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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. 11, Iss. 2 — Feb. 1, 1994
  • pp: 774–778

Numerical solution of the Huygens–Fresnel–Kirchhoff diffraction of spherical waves by a circular aperture

Carl R. Schultheisz  »View Author Affiliations


JOSA A, Vol. 11, Issue 2, pp. 774-778 (1994)
http://dx.doi.org/10.1364/JOSAA.11.000774


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Abstract

Using the rigorous wave-front formulation for scalar wave diffraction of Kraus [ J. Opt. Soc. Am. A 6, 1196 ( 1989); J. Opt. Soc. Am. A 9, 1132 ( 1992)], it is shown that the two-dimensional integral used to calculate the diffraction of spherical waves by a circular aperture may be reduced to a one-dimensional integral by choosing an appropriate coordinate frame. Both the two-dimensional integral and the one-dimensional integral must be evaluated numerically, but because each dimension must be sampled at approximately N locations to calculate accurately the integral (where N is the number of wavelengths across the aperture) the two-dimensional integration will require of the order of N2 evaluations of the integrand, whereas the one-dimensional integration will require of the order of only N evaluations, a substantial decrease in computing time for apertures that are large compared with optical wavelengths.

© 1994 Optical Society of America

History
Original Manuscript: May 4, 1993
Revised Manuscript: September 10, 1993
Manuscript Accepted: September 13, 1993
Published: February 1, 1994

Citation
Carl R. Schultheisz, "Numerical solution of the Huygens–Fresnel–Kirchhoff diffraction of spherical waves by a circular aperture," J. Opt. Soc. Am. A 11, 774-778 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-2-774

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