  If a gravitational microlensing event is caused by a widely separated binary
lens and the source approaches both lens components, the source flux is
successively magnified by the individual lenses: double microlensing events. If
events are observed astrometrically, double lensing events are expected to
occur with an increased frequency due to the long range astrometric effect of
the companion. We find that although the trajectory of the source star image
centroid shifts of an astrometric double lensing event has a distorted shape
from both of the elliptical ones induced by the individual single lens
components, event duplication can be readily identified by the characteristic
loop in the trajectory formed during the source's passage close to the
companion. We determine and compare the probabilities of detecting double
lensing events from both photometric and astrometric lensing observations by
deriving analytic expressions for the relations between binary lensing
parameters to become double lensing events. From this determination, we find
that for a given set of the binary separation and the mass ratio the
astrometric probability is roughly an order higher than the photometric
probability. Therefore, we predict that a significant fraction of events that
will be followed up by using future high precision interferometeric instruments
will be identified as double lensing events.
