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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.
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Keywords:
- Voigt profile function /
- half-width /
- maximum value /
- Fourier transform
[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
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[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
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