Inverse transform sampling for efficient Doppler-averaged spectroscopy simulations

Abstract

We present a thermal velocity sampling method for calculating Doppler-broadened atomic spectra, which more efficiently reaches convergence than regular velocity weighted sampling. The method uses equal-population sampling of the 1D thermal distribution, sampling the “inverse transform” of the cumulative distribution function, and is broadly applicable to normal distributions. We also discuss the efficiency by eliminating velocity classes, which do not significantly contribute to the observed atomic lines, and comment on the application of this method in two- and three-dimensions.