Second derivative of Voigt function

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.