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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 8 — Aug. 1, 2008
  • pp: 1875–1884

Unitary transformation between Cartesian- and polar-pixellated screens

Luis Edgar Vicent and Kurt Bernardo Wolf  »View Author Affiliations


JOSA A, Vol. 25, Issue 8, pp. 1875-1884 (2008)
http://dx.doi.org/10.1364/JOSAA.25.001875


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Abstract

A unitary transformation between Cartesian and polar pixellations of finite two-dimensional images is obtained from the su ( 2 ) model for discrete and finite signals. This transformation analyzes the original image into its finite Cartesian “Laguerre–Kravchuk” modes (involving Wigner little-d functions) and synthesizes it back using a polar mode basis with the same set of mode coefficients. The polar basis is derived from the quantum angular momentum theory, and its modes are given by Clebsch–Gordan coefficients.

© 2008 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(070.2025) Fourier optics and signal processing : Discrete optical signal processing
(070.2465) Fourier optics and signal processing : Finite analogs of Fourier transforms
(270.5585) Quantum optics : Quantum information and processing
(200.6046) Optics in computing : Smart pixel systems

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: March 14, 2008
Manuscript Accepted: May 20, 2008
Published: July 3, 2008

Citation
Luis Edgar Vicent and Kurt Bernardo Wolf, "Unitary transformation between Cartesian- and polar-pixellated screens," J. Opt. Soc. Am. A 25, 1875-1884 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-8-1875

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