Abstract

It is well known that the inversion of a Radon transform can be replaced by an angular Fourier-series expansion, an ensemble of inversions of circular harmonic transforms (CHT’s), and an angular Fourier-series synthesis. The nonunicity of the inverse CHT kernel is a well-established fact that is examined here in detail through a number of enlightening space- and frequency-domain approaches. The extended circular harmonic transform (ECHT) is then introduced as a generalization of the CHT, and the relationship between this transform and the Radon transform is carefully examined. This discussion finally leads to a revised formulation of the principles of coherent optical reconstruction through circular harmonic expansion.

© 1981 Optical Society of America

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