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Optical Engineering

Annular Radon transform and axicon transform
Author(s): Viktor Viktorovich Kotlyar; Alexander Alexeevich Kovalev
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Paper Abstract

We consider integral transforms that can describe ideal imaging optical systems with annular impulse response. The integral transform, referred to as the annular Radon transform (ART), is considered as an average taken along all circles of fixed radius in the plane. The inversion formula for the ART is given. It is shown that for a function of two variables to be reconstructed uniquely, the averaging functions along all circles with at least two different radii need to be known. The ART can be optically realized using a spatial filtering system (SFS) with amplitude filter, its transmittance being proportional to the Bessel function of zero order. Also, an axicon transform (AT) is considered that can be optically realized using a SFS with axicon in the spatial-frequency plane. The inverse and direct ATs are shown to be of the same form (up to a constant). A numerical comparison of the AT and ART has been made when both were used for reconstruction of transformed and distorted images. The relation between the distortion variances of the output functions and the SFS reconstructed input function is derived.

Paper Details

Date Published: 1 July 2006
PDF: 9 pages
Opt. Eng. 45(7) 078201 doi: 10.1117/1.2226990
Published in: Optical Engineering Volume 45, Issue 7
Show Author Affiliations
Viktor Viktorovich Kotlyar, Samara State Aerospace Univ. (Russia)
Alexander Alexeevich Kovalev, Image Processing Systems Institute (Russia)

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