Abstract

The Abel, onion-peeling, and filtered back-projection inversion methods can be inter-compared without assumptions about the object being deconvolved. If the projection data (such as optical absorption, beam deflection, or phase shift) are taken at equally spaced radial positions, the deconvolved field is given by weighted sums of the projections divided by the data spacing. The weighting factors are independent of the data spacing. All the methods are highly similar and have Abel-like behavior: the field at a radial location is primarily determined by the weighted differences of a few projections around that radial position. The weighting factors also determine the relative noise of each method. Based on ease of calculation, robustness, and noise, a three-point Abel inversion is preferred. This analysis also shows that the signal-to-noise ratios of the deconvolutions deteriorate if the projection data are taken too close together.

© 1992 Optical Society of America