Single aperture imaging astrometry with a diffracting pupil: Application to exoplanet mass measurement with a small coronagraphic space telescope

High precision astrometry of nearby bright stars is theoretically (in the photon noise limit) possible with a space corona graph using a wide field diffraction limited camera imaging an annulus of background stars around the central coronagraphic field. With the sub-micro arcsecond accuracy theoretically achievable on a 1.4-m telescope, the mass of all planets that can be imaged by the corona graph would be estimated. Simultaneous imaging and astrometric measurements would reduce the number of astrometric measurements necessary for mass determination, and reduce confusion between multiple planets and possible exozodiacal clouds in the coronagraphic image. While scientifically attractive, this measurement is technically very challenging, and must overcome astrometric distortions, which, in conventional telescopes, are several orders of magnitude above the photon noise limit. In this paper, we propose a new approach to calibrating astrometric distortions in the wide field imaging camera. The astrometric measurement is performed by simultaneously imaging background stars and diffraction spikes from the much brighter coronagraphic target on the same focal plane array. The diffraction spikes are generated by a series of small dark spots on the primary minor to reduce sensitivity to optical and mechanical distortions. Small scale distortions and detector errors are averaged down to sub-micro arcsecond by rolling the telescope around the line of sight. A preliminary error budget is shown and discussed to identify major sources of error for a 1.4-m telescope imaging a 0.25 squaredeg field of view at the galactic pole.