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We implement an efficient method of computation of two dimensionalFourier-type integrals based on approximation of the integrand by Gaussianradial basis functions, which constitute a standard tool in approximationtheory. As a result, we obtain a rapidly converging series expansion for theintegrals, allowing for their accurate calculation. We apply this idea to theevaluation of diffraction integrals, used for the computation of thethrough-focus characteristics of an optical system. We implement this methodand compare it performance in terms of complexity, accuracy and execution timewith several alternative approaches, especially with the extendedNijboer-Zernike theory, which is also outlined in the text for the reader'sconvenience. The proposed method yields a reliable and fast scheme forsimultaneous evaluation of such kind of integrals for several values of thedefocus parameter, as required in the characterization of the through-focusoptics.

Computation of 2D Fourier transforms and diffraction integrals using Gaussian radial basis functions