Paper
27 September 2013 Hybrid fast Hankel transform implementation for optics simulation
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Abstract
The most compute intensive part of a full optics simulation, especially including diffraction effects, is the Fourier transform between pupil and image spaces. This is typically performed as a two dimensional fast discrete transform. For a nearly radially symmetric system there are advantages to using polar coordinates, in which case the radial transform becomes a Hankel transform, using Bessel functions instead of circular functions. However, there are special difficulties in calculating and handling Bessel functions. Several solutions have been proposed. We present a hybrid Hankel transform which divides the domain, calculating a portion using Bessel function approximations but converting most of the domain into a one dimensional Fourier transform which can be handled by standard methods.
© (2013) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Paul K. Davis "Hybrid fast Hankel transform implementation for optics simulation", Proc. SPIE 8840, Optical Modeling and Performance Predictions VI, 884002 (27 September 2013); https://doi.org/10.1117/12.2024530
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KEYWORDS
Fourier transforms

Bessel functions

Optical simulations

Monte Carlo methods

Computer simulations

Convolution

Algorithm development

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