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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: Franco Gori
  • Vol. 27, Iss. 1 — Jan. 1, 2010
  • pp: 21–30

Fast linear canonical transforms

John J. Healy and John T. Sheridan  »View Author Affiliations


JOSA A, Vol. 27, Issue 1, pp. 21-30 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000021


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Abstract

The linear canonical transform provides a mathematical model of paraxial propagation though quadratic phase systems. We review the literature on numerical approximation of this transform, including discretization, sampling, and fast algorithms, and identify key results. We then propose a frequency-division fast linear canonical transform algorithm comparable to the Sande–Tukey fast Fourier transform. Results calculated with an implementation of this algorithm are presented and compared with the corresponding analytic functions.

© 2010 Optical Society of America

OCIS Codes
(070.4560) Fourier optics and signal processing : Data processing by optical means
(080.2730) Geometric optics : Matrix methods in paraxial optics
(100.2000) Image processing : Digital image processing
(200.2610) Optics in computing : Free-space digital optics
(200.3050) Optics in computing : Information processing
(200.4560) Optics in computing : Optical data processing
(200.4740) Optics in computing : Optical processing

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: August 25, 2009
Manuscript Accepted: November 2, 2009
Published: December 3, 2009

Citation
John J. Healy and John T. Sheridan, "Fast linear canonical transforms," J. Opt. Soc. Am. A 27, 21-30 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-1-21


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