  We show that it is possible to prepare and identify ultra--thin sheets of
graphene on crystalline substrates such as SrTiO$_3$, TiO$_2$, Al$_2$O$_3$ and
CaF$_2$ by standard techniques (mechanical exfoliation, optical and atomic
force microscopy). On the substrates under consideration we find a similar
distribution of single, bi- and few layer graphene and graphite flakes as with
conventional SiO$_2$ substrates. The optical contrast $C$ of a single graphene
layer on any of those substrates is determined by calculating the optical
properties of a two-dimensional metallic sheet on the surface of a dielectric,
which yields values between $C=$ ~- 1.5% (G/TiO$_2$) and $C=$ ~- 8.8%
(G/CaF$_2$). This contrast is in reasonable agreement with experimental data
and is sufficient to make identification by an optical microscope possible. The
graphene layers cover the crystalline substrate in a carpet-like mode and the
height of single layer graphene on any of the crystalline substrates as
determined by atomic force microscopy is $d_{SLG}=0.34$ nm and thus much
smaller than on SiO$_2$.
