Theoretical limits on extrasolar terrestrial planet detection with coronagraphs

Many high-contrast coronagraph designs have recently been proposed. In this paper, their suitability for direct imaging of extrasolar terrestrial planets is reviewed. We also develop a linear algebra based model of coronagraphy that can both explain the behavior of existing coronagraphs and quantify the coronagraphic performance limit imposed by fundamental physics. We find that the maximum theoretical throughput of a coronagraph is equal to 1 minus the nonaberrated noncoronagraphic PSF of the telescope. We describe how a coronagraph reaching this fundamental limit may be designed, and how much improvement over the best existing coronagraph design is still possible. Both the analytical model and numerical simulations of existing designs also show that this theoretical limit rapidly degrades as the source size is increased: the "highest performance" coronagraphs, those with the highest throughput and smallest inner working angle (IWA), are the most sensitive to stellar angular diameter. This unfortunately rules out the possibility of using a small IWA (<λ/d) coronagraph for a terrestrial planet imaging mission. Finally, a detailed numerical simulation that accurately accounts for stellar angular size, zodiacal and exozodiacal light is used to quantify the efficiency of coronagraph designs for direct imaging of extrasolar terrestrial planets in a possible real observing program. We find that in the photon noise-limited regime, a 4 m telescope with a theoretically optimal coronagraph is able to detect Earth-like planets around 50 stars with 1 hr exposure time per target (assuming 25% throughput and exozodi levels similar to our solar system). We also show that at least two existing coronagraph design can approach this level of performance in the ideal monochromatic case considered in this study.