Exact analytical formula for Voigt function

which results from the convolution

of a Gaussian profile and a Lorentzian profile

 

H. Amamou*, A. Bois, M. Grimaldi, R. Redon

Laboratoire PROTEE – ISO Université du Sud Toulon-Var, BP 20132, 83957 La Garde Cedex, France

* Corresponding author. E-mail: amamou@univ-tln.fr

Received: 25 January 2006; revised version accepted: 30 May 2007

 

Abstract

     Several works was devoted for the development of the description methods from calculation of the Voigt function. In this article we propose an exact analytical formula of Voigt function. This profile is easily calculable provided that the Gaussian component is not very negligible. This new analytical formula of the Voigt function gives a solution to the mathematical problem which is due at the infinite boundaries of the integral which defines the Voigt function. In this work we explain also the great advantage of this profile during his use for the fit of the spectral lines which results from the convolution between a Lorentzian profile and a Gaussian profile.

 

Keywords: Convolution; Deconvolution; Line profile; Voigt function; Lorentz profile; Doppler profile and Fast Fourier Transform.


 

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