Quick-and-Dirty Computation of Voigt Profiles, Classification of Their Shapes, and Effective Determination of the Shape Parameter

A spectral line is modeled by a Voigt profile, which is a convolution of a Gaussian and a Lorentzian. The width of the Gaussian is described by the standard deviation σ; the width of the Lorentzian, by its lower quartile γ. One common method of computing a Voigt profile uses the real part of the complexvalued Faddeeva function, which is conceptually demanding and whose evaluation is computationally expensive. Other computational methods approximate Voigt profiles by simpler functions. We show that the shape of a Voigt profile only depends on the ratio ρ = γ/σ and, consequently, introduce a one-parameter family of standardized Voigt profiles. Then we present a conceptually simple and efficient numerical method for computing these standardized Voigt profiles – we only require basic numerical integration. Next we compute the second derivative by a finite-difference formula and determine empirically the relationship between the shape parameter ρ and the location of the inflection points described by their quantiles. This empirical relationship suffices to determine the parameters of a Voigt profile directly from data points and thus avoids the use of computationally costly, time-consuming, and sometimes failing general iterative fitting methods. In particular, this new and faster approach allows more real-time analyses of spectral data.