Background-field effects in astrometric microlensing

We consider the motion of the image of a distant radiation source microlensed by one and many point masses in the presence of an external background field, which produces a shear in the lens equation. The trajectories of the image brightness centroid (BC) in a Chang-Refsdal lens are very sensitive to the magnitude of the shear and to the direction of motion of the microlenses, allowing these parameters to be unambiguously determined from the BC motion. Stochastic motions of the BC for an extended source are simulated in a problem with a large number of randomly arranged microlenses. We derive dependences of the root-mean-square variations in BC velocity on microlense density, on external shear, and on the continuous component of the mass density, which may be related to dark matter in extragalactic lenses.