Interferometric signatures of black holes with multiple photon spheres

It has been reported that the photon ring structure in black hole images produces strong and universal interferometric signatures on long interferometric baselines, holding promise for measuring black hole parameters and testing general relativity. This paper investigates the interferometric signatures of black holes with one or two photon spheres, specifically within the framework of Einstein-Maxwell-scalar models. Notably, for black holes possessing two photon spheres, interference between light rays orbiting the inner and outer photon spheres manifests as beat signals in the visibility amplitude, deviating from the universal signatures observed in the single-photon sphere case.