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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. 18, Iss. 11 — Nov. 1, 2001
  • pp: 2707–2716

Talbot effect interpreted by number theory

Marı́a Teresa Flores-Arias, Marı́a Victoria Pérez, Carlos Gómez-Reino, Carmen Bao, and Carlos R. Fernández-Pousa  »View Author Affiliations


JOSA A, Vol. 18, Issue 11, pp. 2707-2716 (2001)
http://dx.doi.org/10.1364/JOSAA.18.002707


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Abstract

An interpretation of the Talbot effect in a tapered gradient-index medium by number theory as the output/input relationship between the integer and the noninteger difference of position and the slope of rays is presented. Unit cell and transverse magnification for Talbot images are evaluated, and two criteria for angular magnification are defined. The study is particularized to a finite set of diffracted rays.

© 2001 Optical Society of America

OCIS Codes
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(110.0110) Imaging systems : Imaging systems

History
Original Manuscript: February 20, 2001
Revised Manuscript: April 26, 2001
Manuscript Accepted: April 30, 2001
Published: November 1, 2001

Citation
Marı́a Teresa Flores-Arias, Marı́a Victoria Pérez, Carlos Gómez-Reino, Carmen Bao, and Carlos R. Fernández-Pousa, "Talbot effect interpreted by number theory," J. Opt. Soc. Am. A 18, 2707-2716 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-11-2707

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