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Modern coronagraph design relies on advanced, large-scale optimizationprocesses that require an ever increasing amount of computational resources. Inthis paper, we restrict ourselves to the design of Apodized Pupil LyotCoronagraphs (APLCs). To produce APLC designs for future giant spacetelescopes, we require a fine sampling for the apodizer to resolve all smallfeatures, such as segment gaps, in the telescope pupil. Additionally, werequire the coronagraph to operate in broadband light and be insensitive tosmall misalignments of the Lyot stop. For future designs we want to includepassive suppression of low-order aberrations and finite stellar diameters. Thememory requirements for such an optimization would exceed multiple terabytesfor the problem matrix alone.  We therefore want to reduce the number of variables and constraints tominimize the size of the problem matrix. We show how symmetries in the pupiland Lyot stop are expressed in the complete optimization problem, and allowremoval of both variables and constraints. Each mirror symmetry reduces theproblem size by a factor of four. Secondly, we introduce progressiverefinement, which uses low-resolution optimizations as a prior for higherresolutions. This lets us remove the majority of variables from thehigh-resolution optimization. Together these two improvements require up to256x less computer memory, with a corresponding speed increase. This allows forgreater exploration of the phase space of the focal-plane mask and Lyot-stopgeometry, and easier simulation of sensitivity to Lyot-stop misalignments.Moreover, apodizers can now be optimized at their native manufacturedresolution.

Exploiting symmetries and progressive refinement for apodized pupil Lyot coronagraph design