Abel inversion using transform techniques

Abstract A method is presented for calculating the reconstruction of a circularly symmetric, two-dimensional function from its projection, a relation known as the Abel inversion. This technique differs from earlier methods by using integral transforms for its implementation. The frequency-domain analysis allows for experimentally obtained data, which are often noisy and off-center, to be processed in a systematic manner. The formulation of the Abel inversion in terms of transforms, filtering of the noise, and estimate of the off-center shift are discussed. Sample calculations of simulated noisy data and the application of the method to an image of a laser-sustained plasma are presented.