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Coronagraph instruments on future space telescopes will enable the directdetection and characterization of Earth-like exoplanets around Sun-like starsfor the first time. The quest for the optimal optical coronagraph designs hasmade rapid progress in recent years thanks to the Segmented Coronagraph Designand Analysis (SCDA) initiative led by the Exoplanet Exploration Program atNASA's Jet Propulsion Laboratory. As a result, several types ofhigh-performance designs have emerged that make use of dual deformable mirrorsto (1) correct for optical aberrations and (2) suppress diffracted starlightfrom obstructions and discontinuities in the telescope pupil. However, thealgorithms used to compute the optimal deformable mirror surface tend to becomputationally intensive, prohibiting large scale design surveys. Here, weutilize the Fast Linearized Coronagraph Optimizer (FALCO), a tool that allowsfor rapid optimization of deformable mirror shapes, to explore trade-offs incoronagraph designs for obstructed and segmented space telescopes. We comparedesigns for representative shaped pupil Lyot and vortex coronagraphs, two ofthe most promising concepts for the LUVOIR space mission concept. We analyzethe optical performance of each design, including their throughput and abilityto passively suppress light from partially resolved stars in the presence oflow-order aberrations. Our main result is that deformable mirror basedapodization can sufficiently suppress diffraction from support struts andinter-segment gaps whose widths are on the order of $\sim$0.1% of the primarymirror diameter to detect Earth-sized planets within a few tens ofmilliarcseconds from the star.

Fast Linearized Coronagraph Optimizer (FALCO) IV. Coronagraph design survey for obstructed and segmented apertures