  Astrometric detection and mass determination of Earth-mass exoplanets
requires sub-microarcsec accuracy, which is theoretically possible with an
imaging space telescope using field stars as an astrometric reference. The
measurement must however overcome astrometric distortions which are much larger
than the photon noise limit. To address this issue, we propose to generate
faint stellar diffraction spikes using a two-dimensional grid of regularly
spaced small dark spots added to the surface of the primary mirror (PM).
Accurate astrometric motion of the host star is obtained by comparing the
position of the spikes to the background field stars. The spikes do not
contribute to scattered light in the central part of the field and therefore
allow unperturbed coronagraphic observation of the star's immediate
surrounding. Because the diffraction spikes are created on the PM and imaged on
the same focal plane detector as the background stars, astrometric distortions
affect equally the diffraction spikes and the background stars, and are
therefore calibrated. We describe the technique, detail how the data collected
by the wide-field camera are used to derive astrometric motion, and identify
the main sources of astrometric error using numerical simulations and
analytical derivations. We find that the 1.4 m diameter telescope, 0.3 sq.deg
field we adopt as a baseline design achieves 0.2 microarcsec single measurement
astrometric accuracy. The diffractive pupil concept thus enables
sub-microarcsec astrometry without relying on the accurate pointing, external
metrology or high stability hardware required with previously proposed high
precision astrometry concepts.
