Abstract

We have significantly accelerated diffraction calculations using three independent acceleration devices. These innovations are restricted to cylindrically symmetrical systems. In the first case, we consider Wolf’s formula for integrated flux in a circular region following diffraction of light from a point source by a circular aperture or a circular lens. Although the formula involves a double sum, we evaluate it with the effort of a single sum by use of fast Fourier transforms (FFTs) to perform 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 the third case, we reduce the number of partial waves, for which the propagation needs to be calculated, to determine 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 second case, we analyze intricate diffraction effects that occur in a satellite-based solar radiometry instrument.

© 2018 Optical Society of America

Two innovations in diffraction calculations for cylindrically symmetrical systems

Eric L. Shirley and Matthew L. Terraciano
Appl. Opt. 40(25) 4463-4472 (2001)

Refined treatment of single-edge diffraction effects in radiometry

Eric L. Shirley
J. Opt. Soc. Am. A 33(8) 1509-1522 (2016)

Diffraction corrections in radiometry: spectral and total power and asymptotic properties

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J. Opt. Soc. Am. A 21(10) 1895-1906 (2004)

Rapid calculation of paraxial wave propagation for cylindrically symmetric optics

Kenan Li and Chris Jacobsen
J. Opt. Soc. Am. A 32(11) 2074-2081 (2015)

Revised formulas for diffraction effects with point and extended sources

Eric L. Shirley
Appl. Opt. 37(28) 6581-6590 (1998)