  Interferometers offer multiple methods for studying microlensing events and
determining the properties of the lenses. We investigate the study of
microlensing events with optical interferometers, focusing on narrow-angle
astrometry, visibility, and closure phase. After introducing the basics of
microlensing and interferometry, we derive expressions for the signals in each
of these three channels. For various forecasts of the instrumental performance,
we discuss which method provides the best means of measuring the lens angular
Einstein radius theta_E, a prerequisite for determining the lens mass. If the
upcoming generation of large-aperture, AO-corrected long baseline
interferometers (e.g. VLTI, Keck, OHANA) perform as well as expected, theta_E
may be determined with signal-to-noise greater than 10 for all bright events.
We estimate that roughly a dozen events per year will be sufficiciently bright
and have long enough durations to allow the measurement of the lens mass and
distance from the ground. We also consider the prospects for a VLTI survey of
all bright lensing events using a Fisher matrix analysis, and find that even
without individual masses, interesting constraints may be placed on the bulge
mass function, although large numbers of events would be required.
