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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. 31, Iss. 4 — Apr. 1, 2014
  • pp: 755–764

Numerical calculation of the Fresnel transform

Damien P. Kelly  »View Author Affiliations


JOSA A, Vol. 31, Issue 4, pp. 755-764 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000755


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Abstract

In this paper, we address the problem of calculating Fresnel diffraction integrals using a finite number of uniformly spaced samples. General and simple sampling rules of thumb are derived that allow the user to calculate the distribution for any propagation distance. It is shown how these rules can be extended to fast-Fourier-transform-based algorithms to increase calculation efficiency. A comparison with other theoretical approaches is made.

© 2014 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(050.1970) Diffraction and gratings : Diffractive optics
(100.5070) Image processing : Phase retrieval
(090.1995) Holography : Digital holography

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: December 10, 2013
Manuscript Accepted: January 24, 2014
Published: March 18, 2014

Citation
Damien P. Kelly, "Numerical calculation of the Fresnel transform," J. Opt. Soc. Am. A 31, 755-764 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-4-755


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