  Imaging a supermassive black hole and extracting physical information
requires good knowledge of both the gravitational and the astrophysical
conditions near the black hole. When the geometrical properties of the black
hole are well understood, extracting information on the emission properties is
possible. Similarly, when the emission properties are well understood,
extracting information on the black-hole geometry is possible. At present
however, uncertainties are present both in the geometry and in the emission,
and this inevitably leads to degeneracies in the interpretation of the
observations. We explore here the impact of varying geometry and emission
coefficient when modelling the imaging of a spherically-accreting black hole.
Adopting the Rezzolla-Zhidenko parametric metric to model arbitrary static
black-holes, we first demonstrate how shadow-size measurements leave
degeneracies in the multidimensional space of metric-deviation parameters, even
in the limit of infinite-precision measurements. Then, at finite precision, we
show that these degenerate regions can be constrained when multiple pieces of
information, such as the shadow-size and the peak image intensity contrast, are
combined. Such degeneracies can potentially be eliminated with measurements at
increased angular-resolution and flux-sensitivity. While our approach is
restricted to spherical symmetry and hence idealised, we expect our results to
hold also when more complex geometries and emission processes are considered.
