Techniques for obtaining velocity distributions of atoms or ions from Doppler-broadened spectral line profiles

Analysis of the doppler-broadened profiles of spectral lines radiated by atoms or ions in plasmas yields information about their velocity distributions. Researchers have analysed profiles of lines radiated by atoms in isotropic velocity distributions in several ways, one being the inversion of the integral equation which relates the velocity distribution to the line profile. This inversion formula was derived for a separate application and was given to within an arbitrary multiplicative constant. This paper presents a new derivation which obtains the inversion exactly, using a method which is easily generalized for determination of anisotropic velocity distribution functions. The technique to obtain an anisotropic velocity distribution function from line profiles measured at different angles is outlined