Abstract

On the basis of experimental Rayleigh-Brillouin scattering data in gaseous nitrogen and air, simulations are performed to describe the observed frequency profiles in analytical form. The experimental data pertain to a λ = 366 nm scattering wavelength, a 90° scattering angle, pressures of 1 and 3 bar, and temperatures in the range 250 – 340 K. Two different models are used to represent the RB-profiles, to distinguish the RB-peaks, and to obtain the Brillouin shift associated with the acoustic waves generated in a gaseous medium. Calculations in the framework of V3 and G3 models, exhibiting composite profiles of three distinct peaks of Voigt or Gaussian functions, are compared to observation. Fitting results show that the V3 model yields an improvement over the G3 model. This mathematical model provides an even better representation of the observed profiles than the Tenti S6 model, which is considered to be the optimum representation in terms of physical parameters. For the derivation of Brillouin shifts, both models perform well at high gas pressure, while at lower pressures, the V3 model yields a higher accuracy than the G3 model.

© 2014 Optical Society of America

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2013 (2)

2012 (6)

Y. Ma, F. Fan, K. Liang, H. Li, Y. Yu, B. Zhou, “An analytical model for Rayleigh–Brillouin scattering spectra in gases,” J. Opt. 14(9), 095703 (2012).
[CrossRef]

Z. Gu, M. O. Vieitez, E. J. van Duijn, W. Ubachs, “A Rayleigh-Brillouin scattering spectrometer for ultraviolet wavelengths,” Rev. Sci. Instrum. 83(5), 053112 (2012).
[CrossRef] [PubMed]

J. Huang, Y. Ma, B. Zhou, H. Li, Y. Yu, K. Liang, “Processing method of spectral measurement using F-P etalon and ICCD,” Opt. Express 20(17), 18568–18578 (2012).
[CrossRef] [PubMed]

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

S. Xie, M. Pang, X. Bao, L. Chen, “Polarization dependence of Brillouin linewidth and peak frequency due to fiber inhomogeneity in single mode fiber and its impact on distributed fiber Brillouin sensing,” Opt. Express 20(6), 6385–6399 (2012).
[CrossRef] [PubMed]

K. Liang, Y. Ma, Y. Yu, J. Huang, H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51(6), 066002 (2012).
[CrossRef]

2011 (3)

X. Bao, L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(12), 4152–4187 (2011).
[CrossRef] [PubMed]

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

B. Witschas, “Analytical model for Rayleigh-Brillouin line shapes in air,” Appl. Opt. 50(3), 267–270 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (1)

K. Schorstein, E. S. Fry, T. Walther, “Depth-resolved temperature measurements of water using the Brillouin lidar technique,” Appl. Phys. B 97(4), 931–934 (2009).
[CrossRef]

2008 (1)

K. Schorstein, A. Popescu, M. Gobel, 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]

2004 (1)

2003 (1)

2002 (3)

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203(3-6), 335–340 (2002).
[CrossRef]

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

X. Pan, P. F. Barker, A. Meschanov, J. H. Grinstead, M. N. Shneider, R. B. Miles, “Temperature measurements by coherent Rayleigh scattering,” Opt. Lett. 27(3), 161–163 (2002).
[CrossRef] [PubMed]

1986 (1)

C. D. Geisler, S. Greenberg, “A two-stage nonlinear cochlear model possesses automatic gain control,” J. Acoust. Soc. Am. 80(5), 1359–1363 (1986).
[CrossRef] [PubMed]

1984 (1)

G. S. K. Wong, T. F. W. Embleton, “Variation of specific heats and of specific heat ratio in air with humidity,” J. Acoust. Soc. Am. 76(2), 555–559 (1984).
[CrossRef]

1974 (1)

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52(4), 285–290 (1974).

1972 (1)

C. Boley, R. Desai, G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50(18), 2158–2173 (1972).
[CrossRef]

1968 (1)

A. Griffin, “Brillouin light scattering from crystals in the hydrodynamic region,” Rev. Mod. Phys. 40(1), 167–205 (1968).
[CrossRef]

1966 (2)

R. D. Mountain, “Thermal relaxation and Brillouin scattering in liquids,” J. Res. Natl. Bur. Stand. Sect. A 70A(3), 207–220 (1966).
[CrossRef]

R. D. Mountain, “Spectral distribution of scattered light in a simple fluid,” Rev. Mod. Phys. 38(1), 205–214 (1966).
[CrossRef]

Afshar V, S.

Bao, X.

Barker, P. F.

Boley, C.

C. Boley, R. Desai, G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50(18), 2158–2173 (1972).
[CrossRef]

Boley, C. D.

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52(4), 285–290 (1974).

Chen, L.

Dai, R.

J. Xu, X. Ren, W. Gong, R. Dai, D. Liu, “Measurement of the bulk viscosity of liquid by Brillouin scattering,” Appl. Opt. 42(33), 6704–6709 (2003).
[CrossRef] [PubMed]

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203(3-6), 335–340 (2002).
[CrossRef]

Desai, R.

C. Boley, R. Desai, G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50(18), 2158–2173 (1972).
[CrossRef]

Desai, R. C.

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52(4), 285–290 (1974).

Embleton, T. F. W.

G. S. K. Wong, T. F. W. Embleton, “Variation of specific heats and of specific heat ratio in air with humidity,” J. Acoust. Soc. Am. 76(2), 555–559 (1984).
[CrossRef]

Fan, F.

Y. Ma, F. Fan, K. Liang, H. Li, Y. Yu, B. Zhou, “An analytical model for Rayleigh–Brillouin scattering spectra in gases,” J. Opt. 14(9), 095703 (2012).
[CrossRef]

Fry, E.

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

Fry, E. S.

K. Schorstein, E. S. Fry, T. Walther, “Depth-resolved temperature measurements of water using the Brillouin lidar technique,” Appl. Phys. B 97(4), 931–934 (2009).
[CrossRef]

Geisler, C. D.

C. D. Geisler, S. Greenberg, “A two-stage nonlinear cochlear model possesses automatic gain control,” J. Acoust. Soc. Am. 80(5), 1359–1363 (1986).
[CrossRef] [PubMed]

Gobel, M.

K. Schorstein, A. Popescu, M. Gobel, 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.

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

J. Xu, X. Ren, W. Gong, R. Dai, D. Liu, “Measurement of the bulk viscosity of liquid by Brillouin scattering,” Appl. Opt. 42(33), 6704–6709 (2003).
[CrossRef] [PubMed]

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203(3-6), 335–340 (2002).
[CrossRef]

Greenberg, S.

C. D. Geisler, S. Greenberg, “A two-stage nonlinear cochlear model possesses automatic gain control,” J. Acoust. Soc. Am. 80(5), 1359–1363 (1986).
[CrossRef] [PubMed]

Griffin, A.

A. Griffin, “Brillouin light scattering from crystals in the hydrodynamic region,” Rev. Mod. Phys. 40(1), 167–205 (1968).
[CrossRef]

Grinstead, J. H.

Gu, Z.

He, X.

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

Huang, J.

K. Liang, Y. Ma, Y. Yu, J. Huang, H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51(6), 066002 (2012).
[CrossRef]

J. Huang, Y. Ma, B. Zhou, H. Li, Y. Yu, K. Liang, “Processing method of spectral measurement using F-P etalon and ICCD,” Opt. Express 20(17), 18568–18578 (2012).
[CrossRef] [PubMed]

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

Katz, J.

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

Li, H.

K. Liang, Y. Ma, Y. Yu, J. Huang, H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51(6), 066002 (2012).
[CrossRef]

Y. Ma, F. Fan, K. Liang, H. Li, Y. Yu, B. Zhou, “An analytical model for Rayleigh–Brillouin scattering spectra in gases,” J. Opt. 14(9), 095703 (2012).
[CrossRef]

J. Huang, Y. Ma, B. Zhou, H. Li, Y. Yu, K. Liang, “Processing method of spectral measurement using F-P etalon and ICCD,” Opt. Express 20(17), 18568–18578 (2012).
[CrossRef] [PubMed]

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

Li, R.

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203(3-6), 335–340 (2002).
[CrossRef]

Liang, K.

Y. Ma, F. Fan, K. Liang, H. Li, Y. Yu, B. Zhou, “An analytical model for Rayleigh–Brillouin scattering spectra in gases,” J. Opt. 14(9), 095703 (2012).
[CrossRef]

K. Liang, Y. Ma, Y. Yu, J. Huang, H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51(6), 066002 (2012).
[CrossRef]

J. Huang, Y. Ma, B. Zhou, H. Li, Y. Yu, K. Liang, “Processing method of spectral measurement using F-P etalon and ICCD,” Opt. Express 20(17), 18568–18578 (2012).
[CrossRef] [PubMed]

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

Liu, D.

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

J. Xu, X. Ren, W. Gong, R. Dai, D. Liu, “Measurement of the bulk viscosity of liquid by Brillouin scattering,” Appl. Opt. 42(33), 6704–6709 (2003).
[CrossRef] [PubMed]

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

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203(3-6), 335–340 (2002).
[CrossRef]

Ma, Y.

K. Liang, Y. Ma, Y. Yu, J. Huang, H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51(6), 066002 (2012).
[CrossRef]

Y. Ma, F. Fan, K. Liang, H. Li, Y. Yu, B. Zhou, “An analytical model for Rayleigh–Brillouin scattering spectra in gases,” J. Opt. 14(9), 095703 (2012).
[CrossRef]

J. Huang, Y. Ma, B. Zhou, H. Li, Y. Yu, K. Liang, “Processing method of spectral measurement using F-P etalon and ICCD,” Opt. Express 20(17), 18568–18578 (2012).
[CrossRef] [PubMed]

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

Meschanov, A.

Miles, R. B.

Mountain, R. D.

R. D. Mountain, “Spectral distribution of scattered light in a simple fluid,” Rev. Mod. Phys. 38(1), 205–214 (1966).
[CrossRef]

R. D. Mountain, “Thermal relaxation and Brillouin scattering in liquids,” J. Res. Natl. Bur. Stand. Sect. A 70A(3), 207–220 (1966).
[CrossRef]

Pan, X.

Pang, M.

Popescu, A.

K. Schorstein, A. Popescu, M. Gobel, 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]

Reitebuch, O.

Ren, X.

Schorstein, K.

K. Schorstein, E. S. Fry, T. Walther, “Depth-resolved temperature measurements of water using the Brillouin lidar technique,” Appl. Phys. B 97(4), 931–934 (2009).
[CrossRef]

K. Schorstein, A. Popescu, M. Gobel, 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]

Shi, J.

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

Shneider, M. N.

Tang, Y.

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

Tenti, G.

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh-Brillouin scattering from molecular gases,” Can. J. Phys. 52(4), 285–290 (1974).

C. Boley, R. Desai, G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50(18), 2158–2173 (1972).
[CrossRef]

Ubachs, W.

van de Water, W.

van Duijn, E. J.

Vieitez, M. O.

Walther, T.

K. Schorstein, E. S. Fry, T. Walther, “Depth-resolved temperature measurements of water using the Brillouin lidar technique,” Appl. Phys. B 97(4), 931–934 (2009).
[CrossRef]

K. Schorstein, A. Popescu, M. Gobel, 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]

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

Wei, H.

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

Witschas, B.

Wong, G. S. K.

G. S. K. Wong, T. F. W. Embleton, “Variation of specific heats and of specific heat ratio in air with humidity,” J. Acoust. Soc. Am. 76(2), 555–559 (1984).
[CrossRef]

Xie, S.

Xu, J.

J. Xu, X. Ren, W. Gong, R. Dai, D. Liu, “Measurement of the bulk viscosity of liquid by Brillouin scattering,” Appl. Opt. 42(33), 6704–6709 (2003).
[CrossRef] [PubMed]

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203(3-6), 335–340 (2002).
[CrossRef]

Yang, K.

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

Yu, Y.

Y. Ma, F. Fan, K. Liang, H. Li, Y. Yu, B. Zhou, “An analytical model for Rayleigh–Brillouin scattering spectra in gases,” J. Opt. 14(9), 095703 (2012).
[CrossRef]

K. Liang, Y. Ma, Y. Yu, J. Huang, H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51(6), 066002 (2012).
[CrossRef]

J. Huang, Y. Ma, B. Zhou, H. Li, Y. Yu, K. Liang, “Processing method of spectral measurement using F-P etalon and ICCD,” Opt. Express 20(17), 18568–18578 (2012).
[CrossRef] [PubMed]

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

Zhang, D.

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

Zhang, L.

J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012).
[CrossRef]

Zhou, B.

Y. Ma, F. Fan, K. Liang, H. Li, Y. Yu, B. Zhou, “An analytical model for Rayleigh–Brillouin scattering spectra in gases,” J. Opt. 14(9), 095703 (2012).
[CrossRef]

J. Huang, Y. Ma, B. Zhou, H. Li, Y. Yu, K. Liang, “Processing method of spectral measurement using F-P etalon and ICCD,” Opt. Express 20(17), 18568–18578 (2012).
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Figures (12)

Fig. 1
Fig. 1

Model description for the RBS spectrum of 1 bar air with the V3 model under different temperature conditions as indicated. Fitted curves are shown with red lines and the experimental RBS spectrum as black dots; lower panels show the residuals between experiment and model description.

Fig. 2
Fig. 2

Model description for the RBS spectrum of 1 bar air with the G3 model under different temperature conditions as indicated. Fitted curves are shown with red lines and the experimental RBS spectrum as black dots; lower panels show the residuals between experiment and model description.

Fig. 3
Fig. 3

Results for 1 bar N2 gas for the V3 model.

Fig. 4
Fig. 4

Results for 1 bar N2 gas for the G3 model.

Fig. 5
Fig. 5

The RMSE values (a) and the χ2 values (b) for V3, G3, and S6 models for conditions of 1 bar air.

Fig. 6
Fig. 6

The RMSE values (a) and the χ2 values (b) for V3, G3, and S6 models for conditions of 1 bar nitrogen.

Fig. 7
Fig. 7

Model description for the RBS spectrum of 3 bar air with the V3 model under different temperature conditions as indicated. Fitted curves are shown with red lines and the experimental RBS spectrum as black dots; lower panels show the residuals between experiment and model description.

Fig. 8
Fig. 8

Model description for the RBS spectrum of 3 bar nitrogen with the G3 model under different temperature conditions.

Fig. 9
Fig. 9

Model description for RBS at 3 bar nitrogen with the V3 model under different temperature conditions.

Fig. 10
Fig. 10

Model description for RBS at 3 bar nitrogen with the G3 model under different temperature conditions.

Fig. 11
Fig. 11

The RMSE values (a) and the χ2 values (b) for V3, G3, and S6 models for conditions of 3 bar air.

Fig. 12
Fig. 12

The RMSE values (a) and the χ2 values (b) for V3, G3, and S6 models for conditions of 3 bar nitrogen.

Tables (5)

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Table 1 Gas conditions and the scattering angles for the RBS experiments

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Table 2 Brillouin Shift Measured Under Conditions of 1 Bar Air, the Fitted Values vbm Using V3 and G3 Models, Predicted Values vbt, Error Δv between vbm and vbt, as well as Relative Error Δvr

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Table 3 Brillouin Shift Measured Under Conditions of 1 Bar Nitrogen, Fitted Values vbm Using V3 and G3 Models, Predicted Values vbt, Error Δv between vbm and vbt, as well as Relative Error Δvr

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Table 4 Brillouin Shift Obtained from Experimental Data for 3 Bar Air, Fitted Values vbm Using V3 and G3 Models, Predicted Values vbt, Error Δv between vbm and vbt, as well as Relative Error Δvr

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Table 5 Brillouin Shift Obtained from Experimental for 3 Bar Nitrogen, Fitted Values vbm Using V3 and G3 Model, Predicted Values vbt, Error Δv between vbm and vbt, as well as Relative Error Δvr

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

G(v)= 1 2π Г R Aexp[ 1 2 ( v Г R ) 2 ]+ 1A 2 2π Г B exp[ 1 2 ( v+ v B Г B ) 2 ] + 1A 2 2π Г B exp[ 1 2 ( v v B Г B ) 2 ]
V(v)=ρL(v; Г L , v L )+( 1ρ )G(v; Г G , v L )
G(v; Г G , v G )= 2 ln2 π Г G exp{ 4ln2 ( v v G ) 2 Г G 2 }
L(v; Г L , v L )= 2 π Г L 4 ( v v L ) 2 + Г L 2
V RB = C T { Diag(ρ) G+[ I 3 Diag(ρ)] L }
RMSE= i=1 N [ I e ( f i ) I m ( f i )] 2 N
χ 2 = 1 N i=1 N [ I e ( f i ) I m ( f i )] 2 σ 2 ( f i )
v bt = 2n λ v S sin(θ/2)
v s = γRT/m

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