  Interpreting horizon-scale observations of astrophysical black holes demands
a general understanding of null geodesics in the Kerr spacetime. These may be
divided into two classes: "direct" rays that primarily determine the
observational appearance of a given source, and highly bent rays that produce a
nested sequence of exponentially demagnified images of the main emission: the
so-called "photon ring". We develop heuristics that characterize the direct
rays and study the highly bent geodesics analytically. We define three critical
parameters $\gamma$, $\delta$, and $\tau$ that respectively control the
demagnification, rotation, and time delay of successive images of the source,
thereby providing an analytic theory of the photon ring. These observable
parameters encode universal effects of general relativity, independent of the
details of the emitting matter.
