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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: Steven A. Burns
  • Vol. 24, Iss. 9 — Sep. 1, 2007
  • pp: 2568–2577

Geometry and dynamics in the Fresnel transforms of discrete systems

Kurt Bernardo Wolf and Guillermo Krötzsch  »View Author Affiliations


JOSA A, Vol. 24, Issue 9, pp. 2568-2577 (2007)
http://dx.doi.org/10.1364/JOSAA.24.002568


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Abstract

Free propagation in continuous optical and mechanical systems is generated by the momentum-squared operator and results in a shear of the phase space plane along the position coordinate. We examine three discrete versions of the Fresnel transform in periodic systems through their Wigner function on a toroidal phase space. But since it is topologically impossible to continuously and globally shear a torus, we examine a fourth version of the Fresnel transform on a spherical phase space, in a model based on the Lie algebra of angular momentum, where the corresponding Fresnel transform wrings the sphere.

© 2007 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(090.1970) Holography : Diffractive optics

ToC Category:
Fourier optics and signal processing

History
Original Manuscript: March 6, 2007
Revised Manuscript: April 11, 2007
Manuscript Accepted: April 16, 2007
Published: July 19, 2007

Citation
Kurt Bernardo Wolf and Guillermo Krötzsch, "Geometry and dynamics in the Fresnel transforms of discrete systems," J. Opt. Soc. Am. A 24, 2568-2577 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-9-2568

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