Abstract

We investigate the problem of representing an arbitrary class of real functions f(·) in terms of their sampled values along the radius r and at equal angular increments of the azimuthal angle θ. Two different bandwidth constraints on f(r,θ) are considered: Fourier and Hankel. The end result is two theorems which enable images to be reconstructed from their samples. The theorems have potential application in image storage, image encoding, and computer-aided tomography.

© 1979 Optical Society of America

Image reconstruction using polar sampling theorems

H. Stark and C. S. Sarna
Appl. Opt. 18(13) 2086-2088 (1979)

Cauchy and polar-sampling theorems

J. L. Brown
J. Opt. Soc. Am. A 1(10) 1054-1056 (1984)

Application of the Sampling Theorem to Optical Diffraction Theory

Richard Barakat
J. Opt. Soc. Am. 54(7) 920-930 (1964)

Image Evaluation by Use of the Sampling Theorem*

B. Roy Frieden
J. Opt. Soc. Am. 56(10) 1355-1362 (1966)

New equivalence theorems for planar sources that generate the same distributions of radiant intensity*

E. Collett and E. Wolf
J. Opt. Soc. Am. 69(7) 942-950 (1979)