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.