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The gas pressure is an important parameter describing the status of system and relating to many properties of physics and chemistry. The traditional intrusive method for pressure measurement has some effects on the gas status and the measurement accuracy. Therefore, it is desired to develop a non-intrusive method. The spontaneous Rayleigh-Brillouin scattering (SRBS) is a potential tool for accurate, remote, and non-intrusive pressure measurement. In this paper, the SRBS spectra are simulated using the Tenti S6 model convolved with the instrument function of the measurement system at a 90 scattering angle and pressures of 2, 4, and 6 atm (1 atm = 1.01325105 Pa). In order to eliminate the effect of the instrument function of the measurement system, we propose a deconvolution method by comparing the traditional convolved SRBS method in this paper. According to the principle of the Wiener filter and the truncated singular value decomposition method, the Wiener filtering factor can be obtained. And the deconvolved spectra are obtained by convolving the stimulated spectra with the Wiener filtering factor. We find that the deconvolved spectra are coincident well with those from the Tenti S6 model without convolving with system transmission function. In order to compare the accuracy of the convolution method with that of the deconvolution method in experiment, the SRBS spectra of N2 mixed with aerosols are measured at a 90 scattering angle and pressures of 2, 4, and 6 atm respectively. The experimentally obtained raw spectra are fitted with the theoretical spectra, which are obtained by convolving the Tenti S6 model with the instrument function of the measurement system. The relative errors of retrieved pressure are all less than 6.0%, and the normalized root-mean-square deviation is calculated and found to be less than 6.5%. On the other hand, the deconvolved spectra are obtained by convolving the experimentally obtained raw spectra with the Wiener filtering factor and then fitted with theoretical calculated spectra from Tenti S6 model without convolving with system transmission function. The relative errors of retrieved pressure are all less than 5.0%, and the normalized root-mean-square error is less than 6.0%. By comparing the two methods, it can be found that the deconvolution method can eliminate the effect of instrument function of the measurement system and improve the resolution of Rayleigh-Brillouin scattering spectrum. The performance of fitting and the accuracy of pressure retrieving show that the deconvolution method is better than the convolution method under lower pressure (2 atm), but worse than the convolution method under higher pressure (2 atm). The comparison result demonstrates that the deconvolution based on the Wiener filter is likely to be directly applied to the exploring of the properties of the combustor in aero engine, such as pressure profile retrieval or temperature measurements.
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Keywords:
- Rayleigh scattering /
- Brillouin scattering /
- deconvolution /
- pressure retrieving
[1] Boley C D, Desai R C, Tenti G 1972 Can. J. Phys. 50 2158
[2] Ma Y, Liang K, Lin H, Ji H 2007 Acta Opt. Sin. 27 962 (in Chinese) [马泳, 梁琨, 林宏, 冀航 2007 光学学报 27 962]
[3] Gu Z, Ubachs W, Marques Jr W, van de Water W 2015 Phys. Rev. Lett. 114 243902
[4] Cao C L, Xu S L, Liu E W 2013 J. Univ. Sci. Tech. China 43 510 (in Chinese) [曹春丽, 徐胜利, 刘二伟 2013 中国科学技术大学学报 43 510]
[5] Gu Z Y, Ubachs W, van de Water W 2014 Opt. Lett. 39 3301
[6] Meijer A S, de Wijn A S, Peters M F E, Dam N J, van de Water W 2010 J. Chem. Phys. 133 164315
[7] Gerakis A, Shneider M N, Stratton B C 2016 Appl. Phys. Lett. 109 031112
[8] Lock J A, Seasholtz R G, John W T 1992 Appl. Opt. 31 2839
[9] Pan X G, Shneider M N, Miles R B 2005 Phys. Rew. A 71 045801
[10] Witschas B, Gu Z, Ubachs W 2014 Opt. Express 22 29655
[11] Tenti G, Boley C D, Desai R C 1974 Can. J. Phys. 52 285
[12] Gu Z, Witschas B, van de Water W 2013 Appl. Opt. 52 4640
[13] Vieitez M O, van Duijn E J, Ubachs W 2010 Phys. Rev. A 82 043836
[14] Witschas B, Vieitez M O, van Duijn E J, Reitebuch O, van de Water W, Ubachs W 2010 Appl. Opt. 49 4217
[15] Witschas B, Lemmerz C, Reitebuch O 2012 Appl. Opt. 51 6207
[16] Witschas B, Lemmerz C, Reitebuch O 2014 Opt. Lett. 39 1972
[17] Mielke A F, Seasholtz R G, Elam K A 2005 Exp. Fluids 39 441
[18] Wang Y Q, Yu Y, Liang K, Marques Jr W, van de Water W, Ubachs W 2017 Chem. Phys. Lett. 669 137
[19] Levinson N 1946 Stud. Appl. Math. 25 261
[20] Golub G H, Reinsch C 1970 Numer. Math. 14 403
[21] Henry E R, Hofrichter J 1992 Meth. Enzymol. 210 129
[22] Hansen P C 1990 SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 11 503
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[1] Boley C D, Desai R C, Tenti G 1972 Can. J. Phys. 50 2158
[2] Ma Y, Liang K, Lin H, Ji H 2007 Acta Opt. Sin. 27 962 (in Chinese) [马泳, 梁琨, 林宏, 冀航 2007 光学学报 27 962]
[3] Gu Z, Ubachs W, Marques Jr W, van de Water W 2015 Phys. Rev. Lett. 114 243902
[4] Cao C L, Xu S L, Liu E W 2013 J. Univ. Sci. Tech. China 43 510 (in Chinese) [曹春丽, 徐胜利, 刘二伟 2013 中国科学技术大学学报 43 510]
[5] Gu Z Y, Ubachs W, van de Water W 2014 Opt. Lett. 39 3301
[6] Meijer A S, de Wijn A S, Peters M F E, Dam N J, van de Water W 2010 J. Chem. Phys. 133 164315
[7] Gerakis A, Shneider M N, Stratton B C 2016 Appl. Phys. Lett. 109 031112
[8] Lock J A, Seasholtz R G, John W T 1992 Appl. Opt. 31 2839
[9] Pan X G, Shneider M N, Miles R B 2005 Phys. Rew. A 71 045801
[10] Witschas B, Gu Z, Ubachs W 2014 Opt. Express 22 29655
[11] Tenti G, Boley C D, Desai R C 1974 Can. J. Phys. 52 285
[12] Gu Z, Witschas B, van de Water W 2013 Appl. Opt. 52 4640
[13] Vieitez M O, van Duijn E J, Ubachs W 2010 Phys. Rev. A 82 043836
[14] Witschas B, Vieitez M O, van Duijn E J, Reitebuch O, van de Water W, Ubachs W 2010 Appl. Opt. 49 4217
[15] Witschas B, Lemmerz C, Reitebuch O 2012 Appl. Opt. 51 6207
[16] Witschas B, Lemmerz C, Reitebuch O 2014 Opt. Lett. 39 1972
[17] Mielke A F, Seasholtz R G, Elam K A 2005 Exp. Fluids 39 441
[18] Wang Y Q, Yu Y, Liang K, Marques Jr W, van de Water W, Ubachs W 2017 Chem. Phys. Lett. 669 137
[19] Levinson N 1946 Stud. Appl. Math. 25 261
[20] Golub G H, Reinsch C 1970 Numer. Math. 14 403
[21] Henry E R, Hofrichter J 1992 Meth. Enzymol. 210 129
[22] Hansen P C 1990 SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 11 503
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