  The ``screen mapping" introduced by Susskind to implement 't Hooft's
holographic hypothesis is studied. For a single screen time, there are an
infinite number of images of a black hole event horizon, almost all of which
have smaller area on the screen than the horizon area. This is consistent with
the focusing equation because of the existence of focal points. However, the
{\it boundary} of the past (or future) of the screen obeys the area theorem,
and so always gives an expanding map to the screen, as required by the
holographic hypothesis. These considerations are illustrated with several
axisymmetric static black hole spacetimes.
