Computation of the Fresnel diffraction of starshades based on a polygonal approximation

TL;DR

This paper introduces a fast, accurate method for computing Fresnel diffraction patterns of starshades using polygonal approximations, improving efficiency and avoiding aliasing compared to existing techniques.

Contribution

A novel polygonal approximation method for starshade diffraction computation that enhances speed and accuracy over traditional Fourier and Boundary Diffraction Wave methods.

Findings

Method is faster than traditional Fourier-based approaches.

Avoids aliasing artifacts common in other methods.

Comparable or superior accuracy in diffraction pattern calculations.

Abstract

The design of starshades, i.e. external occulters for stellar coronography, relies on the fast and precise computation of their associated diffraction patterns of incoming plane waves in the telescope aperture plane. We present here a method based on a polygonal approximation of the occulter's shape, that allows fast computation of their diffraction patterns in the Fresnel approximation, without aliasing artefacts. It is competitive with respect to methods based on direct 2D Fourier transforms, or Boundary Diffraction Wave algorithms.