Abstract

Utilizing the large effective area non-zero dispersion-shifted fiber (LEAF), a multi-parameter optical-fiber sensor has been proposed and experimentally demonstrated for distributed simultaneous temperature and strain measurement, which is based on multiple acoustic modes in spontaneous Brillouin scattering (SpBS) effect. Proof-of-concept experiments demonstrate 3 m spatial resolution over 2.5 km sensing LEAF with 2°C temperature accuracy and 60µɛ strain accuracy. The proposed distributed Brillouin optical fiber sensor allows simultaneously temperature and strain measurement, thus opening a door for practical application such as superconducting cable.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (3)

2018 (1)

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

2017 (1)

2016 (3)

2015 (1)

Y. Mizuno, N. Hayashi, H. Tanaka, Y. Wada, and K. Nakamura, “Brillouin scattering in multi-core optical fibers for sensing applications,” Sci. Rep. 5(1), 11388 (2015).
[Crossref]

2013 (1)

Z. Y. He, Q. W. Liu, and T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonics Sens. 3(4), 295–303 (2013).
[Crossref]

2012 (2)

2011 (1)

X. Y. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors 11(4), 4152–4187 (2011).
[Crossref]

2001 (1)

C. C. Lee, P. W. Chiang, and S. Chi, “Utilization of a dispersion-shifted fiber for simultaneous measurement of distributed strain and temperature through Brillouin frequency shift,” IEEE Photonics Technol. Lett. 13(10), 1094–1096 (2001).
[Crossref]

1997 (2)

M. A. Davis and A. D. Kersey, “Simultaneous measurement of temperature and strain using fibre Bragg gratings and Brillouin scattering,” IEE Proc.: Optoelectron. 144(3), 151–155 (1997).
[Crossref]

T. R. Parker, M. F. Farhadiroushan, V. A. Handerek, and A. J. Rogers, “The simultaneous measurement of strain and temperature distributionsfrom Brillouin backscatterm,” IEEE Photonics Technol. Lett. 9(7), 979–981 (1997).
[Crossref]

1993 (2)

X. Y. Bao, K. J. Webb, and D. A. Jackson, “32-km distributed temperature sensor based on Brillouin loss in an optical fiber,” Opt. Lett. 18(18), 1561–1563 (1993).
[Crossref]

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

Ba, D. X.

B. Z. Wang, B. Fan, D. W. Zhou, C. Pang, Y. Li, D. X. Ba, and Y. K. Dong, “High-performance optical chirp chain BOTDA by using a pattern recognition algorithm and the differential pulse-width pair technique,” Photonics Res. 7(6), 652–658 (2019).
[Crossref]

D. X. Ba, Y. Li, J. L. Yan, X. P. Zhang, and Y. K. Dong, “Phase-coded Brillouin optical correlation domain analysis with 2-mm resolution based on phase-shift keying,” Opt. Express 27(25), 36197–36205 (2019).
[Crossref]

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

D. X. Ba, B. Z. Wang, D. W. Zhou, M. J. Yin, Y. K. Dong, H. Li, Z. W. Lu, and Z. G. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref]

Bao, X. Y.

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

X. Y. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors 12(7), 8601–8639 (2012).
[Crossref]

X. Liu and X. Y. Bao, “Brillouin spectrum in LEAF and simultaneous temperature and strain measurement,” J. Lightwave Technol. 30(8), 1053–1059 (2012).
[Crossref]

X. Y. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors 11(4), 4152–4187 (2011).
[Crossref]

X. Y. Bao, K. J. Webb, and D. A. Jackson, “32-km distributed temperature sensor based on Brillouin loss in an optical fiber,” Opt. Lett. 18(18), 1561–1563 (1993).
[Crossref]

Chen, L.

X. Y. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors 12(7), 8601–8639 (2012).
[Crossref]

X. Y. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors 11(4), 4152–4187 (2011).
[Crossref]

Chi, S.

C. C. Lee, P. W. Chiang, and S. Chi, “Utilization of a dispersion-shifted fiber for simultaneous measurement of distributed strain and temperature through Brillouin frequency shift,” IEEE Photonics Technol. Lett. 13(10), 1094–1096 (2001).
[Crossref]

Chiang, P. W.

C. C. Lee, P. W. Chiang, and S. Chi, “Utilization of a dispersion-shifted fiber for simultaneous measurement of distributed strain and temperature through Brillouin frequency shift,” IEEE Photonics Technol. Lett. 13(10), 1094–1096 (2001).
[Crossref]

Dang, Y. L.

Davis, M. A.

M. A. Davis and A. D. Kersey, “Simultaneous measurement of temperature and strain using fibre Bragg gratings and Brillouin scattering,” IEE Proc.: Optoelectron. 144(3), 151–155 (1997).
[Crossref]

Dong, Y. K.

B. Z. Wang, B. Fan, D. W. Zhou, C. Pang, Y. Li, D. X. Ba, and Y. K. Dong, “High-performance optical chirp chain BOTDA by using a pattern recognition algorithm and the differential pulse-width pair technique,” Photonics Res. 7(6), 652–658 (2019).
[Crossref]

D. X. Ba, Y. Li, J. L. Yan, X. P. Zhang, and Y. K. Dong, “Phase-coded Brillouin optical correlation domain analysis with 2-mm resolution based on phase-shift keying,” Opt. Express 27(25), 36197–36205 (2019).
[Crossref]

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

D. X. Ba, B. Z. Wang, D. W. Zhou, M. J. Yin, Y. K. Dong, H. Li, Z. W. Lu, and Z. G. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref]

Duan, L.

Fan, B.

B. Z. Wang, B. Fan, D. W. Zhou, C. Pang, Y. Li, D. X. Ba, and Y. K. Dong, “High-performance optical chirp chain BOTDA by using a pattern recognition algorithm and the differential pulse-width pair technique,” Photonics Res. 7(6), 652–658 (2019).
[Crossref]

Fan, Z. G.

Farhadiroushan, M. F.

T. R. Parker, M. F. Farhadiroushan, V. A. Handerek, and A. J. Rogers, “The simultaneous measurement of strain and temperature distributionsfrom Brillouin backscatterm,” IEEE Photonics Technol. Lett. 9(7), 979–981 (1997).
[Crossref]

Fu, S. N.

Furukawa, S.

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

Gan, L.

Guo, N.

Handerek, V. A.

T. R. Parker, M. F. Farhadiroushan, V. A. Handerek, and A. J. Rogers, “The simultaneous measurement of strain and temperature distributionsfrom Brillouin backscatterm,” IEEE Photonics Technol. Lett. 9(7), 979–981 (1997).
[Crossref]

Hayashi, N.

Y. Mizuno, N. Hayashi, H. Tanaka, Y. Wada, and K. Nakamura, “Brillouin scattering in multi-core optical fibers for sensing applications,” Sci. Rep. 5(1), 11388 (2015).
[Crossref]

He, Z. Y.

Z. Y. He, Q. W. Liu, and T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonics Sens. 3(4), 295–303 (2013).
[Crossref]

Horiguchi, T.

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

Huang, S.

Huang, W.

Huang, W. Z.

W. T. Zhang, W. Z. Huang, L. Li, W. Y. Liu, and F. Li, “High resolution strain sensor for earthquake precursor observation and earthquake monitoring,” Proceedings of the 6th European Workshop on Optical Fibre Sensors. (2016).

Izumita, H.

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

Jackson, D. A.

Kersey, A. D.

M. A. Davis and A. D. Kersey, “Simultaneous measurement of temperature and strain using fibre Bragg gratings and Brillouin scattering,” IEE Proc.: Optoelectron. 144(3), 151–155 (1997).
[Crossref]

Koyamada, Y.

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

Kurashima, T.

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

Lee, C. C.

C. C. Lee, P. W. Chiang, and S. Chi, “Utilization of a dispersion-shifted fiber for simultaneous measurement of distributed strain and temperature through Brillouin frequency shift,” IEEE Photonics Technol. Lett. 13(10), 1094–1096 (2001).
[Crossref]

Li, B. R.

Li, F.

W. T. Zhang, W. Z. Huang, L. Li, W. Y. Liu, and F. Li, “High resolution strain sensor for earthquake precursor observation and earthquake monitoring,” Proceedings of the 6th European Workshop on Optical Fibre Sensors. (2016).

Li, H.

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

D. X. Ba, B. Z. Wang, D. W. Zhou, M. J. Yin, Y. K. Dong, H. Li, Z. W. Lu, and Z. G. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref]

Li, L.

W. T. Zhang, W. Z. Huang, L. Li, W. Y. Liu, and F. Li, “High resolution strain sensor for earthquake precursor observation and earthquake monitoring,” Proceedings of the 6th European Workshop on Optical Fibre Sensors. (2016).

Li, Y.

B. Z. Wang, B. Fan, D. W. Zhou, C. Pang, Y. Li, D. X. Ba, and Y. K. Dong, “High-performance optical chirp chain BOTDA by using a pattern recognition algorithm and the differential pulse-width pair technique,” Photonics Res. 7(6), 652–658 (2019).
[Crossref]

D. X. Ba, Y. Li, J. L. Yan, X. P. Zhang, and Y. K. Dong, “Phase-coded Brillouin optical correlation domain analysis with 2-mm resolution based on phase-shift keying,” Opt. Express 27(25), 36197–36205 (2019).
[Crossref]

Liu, D. M.

Liu, M.

Liu, Q. W.

Z. Y. He, Q. W. Liu, and T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonics Sens. 3(4), 295–303 (2013).
[Crossref]

Liu, W. Y.

W. T. Zhang, W. Z. Huang, L. Li, W. Y. Liu, and F. Li, “High resolution strain sensor for earthquake precursor observation and earthquake monitoring,” Proceedings of the 6th European Workshop on Optical Fibre Sensors. (2016).

Liu, X.

Lu, C.

Lu, Z. W.

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

D. X. Ba, B. Z. Wang, D. W. Zhou, M. J. Yin, Y. K. Dong, H. Li, Z. W. Lu, and Z. G. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref]

Mizuno, Y.

Y. Mizuno, N. Hayashi, H. Tanaka, Y. Wada, and K. Nakamura, “Brillouin scattering in multi-core optical fibers for sensing applications,” Sci. Rep. 5(1), 11388 (2015).
[Crossref]

Nakamura, K.

Y. Mizuno, N. Hayashi, H. Tanaka, Y. Wada, and K. Nakamura, “Brillouin scattering in multi-core optical fibers for sensing applications,” Sci. Rep. 5(1), 11388 (2015).
[Crossref]

Pang, C.

B. Z. Wang, B. Fan, D. W. Zhou, C. Pang, Y. Li, D. X. Ba, and Y. K. Dong, “High-performance optical chirp chain BOTDA by using a pattern recognition algorithm and the differential pulse-width pair technique,” Photonics Res. 7(6), 652–658 (2019).
[Crossref]

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Parker, T. R.

T. R. Parker, M. F. Farhadiroushan, V. A. Handerek, and A. J. Rogers, “The simultaneous measurement of strain and temperature distributionsfrom Brillouin backscatterm,” IEEE Photonics Technol. Lett. 9(7), 979–981 (1997).
[Crossref]

Rogers, A. J.

T. R. Parker, M. F. Farhadiroushan, V. A. Handerek, and A. J. Rogers, “The simultaneous measurement of strain and temperature distributionsfrom Brillouin backscatterm,” IEEE Photonics Technol. Lett. 9(7), 979–981 (1997).
[Crossref]

Shum, P.

Shum, P. P.

Tanaka, H.

Y. Mizuno, N. Hayashi, H. Tanaka, Y. Wada, and K. Nakamura, “Brillouin scattering in multi-core optical fibers for sensing applications,” Sci. Rep. 5(1), 11388 (2015).
[Crossref]

Tang, M.

Tokunaga, T.

Z. Y. He, Q. W. Liu, and T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonics Sens. 3(4), 295–303 (2013).
[Crossref]

Tong, W. J.

Wada, Y.

Y. Mizuno, N. Hayashi, H. Tanaka, Y. Wada, and K. Nakamura, “Brillouin scattering in multi-core optical fibers for sensing applications,” Sci. Rep. 5(1), 11388 (2015).
[Crossref]

Wang, B. W.

Wang, B. Z.

B. Z. Wang, B. Fan, D. W. Zhou, C. Pang, Y. Li, D. X. Ba, and Y. K. Dong, “High-performance optical chirp chain BOTDA by using a pattern recognition algorithm and the differential pulse-width pair technique,” Photonics Res. 7(6), 652–658 (2019).
[Crossref]

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

D. X. Ba, B. Z. Wang, D. W. Zhou, M. J. Yin, Y. K. Dong, H. Li, Z. W. Lu, and Z. G. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref]

Wang, L.

Wang, M.

Webb, K. J.

Wei, H. F.

Wu, H.

Yan, J. L.

Yin, M. J.

Yu, C. Y.

Zhang, H. Y.

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Zhang, J.

Zhang, W. T.

W. T. Zhang, W. Z. Huang, L. Li, W. Y. Liu, and F. Li, “High resolution strain sensor for earthquake precursor observation and earthquake monitoring,” Proceedings of the 6th European Workshop on Optical Fibre Sensors. (2016).

Zhang, X. P.

Zhao, Z. Y.

Zhou, D. W.

B. Z. Wang, B. Fan, D. W. Zhou, C. Pang, Y. Li, D. X. Ba, and Y. K. Dong, “High-performance optical chirp chain BOTDA by using a pattern recognition algorithm and the differential pulse-width pair technique,” Photonics Res. 7(6), 652–658 (2019).
[Crossref]

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

D. X. Ba, B. Z. Wang, D. W. Zhou, M. J. Yin, Y. K. Dong, H. Li, Z. W. Lu, and Z. G. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref]

Zhou, H.

Zhu, T.

IEE Proc.: Optoelectron. (1)

M. A. Davis and A. D. Kersey, “Simultaneous measurement of temperature and strain using fibre Bragg gratings and Brillouin scattering,” IEE Proc.: Optoelectron. 144(3), 151–155 (1997).
[Crossref]

IEEE Photonics Technol. Lett. (2)

T. R. Parker, M. F. Farhadiroushan, V. A. Handerek, and A. J. Rogers, “The simultaneous measurement of strain and temperature distributionsfrom Brillouin backscatterm,” IEEE Photonics Technol. Lett. 9(7), 979–981 (1997).
[Crossref]

C. C. Lee, P. W. Chiang, and S. Chi, “Utilization of a dispersion-shifted fiber for simultaneous measurement of distributed strain and temperature through Brillouin frequency shift,” IEEE Photonics Technol. Lett. 13(10), 1094–1096 (2001).
[Crossref]

IEICE Trans. Commun. (1)

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

J. Lightwave Technol. (1)

Light: Sci. Appl. (1)

D. W. Zhou, Y. K. Dong, B. Z. Wang, C. Pang, D. X. Ba, H. Y. Zhang, Z. W. Lu, H. Li, and X. Y. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Photonics Res. (1)

B. Z. Wang, B. Fan, D. W. Zhou, C. Pang, Y. Li, D. X. Ba, and Y. K. Dong, “High-performance optical chirp chain BOTDA by using a pattern recognition algorithm and the differential pulse-width pair technique,” Photonics Res. 7(6), 652–658 (2019).
[Crossref]

Photonics Sens. (1)

Z. Y. He, Q. W. Liu, and T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonics Sens. 3(4), 295–303 (2013).
[Crossref]

Sci. Rep. (1)

Y. Mizuno, N. Hayashi, H. Tanaka, Y. Wada, and K. Nakamura, “Brillouin scattering in multi-core optical fibers for sensing applications,” Sci. Rep. 5(1), 11388 (2015).
[Crossref]

Sensors (2)

X. Y. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors 12(7), 8601–8639 (2012).
[Crossref]

X. Y. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors 11(4), 4152–4187 (2011).
[Crossref]

Other (1)

W. T. Zhang, W. Z. Huang, L. Li, W. Y. Liu, and F. Li, “High resolution strain sensor for earthquake precursor observation and earthquake monitoring,” Proceedings of the 6th European Workshop on Optical Fibre Sensors. (2016).

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Figures (9)

Fig. 1.
Fig. 1. Schematic diagram of experimental setup. EOM, electro-optic modulator; EDFA, erbium doped fiber amplifier; FUT, fiber under test; PC, polarization controller; AWG, arbitrary waveform generator; OI, optical isolator; PD, photodetector; AWG, arbitrary waveform generator; FBG, fiber Bragg grating, VOA, variable optical attenuator; OC, optical coupler; DAQ, data acquisition; CIR, circulator.
Fig. 2.
Fig. 2. The detail arrangement diagram of sensing fiber for the sensing measurement: (a) Temperature measurement; (b) Strain measurement.
Fig. 3.
Fig. 3. Measured multi-peak BGS of LEAF after Lorentz fitting under heated temperature of 30°C and strain of 0µɛ.
Fig. 4.
Fig. 4. The measured BGSs of Peak1 at different temperatures with a step of 10°C.
Fig. 5.
Fig. 5. The measured BGSs of Peak2 at different temperatures with a step of 10°C.
Fig. 6.
Fig. 6. The measured BFS-temperature relations for Peak1 (lower) and Peak2 (upper).
Fig. 7.
Fig. 7. Measurement results of BFS distribution at different temperatures.
Fig. 8.
Fig. 8. The measured BFS-strain relations for Peak1 (lower) and Peak2 (upper).
Fig. 9.
Fig. 9. The measured change in BFS of Peak1 and Peak2 versus distance in the testing case of 50.8°C/220µɛ.

Equations (3)

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( Δ ν B 1 Δ ν B m ) = ( C T 1 C T m C ε 1 C ε m ) ( Δ T Δ ε )
Δ T = Δ ν B 1 Δ ν B m C T 1 C T m
Δ ε = Δ ν B 1 C T 1 Δ T C ε 1