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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. 20, Iss. 4 — Apr. 1, 2003
  • pp: 661–667

Generalized Jinc functions and their application to focusing and diffraction of circular apertures

Qing Cao  »View Author Affiliations


JOSA A, Vol. 20, Issue 4, pp. 661-667 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000661


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Abstract

A family of generalized Jinc functions is defined and analyzed. The zero-order one is just the traditional Jinc function. In terms of these functions, series-form expressions are presented for the Fresnel diffraction of a circular aperture illuminated by converging spherical waves or plane waves. The leading term is nothing but the Airy formula for the Fraunhofer diffraction of circular apertures, and those high-order terms are directly related to those high-order Jinc functions. The truncation error of the retained terms is also analytically investigated. We show that, for the illumination of a converging spherical wave, the first 19 terms are sufficient for describing the three-dimensional field distribution in the whole focal region.

© 2003 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(220.2560) Optical design and fabrication : Propagating methods

History
Original Manuscript: October 7, 2002
Revised Manuscript: December 2, 2002
Manuscript Accepted: December 2, 2002
Published: April 1, 2003

Citation
Qing Cao, "Generalized Jinc functions and their application to focusing and diffraction of circular apertures," J. Opt. Soc. Am. A 20, 661-667 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-4-661

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