  Black holes hold a tremendous discovery potential. In this paper the extent
to which the Event Horizon Telescope and its next generation upgrade can
resolve their structure is quantified. Black holes are characterized by a
perfectly absorptive boundary, with a specific area determined by intrinsic
parameters of the black hole. We use a general parametrization of spherically
symmetric spacetimes describing deviations from this behavior, with parameters
controlling the size of the central object and its interaction with light, in
particular through a specular reflection coefficient $\Gamma$ and an intrinsic
luminosity measured as a fraction $\eta$ of that of the accretion disc. This
enables us to study exotic compact objects and compare them with black holes in
a model-independent manner. We determine the image features associated with the
existence of a surface in the presence of a geometrically thin and optically
thick accretion disc, identifying requirements for VLBI observations to be able
to cast meaningful constraints on these parameters, in particular regarding
angular resolution and image dynamic range. For face-on observations,
constraints of order $\eta\lesssim 10^{-4}, \Gamma\lesssim 10^{-1}$ are
possible with an enhanced EHT array, imposing strong constraints on the nature
of the central object.
