Method for deriving optical telescope performance specifications for Earth-detecting coronagraphs

Direct detection and characterization of extrasolar planets has become possible with powerful new coronagraphs on ground-based telescopes. Space telescopes with active optics and coronagraphs will expand the frontier to imaging Earth-sized planets in the habitable zones of nearby Sun-like stars. Currently, NASA is studying potential space missions to detect and characterize such planets, which are dimmer than their host stars by a factor of 10¹⁰. One approach is to use a star-shade occulter. Another is to use an internal coronagraph. The advantages of a coronagraph are its greater targeting versatility and higher technology readiness, but one disadvantage is its need for an ultrastable wavefront when operated open-loop. Achieving this requires a system-engineering approach, which specifies and designs the telescope and coronagraph as an integrated system. We describe a systems engineering process for deriving a wavefront stability error budget for any potential telescope/coronagraph combination. The first step is to calculate a given coronagraph’s basic performance metrics, such as contrast. The second step is to calculate the sensitivity of that coronagraph’s performance to its telescope’s wavefront stability. The utility of the method is demonstrated by intercomparing the ability of several monolithic and segmented telescope and coronagraph combinations to detect an exo-Earth at 10 pc