  In current microlensing experiments, the information about the physical
parameters of individual lenses are obtained from the Einstein timescales.
However, the nature of MACHOs is still very uncertain despite the large number
of detected events. This uncertainty is mainly due to the degeneracy of the
lens parameters in the measured Einstein timescales. The degeneracy can be
lifted in a general fashion if the angular Einstein ring radius $\theta_{\rm
E}$, and thus the MACHO proper motion, can be measured by conducting accurate
astrometric measurements of centroid displacement in the source star image.
  In this paper, we analyze the influence of bright lenses on the astrometric
measurements of the centroid displacement and investigate this effect on the
determination of $\theta_{\rm E}$. We find that if an event is caused by a
bright lens, the centroid displacement is distorted by the flux of the lens and
resulting astrometric ellipse becomes rounder and smaller with increasing lens
brightness, causing an incorrect determination of the angular Einstein ring
radius. A lens-blended event cannot be distinguished from a dark lens event
from the trajectory of the measured centroid displacements alone because both
events have elliptical trajectories: the degeneracy between dark and bright
lens events. We also find that even with information from the analysis of the
light curve of the event it will still be difficult to resolve the degeneracy
caused by the bright lens because the light curve is also affected by lens
blending.
