  While dozens of stellar mass black holes have been discovered in binary
systems, isolated black holes have eluded detection. Their presence can be
inferred when they lens light from a background star. We attempt to detect the
astrometric lensing signatures of three photometrically identified microlensing
events, OGLE-2011-BLG-0022, OGLE-2011-BLG-0125, and OGLE-2012-BLG-0169
(OB110022, OB110125, and OB120169), located toward the Galactic Bulge. These
events were selected because of their long durations, which statistically
favors more massive lenses. Astrometric measurements were made over 1-2 years
using laser-guided adaptive optics observations from the W. M. Keck
Observatory. Lens model parameters were first constrained by the photometric
light curves. The OB120169 light curve is well-fit by a single-lens model,
while both OB110022 and OB110125 light curves favor binary-lens models. Using
the photometric fits as prior information, no significant astrometric lensing
signal was detected and all targets were consistent with linear motion. The
significant lack of astrometric signal constrains the lens mass of OB110022 to
0.05-1.79 Msun in a 99.7% confidence interval, which disfavors a black hole
lens. Fits to OB110125 yielded a reduced Einstein crossing time and
insufficient observations during the peak, so no mass limits were obtained. Two
degenerate solutions exist for OB120169, which have a lens mass between
0.2-38.8 Msun and 0.4-39.8 Msun for a 99.7% confidence interval. Follow-up
observations of OB120169 will further constrain the lens mass. Based on our
experience, we use simulations to design optimal astrometric observing
strategies and show that, with more typical observing conditions, detection of
black holes is feasible.
