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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. 28, Iss. 5 — May. 1, 2011
  • pp: 786–790

Space–bandwidth ratio as a means of choosing between Fresnel and other linear canonical transform algorithms

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


JOSA A, Vol. 28, Issue 5, pp. 786-790 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000786


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Abstract

The product of the spatial and spatial frequency extents of a wave field has proven useful in the analysis of the sampling requirements of numerical simulations. We propose that the ratio of these quantities is also illuminating. We have shown that the distance at which the so-called “direct method” becomes more efficient than the so-called “spectral method” for simulations of Fresnel transforms may be written in terms of this space–bandwidth ratio. We have proposed generalizations of these algorithms for numerical simulations of general ABCD systems and derived expressions for the “transition space–bandwidth ratio,” above which the generalization of the spectral method is the more efficient algorithm and below which the generalization of the direct method is preferable.

© 2011 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.1510) Geometric optics : Propagation methods
(080.2730) Geometric optics : Matrix methods in paraxial optics
(090.1760) Holography : Computer holography
(090.1995) Holography : Digital holography

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: January 4, 2011
Revised Manuscript: February 2, 2011
Manuscript Accepted: February 24, 2011
Published: April 15, 2011

Citation
John J. Healy and John T. Sheridan, "Space–bandwidth ratio as a means of choosing between Fresnel and other linear canonical transform algorithms," J. Opt. Soc. Am. A 28, 786-790 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-5-786

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