  When a source star is gravitationally microlensed by a dark lens, the
centroid of the source star image is displaced relative to the position of the
unlensed source star with an elliptical trajectory. Recently, routine
astrometric follow-up measurements of these source star image centroid shifts
by using high precision interferometers are proposed to measure the lens proper
motion which can resolve the lens parameter degeneracy in the photometrically
determined Einstein time scale. When an event is caused by a bright lens, on
the other hand, the astrometric shift is affected by the light from the lens,
but one cannot identify the existence of the bright lens from the observed
trajectory because the resulting trajectory of the bright lens event is also an
ellipse. As results, lensing parameters determined from the trajectory differ
from those of a dark lens event, causing wrong identification of lens
population. In this paper, we show that although the shape and size of the
astrometric centroid shift trajectory are changed due to the bright lens, the
angular speed of centroid shifts around the apparent position of the unlensed
source star is not affected by the lens brightness. Then, one can identify the
existence of the bright lens and determine its brightness by comparing the lens
parameters determined from the angular speed curve with those determined from
the trajectory of observed centroid shifts. Once the lens brightness is
determined, one can correct for the lens proper motion. Since the proposed
method provides both information about the lens brightness (dark or bright) and
the corrected values of the physical parameters of the lens, one can
significantly better constrain the nature of MACHOs.
