  We implement an efficient method of computation of two dimensional
Fourier-type integrals based on approximation of the integrand by Gaussian
radial basis functions, which constitute a standard tool in approximation
theory. As a result, we obtain a rapidly converging series expansion for the
integrals, allowing for their accurate calculation. We apply this idea to the
evaluation of diffraction integrals, used for the computation of the
through-focus characteristics of an optical system. We implement this method
and compare it performance in terms of complexity, accuracy and execution time
with several alternative approaches, especially with the extended
Nijboer-Zernike theory, which is also outlined in the text for the reader's
convenience. The proposed method yields a reliable and fast scheme for
simultaneous evaluation of such kind of integrals for several values of the
defocus parameter, as required in the characterization of the through-focus
optics.
