  Microlensing events are now regularly being detected by monitoring the flux
of a large number of potential sources and measuring the combined magnification
of the images. This phenomenon could also be detected directly from the
gravitational deflection, by means of high precision astrometry using
interferometry. Relative astrometry at the level of $10\muas$ may become
possible in the near future. The gravitational deflection can be measured by
astrometric monitoring of a bright star having a background star within a small
angular separation. This type of monitoring program will be carried out for the
independent reasons of discovering planets from the angular motion they induce
on the nearby star around which they are orbiting, and for measuring
parallaxes, proper motions and orbits of binary stars. We discuss three
applications of the measurement of gravitational deflections by astrometric
monitoring: measuring the mass of the bright stars that are monitored,
measuring the mass of brown dwarfs or giant planets around the bright stars,
and detecting microlensing events by unrelated objects near the line of sight
to the two stars. We discuss the number of stars whose mass could be measured
by this procedure. We also give expressions for the number of expected
microlensing events by unrelated objects, which could be stars, brown dwarfs,
or other compact objects accounting for dark matter in the halo or in the disk.
