  Recent observations indicate that many if not all galaxies host massive
central black holes (BHs). In this paper we explore the influence of
supermassive binary black holes (SMBBHs) on their actions as gravitational
lenses. When lenses are modelled as singular isothermal ellipsoids, binary
black holes change the critical curves and caustics differently as a function
of distance. Each black hole can in principle create at least one additional
image, which, if observed, provides evidence of black holes. By studying how
SMBBHs affect the cumulative distribution of magnification for images created
by black holes, we find that the cross section for at least one such additional
image to have a magnification larger than $10^{-5}$ is comparable to the cross
section for producing multiple-images in singular isothermal lenses. Such
additional images may be detectable with high-resolution and large dynamic
range maps of multiply-imaged systems from future facilities, such as the SKA.
The probability of detecting at least one image (two images) with magnification
above $10^{-3}$ is $\sim 0.2 \fBH$ ($\sim 0.05 \fBH$) in a multiply-imaged lens
system, where $\fBH$ is the fraction of galaxies housing binary black holes. We
also study the effects of SMBBHs on the core images when galaxies have
shallower central density profiles (modelled as non-singular isothermal
ellipsoids). We find that the cross section of the usually faint core images is
further suppressed by SMBBHs. Thus their presence should also be taken into
account when one constrains the core radius from the lack of central images in
gravitational lenses.
