Notes: An assessment of some closed-form expressions for the Voigt function III: Combinations of the Lorentz and Gauss functions

@article{Schreier2019NotesAA,
  title={Notes: An assessment of some closed-form expressions for the Voigt function III: Combinations of the Lorentz and Gauss functions},
  author={Franz Schreier},
  journal={Journal of Quantitative Spectroscopy and Radiative Transfer},
  year={2019}
}
  • F. Schreier
  • Published 24 January 2019
  • Physics
  • Journal of Quantitative Spectroscopy and Radiative Transfer

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TLDR
The object of the work reported in this paper was to find a simple and easy to calculate approximation to the Voigt function using the Padé method, which can be used instead of the exact function in experiments that do not require great accuracy.
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An approximation to the Voigt function is described, which is valid over the entire domain of the independent variables that characterize it and which is accurate to the order of 0.0001 of the peak
Determination of the Gaussian and Lorentzian content of experimental line shapes
The approximation of the Voigt line shape by the sum of a Gaussian and a Lorentzian of equal width is explored. The relative intensities of these two lines in the approximate function are related to
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The formula of the pseudo-Voigt function expressed by a weighted sum of Gaussian and Lorentzian functions is extended by adding two other types of peak functions in order to improve the accuracy when
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TLDR
Three and four generalized Lorentzians in two variables have been obtained to approximate the Voigt function by using the asymptotical Padé method and give a reliable and easily calculable approximation for most of the experimental needs.
Simple empirical analytical approximation to the Voigt profile
A simple empirical analytical approximation to the Voigt profile is proposed as a weighted sum of Lorentzian and Gaussian functions. It is prevalent in the analysis of complicated experimental
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