Fast computation of Lyot-style coronagraph propagation

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.