Abstract

Modified Zernike polynomials and also a set of generalized functions W_m^ν(γ,u) are introduced. These polynomials and functions are then applied to the analysis of the Fresnel region field of circular apertures with nonuniform and nonsymmetric illumination. With m=0, the general result obtained in this paper reduces to the case of nonuniform but circular symmetric illumination obtained by the author in a previous paper. A general expression for the far field (Fraunhofer field) of circular apertures with general illumination is also derived. Finally, a simple example is given as an illustration.

© 1963 Optical Society of America

Fresnel Diffraction of the Plane Phase Grating

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J. Opt. Soc. Am. 53(2) 267-273 (1963)

Transfer Functions and Total Illuminance of High Numerical Aperture Systems Obeying the Sine Condition*

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Application of Apodization to Increase Two-Point Resolution by the Sparrow Criterion. II. Incoherent Illumination

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Zernike annular polynomials for imaging systems with annular pupils

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