  We report on the expected astrometric performance of the Thirty Meter
Telescope's InfraRed Imaging Spectrometer (IRIS) as determined using simulated
images of the Galactic center. This region of the Galaxy harbors a supermassive
black hole and a dense nuclear stellar cluster, thus providing an ideal
laboratory for testing crowded-field astrometry with the IRIS imager.
Understanding the sources of astrometric error is also important for making
precision measurements of the short-period stars orbiting the supermassive
black hole in order to probe the curvature of space-time as predicted by
General Relativity. Various sources of error are investigated, including
read-out and photon noise, spatially variable point spread functions,
confusion, static distortion for the IRIS imager, and the quadratic probe arm
distortion. Optical distortion is the limiting source of error for bright stars
(K < 15), while fainter sources will be limited by the effects of source
confusion. A detailed astrometric error budget for the Galactic center science
case is provided.
