Abstract

A processing method for the precise acquisition of 1D interference spectrum from the 2D Fabry-Pérot(F-P) fringe pattern is proposed in the paper. Current methods can only measure the spectrum with full-pixel accuracy. The new method is capable to achieve the sub-pixel accuracy as well as reduce the noise by taking full advantage of the 2D image information and analyzing the statistical values of pixels in a comprehensive way. Experimental results show that the accuracy of the measured Brillouin shift and linewidth is around several MHzs, which is significantly improved compared to methods with full-pixel accuracy.

© 2012 OSA

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2011 (4)

L. Zhang, D. Zhang, Z. Yang, J. Shi, D. Liu, W. Gong, and E. S. Fry. “Experimental investigation on line width compression of stimulated Brillouin scattering in water,” Appl. Phys. Lett.98(22), 221106 (2011).
[CrossRef]

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, “Precise measurement of Brillouin scattering spectrum in the ocean using F–P etalon and ICCD,” Appl. Phys. B-Lasers Opt.105(2), 421–425 (2011).
[CrossRef]

M. Hirschberger and G. Ehret, “Simulation and high-precision wavelength determination of noisy 2D Fabry–Pérot interferometric rings for direct-detection Doppler lidar and laser spectroscopy,” Appl. Phys. B-Lasers Opt.103(1), 207–222 (2011).
[CrossRef]

Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express19(21), 19845–19854 (2011).
[CrossRef] [PubMed]

2009 (2)

2008 (3)

M. Ouyang, J. Shi, L. Zhao, X. Chen, H. Jing, and D. Liu, “Real time measurement of the attenuation coefficient of water in open ocean based on stimulated Brillouin scattering,” Appl. Phys. B-Lasers Opt.91(2), 381–385 (2008).
[CrossRef]

K. Schorstein, A. Popescu, M. Gobel, and T. Walther, “Remote water temperature measurements based on Brillouin scattering with a frequency doubled pulsed Yb:doped fiber amplifier,” Sensors (Basel Switzerland)8(9), 5820–5831 (2008).
[CrossRef]

J. Shi, M. Ouyang, W. Gong, S. Li, and D. Liu, “A Brillouin lidar system using F-P etalon and ICCD for remote sensing of the ocean,” Appl. Phys. B-Lasers Opt.90(3-4), 569–571 (2008).
[CrossRef]

2007 (1)

X. He, S. Li, and D. Liu, “Detecting of Brillouin shift and sound speed in water with the method of ICCD image by time oriented sequential control,” Proc. SPIE6837(683719), 683719, 683719-7 (2007).
[CrossRef]

2006 (3)

S. Li, J. Shi, W. Gong, X. He, and D. Liu, “Real-time detecting of Brillouin scattering in water with ICCD,” Proc. SPIE6028(60281J), 60281J, 60281J-6 (2006).
[CrossRef]

W. Gong, J. Shi, G. Li, D. Liu, J. W. Katz, and E. S. Fry, “Calibration of edge technique considering variation of Brillouin line width at different temperatures of water,” Appl. Phys. B-Lasers Opt.83(2), 319–322 (2006).
[CrossRef]

W. Gao, Z. Lv, Y. Dong, and W. He, “A new approach to measure the ocean temperature using Brillouin lidar,” Chin. Opt. Lett.4, 428–431 (2006).

2004 (2)

A. Popescu, K. Schorstein, and T. Walther, “A novel approach to a Brillouin–LIDAR for remote sensing of the ocean temperature,” Appl. Phys. B-Lasers Opt.79(8), 955–961 (2004).
[CrossRef]

W. Gong, R. Dai, Z. Sun, X. Ren, J. Shi, G. Li, and D. Liu, “Detecting submerged objects by Brillouin scattering,” Appl. Phys. B-Lasers Opt.79(5), 635–639 (2004).
[CrossRef]

2002 (1)

E. S. Fry, J. Katz, D. Liu, and T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt.49(3-4), 411–418 (2002).
[CrossRef]

2000 (1)

1999 (1)

1997 (1)

1990 (1)

Bao, X.

Brown, S.

Chen, L.

Chen, X.

M. Ouyang, J. Shi, L. Zhao, X. Chen, H. Jing, and D. Liu, “Real time measurement of the attenuation coefficient of water in open ocean based on stimulated Brillouin scattering,” Appl. Phys. B-Lasers Opt.91(2), 381–385 (2008).
[CrossRef]

Dai, R.

W. Gong, R. Dai, Z. Sun, X. Ren, J. Shi, G. Li, and D. Liu, “Detecting submerged objects by Brillouin scattering,” Appl. Phys. B-Lasers Opt.79(5), 635–639 (2004).
[CrossRef]

Dong, Y.

Ehret, G.

M. Hirschberger and G. Ehret, “Simulation and high-precision wavelength determination of noisy 2D Fabry–Pérot interferometric rings for direct-detection Doppler lidar and laser spectroscopy,” Appl. Phys. B-Lasers Opt.103(1), 207–222 (2011).
[CrossRef]

Emery, Y.

Fisher, G. M.

Flesia, C.

Fry, E. S.

L. Zhang, D. Zhang, Z. Yang, J. Shi, D. Liu, W. Gong, and E. S. Fry. “Experimental investigation on line width compression of stimulated Brillouin scattering in water,” Appl. Phys. Lett.98(22), 221106 (2011).
[CrossRef]

W. Gong, J. Shi, G. Li, D. Liu, J. W. Katz, and E. S. Fry, “Calibration of edge technique considering variation of Brillouin line width at different temperatures of water,” Appl. Phys. B-Lasers Opt.83(2), 319–322 (2006).
[CrossRef]

E. S. Fry, J. Katz, D. Liu, and T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt.49(3-4), 411–418 (2002).
[CrossRef]

E. S. Fry, Y. Emery, X. Quan, and J. W. Katz, “Accuracy limitations on Brillouin lidar measurements of temperature and sound speed in the ocean,” Appl. Opt.36(27), 6887–6894 (1997).
[CrossRef] [PubMed]

Gao, W.

Gault, W. A.

Gobel, M.

K. Schorstein, A. Popescu, M. Gobel, and T. Walther, “Remote water temperature measurements based on Brillouin scattering with a frequency doubled pulsed Yb:doped fiber amplifier,” Sensors (Basel Switzerland)8(9), 5820–5831 (2008).
[CrossRef]

Gong, W.

L. Zhang, D. Zhang, Z. Yang, J. Shi, D. Liu, W. Gong, and E. S. Fry. “Experimental investigation on line width compression of stimulated Brillouin scattering in water,” Appl. Phys. Lett.98(22), 221106 (2011).
[CrossRef]

J. Shi, M. Ouyang, W. Gong, S. Li, and D. Liu, “A Brillouin lidar system using F-P etalon and ICCD for remote sensing of the ocean,” Appl. Phys. B-Lasers Opt.90(3-4), 569–571 (2008).
[CrossRef]

S. Li, J. Shi, W. Gong, X. He, and D. Liu, “Real-time detecting of Brillouin scattering in water with ICCD,” Proc. SPIE6028(60281J), 60281J, 60281J-6 (2006).
[CrossRef]

W. Gong, J. Shi, G. Li, D. Liu, J. W. Katz, and E. S. Fry, “Calibration of edge technique considering variation of Brillouin line width at different temperatures of water,” Appl. Phys. B-Lasers Opt.83(2), 319–322 (2006).
[CrossRef]

W. Gong, R. Dai, Z. Sun, X. Ren, J. Shi, G. Li, and D. Liu, “Detecting submerged objects by Brillouin scattering,” Appl. Phys. B-Lasers Opt.79(5), 635–639 (2004).
[CrossRef]

Hays, P. B.

He, W.

He, X.

X. He, S. Li, and D. Liu, “Detecting of Brillouin shift and sound speed in water with the method of ICCD image by time oriented sequential control,” Proc. SPIE6837(683719), 683719, 683719-7 (2007).
[CrossRef]

S. Li, J. Shi, W. Gong, X. He, and D. Liu, “Real-time detecting of Brillouin scattering in water with ICCD,” Proc. SPIE6028(60281J), 60281J, 60281J-6 (2006).
[CrossRef]

He, Z.

Hirschberger, M.

M. Hirschberger and G. Ehret, “Simulation and high-precision wavelength determination of noisy 2D Fabry–Pérot interferometric rings for direct-detection Doppler lidar and laser spectroscopy,” Appl. Phys. B-Lasers Opt.103(1), 207–222 (2011).
[CrossRef]

Hotate, K.

Huang, J.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, “Precise measurement of Brillouin scattering spectrum in the ocean using F–P etalon and ICCD,” Appl. Phys. B-Lasers Opt.105(2), 421–425 (2011).
[CrossRef]

Jing, H.

M. Ouyang, J. Shi, L. Zhao, X. Chen, H. Jing, and D. Liu, “Real time measurement of the attenuation coefficient of water in open ocean based on stimulated Brillouin scattering,” Appl. Phys. B-Lasers Opt.91(2), 381–385 (2008).
[CrossRef]

Katz, J.

E. S. Fry, J. Katz, D. Liu, and T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt.49(3-4), 411–418 (2002).
[CrossRef]

Katz, J. W.

W. Gong, J. Shi, G. Li, D. Liu, J. W. Katz, and E. S. Fry, “Calibration of edge technique considering variation of Brillouin line width at different temperatures of water,” Appl. Phys. B-Lasers Opt.83(2), 319–322 (2006).
[CrossRef]

E. S. Fry, Y. Emery, X. Quan, and J. W. Katz, “Accuracy limitations on Brillouin lidar measurements of temperature and sound speed in the ocean,” Appl. Opt.36(27), 6887–6894 (1997).
[CrossRef] [PubMed]

Killeen, T. L.

Korb, C. L.

Li, G.

W. Gong, J. Shi, G. Li, D. Liu, J. W. Katz, and E. S. Fry, “Calibration of edge technique considering variation of Brillouin line width at different temperatures of water,” Appl. Phys. B-Lasers Opt.83(2), 319–322 (2006).
[CrossRef]

W. Gong, R. Dai, Z. Sun, X. Ren, J. Shi, G. Li, and D. Liu, “Detecting submerged objects by Brillouin scattering,” Appl. Phys. B-Lasers Opt.79(5), 635–639 (2004).
[CrossRef]

Li, H.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, “Precise measurement of Brillouin scattering spectrum in the ocean using F–P etalon and ICCD,” Appl. Phys. B-Lasers Opt.105(2), 421–425 (2011).
[CrossRef]

Li, S.

J. Shi, M. Ouyang, W. Gong, S. Li, and D. Liu, “A Brillouin lidar system using F-P etalon and ICCD for remote sensing of the ocean,” Appl. Phys. B-Lasers Opt.90(3-4), 569–571 (2008).
[CrossRef]

X. He, S. Li, and D. Liu, “Detecting of Brillouin shift and sound speed in water with the method of ICCD image by time oriented sequential control,” Proc. SPIE6837(683719), 683719, 683719-7 (2007).
[CrossRef]

S. Li, J. Shi, W. Gong, X. He, and D. Liu, “Real-time detecting of Brillouin scattering in water with ICCD,” Proc. SPIE6028(60281J), 60281J, 60281J-6 (2006).
[CrossRef]

Liang, K.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, “Precise measurement of Brillouin scattering spectrum in the ocean using F–P etalon and ICCD,” Appl. Phys. B-Lasers Opt.105(2), 421–425 (2011).
[CrossRef]

Liu, D.

L. Zhang, D. Zhang, Z. Yang, J. Shi, D. Liu, W. Gong, and E. S. Fry. “Experimental investigation on line width compression of stimulated Brillouin scattering in water,” Appl. Phys. Lett.98(22), 221106 (2011).
[CrossRef]

J. Shi, M. Ouyang, W. Gong, S. Li, and D. Liu, “A Brillouin lidar system using F-P etalon and ICCD for remote sensing of the ocean,” Appl. Phys. B-Lasers Opt.90(3-4), 569–571 (2008).
[CrossRef]

M. Ouyang, J. Shi, L. Zhao, X. Chen, H. Jing, and D. Liu, “Real time measurement of the attenuation coefficient of water in open ocean based on stimulated Brillouin scattering,” Appl. Phys. B-Lasers Opt.91(2), 381–385 (2008).
[CrossRef]

X. He, S. Li, and D. Liu, “Detecting of Brillouin shift and sound speed in water with the method of ICCD image by time oriented sequential control,” Proc. SPIE6837(683719), 683719, 683719-7 (2007).
[CrossRef]

S. Li, J. Shi, W. Gong, X. He, and D. Liu, “Real-time detecting of Brillouin scattering in water with ICCD,” Proc. SPIE6028(60281J), 60281J, 60281J-6 (2006).
[CrossRef]

W. Gong, J. Shi, G. Li, D. Liu, J. W. Katz, and E. S. Fry, “Calibration of edge technique considering variation of Brillouin line width at different temperatures of water,” Appl. Phys. B-Lasers Opt.83(2), 319–322 (2006).
[CrossRef]

W. Gong, R. Dai, Z. Sun, X. Ren, J. Shi, G. Li, and D. Liu, “Detecting submerged objects by Brillouin scattering,” Appl. Phys. B-Lasers Opt.79(5), 635–639 (2004).
[CrossRef]

E. S. Fry, J. Katz, D. Liu, and T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt.49(3-4), 411–418 (2002).
[CrossRef]

Lv, Z.

Ma, Y.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, “Precise measurement of Brillouin scattering spectrum in the ocean using F–P etalon and ICCD,” Appl. Phys. B-Lasers Opt.105(2), 421–425 (2011).
[CrossRef]

Motil, A.

Ouyang, M.

M. Ouyang, J. Shi, L. Zhao, X. Chen, H. Jing, and D. Liu, “Real time measurement of the attenuation coefficient of water in open ocean based on stimulated Brillouin scattering,” Appl. Phys. B-Lasers Opt.91(2), 381–385 (2008).
[CrossRef]

J. Shi, M. Ouyang, W. Gong, S. Li, and D. Liu, “A Brillouin lidar system using F-P etalon and ICCD for remote sensing of the ocean,” Appl. Phys. B-Lasers Opt.90(3-4), 569–571 (2008).
[CrossRef]

Peled, Y.

Popescu, A.

K. Schorstein, A. Popescu, M. Gobel, and T. Walther, “Remote water temperature measurements based on Brillouin scattering with a frequency doubled pulsed Yb:doped fiber amplifier,” Sensors (Basel Switzerland)8(9), 5820–5831 (2008).
[CrossRef]

A. Popescu, K. Schorstein, and T. Walther, “A novel approach to a Brillouin–LIDAR for remote sensing of the ocean temperature,” Appl. Phys. B-Lasers Opt.79(8), 955–961 (2004).
[CrossRef]

Quan, X.

Reeves, J. M.

Ren, X.

W. Gong, R. Dai, Z. Sun, X. Ren, J. Shi, G. Li, and D. Liu, “Detecting submerged objects by Brillouin scattering,” Appl. Phys. B-Lasers Opt.79(5), 635–639 (2004).
[CrossRef]

Schorstein, K.

K. Schorstein, A. Popescu, M. Gobel, and T. Walther, “Remote water temperature measurements based on Brillouin scattering with a frequency doubled pulsed Yb:doped fiber amplifier,” Sensors (Basel Switzerland)8(9), 5820–5831 (2008).
[CrossRef]

A. Popescu, K. Schorstein, and T. Walther, “A novel approach to a Brillouin–LIDAR for remote sensing of the ocean temperature,” Appl. Phys. B-Lasers Opt.79(8), 955–961 (2004).
[CrossRef]

Shepherd, G. G.

Shi, J.

L. Zhang, D. Zhang, Z. Yang, J. Shi, D. Liu, W. Gong, and E. S. Fry. “Experimental investigation on line width compression of stimulated Brillouin scattering in water,” Appl. Phys. Lett.98(22), 221106 (2011).
[CrossRef]

J. Shi, M. Ouyang, W. Gong, S. Li, and D. Liu, “A Brillouin lidar system using F-P etalon and ICCD for remote sensing of the ocean,” Appl. Phys. B-Lasers Opt.90(3-4), 569–571 (2008).
[CrossRef]

M. Ouyang, J. Shi, L. Zhao, X. Chen, H. Jing, and D. Liu, “Real time measurement of the attenuation coefficient of water in open ocean based on stimulated Brillouin scattering,” Appl. Phys. B-Lasers Opt.91(2), 381–385 (2008).
[CrossRef]

W. Gong, J. Shi, G. Li, D. Liu, J. W. Katz, and E. S. Fry, “Calibration of edge technique considering variation of Brillouin line width at different temperatures of water,” Appl. Phys. B-Lasers Opt.83(2), 319–322 (2006).
[CrossRef]

S. Li, J. Shi, W. Gong, X. He, and D. Liu, “Real-time detecting of Brillouin scattering in water with ICCD,” Proc. SPIE6028(60281J), 60281J, 60281J-6 (2006).
[CrossRef]

W. Gong, R. Dai, Z. Sun, X. Ren, J. Shi, G. Li, and D. Liu, “Detecting submerged objects by Brillouin scattering,” Appl. Phys. B-Lasers Opt.79(5), 635–639 (2004).
[CrossRef]

Sun, Z.

W. Gong, R. Dai, Z. Sun, X. Ren, J. Shi, G. Li, and D. Liu, “Detecting submerged objects by Brillouin scattering,” Appl. Phys. B-Lasers Opt.79(5), 635–639 (2004).
[CrossRef]

Tur, M.

Walther, T.

K. Schorstein, A. Popescu, M. Gobel, and T. Walther, “Remote water temperature measurements based on Brillouin scattering with a frequency doubled pulsed Yb:doped fiber amplifier,” Sensors (Basel Switzerland)8(9), 5820–5831 (2008).
[CrossRef]

A. Popescu, K. Schorstein, and T. Walther, “A novel approach to a Brillouin–LIDAR for remote sensing of the ocean temperature,” Appl. Phys. B-Lasers Opt.79(8), 955–961 (2004).
[CrossRef]

E. S. Fry, J. Katz, D. Liu, and T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt.49(3-4), 411–418 (2002).
[CrossRef]

Wu, Q.

Yang, Z.

L. Zhang, D. Zhang, Z. Yang, J. Shi, D. Liu, W. Gong, and E. S. Fry. “Experimental investigation on line width compression of stimulated Brillouin scattering in water,” Appl. Phys. Lett.98(22), 221106 (2011).
[CrossRef]

Yaron, L.

Yu, Y.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, “Precise measurement of Brillouin scattering spectrum in the ocean using F–P etalon and ICCD,” Appl. Phys. B-Lasers Opt.105(2), 421–425 (2011).
[CrossRef]

Zhang, D.

L. Zhang, D. Zhang, Z. Yang, J. Shi, D. Liu, W. Gong, and E. S. Fry. “Experimental investigation on line width compression of stimulated Brillouin scattering in water,” Appl. Phys. Lett.98(22), 221106 (2011).
[CrossRef]

Zhang, L.

L. Zhang, D. Zhang, Z. Yang, J. Shi, D. Liu, W. Gong, and E. S. Fry. “Experimental investigation on line width compression of stimulated Brillouin scattering in water,” Appl. Phys. Lett.98(22), 221106 (2011).
[CrossRef]

Zhao, L.

M. Ouyang, J. Shi, L. Zhao, X. Chen, H. Jing, and D. Liu, “Real time measurement of the attenuation coefficient of water in open ocean based on stimulated Brillouin scattering,” Appl. Phys. B-Lasers Opt.91(2), 381–385 (2008).
[CrossRef]

Zou, W.

Appl. Opt. (4)

Appl. Phys. B-Lasers Opt. (7)

A. Popescu, K. Schorstein, and T. Walther, “A novel approach to a Brillouin–LIDAR for remote sensing of the ocean temperature,” Appl. Phys. B-Lasers Opt.79(8), 955–961 (2004).
[CrossRef]

M. Ouyang, J. Shi, L. Zhao, X. Chen, H. Jing, and D. Liu, “Real time measurement of the attenuation coefficient of water in open ocean based on stimulated Brillouin scattering,” Appl. Phys. B-Lasers Opt.91(2), 381–385 (2008).
[CrossRef]

M. Hirschberger and G. Ehret, “Simulation and high-precision wavelength determination of noisy 2D Fabry–Pérot interferometric rings for direct-detection Doppler lidar and laser spectroscopy,” Appl. Phys. B-Lasers Opt.103(1), 207–222 (2011).
[CrossRef]

W. Gong, J. Shi, G. Li, D. Liu, J. W. Katz, and E. S. Fry, “Calibration of edge technique considering variation of Brillouin line width at different temperatures of water,” Appl. Phys. B-Lasers Opt.83(2), 319–322 (2006).
[CrossRef]

W. Gong, R. Dai, Z. Sun, X. Ren, J. Shi, G. Li, and D. Liu, “Detecting submerged objects by Brillouin scattering,” Appl. Phys. B-Lasers Opt.79(5), 635–639 (2004).
[CrossRef]

J. Shi, M. Ouyang, W. Gong, S. Li, and D. Liu, “A Brillouin lidar system using F-P etalon and ICCD for remote sensing of the ocean,” Appl. Phys. B-Lasers Opt.90(3-4), 569–571 (2008).
[CrossRef]

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, “Precise measurement of Brillouin scattering spectrum in the ocean using F–P etalon and ICCD,” Appl. Phys. B-Lasers Opt.105(2), 421–425 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

L. Zhang, D. Zhang, Z. Yang, J. Shi, D. Liu, W. Gong, and E. S. Fry. “Experimental investigation on line width compression of stimulated Brillouin scattering in water,” Appl. Phys. Lett.98(22), 221106 (2011).
[CrossRef]

Chin. Opt. Lett. (1)

J. Mod. Opt. (1)

E. S. Fry, J. Katz, D. Liu, and T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt.49(3-4), 411–418 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (2)

S. Li, J. Shi, W. Gong, X. He, and D. Liu, “Real-time detecting of Brillouin scattering in water with ICCD,” Proc. SPIE6028(60281J), 60281J, 60281J-6 (2006).
[CrossRef]

X. He, S. Li, and D. Liu, “Detecting of Brillouin shift and sound speed in water with the method of ICCD image by time oriented sequential control,” Proc. SPIE6837(683719), 683719, 683719-7 (2007).
[CrossRef]

Sensors (Basel Switzerland) (1)

K. Schorstein, A. Popescu, M. Gobel, and T. Walther, “Remote water temperature measurements based on Brillouin scattering with a frequency doubled pulsed Yb:doped fiber amplifier,” Sensors (Basel Switzerland)8(9), 5820–5831 (2008).
[CrossRef]

Other (1)

Q. Zheng, “On the Rayleigh-Brillouin scattering in air,” PhD thesis, University of New Hampshire (2004).

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Figures (7)

Fig. 1
Fig. 1

Schematics for Brillouin lidar system using F-P etalon and ICCD.

Fig. 2
Fig. 2

An interference pattern taken from the experiment.

Fig. 3
Fig. 3

Schematic of the determination of the center.

Fig. 4
Fig. 4

Schematic of the data folding operation.

Fig. 5
Fig. 5

The interference spectrum obtained by data folding algorithm.

Fig. 6
Fig. 6

Performance of low-pass filtering with FFT.

Fig. 7
Fig. 7

The 1D Rayleigh-Brillouin spectra obtained by three independent experiments.

Tables (4)

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Table 1 Midpoints Calculated by Three Randomly Chosen Strings and Their Error with Center Position Calculated by the Proposed Method

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Table 2 Retrieved Brillouin Shifts VB, Brillouin Linewidths ГB, Temperatures TV Calculated by VB, Temperatures TГ Calculated byГB with Their Measured Uncertainties

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Table 3 Brillouin Shifts VB and Linewidths ГB Measured by the Proposed Method (Folded) and Measured from a Single Cut through the Fringes (Single)

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Table 4 Temperatures Measured by the Proposed Method (Folded) and Measured from a Single Cut through the Fringes (Single)

Equations (6)

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x O' = x A + x A' 2
x ˜ O' = 1 2n i=1 n ( x A i + x A ' i )
y O' = y A + y A'' 2
y ˜ O' = 1 2n j=1 n ( y A j + y A j )
d (i,i)=d( 2 i,0)
d ij = r ij = ( x ij x O' ) 2 + ( y ij y O' ) 2 ,i=1,2,,n;j=1,2,,m

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