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• W3093334156 abstract "We present a fast algorithm for computing the diffracted field from arbitrary binary (sharp-edged) planar apertures and occulters in the scalar Fresnel approximation, for up to moderately high Fresnel numbers ($lesssim 10^3$). It uses a high-order areal quadrature over the aperture, then exploits a single 2D nonuniform fast Fourier transform (NUFFT) to evaluate rapidly at target points (of order $10^7$ such points per second, independent of aperture complexity). It thus combines the high accuracy of edge integral methods with the high speed of Fourier methods. Its cost is ${mathcal O}(n^2 log n)$, where $n$ is the linear resolution required in source and target planes, to be compared with ${mathcal O}(n^3)$ for edge integral methods. In tests with several aperture shapes, this translates to between 2 and 5 orders of magnitude acceleration. In starshade modeling for exoplanet astronomy, we find that it is roughly $10^4 times$ faster than the state of the art in accurately computing the set of telescope pupil wavefronts. We provide a documented, tested MATLAB/Octave implementation. An appendix shows the mathematical equivalence of the boundary diffraction wave, angular integration, and line integral formulae, then analyzes a new non-singular reformulation that eliminates their common difficulties near the geometric shadow edge. This supplies a robust edge integral reference against which to validate the main proposal." @default.
• W3093334156 created "2020-10-22" @default.
• W3093334156 creator A5037306695 @default.
• W3093334156 date "2020-10-12" @default.
• W3093334156 modified "2023-09-27" @default.
• W3093334156 title "Efficient high-order accurate Fresnel diffraction via areal quadrature and the nonuniform FFT." @default.
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• W3093334156 hasPublicationYear "2020" @default.
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