Astrometry with MCAO at Gemini and at ELTs

We present in this study a first analysis of the astrometric error budget of absolute astrometry relative to back- ground galaxies using adaptive optics. We use for this analysis multi-conjugated adaptive optics (MCAO) images obtained with GeMS/GSAOI at Gemini South. We find that it is possible to obtain 0.3 mas reference precision in a random field with 1 hour on source using faint background galaxies. Systematic errors are correctable below that level, such that the overall error is approximately 0.4 mas. Because the reference sources are extended, we find it necessary to correct for the dependency of the PSF centroid on the used aperture size, which would oth- erwise cause an important bias. This effect needs also to be considered for Extremely Large Telescopes (ELTs). When this effect is corrected, ELTs have the potential to measure proper motions of dwarfs galaxies around M31 with 10 km/s accuracy over a baseline of 5 years