  Recent interferometric observations by the Event Horizon Telescope have
resolved the horizon-scale emission from sources in the vicinity of nearby
supermassive black holes. Future space-based interferometers promise to measure
the "photon ring"--a narrow, ring-shaped, lensed feature predicted by general
relativity, but not yet observed--and thereby open a new window into strong
gravity. Here we present AART: an Adaptive Analytical Ray-Tracing code that
exploits the integrability of light propagation in the Kerr spacetime to
rapidly compute high-resolution simulated black hole images, together with the
corresponding radio visibility accessible on very long space-ground baselines.
The code samples images on a nonuniform adaptive grid that is specially
tailored to the lensing behavior of the Kerr geometry and is therefore
particularly well-suited to studying photon rings. This numerical approach
guarantees that interferometric signatures are correctly computed on long
baselines, and the modularity of the code allows for detailed studies of
equatorial sources with complex emission profiles and time variability. To
demonstrate its capabilities, we use AART to simulate a black hole movie of a
stochastic, non-stationary, non-axisymmetric equatorial source; by
time-averaging the visibility amplitude of each snapshot, we are able to
extract the projected diameter of the photon ring and recover the shape
predicted by general relativity.
