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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

  • Vol. 22, Iss. 3 — Mar. 1, 2005
  • pp: 460–474

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms

Soo-Chang Pei and Jian-Jiun Ding  »View Author Affiliations


JOSA A, Vol. 22, Issue 3, pp. 460-474 (2005)
http://dx.doi.org/10.1364/JOSAA.22.000460


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Abstract

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

© 2005 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(350.6980) Other areas of optics : Transforms

History
Original Manuscript: May 13, 2004
Revised Manuscript: September 14, 2004
Manuscript Accepted: September 16, 2004
Published: March 1, 2005

Citation
Soo-Chang Pei and Jian-Jiun Ding, "Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms," J. Opt. Soc. Am. A 22, 460-474 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-3-460


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