Abstract

In this paper, we propose and demonstrate an ultrahigh-speed Brillouin optical correlation domain analysis (BOCDA) with a single-position sampling rate of 200 kS/s and a spatial resolution of 8 cm. The Brillouin gain spectrum (BGS) is obtained by using a data subtraction scheme rather than the conventional lock-in amplifier (LIA) detection configuration, thus removing the limitation of measurement speed imposed by the LIA. Meanwhile, a voltage controlled oscillator (VCO) is used to sweep the frequency interval between the pump and the probe rapidly. As a proof of concept, we implement measurements of various dynamic strains with frequencies up to 20 kHz at arbitrary position. Moreover, to implement high-speed distributed measurements of Brillouin frequency shift (BFS) along the whole fiber under test (FUT), we propose a novel measuring method which moves the correlation peak and sweeps the pump-probe frequency interval simultaneously. A repetition rate of 1 kHz is verified by measuring dynamic strains with frequencies up to 200 Hz, for distributed measurements performed with 200 points.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
  22. 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] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  33. D. Elooz, Y. Antman, N. Levanon, and A. Zadok, “High-resolution long-reach distributed Brillouin sensing based on combined time-domain and correlation-domain analysis,” Opt. Express 22(6), 6453–6463 (2014).
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    [Crossref]

2017 (4)

2016 (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]

2015 (4)

F. Wei, B. Lu, J. Wang, D. Xu, Z. Pan, D. Chen, H. Cai, and R. Qu, “Precision and broadband frequency swept laser source based on high-order modulation-sideband injection-locking,” Opt. Express 23(4), 4970–4980 (2015).
[Crossref] [PubMed]

J. Wang, D. Chen, H. Cai, F. Wei, and R. Qu, “Fast optical frequency sweeping using voltage controlled oscillator driven single sideband modulation combined with injection locking,” Opt. Express 23(6), 7038–7043 (2015).
[Crossref] [PubMed]

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]

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]

2014 (1)

2013 (1)

2012 (4)

2011 (6)

2010 (1)

2009 (1)

2008 (1)

2007 (2)

A. W. Brown, B. G. Colpitts, and K. Brown, “Dark-pulse Brillouin optical time-domain sensor with 20-mm spatial resolution,” J. Lightwave Technol. 25(1), 381–386 (2007).
[Crossref]

K. Y. Song and K. Hotate, “Distributed Fiber Strain Sensor with 1-kHz Sampling Rate Based on Brillouin Optical Correlation Domain Analysis,” IEEE Photonics Technol. Lett. 19(23), 1928–1930 (2007).
[Crossref]

2006 (1)

2004 (1)

L. Thévenaz, S. Le Floch, D. Alasia, and J. Troger, “Novel schemes for optical signal generation using laser injection locking with application to Brillouin sensing,” Meas. Sci. Technol. 15(8), 1519–1524 (2004).
[Crossref]

2000 (1)

K. Hotate, “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), 405–411 (2000).

1996 (2)

1993 (2)

X. Bao, D. J. Webb, and D. A. Jackson, “22-km distributed temperature sensor using Brillouin gain in an optical fiber,” Opt. Lett. 18(7), 552–554 (1993).
[Crossref] [PubMed]

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

Alasia, D.

L. Thévenaz, S. Le Floch, D. Alasia, and J. Troger, “Novel schemes for optical signal generation using laser injection locking with application to Brillouin sensing,” Meas. Sci. Technol. 15(8), 1519–1524 (2004).
[Crossref]

Angulo-Vinuesa, X.

Ania-Castañon, J. D.

Antman, Y.

Bao, X.

Beugnot, J.-C.

Bolognini, G.

Brown, A. W.

Brown, K.

Cai, H.

Chen, D.

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.

Colpitts, B. G.

Corredera, P.

Di Pasquale, F.

Dong, Y.

Du, J.

Elooz, D.

Fan, X.

G. Yang, X. Fan, and Z. He, “Strain Dynamic Range Enlargement of Slope-Assisted BOTDA by Using Brillouin Phase-Gain Ratio,” J. Lightwave Technol. 35(20), 4451–4458 (2017).
[Crossref]

B. Wang, X. Fan, J. Du, and Z. He, “Performance enhancement of Brillouin optical correlation domain analysis based on frequency chirp magnification,” Chin. Opt. Lett. 15(12), 120601 (2017).
[Crossref]

B. Wang, X. Fan, S. Wang, J. Du, and Z. He, “Millimeter-resolution long-range OFDR using ultra-linearly 100 GHz-swept optical source realized by injection-locking technique and cascaded FWM process,” Opt. Express 25(4), 3514–3524 (2017).
[Crossref] [PubMed]

B. Wang, X. Fan, G. Yang, Q. Liu, and Z. He, “Millimeter-resolution long range optical frequency domain reflectometry for health monitoring of access network,” in Proceedings of European Conference on Optical Communication (ECOC) (2016).

B. Wang, X. Fan, Q. Liu, and Z. He, “Increasing effective sensing points of Brillouin optical correlation domain analysis using four-wave-mixing process,” in Proceedings of Optical Fiber Sensors Conference (OFS) (2017).

Foaleng, S. M.

Fukuda, H.

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, S.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

Garus, D.

Gogolla, T.

González-Herráez, M.

Hayashi, N.

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]

He, Z.

B. Wang, X. Fan, S. Wang, J. Du, and Z. He, “Millimeter-resolution long-range OFDR using ultra-linearly 100 GHz-swept optical source realized by injection-locking technique and cascaded FWM process,” Opt. Express 25(4), 3514–3524 (2017).
[Crossref] [PubMed]

G. Yang, X. Fan, and Z. He, “Strain Dynamic Range Enlargement of Slope-Assisted BOTDA by Using Brillouin Phase-Gain Ratio,” J. Lightwave Technol. 35(20), 4451–4458 (2017).
[Crossref]

B. Wang, X. Fan, J. Du, and Z. He, “Performance enhancement of Brillouin optical correlation domain analysis based on frequency chirp magnification,” Chin. Opt. Lett. 15(12), 120601 (2017).
[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] [PubMed]

K. Y. Song, Z. He, and K. Hotate, “Distributed strain measurement with millimeter-order spatial resolution based on Brillouin optical correlation domain analysis,” Opt. Lett. 31(17), 2526–2528 (2006).
[Crossref] [PubMed]

B. Wang, X. Fan, G. Yang, Q. Liu, and Z. He, “Millimeter-resolution long range optical frequency domain reflectometry for health monitoring of access network,” in Proceedings of European Conference on Optical Communication (ECOC) (2016).

B. Wang, X. Fan, Q. Liu, and Z. He, “Increasing effective sensing points of Brillouin optical correlation domain analysis using four-wave-mixing process,” in Proceedings of Optical Fiber Sensors Conference (OFS) (2017).

Horiguchi, T.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

Hotate, K.

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] [PubMed]

K. Y. Song and K. Hotate, “Distributed Fiber Strain Sensor with 1-kHz Sampling Rate Based on Brillouin Optical Correlation Domain Analysis,” IEEE Photonics Technol. Lett. 19(23), 1928–1930 (2007).
[Crossref]

K. Y. Song, Z. He, and K. Hotate, “Distributed strain measurement with millimeter-order spatial resolution based on Brillouin optical correlation domain analysis,” Opt. Lett. 31(17), 2526–2528 (2006).
[Crossref] [PubMed]

K. Hotate, “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), 405–411 (2000).

Izumita, H.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 382–390 (1993).

Jackson, D. A.

Jeong, J. H.

Jeong, J.-M.

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]

Kim, G. T.

Kishi, M.

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] [PubMed]

Koyamada, Y.

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE Trans. Commun. 76, 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. 76, 382–390 (1993).

Le Floch, S.

M. A. Soto, S. Le Floch, and L. Thévenaz, “Bipolar optical pulse coding for performance enhancement in BOTDA sensors,” Opt. Express 21(14), 16390–16397 (2013).
[Crossref] [PubMed]

L. Thévenaz, S. Le Floch, D. Alasia, and J. Troger, “Novel schemes for optical signal generation using laser injection locking with application to Brillouin sensing,” Meas. Sci. Technol. 15(8), 1519–1524 (2004).
[Crossref]

Lee, K.

Lee, S. B.

Levanon, N.

Li, W.

Li, Y.

Liu, Q.

B. Wang, X. Fan, Q. Liu, and Z. He, “Increasing effective sensing points of Brillouin optical correlation domain analysis using four-wave-mixing process,” in Proceedings of Optical Fiber Sensors Conference (OFS) (2017).

B. Wang, X. Fan, G. Yang, Q. Liu, and Z. He, “Millimeter-resolution long range optical frequency domain reflectometry for health monitoring of access network,” in Proceedings of European Conference on Optical Communication (ECOC) (2016).

Lu, B.

Martin-Lopez, S.

Mizuno, Y.

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]

Motil, A.

Nakamura, K.

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]

Niklès, M.

Nuño, J.

Pan, Z.

Peled, Y.

Qu, R.

Robert, P. A.

Ryu, G.

Schliep, F.

Song, K. Y.

Soto, M. A.

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]

Thevenaz, L.

Thévenaz, L.

Troger, J.

L. Thévenaz, S. Le Floch, D. Alasia, and J. Troger, “Novel schemes for optical signal generation using laser injection locking with application to Brillouin sensing,” Meas. Sci. Technol. 15(8), 1519–1524 (2004).
[Crossref]

Tur, M.

Voskoboinik, A.

Wang, B.

B. Wang, X. Fan, J. Du, and Z. He, “Performance enhancement of Brillouin optical correlation domain analysis based on frequency chirp magnification,” Chin. Opt. Lett. 15(12), 120601 (2017).
[Crossref]

B. Wang, X. Fan, S. Wang, J. Du, and Z. He, “Millimeter-resolution long-range OFDR using ultra-linearly 100 GHz-swept optical source realized by injection-locking technique and cascaded FWM process,” Opt. Express 25(4), 3514–3524 (2017).
[Crossref] [PubMed]

B. Wang, X. Fan, G. Yang, Q. Liu, and Z. He, “Millimeter-resolution long range optical frequency domain reflectometry for health monitoring of access network,” in Proceedings of European Conference on Optical Communication (ECOC) (2016).

B. Wang, X. Fan, Q. Liu, and Z. He, “Increasing effective sensing points of Brillouin optical correlation domain analysis using four-wave-mixing process,” in Proceedings of Optical Fiber Sensors Conference (OFS) (2017).

Wang, J.

Wang, S.

Webb, D. J.

Wei, F.

Willner, A. W.

Xu, D.

Yang, G.

G. Yang, X. Fan, and Z. He, “Strain Dynamic Range Enlargement of Slope-Assisted BOTDA by Using Brillouin Phase-Gain Ratio,” J. Lightwave Technol. 35(20), 4451–4458 (2017).
[Crossref]

B. Wang, X. Fan, G. Yang, Q. Liu, and Z. He, “Millimeter-resolution long range optical frequency domain reflectometry for health monitoring of access network,” in Proceedings of European Conference on Optical Communication (ECOC) (2016).

Yaron, L.

Yilmaz, O. F.

Zadok, A.

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, H.

Zou, W.

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]

Appl. Opt. (2)

Appl. Phys. Express (2)

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]

Chin. Opt. Lett. (1)

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]

K. Y. Song and K. Hotate, “Distributed Fiber Strain Sensor with 1-kHz Sampling Rate Based on Brillouin Optical Correlation Domain Analysis,” IEEE Photonics Technol. Lett. 19(23), 1928–1930 (2007).
[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. 76, 382–390 (1993).

IEICE Trans. Electron. (1)

K. Hotate, “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), 405–411 (2000).

J. Lightwave Technol. (5)

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]

Meas. Sci. Technol. (1)

L. Thévenaz, S. Le Floch, D. Alasia, and J. Troger, “Novel schemes for optical signal generation using laser injection locking with application to Brillouin sensing,” Meas. Sci. Technol. 15(8), 1519–1524 (2004).
[Crossref]

Opt. Express (10)

D. Elooz, Y. Antman, N. Levanon, and A. Zadok, “High-resolution long-reach distributed Brillouin sensing based on combined time-domain and correlation-domain analysis,” Opt. Express 22(6), 6453–6463 (2014).
[Crossref] [PubMed]

J. H. Jeong, K. Lee, K. Y. Song, J.-M. Jeong, and S. B. Lee, “Variable-frequency lock-in detection for the suppression of beat noise in Brillouin optical correlation domain analysis,” Opt. Express 19(19), 18721–18728 (2011).
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F. Wei, B. Lu, J. Wang, D. Xu, Z. Pan, D. Chen, H. Cai, and R. Qu, “Precision and broadband frequency swept laser source based on high-order modulation-sideband injection-locking,” Opt. Express 23(4), 4970–4980 (2015).
[Crossref] [PubMed]

J. Wang, D. Chen, H. Cai, F. Wei, and R. Qu, “Fast optical frequency sweeping using voltage controlled oscillator driven single sideband modulation combined with injection locking,” Opt. Express 23(6), 7038–7043 (2015).
[Crossref] [PubMed]

B. Wang, X. Fan, S. Wang, J. Du, and Z. He, “Millimeter-resolution long-range OFDR using ultra-linearly 100 GHz-swept optical source realized by injection-locking technique and cascaded FWM process,” Opt. Express 25(4), 3514–3524 (2017).
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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).
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Opt. Lett. (7)

Other (2)

B. Wang, X. Fan, G. Yang, Q. Liu, and Z. He, “Millimeter-resolution long range optical frequency domain reflectometry for health monitoring of access network,” in Proceedings of European Conference on Optical Communication (ECOC) (2016).

B. Wang, X. Fan, Q. Liu, and Z. He, “Increasing effective sensing points of Brillouin optical correlation domain analysis using four-wave-mixing process,” in Proceedings of Optical Fiber Sensors Conference (OFS) (2017).

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Figures (12)

Fig. 1
Fig. 1 (a) Schematic of the conventional detection scheme using lock-in amplifier (LIA). IM: intensity modulator; AWG: arbitrary wave generator; LIA: lock-in amplifier. (b) Brillouin gain spectrum (BGS) measured by using LIA when the sampling is set to be 100 S/s (red line) and 500 S/s (gray line).
Fig. 2
Fig. 2 Schematic of the proposed LIA-free BOCDA scheme. FUT: fiber under test; PD: photodetector; LPF: low-pass filter.
Fig. 3
Fig. 3 The schematic illustration of the proposed measuring method without point-by-point shifting. The blue line shows the sweeping of the pump-probe frequency difference, while the red line shows the scanning of the measurement position (correlation peak). Ts is the sweep time of the voltage controlled oscillator (VCO), and NTs is the total measurement time for N-points when the correlation peak is moved from 0 to LFUT.
Fig. 4
Fig. 4 Experimental setup of the proposed LIA-free BOCDA. DFB: distributed feedback laser diode; SSBM: single-sideband modulator; VCO: voltage-controlled oscillator; PC: polarization controller; CIR: optical circulator; EDFA: erbium-doped fiber amplifier; ISO: optical isolator; PMF: polarization-maintaining fiber; VOA: variable attenuator; PD: photodetector; ADC: analog-to-digital converter.
Fig. 5
Fig. 5 (a) Experimental configuration used to measurement the output frequency of the VCO. The VCO operates with a repetition rate of 200 kHz. (b) Linearly applied voltage (blue line) and nonlinear output frequency of the VCO (red line). The residual errors shown in the inset figure is near 40 MHz. (c) Pre-distorted applied voltage (blue line) and the linear output frequency of the VCO (red line). The residual errors shown in the inset figure is decreased to less than 1 MHz with pre-distortion.
Fig. 6
Fig. 6 (a) Optical spectra and (b) power fluctuation of the probe lightwave without (blue line) and with (red line) injection locking. The measured Brillouin signals (c) without and (d) with injection locking. The sampling rate is set to be 10 kS/s.
Fig. 7
Fig. 7 Strain dependence of the measured BGS when the sampling rate is set to be 200 kS/s. The spatial resolution is 8 cm, and the stretched length is 19 cm.
Fig. 8
Fig. 8 Measured BGSs when the single-position sampling rate is set to be (a) 10 kS/s, (b) 100 kS/s, and (c) 200 kS/s. The correlation peak is fixed at a certain position, and the measurement time is 5 ms. (d), (e), and (f) are the Brillouin frequency shift (BFS) variation obtained from (a), (b), and (c). The standard deviations of BFS variation are calculated to 1 MHz, 2.7 MHz, and 4.2 MHz for sampling rates of 10 kS/s, 100 kS/s, and 200 kS/s, respectively.
Fig. 9
Fig. 9 The measured BFS variation when dynamic strains with frequency of (a) 150 Hz, (b) 600 Hz, (c) 5,000 Hz, and (d) 20,000 Hz are applied to the fiber. The blue line is the measured data and the red line is the sinusoidally-fitted data.
Fig. 10
Fig. 10 (a) Measured BFS distribution along the whole FUT (200 effective sensing points) with a repetition rate of 1 kHz. The inset figure shows the BGS without (gray line) and with (red) strain. (b) Measured BGSs around the stretched section whose length is 19 cm.
Fig. 11
Fig. 11 Three-dimensional plot of the distributed BFS change measured by the LIA-free BOCDA at a repetition rate of 1 kHz during 60 ms when dynamic strains with frequencies of (a) 50 Hz, (b) 100 Hz, and (c) 200 Hz are applied to the FUT. (d) The BFS variation at 11 m where no strains are applied. The BFS variation at 7.9 m when dynamic strains with frequencies of (e) 50 Hz, (f) 100 Hz, and (g) 200 Hz are applied. The blue line is the measured data and the red line is the sinusoidally-fitted data.
Fig. 12
Fig. 12 (a) Comparison between two measurement methods based on step-by-step changing fm (blue line) or continuously sweeping fm (red line). (b) Schematic analysis of the distributed measurement process based on continuously sweeping scheme. TS is the sweeping period of the VCO, and Δx is the distance corresponding to the frequency change within Ts.

Tables (1)

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Table 1 The parameters of the PMF.

Equations (6)

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d m = V g 2 f m
Δz= V g Δ v B 2π f m Δf
E(t) k= A k (t) e j2π( v 0 (t)+k f r )t
E(t) P s e j2π( v 0 (t) f r )t
- c 2nL (1+ β 2 )ρ <Δω<- c 2nL ρ
P(t,v)= P probe (t)+ g B (v) P probe (t) P pump (t)Δz

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