Optimal deformable mirror and pupil apodization combinations for apodized pupil Lyot coronagraphs with obstructed pupils

Combining active pupil correction via deformable mirrors (DMs) with coronagraphs such as the Apodized Pupil Lyot Coronagraph (APLC) provides a powerful tool for creating high contrast dark holes with obstructed pupils featuring central obstructions, spiders, and gaps. We investigate optimal combinations of DM pupil remapping via Active Compensation of Aperture Discontinuities- Optimized Stroke Minimization (ACAD-OSM) and binary mask pupil apodization to obtain dark holes with contrasts of 1010 for the APLC. We examine the space of possible configurations for an APLC apodized with a circularly symmetric pupil mask and a pair of DMs using a modified MCMC algorithm that allows us to probe previously unexamined combinations of pupil apodization, focal plane mask size, and Lyot stop size. We find designs with ~ 20% encircled energy throughput for a focal plane mask radius of 4.5λ/D and a bandwidth of 20%, as well as for a focal plane mask radius of 3.18 λ/D and a bandwidth of 10%. We also find solutions for focal plane mask radii of 2 λ/D and 20% bandwidths that can obtain encircled energy throughputs of up to ~ 4%. Our strategy of combining circularly symmetric binary masks with DMs to create dark holes with obstructed pupils can be expanded to optimize the APLC for terrestrial exoplanet yield, and we conclude by exploring the possibility of optimizing coronagraphs using a simple parametric expression for yield.