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Black hole images are theoretically predicted (under mild astrophysicalassumptions) to display a stack of lensed "photon rings" that carry informationabout the underlying spacetime geometry. Despite vigorous efforts, no such ringhas been observationally resolved thus far. However, planning is now activelyunder way for space missions targeting the first (and possibly the second)photon rings of the supermassive black holes M87* and Sgr A*. In this work, westudy interferometric photon ring signatures in time-averaged images of Kerrblack holes surrounded by different astrophysical profiles. We focus on thefirst, most easily accessible photon ring, which has a larger width-to-diameterratio than subsequent rings and whose image consequently lacks a sharplydefined diameter. Nonetheless, we show that it does admit a preciseangle-dependent diameter in visibility space, for which the Kerr metricpredicts a specific functional form that tracks the critical curve. We findthat a measurement of this interferometric ring diameter is possible for mostastrophysical profiles, paving the way for precision tests of strong-fieldgeneral relativity via near-future observations of the first photon ring.

Prediction for the interferometric shape of the first black hole photon ring