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# 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