Black holes hold a tremendous discovery potential, and experiments such as the Event Horizon Telescope and its next generation upgrade could provide important cues about their structure. New physics beyond general relativity can modify the structure of black holes and leave imprints on image features, for instance changing the separation between photon rings or generating additional sets of photon rings. Both cases motivate the study of the detectability of two rings in black hole images. In this talk, I will discuss: (1) the current knowledge about the structure of black holes beyond general relativity, (2) how image features could change due to new physics associated with this modified structure, and (3) the detectability of these features using closure quantities for various telescope arrays.