Interferometric signature of higher-order images in a parametrized framework

This paper investigates gravitational lensing in the strong deflection limit, focusing particularly on higher-order images produced near compact objects such as black holes and their observable impact through the visibility function. Employing a robust parametrization framework proposed by Rezzolla and Zhidenko, the study systematically explores deviations from the Schwarzschild metric. A detailed theoretical analysis of interferometric observables is provided, highlighting how higher-order images imprint distinctive, measurable patterns in the visibility function, notably characterized by a staircaselike structure. By parametrically varying metric coefficients, the analysis reveals clear dependencies between spacetime deviations and key observational signatures, specifically the step heights and periodicities in the interferometric visibility. The results enhance the theoretical groundwork for interpreting data from advanced interferometric observations, potentially enabling precise tests of general relativity and the discrimination among alternative gravitational theories.