Acceleration of diffraction calculations in cylindrically symmetrical optics by use of discrete fast Fourier transforms

Published

January 30, 2018

Author(s)

Jeremy S. Rubin, Eric L. Shirley, Zachary H. Levine

Abstract

We have achieved significant acceleration of diffraction calculations in two different, though related contexts. In the first case, we consider Wolf's formula for integrated flux in a circular region following diffraction of a point source's light by a circular aperture or lens. Although the formula involves a double sum, we have found a way to evaluate it with the effort of a single sum by use of fast Fourier transforms (FFTs) to carry out convolutions. In the second case, we exploit properties of the Fresnel-Kirchhoff propagator in the Gaussian, paraxial optics approximation to achieve the propagation of a partial wave from one optical element to the next. Ordinarily, this would involve a double loop over the radial variables on each element, but we have reduced the computational cost by a factor approximately equal to the smaller number of radius values. In addition, one can reduce the number of partial waves required to calculate the throughput of an optical system of interest in radiometry when at least one element is very small, such as a pinhole aperture. As a demonstration of the benefits of the acceleration, we analyze intricate diffraction effects that occur in a satellite-based solar radiometry instrument.

Citation

Applied Optics

Volume

57

Issue

4

Pub Type

Journals

Download Paper

DOI Link

Keywords

convolution, diffraction, fast Fourier transform, radiometry, Wolf

Citation

Rubin, J. , Shirley, E. and Levine, Z. (2018), Acceleration of diffraction calculations in cylindrically symmetrical optics by use of discrete fast Fourier transforms, Applied Optics, [online], https://doi.org/10.1364/AO.57.000788 (Accessed March 16, 2025)