Voigt

Description

A Voigt function is a convolution between a Lorentzian and Gaussian and is defined as:

\[V(X,Y) = \frac{Y}{\pi}\int_{-\infty}^{+\infty}dz\frac{\exp^{-z^2}}{Y^2 + (X - z)^2},\]

where

• X - Normalized line separation width;

• Y - Normalized collision separation width.

Generally, the Voigt function involves a numerical integral and is therefore a computational intensive task. However, several approximations to the Voigt function exist making it palatable for fitting in a least-squares algorithm. The approximation used here is described in

• A.B. McLean, C.E.J. Mitchell, and D.M. Swanston. Implementation of an Efficient Analytical Approximation to the Voigt Function for Photoemission Lineshape Analysis. Journal of Electron Spectroscopy and Related Phenomena 69.2 (1994): 125–132 doi:10.1016/0368-2048(94)02189-7

The approximation uses a combination of 4 Lorentzians in two variables to generate good approximation to the true function.

Properties (fitting parameters)

Name	Default	Description
LorentzAmp	0.0	Value of the Lorentzian amplitude
LorentzPos	0.0	Position of the Lorentzian peak
LorentzFWHM	0.0	Value of the full-width half-maximum for the Lorentzian
GaussianFWHM	0.0	Value of the full-width half-maximum for the Gaussian

Categories: FitFunctions | General

Source

C++ header: Voigt.h

C++ source: Voigt.cpp