Open AccessSecond derivative of Voigt function
Author(s) -
Chenguang Yang,
Ruifeng Kan,
Zhenyu Xu,
Guangle Zhang,
Jianguo Liu
Publication year - 2014
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.63.223301
Subject(s) - second derivative , derivative (finance) , maxima and minima , lorentz transformation , voigt profile , optics , function (biology) , physics , doppler effect , mathematical analysis , signal (programming language) , maxima , spectral line , computational physics , materials science , mathematics , quantum mechanics , computer science , evolutionary biology , biology , art , performance art , financial economics , art history , economics , programming language
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.