  The primary optical caustic surface behind a Kerr black hole is a four-cusped
tube displaced from the line of sight. We derive the caustic surface in the
nearly asymptotic region far from the black hole through a Taylor expansion of
the lightlike geodesics up to and including fourth-order terms in m/b and a/b,
where $m$ is the black hole mass, a the spin and b the impact parameter. The
corresponding critical locus in the observer's sky is elliptical and a
point-like source inside the caustics will be imaged as an Einstein cross. With
regard to lensing near critical points, a Kerr lens is analogous to a circular
lens perturbed by a dipole and a quadrupole potential. The caustic structure of
the supermassive black hole in the Galactic center could be probed by lensing
of low mass X-ray binaries in the Galactic inner regions or by hot spots in the
accretion disk.
