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Appl Opt. 2009 Aug 1;48(22):4310-9.

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

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  • 1Laser Department, National Institute for Laser, Plasma and Radiation Physics, P.O. Box MG-36, Măgurele 077125, Romania.


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.

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