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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

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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References

  1. M. Born and E. Wolf, Principles of Optics, 6th ed (Pergamon, Oxford, UK, 1980), pp. 1–104, 370–455, 556–591.
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 30–76.
  3. H. Osterberg and L. Smith, “Closed solutions of Rayleigh’s diffraction integral for axial points,” J. Opt. Soc. Am. 51, 1050–1054 (1961).
  4. J. C. Heurtley, “Scalar Rayleigh–Sommerfeld and Kirchhoff diffraction integrals: a comparison of exact evaluations for axial points,” J. Opt. Soc. Am. 63, 1003–1008 (1973).
  5. E. Marchand and E. Wolf, “Boundary diffraction wave in the domain of the Rayleigh–Kirchhoff diffraction theory,” J. Opt. Soc. Am. 52, 761–767 (1962).
  6. A. Rubinowicz, “Boundary wave diffraction,” in Progress in Optics, Vol. IV, E. Wolf, ed. (North-Holland, Amsterdam, 1965), p. 199.
  7. T. Young,”Bakerian lecture on the mechanism of the theory of light and colour,” Philos. Trans. 12–48 (1802).

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