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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. 21, Iss. 4 — Apr. 1, 2004
  • pp: 510–516

On the usual approximation used in the Rayleigh–Sommerfeld diffraction theory

Arvind S. Marathay and John F. McCalmont  »View Author Affiliations


JOSA A, Vol. 21, Issue 4, pp. 510-516 (2004)
http://dx.doi.org/10.1364/JOSAA.21.000510


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Abstract

The complete Rayleigh–Sommerfeld scalar diffraction formula contains (1-ikR) in the integrand. Usually the wavelength is small compared with the distance of the observation point from the aperture and (1-ikR) is approximated by -ikR alone. Other approximations usually made in the Rayleigh–Sommerfeld formula are addressed as well. Closed-form solutions, without approximations, are possible wherein interesting consequences of these approximations become apparent.

© 2004 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(260.1960) Physical optics : Diffraction theory

History
Original Manuscript: April 15, 2003
Manuscript Accepted: December 5, 2003
Published: April 1, 2004

Citation
Arvind S. Marathay and John F. McCalmont, "On the usual approximation used in the Rayleigh–Sommerfeld diffraction theory," J. Opt. Soc. Am. A 21, 510-516 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-4-510

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