Sebastian Ament, Accurate & Efficient Numerical Calculation of Voigt Profile via Optimized...

The Voigt profile is defined as the convolution of a Gaussian and a Lorentzian function. It occurs frequently in spectroscopy and astronomy, but is approximated in applications by sums of Gaussian and Lorentzian functions, called pseudo-Voigt profiles. These approximations tend to be accurate to only 3-4 digits, which is insufficient for high precision data. The goal of this work is to provide an accurate and efficient means of calculating the Voigt profile and its gradient directly. In addition, a method for the calculation for the full width at half maximum (FWHM) of the Voigt profile is given. The novel methods are based on the low-rank approximation of the Voigt characteristic function, generalized Gaussian quadrature, and specially derived asymptotic expansions. Numerical experiments of the schemes display their speed and machine-precision accuracy.