Fast computation of Lyot-style coronagraph propagation

TL;DR

This paper introduces a fast, memory-efficient numerical method for simulating Lyot-style coronagraphs, significantly reducing computation time and memory use, enabling practical ELT coronagraph design on standard computers.

Contribution

A novel semi-analytical, non-FFT based approach that accelerates coronagraph simulations without approximations, suitable for large telescopes.

Findings

Speed improvements of 10 to 50 times over standard FFT methods.

Memory reduction by a factor of 30 to 60.

Enables coronagraph simulations on standard laptops.

Abstract

We present a new method for numerical propagation through Lyot-style coronagraphs using finite occulting masks. Standard methods for coronagraphic simulations involve Fast Fourier Transforms (FFT) of very large arrays, and computing power is an issue for the design and tolerancing of coronagraphs on segmented Extremely Large Telescopes (ELT) in order to handle both the speed and memory requirements. Our method combines a semi-analytical approach with non-FFT based Fourier transform algorithms. It enables both fast and memory-efficient computations without introducing any additional approximations. Typical speed improvements based on computation costs are of about ten to fifty for propagations from pupil to Lyot plane, with thirty to sixty times less memory needed. Our method makes it possible to perform numerical coronagraphic studies even in the case of ELTs using a contemporary commercial laptop computer, or any standard commercial workstation computer.