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In high-temperature high-pressure environment, the measurement precisions of tunable diode laser absorption spectroscopy and other laser spectrum technologies are influenced by spectral overlap because of Doppler and Lorentz broadenings. One of the potential methods to improve precision is to use the second derivative spectral signal, which has less overlap. This paper deals with the second derivative of Voigt function. The integration of its second derivative from negative to positive infinity is proved to be zero. And the analytical results of its second derivative minimum and the maxima or minima of its even-order derivatives are obtained. It is also shown that there is the relationship between the ratio of second derivative maximum point location to zero point location and the ratio of Lorentz half-width to Doppler half-width. These results provide the basis for inversing precision information from second derivative spectral signal.
[1] Demtroder W 2008 Laser Spectroscopy (Vol. 1) (Berlin: Springer-Verlag) p61
[2] Xu Z Y, Liu W Q, Liu J G, He J F, Yao L, Ruan J, Chen J Y, Li H, Yuan S, Geng H, Kan R F 2012 Acta Phys. Sin. 61 234204 (in Chinese) [许振宇, 刘文清, 刘建国, 何俊峰, 姚路, 阮俊, 陈玖英, 李晗, 袁松, 耿辉, 阚瑞峰 2012 61 234204]
[3] Chen J Y, Liu J G, He Y B, Wang L, Gang Q, Xu Z Y, Yao L, Yuan S, Ruan J, He J F, Dai Y H, Kan R F 2013 Acta Phys. Sin. 62 224206 (in Chinese) [陈玖英, 刘建国, 何亚柏, 王辽, 冮强, 许振宇, 姚路, 袁松, 阮俊, 何俊峰, 戴云海, 阚瑞峰 2013 62 224206]
[4] Kan R F, Dong F Z, Zhang Y J, Liu J G, Liu C, Wang M, Gao S H, Chen J 2005 Chin. Phys. B 14 1904
[5] Shao J, Zhang W J, Gao X M, Ning L X, Yuan Y Q 2005 Chin. Phys. B 14 482
[6] Yin Z Q, Wu C, Gong W Y, Gong Z K, Wang Y J 2013 Acta Phys. Sin. 62 123301 (in Chinese) [尹增谦, 武臣, 宫琬钰, 龚之珂, 王永杰 2013 62 123301]
[7] Schreier F 1992 J. Quant. Spectrosc. Radiat. Transfer. 48 743
[8] Abrarov S M, Quine B M, Jagpal R K 2010 Comput. Phys. Commun. 181 876
[9] Schreier F 2011 J. Quant. Spectrosc. Radiat. Transfer. 112 1010
[10] Weng S F 2010 Fourier Transform Infrared Spectroscopic Analysis (Beijing: Chemical Industrial Press) p254 (in Chinese) [翁诗甫 2010 傅里叶变换红外光谱分析 (北京: 化学工业出版社) 第254页]
[11] Sampoorna M, Nagendra K N, Frisch H 2007 J. Quant. Spectrosc. Radiat. Transfer. 104 71
[12] Jeffery A, Zwillinger D 2007 Table of Integrals, Series, and Products (London: Academic Press) p1028
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[1] Demtroder W 2008 Laser Spectroscopy (Vol. 1) (Berlin: Springer-Verlag) p61
[2] Xu Z Y, Liu W Q, Liu J G, He J F, Yao L, Ruan J, Chen J Y, Li H, Yuan S, Geng H, Kan R F 2012 Acta Phys. Sin. 61 234204 (in Chinese) [许振宇, 刘文清, 刘建国, 何俊峰, 姚路, 阮俊, 陈玖英, 李晗, 袁松, 耿辉, 阚瑞峰 2012 61 234204]
[3] Chen J Y, Liu J G, He Y B, Wang L, Gang Q, Xu Z Y, Yao L, Yuan S, Ruan J, He J F, Dai Y H, Kan R F 2013 Acta Phys. Sin. 62 224206 (in Chinese) [陈玖英, 刘建国, 何亚柏, 王辽, 冮强, 许振宇, 姚路, 袁松, 阮俊, 何俊峰, 戴云海, 阚瑞峰 2013 62 224206]
[4] Kan R F, Dong F Z, Zhang Y J, Liu J G, Liu C, Wang M, Gao S H, Chen J 2005 Chin. Phys. B 14 1904
[5] Shao J, Zhang W J, Gao X M, Ning L X, Yuan Y Q 2005 Chin. Phys. B 14 482
[6] Yin Z Q, Wu C, Gong W Y, Gong Z K, Wang Y J 2013 Acta Phys. Sin. 62 123301 (in Chinese) [尹增谦, 武臣, 宫琬钰, 龚之珂, 王永杰 2013 62 123301]
[7] Schreier F 1992 J. Quant. Spectrosc. Radiat. Transfer. 48 743
[8] Abrarov S M, Quine B M, Jagpal R K 2010 Comput. Phys. Commun. 181 876
[9] Schreier F 2011 J. Quant. Spectrosc. Radiat. Transfer. 112 1010
[10] Weng S F 2010 Fourier Transform Infrared Spectroscopic Analysis (Beijing: Chemical Industrial Press) p254 (in Chinese) [翁诗甫 2010 傅里叶变换红外光谱分析 (北京: 化学工业出版社) 第254页]
[11] Sampoorna M, Nagendra K N, Frisch H 2007 J. Quant. Spectrosc. Radiat. Transfer. 104 71
[12] Jeffery A, Zwillinger D 2007 Table of Integrals, Series, and Products (London: Academic Press) p1028
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