Computation of 2D Fourier transforms and diffraction integrals using Gaussian radial basis functions
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 int...
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
2018
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| Online Access: | http://hdl.handle.net/10835/5670 http://dx.doi.org/10.1016/j.acha.2016.01.007 |
| Summary: | 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 Fourier transform, Diffraction integrals, Radial Basis Functions,
Extended Nijboer–Zernike theory, Through-focus characteristics of an optical
system. |
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