Computation of 2D Fourier transforms and diffraction integrals using Gaussian radial basis functions
Identificadores
URI: http://hdl.handle.net/10835/5670
ISSN: 1063-5203
DOI: http://dx.doi.org/10.1016/j.acha.2016.01.007
ISSN: 1063-5203
DOI: http://dx.doi.org/10.1016/j.acha.2016.01.007
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Ramos López, DaríoFecha
2016Resumen
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.
Keywords: 2D F...