Voigt线型函数及其最大值的研究

尹增谦; 武臣; 宫琬钰; 龚之珂; 王永杰

doi:10.7498/aps.62.123301

摘要

研究了多普勒和洛伦兹线型函数卷积形式的Voigt线型函数, 给出了它的最大值.结果表明, Voigt线型函数是关于中心频率的对称函数, Voigt线型函数的最大值由多普勒和洛伦兹线型函数的半宽度决定, 与中心频率无关, 且比洛伦兹和多普勒线型函数的最大值都小.提出了利用Voigt线型函数最大值和半宽度获得多普勒线型函数和洛伦兹线型函数的方法, 并利用Monte Carlo方法进行了验证.

关键词:

The Voigt profile function which is the convolution of the Doppler and Lorentzian function is investigated analytically and its maximum is obtained. The results indicate that the maximum of the Voigt profile function is smaller than maxima of Doppler and Lorentzian profile function, which is determined by the half-widths of Doppler and Lorentzian profile function. The Voigt profile function is a symmetric function about the central frequency. A new technique is presented, with which the Doppler and Lorentzian profile function can be obtained by using the maximum and half-width of the Voigt profile function, and the technique is verified by the Monte Carlo method.

Keywords:

作者及机构信息

1.
华北电力大学数理系, 保定 071003

基金项目: 中央高校基本科研业务费(批准号: 10ML40)资助的课题.

Authors and contacts

1.
Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China

Funds: Project supported by the Fundamental Research Fund for the Central Universities, China (Grant No. 10ML40).

参考文献

[1]	Dong L F, Ran J X, Mao Z G 2005 Atca Phys. Sin. 54 2167 (in Chinese) [董丽芳, 冉俊霞, 毛志国 2005物理学报 54 2167]
[2]	Lin J L 2000 Ph. D. Dissertation (Wuhan: Institute of Physics and Mathematics) (in Chinese) [林洁丽 2000 博士学位论文(武汉: 中国科学院武汉物理与数学研究所)]
[3]	He J, Zhang C M, Zhang Q G 2007 Spectrosc. Spectr. Anal. 27 423 (in Chinese) [贺健, 张淳民, 张庆国 2007光谱学与光谱分析 27 423]
[4]	Dobryakow S N, Lebedev Y S 1969 Sov. Phys. Dokl. 9 13
[5]	Roston G D, Obaid F S 2005 J. Quant. Spectrosc. Radiat. Transfer. 94 255
[6]	Belafhal A 2000 Opt. Commun. 177 111
[7]	Dulov E N, Khripunov D M 2007 J. Quant. Spectrosc. Radiat. Transfer. 107 421
[8]	Gianni P, Francesco M 2010 J. Comput. Appl. Math. 233 1590
[9]	Abrarov S M, Quine B M 2011 Appl. Math. Comput. 218 1894
[10]	Yin Z Q, Wu C, WangY J, Li X C 2012 Spectrosc. Spectr. Anal. 32 1189 (in Chinese) [尹增谦, 武臣, 王永杰, 李雪辰 2012 光谱学与光谱分析 32 1189]
[11]	Feng W G 2000 Integral Transformation (Shanghai: Shanghai Jiaotong University Press) p44 (in Chinese) [冯卫国 2000 积分变换 (上海: 上海交通大学出版社) 第44页]
[12]	Wang L X, Fang D Z 1998 Handbook of Mathematics (Beijing: Higher Education Press) p595 (in Chinese) [王连祥, 方德植 1998 数学手册 (北京: 高等教育出版社)第595页]
[13]	Olivero J J, Longbothum R L 1977 J. Quant. Spectrosc. Radiat. Transfer. 17 233

施引文献

[1]	Dong L F, Ran J X, Mao Z G 2005 Atca Phys. Sin. 54 2167 (in Chinese) [董丽芳, 冉俊霞, 毛志国 2005物理学报 54 2167]
[2]	Lin J L 2000 Ph. D. Dissertation (Wuhan: Institute of Physics and Mathematics) (in Chinese) [林洁丽 2000 博士学位论文(武汉: 中国科学院武汉物理与数学研究所)]
[3]	He J, Zhang C M, Zhang Q G 2007 Spectrosc. Spectr. Anal. 27 423 (in Chinese) [贺健, 张淳民, 张庆国 2007光谱学与光谱分析 27 423]
[4]	Dobryakow S N, Lebedev Y S 1969 Sov. Phys. Dokl. 9 13
[5]	Roston G D, Obaid F S 2005 J. Quant. Spectrosc. Radiat. Transfer. 94 255
[6]	Belafhal A 2000 Opt. Commun. 177 111
[7]	Dulov E N, Khripunov D M 2007 J. Quant. Spectrosc. Radiat. Transfer. 107 421
[8]	Gianni P, Francesco M 2010 J. Comput. Appl. Math. 233 1590
[9]	Abrarov S M, Quine B M 2011 Appl. Math. Comput. 218 1894
[10]	Yin Z Q, Wu C, WangY J, Li X C 2012 Spectrosc. Spectr. Anal. 32 1189 (in Chinese) [尹增谦, 武臣, 王永杰, 李雪辰 2012 光谱学与光谱分析 32 1189]
[11]	Feng W G 2000 Integral Transformation (Shanghai: Shanghai Jiaotong University Press) p44 (in Chinese) [冯卫国 2000 积分变换 (上海: 上海交通大学出版社) 第44页]
[12]	Wang L X, Fang D Z 1998 Handbook of Mathematics (Beijing: Higher Education Press) p595 (in Chinese) [王连祥, 方德植 1998 数学手册 (北京: 高等教育出版社)第595页]
[13]	Olivero J J, Longbothum R L 1977 J. Quant. Spectrosc. Radiat. Transfer. 17 233

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板