Three and four generalized Lorentzian approximations for the Voigt line shape

Area of Science:

• Spectroscopy
• Computational Physics
• Mathematical Modeling

Background:

• The Voigt function is crucial in spectroscopy for modeling spectral line shapes.
• Previous approximations using one or two generalized Lorentzians had limitations in accuracy.
• Accurate Voigt function approximations are needed for data analysis in various scientific fields.

Purpose of the Study:

• To develop a more accurate approximation of the Voigt function.
• To investigate the use of three and four generalized Lorentzians for Voigt function approximation.
• To assess the accuracy and applicability of the proposed approximation method.

Main Methods:

• Utilized the asymptotical Padé method to derive generalized Lorentzian approximations.
• Developed approximations using three and four generalized Lorentzians in two variables.
• Evaluated the approximation accuracy across different normalized collision widths and line separations.

Main Results:

• Achieved significantly improved accuracy compared to one and two generalized Lorentzian approximations.
• The four generalized Lorentzian function demonstrated positivity for all tested parameters.
• Accuracy better than 0.0001 was obtained for most values, with a worst-case absolute error of ~0.001.
• Adequate limit functions were derived for low and high pressure regimes.

Conclusions:

• A four generalized Lorentzian approximation provides a reliable and computationally accessible method for approximating the Voigt function.
• This method offers high accuracy suitable for a wide range of experimental requirements in spectroscopy and related fields.
• The developed approximation addresses limitations of previous methods, enhancing quantitative analysis in spectral data interpretation.