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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 22 — Aug. 1, 2009
  • pp: 4310–4319

Fast computation algorithm for the Rayleigh–Sommerfeld diffraction formula using a type of scaled convolution

Victor Nascov and Petre Cătălin Logofătu  »View Author Affiliations

Applied Optics, Vol. 48, Issue 22, pp. 4310-4319 (2009)

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We describe a fast computational algorithm able to evaluate the Rayleigh–Sommerfeld diffraction formula, based on a special formulation of the convolution theorem and the fast Fourier transform. What is new in our approach compared to other algorithms is the use of a more general type of convolution with a scale parameter, which allows for independent sampling intervals in the input and output computation windows. Comparison between the calculations made using our algorithm and direct numeric integration show a very good agreement, while the computation speed is increased by orders of magnitude.

© 2009 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(260.1960) Physical optics : Diffraction theory
(070.2025) Fourier optics and signal processing : Discrete optical signal processing
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: April 22, 2009
Revised Manuscript: June 24, 2009
Manuscript Accepted: June 26, 2009
Published: July 21, 2009

Victor Nascov and Petre Cătălin Logofătu, "Fast computation algorithm for the Rayleigh-Sommerfeld diffraction formula using a type of scaled convolution," Appl. Opt. 48, 4310-4319 (2009)

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