Reconstruction of an axisymmetric image from its blurred and noisy projection

The 3-D velocity distribution of ionized photofragments resulting from the dissociation of methyl iodide is recovered by digitally deblurring and Abel inverting a single measured 2-D projection. The reconstructed distribution reveals two rings which are the dissociation channels corresponding to ground state and excited state iodine. A channel resolution improvement factor of 1.6 is achieved by deconvolving the 2-D projection using a line-by-line implementation of Kawata´s (1980) reblur algorithm. This technique guarantees noise-smoothed projections for the notoriously sensitive Abel inversion procedure, which in this paper is implemented using discrete Fourier and Hankel transforms