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

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