Advances in edge diffraction algorithms

Starshade external occulters are a leading technology that provide the starlight suppression needed to directly image and spectroscopically characterize Earth-sized exoplanets in the habitable zone of nearby stars. A high-priority technology area identified in need of development for a future starshade mission is the development and validation of high-fidelity optical models to predict the performance of a full-scale starshade. We present the generalization of an algorithm to formulate the Fresnel diffraction equation as a one-dimensional integral around the edge of an arbitrary binary diffraction screen. Our edge integral provides an efficient method for capturing diffraction over a large range of size scales and is computationally superior to standard two-dimensional codes. We also present a novel method to implement wavefront errors with the edge integral. This paper provides the derivation of the algorithms and their validation with comparisons to known solutions and results from standard Fresnel propagation codes.