Abstract

A diffraction image is analyzed using the generalized prolate spheroidal wavefunctions (GPSWF) introduced by Slepian. The pupil function of an optical system is expanded exactly in terms of these functions, irrespective of the amounts of residual aberrations. The encircled flux is given by (2π/a)2N=0n=0|aN,n|2λN,n, where a is the radius of the encircled region, aN,n is an expansion coefficient of the pupil function in terms of the GPSWF, and λN,n is the eigenvalue corresponding to the GPSWF that satisfies an integral equation related to the Fraunhofer diffraction integral. Several numerical results are shown for the encircled flux in the presence of the third- and fifth-order spherical aberrations which vary from 1 to 20 wavelengths.

© 1970 Optical Society of America

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