys. Express 8(4), 042501 (2015).
[Crossref]

K. Y. Song, M. Kishi, Z. He, and K. Hotate, “High-repetition-rate distributed Brillouin sensor based on optical correlation-domain analysis with differential frequency modulation,” Opt. Lett. 36(11), 2062–2064 (2011).
[Crossref]

Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Operation of Brillouin optical correlation-domain reflectometry: theoretical analysis and experimental validation,” J. Lightwave Technol. 28(22), 3300–3306 (2010).
[Crossref]

Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR),” Opt. Express 16(16), 12148–12153 (2008).
[Crossref]

K. Y. Song, Z. He, and K. Hotate, “Optimization of Brillouin optical correlation domain analysis system based on intensity modulation scheme,” Opt. Express 14(10), 4256–4263 (2006).
[Crossref]

K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique–Proposal, experiment and simulation–,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).

Izumita, H.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993).

Jin, C.

W. Zou, C. Jin, and J. Chen, “Distributed strain sensing based on combination of Brillouin gain and loss effects in Brillouin optical correlation domain analysis,” Appl. Phys. Express 5(8), 082503 (2012).
[Crossref]

Kishi, M.

O. Furukawa, S. Tezuka, M. Tsukamoto, S. Matsuura, M. Kishi, and K. Hotate, “Beyond 21 km distributed strain measurement with Brillouin optical correlation-domain reflectometry using polarization diversity method and temporal gating scheme,” IEEJ Trans. Fund. Mater. 137(1), 52–57 (2017). [In Japanese]
[Crossref]

R. Shimizu, M. Kishi, and K. Hotate, “Enlargement of measurement function in Brillouin optical correlation-domain reflectometry with combining four performance improvement schemes,” Proc. SPIE 10323, 1032390 (2017).
[Crossref]

Y. Yao, M. Kishi, and K. Hotate, “Brillouin optical correlation domain reflectometry with lock-in detection scheme,” Appl. Phys. Express 9(7), 072501 (2016).
[Crossref]

C. Zhang, M. Kishi, and K. Hotate, “5,000 points/s high-speed random accessibility for dynamic strain measurement at arbitrary multiple points along a fiber by Brillouin optical correlation domain analysis,” Appl. Phys. Express 8(4), 042501 (2015).
[Crossref]

K. Y. Song, M. Kishi, Z. He, and K. Hotate, “High-repetition-rate distributed Brillouin sensor based on optical correlation-domain analysis with differential frequency modulation,” Opt. Lett. 36(11), 2062–2064 (2011).
[Crossref]

Koyamada, Y.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993).

Krebber, K.

Kurashima, T.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993).

T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects on the Brillouin frequency shift in jacketed optical silica fibers,” Appl. Opt. 29(15), 2219–2222 (1990).
[Crossref]

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

Lee, H.

H. Lee, Y. Mizuno, and K. Nakamura, “Detection of 2-mm-long strained section in silica fiber using slope-assisted Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 57(2), 020303 (2018).
[Crossref]

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

H. Lee, Y. Mizuno, and K. Nakamura, “Measurement sensitivity dependencies on incident power and spatial resolution in slope-assisted Brillouin optical correlation-domain reflectometry,” Sens. Actuators A 268, 68–71 (2017).
[Crossref]

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Operation of slope-assisted Brillouin optical correlation-domain reflectometry: comparison of system output with actual frequency shift distribution,” Opt. Express 24(25), 29190–29197 (2016).
[Crossref]

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Slope-assisted Brillouin optical correlation-domain reflectometry: proof of concept,” IEEE Photon. J. 8(3), 1–7 (2016).
[Crossref]

López-Gil, A.

Lopez-Higuera, J. M.

Lv, L.

G. Tu, X. Zhang, Y. Zhang, Z. Ying, and L. Lv, “Strain variation measurement with short time Fourier transform-based Brillouin optical time-domain reflectometry sensing system,” Electron. Lett. 50(22), 1624–1626 (2014).
[Crossref]

Magi, E.

Martin-Lopez, S.

Masoudi, A.

Matsui, T.

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

Matsumoto, Y.

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

Matsuura, S.

O. Furukawa, S. Tezuka, M. Tsukamoto, S. Matsuura, M. Kishi, and K. Hotate, “Beyond 21 km distributed strain measurement with Brillouin optical correlation-domain reflectometry using polarization diversity method and temporal gating scheme,” IEEJ Trans. Fund. Mater. 137(1), 52–57 (2017). [In Japanese]
[Crossref]

Minardo, A.

A. Minardo, R. Bernini, R. Ruiz-Lombera, J. Mirapeix, J. M. Lopez-Higuera, and L. Zeni, “Proposal of Brillouin optical frequency-domain reflectometry (BOFDR),” Opt. Express 24(26), 29994–20001 (2016).
[Crossref]

A. Minardo, R. Bernini, and L. Zeni, “Distributed temperature sensing in polymer optical fiber by BOFDA,” IEEE Photon. Technol. Lett. 26(4), 387–390 (2014).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Distributed sensing at centimeter-scale spatial resolution by BOFDA: Measurements and signal processing,” IEEE Photon. J. 4(1), 48–56 (2012).
[Crossref]

Mirapeix, J.

Mizuno, Y.

H. Lee, Y. Mizuno, and K. Nakamura, “Detection of 2-mm-long strained section in silica fiber using slope-assisted Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 57(2), 020303 (2018).
[Crossref]

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, and K. Nakamura, “Single-end-access distributed strain sensing with wide dynamic range using higher-speed Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 56(7), 072501 (2017).
[Crossref]

H. Lee, Y. Mizuno, and K. Nakamura, “Measurement sensitivity dependencies on incident power and spatial resolution in slope-assisted Brillouin optical correlation-domain reflectometry,” Sens. Actuators A 268, 68–71 (2017).
[Crossref]

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Operation of slope-assisted Brillouin optical correlation-domain reflectometry: comparison of system output with actual frequency shift distribution,” Opt. Express 24(25), 29190–29197 (2016).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5(12), e16184 (2016).
[Crossref]

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Slope-assisted Brillouin optical correlation-domain reflectometry: proof of concept,” IEEE Photon. J. 8(3), 1–7 (2016).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Distributed Brillouin sensing with centimeter-order spatial resolution in polymer optical fibers,” J. Lightwave Technol. 32(21), 3999–4003 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Characterization of stimulated Brillouin scattering in polymer optical fibers based on lock-in-free pump-probe technique,” J. Lightwave Technol. 31(19), 3162–3166 (2013).
[Crossref]

Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Operation of Brillouin optical correlation-domain reflectometry: theoretical analysis and experimental validation,” J. Lightwave Technol. 28(22), 3300–3306 (2010).
[Crossref]

Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR),” Opt. Express 16(16), 12148–12153 (2008).
[Crossref]

Motil, A.

Nakamura, H.

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

Nakamura, K.

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

H. Lee, Y. Mizuno, and K. Nakamura, “Detection of 2-mm-long strained section in silica fiber using slope-assisted Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 57(2), 020303 (2018).
[Crossref]

H. Lee, Y. Mizuno, and K. Nakamura, “Measurement sensitivity dependencies on incident power and spatial resolution in slope-assisted Brillouin optical correlation-domain reflectometry,” Sens. Actuators A 268, 68–71 (2017).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, and K. Nakamura, “Single-end-access distributed strain sensing with wide dynamic range using higher-speed Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 56(7), 072501 (2017).
[Crossref]

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Slope-assisted Brillouin optical correlation-domain reflectometry: proof of concept,” IEEE Photon. J. 8(3), 1–7 (2016).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5(12), e16184 (2016).
[Crossref]

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Operation of slope-assisted Brillouin optical correlation-domain reflectometry: comparison of system output with actual frequency shift distribution,” Opt. Express 24(25), 29190–29197 (2016).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Distributed Brillouin sensing with centimeter-order spatial resolution in polymer optical fibers,” J. Lightwave Technol. 32(21), 3999–4003 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Characterization of stimulated Brillouin scattering in polymer optical fibers based on lock-in-free pump-probe technique,” J. Lightwave Technol. 31(19), 3162–3166 (2013).
[Crossref]

Newson, T. P.

Ochi, Y.

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

Okamoto, K.

Y. Sasaki, K. Okamoto, T. Hosaka, and N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Optical Fiber Communication Conference, 1982 OSA Technical Digest Series (Optical Society of America, 1982), paper ThCC6.

Peled, Y.

Ruiz-Lombera, R.

Sasaki, Y.

Y. Sasaki, K. Okamoto, T. Hosaka, and N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Optical Fiber Communication Conference, 1982 OSA Technical Digest Series (Optical Society of America, 1982), paper ThCC6.

Schliep, F.

Shibata, N.

Y. Sasaki, K. Okamoto, T. Hosaka, and N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Optical Fiber Communication Conference, 1982 OSA Technical Digest Series (Optical Society of America, 1982), paper ThCC6.

Shimizu, R.

R. Shimizu, M. Kishi, and K. Hotate, “Enlargement of measurement function in Brillouin optical correlation-domain reflectometry with combining four performance improvement schemes,” Proc. SPIE 10323, 1032390 (2017).
[Crossref]

Song, K. Y.

Tanaka, Y.

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

Tateda, M.

T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects on the Brillouin frequency shift in jacketed optical silica fibers,” Appl. Opt. 29(15), 2219–2222 (1990).
[Crossref]

T. Horiguchi and M. Tateda, “BOTDA–nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
[Crossref]

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

Tezuka, S.

O. Furukawa, S. Tezuka, M. Tsukamoto, S. Matsuura, M. Kishi, and K. Hotate, “Beyond 21 km distributed strain measurement with Brillouin optical correlation-domain reflectometry using polarization diversity method and temporal gating scheme,” IEEJ Trans. Fund. Mater. 137(1), 52–57 (2017). [In Japanese]
[Crossref]

Tsukamoto, M.

O. Furukawa, S. Tezuka, M. Tsukamoto, S. Matsuura, M. Kishi, and K. Hotate, “Beyond 21 km distributed strain measurement with Brillouin optical correlation-domain reflectometry using polarization diversity method and temporal gating scheme,” IEEJ Trans. Fund. Mater. 137(1), 52–57 (2017). [In Japanese]
[Crossref]

Tu, G.

G. Tu, X. Zhang, Y. Zhang, Z. Ying, and L. Lv, “Strain variation measurement with short time Fourier transform-based Brillouin optical time-domain reflectometry sensing system,” Electron. Lett. 50(22), 1624–1626 (2014).
[Crossref]

Tur, M.

van Deventer, M. O.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[Crossref]

Vo, T. D.

Xiong, C.

Yao, Y.

Y. Yao, M. Kishi, and K. Hotate, “Brillouin optical correlation domain reflectometry with lock-in detection scheme,” Appl. Phys. Express 9(7), 072501 (2016).
[Crossref]

Yaron, L.

Ying, Z.

G. Tu, X. Zhang, Y. Zhang, Z. Ying, and L. Lv, “Strain variation measurement with short time Fourier transform-based Brillouin optical time-domain reflectometry sensing system,” Electron. Lett. 50(22), 1624–1626 (2014).
[Crossref]

Zeni, L.

A. Minardo, R. Bernini, R. Ruiz-Lombera, J. Mirapeix, J. M. Lopez-Higuera, and L. Zeni, “Proposal of Brillouin optical frequency-domain reflectometry (BOFDR),” Opt. Express 24(26), 29994–20001 (2016).
[Crossref]

A. Minardo, R. Bernini, and L. Zeni, “Distributed temperature sensing in polymer optical fiber by BOFDA,” IEEE Photon. Technol. Lett. 26(4), 387–390 (2014).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Distributed sensing at centimeter-scale spatial resolution by BOFDA: Measurements and signal processing,” IEEE Photon. J. 4(1), 48–56 (2012).
[Crossref]

Zhang, C.

C. Zhang, M. Kishi, and K. Hotate, “5,000 points/s high-speed random accessibility for dynamic strain measurement at arbitrary multiple points along a fiber by Brillouin optical correlation domain analysis,” Appl. Phys. Express 8(4), 042501 (2015).
[Crossref]

Zhang, X.

G. Tu, X. Zhang, Y. Zhang, Z. Ying, and L. Lv, “Strain variation measurement with short time Fourier transform-based Brillouin optical time-domain reflectometry sensing system,” Electron. Lett. 50(22), 1624–1626 (2014).
[Crossref]

Zhang, Y.

G. Tu, X. Zhang, Y. Zhang, Z. Ying, and L. Lv, “Strain variation measurement with short time Fourier transform-based Brillouin optical time-domain reflectometry sensing system,” Electron. Lett. 50(22), 1624–1626 (2014).
[Crossref]

Zou, W.

Appl. Opt. (1)

Appl. Phys. Express (4)

C. Zhang, M. Kishi, and K. Hotate, “5,000 points/s high-speed random accessibility for dynamic strain measurement at arbitrary multiple points along a fiber by Brillouin optical correlation domain analysis,” Appl. Phys. Express 8(4), 042501 (2015).
[Crossref]

W. Zou, C. Jin, and J. Chen, “Distributed strain sensing based on combination of Brillouin gain and loss effects in Brillouin optical correlation domain analysis,” Appl. Phys. Express 5(8), 082503 (2012).
[Crossref]

Y. Yao, M. Kishi, and K. Hotate, “Brillouin optical correlation domain reflectometry with lock-in detection scheme,” Appl. Phys. Express 9(7), 072501 (2016).
[Crossref]

H. Lee, Y. Ochi, T. Matsui, Y. Matsumoto, Y. Tanaka, H. Nakamura, Y. Mizuno, and K. Nakamura, “Distributed strain measurement and possible breakage detection of optical-fiber-embedded composite structure using slope-assisted Brillouin optical correlation-domain reflectometry,” Appl. Phys. Express 11(7), 072501 (2018).
[Crossref]

Electron. Lett. (1)

G. Tu, X. Zhang, Y. Zhang, Z. Ying, and L. Lv, “Strain variation measurement with short time Fourier transform-based Brillouin optical time-domain reflectometry sensing system,” Electron. Lett. 50(22), 1624–1626 (2014).
[Crossref]

IEEE Photon. J. (2)

H. Lee, N. Hayashi, Y. Mizuno, and K. Nakamura, “Slope-assisted Brillouin optical correlation-domain reflectometry: proof of concept,” IEEE Photon. J. 8(3), 1–7 (2016).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Distributed sensing at centimeter-scale spatial resolution by BOFDA: Measurements and signal processing,” IEEE Photon. J. 4(1), 48–56 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (2)

A. Minardo, R. Bernini, and L. Zeni, “Distributed temperature sensing in polymer optical fiber by BOFDA,” IEEE Photon. Technol. Lett. 26(4), 387–390 (2014).
[Crossref]

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photon. Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

IEEJ Trans. Fund. Mater. (1)

O. Furukawa, S. Tezuka, M. Tsukamoto, S. Matsuura, M. Kishi, and K. Hotate, “Beyond 21 km distributed strain measurement with Brillouin optical correlation-domain reflectometry using polarization diversity method and temporal gating scheme,” IEEJ Trans. Fund. Mater. 137(1), 52–57 (2017). [In Japanese]
[Crossref]

IEICE Trans. Commun. (1)

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. E76-B(4), 382–390 (1993).

IEICE Trans. Electron. (1)

K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique–Proposal, experiment and simulation–,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).

J. Lightwave Technol. (5)

T. Horiguchi and M. Tateda, “BOTDA–nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Distributed Brillouin sensing with centimeter-order spatial resolution in polymer optical fibers,” J. Lightwave Technol. 32(21), 3999–4003 (2014).
[Crossref]

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[Crossref]

Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Operation of Brillouin optical correlation-domain reflectometry: theoretical analysis and experimental validation,” J. Lightwave Technol. 28(22), 3300–3306 (2010).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Characterization of stimulated Brillouin scattering in polymer optical fibers based on lock-in-free pump-probe technique,” J. Lightwave Technol. 31(19), 3162–3166 (2013).
[Crossref]

Jpn. J. Appl. Phys. (2)

Y. Mizuno, N. Hayashi, H. Fukuda, and K. Nakamura, “Single-end-access distributed strain sensing with wide dynamic range using higher-speed Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 56(7), 072501 (2017).
[Crossref]

H. Lee, Y. Mizuno, and K. Nakamura, “Detection of 2-mm-long strained section in silica fiber using slope-assisted Brillouin optical correlation-domain reflectometry,” Jpn. J. Appl. Phys. 57(2), 020303 (2018).
[Crossref]

Light: Sci. Appl. (1)

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5(12), e16184 (2016).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

Proc. SPIE (1)

R. Shimizu, M. Kishi, and K. Hotate, “Enlargement of measurement function in Brillouin optical correlation-domain reflectometry with combining four performance improvement schemes,” Proc. SPIE 10323, 1032390 (2017).
[Crossref]

Sens. Actuators A (1)

H. Lee, Y. Mizuno, and K. Nakamura, “Measurement sensitivity dependencies on incident power and spatial resolution in slope-assisted Brillouin optical correlation-domain reflectometry,” Sens. Actuators A 268, 68–71 (2017).
[Crossref]

Other (2)

Y. Sasaki, K. Okamoto, T. Hosaka, and N. Shibata, “Polarization-maintaining and absorption-reducing fibers,” in Optical Fiber Communication Conference, 1982 OSA Technical Digest Series (Optical Society of America, 1982), paper ThCC6.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).

Supplementary Material (2)

NameDescription
» Visualization 1       Demonstration movie of distributed temperature measurement using PMF-based SA-BOCDR with a lower spatial resolution.
» Visualization 2       Demonstration movie of distributed temperature measurement using PMF-based SA-BOCDR with a higher spatial resolution.

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Figures (5)

Fig. 1.
Fig. 1. Experimental setup of SA-BOCDR, in which the polarization scrambler (PSCR) can be switched on and off. EDFA, erbium-doped fiber amplifier; ESA, electrical spectrum analyzer; OSC, oscilloscope; PC, polarization controller; PD, photodetector; PMF, polarization-maintaining fiber.
Fig. 2.
Fig. 2. Spectral power distributions along (a) the SMF and (b) the PMF measured at three different states of polarization, when 1000 µε strain was applied to the FUTs (7.0–7.3 m).
Fig. 3.
Fig. 3. (a) Measured BGS in the PANDA-type PMF at three different SOPs. (b) Spectral power plotted as a function of the applied strain at three different SOPs. The dotted lines are linear fits.
Fig. 4.
Fig. 4. Demonstration movies of distributed temperature measurement using PMF-based SA-BOCDR. (a) Lower spatial resolution (Visualization 1) and (b) higher spatial resolution (Visualization 2).
Fig. 5.
Fig. 5. BFS dependencies on (a) strain and (b) temperature in the PANDA-type PMF. The dotted lines are linear fits.

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