  We systematically investigate the error sources for high-precision astrometry
from adaptive optics based near-infrared imaging data. We focus on the
application in the crowded stellar field in the Galactic Center. We show that
at the level of <=100 micro-arcseconds a number of effects are limiting the
accuracy. Most important are the imperfectly subtracted seeing halos of
neighboring stars, residual image distortions and unrecognized confusion of the
target source with fainter sources in the background. Further contributors to
the error budget are the uncertainty in estimating the point spread function,
the signal-to-noise ratio induced statistical uncertainty, coordinate
transformation errors, the chromaticity of refraction in Earth's atmosphere,
the post adaptive optics differential tilt jitter and anisoplanatism. For stars
as bright as mK=14, residual image distortions limit the astrometry, for
fainter stars the limitation is set by the seeing halos of the surrounding
stars. In order to improve the astrometry substantially at the current
generation of telescopes, an adaptive optics system with high performance and
weak seeing halos over a relatively small field (r<=3") is suited best.
Furthermore, techniques to estimate or reconstruct the seeing halo could be
promising.
