Abel inversion of optical beam deflection signals from photoacoustic waves with symmetry in one, two, and three dimensions

Abstract

Photoacoustic waves can be detected by recording optical beam deflection as a result of density gradients inherent in the waves. Beam deflection can be recorded from a single laser beam placed at a distance from the source where data are generated as a function of time, or by recording beam deflections at a single time as the position of the probe beam is varied. For either case, the deflection signal is shown to be described by an Abel transform of the pressure gradient. Here, the inversion of beam deflection data from photoacoustic sources with symmetry in one, two, and three dimensions is investigated. An iterative method based on total variation regularization and a regression procedure based on Lasso regularization are shown to result in accurate reproductions of the theoretical expressions that describe photoacoustic waves from simple sources.