An Analytical Method for the Deconvolution of Voigtian Profiles

Abstract

In spectroscopy, the spectral lineshape is often well described by a Voigtian function, which is the convolution of a Lorentzian function and a Gaussian function. A number of researchers have suggested ways to approximate the Voigtian profile. Herein, we report an analytical method to deconvolve it. Our method calculates the component Lorentzian and Gaussian linewidth of a Voigtian function by solving some polynomial equations in terms of even-order derivatives of the Voigtian function evaluated at the center. In the absence of noise, the Lorentzian and Gaussian linewidths obtained by the deconvolution of computer-generated Voigtian absorption spectra are accurate within an error of 0.01 %. While the accuracy of our new method is affected by noise, it can be improved by employing a Savitzky–Golay filter and/or a Lorentzian filter function. Our new method will be useful in magnetic resonance spectroscopy, optical spectroscopy, and other fields of science.