Inverse Transform Sampling for Efficient Doppler-Averaged Spectroscopy Simulations

We present a thermal velocity sampling method for calculating Doppler-broadened atomic spectra, which more efficiently reaches a smooth limit than regular velocity weighted sampling. The method uses equal-population sampling of the 1-D thermal distribution, sampling the 'inverse transform' of the cumulative distribution function, and is broadly applicable to normal distributions. We also discuss efficiencies from eliminating velocity classes which don't significantly contribute to observed atomic lines, and comment on the application of this method in 2- and 3-dimensions.