The accuracy of differential astrometry limited by the atmospheric turbulence

In differential astrometry from the ground, the random motion of a stellar image due to atmospheric turbulence is a main source of error. Lindegren (1980) derived the astrometric accuracy as a function of the integration time and the field size. In this paper, data obtained from the MAP (Multichannel Astrometric Photometer, Gatewood 1987), are obtained and compared with Lindegren's predictions. The data show that sigma, the standard error of the differential image motion, for modest seeing is well approximated by S.E. (mas) = 140 (S/10 arcmin) exp 0.32/sq rt(T), for T of much greater than 10 s, where S is the separation between two stars, T is the integration time in seconds, and arcmin and mas are used for arcminute and milliarc-second, respectively.