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气体自发瑞利-布里渊散射的理论分析及压强反演

商景诚 吴涛 何兴道 杨传音

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气体自发瑞利-布里渊散射的理论分析及压强反演

商景诚, 吴涛, 何兴道, 杨传音

Theoretical analyses of gaseous spontaneous Rayleigh-Brillouin scattering and pressure retrieving

Shang Jing-Cheng, Wu Tao, He Xing-Dao, Yang Chuan-Yin
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  • 气体压力是描述体系状态的重要参数,许多物理、化学性质都与压力有关.传统侵入式的压力测量方法会对气体状态产生干扰,影响测量精度,因此需要一种无扰式的测量方法.本实验测量了压强为2,4和6 atm(1 atm=1.01325105 Pa)下加入气溶胶的N2在90散射方向的自发瑞利-布里渊散射光谱,利用卷积后的Tenti S6模型对测量光谱进行直接拟合,拟合得到的压强值总体误差小于6.0%,求和归一化的均方根误差总体小于6.5%;利用理想的Tenti S6模型对经维纳滤波器反卷积处理后的测量光谱进行拟合,拟合得到的压强值误差总体小于5.0%,求和归一化的均方根误差总体小于6.0%.通过对两种方法的详细对比,发现压强低于2 atm时,对测量光谱进行反卷积处理在一定程度上可以消除仪器函数的影响,提高测量光谱的准确性,其光谱拟合效果和压强反演精度要优于卷积光谱.而在压强高于2 atm的情况下,卷积光谱的拟合效果和压强反演精度要优于反卷积光谱.
    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.
      通信作者: 吴涛, wutccnu@nchu.edu.cn
    • 基金项目: 国家自然科学基金(批准号:41665001,61177096)和航空科学基金(批准号:2015ZC56006)资助的课题.
      Corresponding author: Wu Tao, wutccnu@nchu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41665001, 61177096) and the Aeronautical Science Fund, China (Grant No. 2015ZC56006).
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    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

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    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]

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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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出版历程
  • 收稿日期:  2017-07-20
  • 修回日期:  2017-10-09
  • 刊出日期:  2018-02-05

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