Voigt线形函数二阶导数研究

Second derivative of Voigt function

在强展宽条件下,光谱信号二阶导数相互的交叠影响较小,是一种潜在的反演光谱信息的手段.本文研究了光谱Voigt线形函数的二阶导数,得出了其二阶导数全域积分为0的性质,计算了二阶导数最小值与偶数高阶导数最大值和最小值的解析结果,并通过数值计算与曲线拟合得出了其极大值位置与零点位置的比例与洛仑兹-多普勒半宽比的关系,为强展宽下由光谱二阶导数准确反演光谱信息提供了理论基础.

In high-temperature high-pressure environment, the measurement precisions of tunable diode laser absorption spec-troscopy 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.