Astrometric precision of observations at VLT/FORS2

In this paper we test the astrometric precision of VLT/FORS2 observations using a series of CCD frames taken in the Galactic bulge area. A special reduction method based on symmetrization of reference fields was used to reduce the atmospheric image motion. The positional precision of unsaturated R=16 mag star images at a 17 s exposure and 0.55 '' seeing was found to be equal to 300 mu as. The total error of observations was decomposed into components. It was shown that astrometric error depends mainly on the photon centroiding error of the target (250 mu as for 16 mag stars), while the image motion was much less (110 mu as). At galactic latitudes to about 20 degrees, precision for a series of frames with a 10 min total exposure was estimated to be 30-50 mu as for 14-16 mag stars, providing the images were not overexposed and the filter R-special was used. Error estimates for fields with smaller sky star density are given. We conclude that astrometric observations with large telescopes, under optimal reduction, are never atmospheric limited. The bias caused by differential chromatic refraction and the residual chromatism of LADC are considered and expressions that are valid for correcting color effects in the measured positions are given.