A simple quasi-analytical method for the deconvolution of Voigtian profiles

Abstract

In electron spin resonance spectroscopy, spectral lineshapes are often assumed to be Voigtian. A number of researchers have suggested ways to approximate the Voigtian profile. Herein, we have devised a new quasi-analytical method to deconvolve it. In particular, we have derived an equation that relates the Lorentzian-to-Gaussian linewidth ratio directly to the product of the linewidth and the maximum value of a normalized Voigtian profile. Our calculations show that the Lorentzian and Gaussian linewidths obtained by the quasi-analytical deconvolution of computer-generated Voigtian absorption spectra are accurate within an error range of 1% in the absence of noise. Also, simulations with noise-added spectra reveal that, in the presence of white noise, our method is valid to a certain extent that depends on several factors such as the number of data points and the spectral sweep width. The new deconvolution method is valuable in that it estimates the Lorentzian and Gaussian linewidth in a rapid manner. The method may be also useful in other fields of science, such as optical spectroscopy, especially if some a priori knowledge about the lineshape is given.