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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 45, Iss. 6 — Feb. 20, 2006
  • pp: 1102–1110

Fast-Fourier-transform based numerical integration method for the Rayleigh–Sommerfeld diffraction formula

Fabin Shen and Anbo Wang  »View Author Affiliations


Applied Optics, Vol. 45, Issue 6, pp. 1102-1110 (2006)
http://dx.doi.org/10.1364/AO.45.001102


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Abstract

The numerical calculation of the Rayleigh–Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical accuracy and on computational complexity are discussed for the FFT-DI and the FFT-based angular spectrum (FFT-AS) methods. The performance of the FFT-DI method is verified by numerical simulation and compared with that of the FFT-AS method.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Diffraction and Gratings

History
Original Manuscript: March 15, 2005
Revised Manuscript: September 9, 2005
Manuscript Accepted: September 22, 2005

Citation
Fabin Shen and Anbo Wang, "Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula," Appl. Opt. 45, 1102-1110 (2006)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-6-1102

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