Atmospheric limitations of narrow-field optical astrometry

The influence of refraction anomalies on optical differential astrometry is analyzed by means of a simple model of the large-scale wavefront distortion caused by atmospheric turbulence. The few model parameters are determined from the empirical power spectrum of image motion and meteorological data. It is found that the mean error of the measured angle theta (rad) between two objects near zenith is 1.3 arcsec theta to the 0.25th T to the -0.5th, where T much greater than 300 theta is the integration time in seconds. This is consistent with observed apparent fluctuations of the solar diameter. If the position of a star is measured relative to the centroid of several reference stars within a radius R(rad), the mean error in each coordinate is 0.8 arcsec R to the 0.25th T to the -0.5th or 0.003 arcsec for R = 10 arcmin and T = 1 h.