  X-ray observations suggest high compactness of coronae in active galactic
nuclei as well as in X-ray binaries. The compactness of the source implies a
strong radial dependence in the illumination of the accretion disc. This will,
for any reasonable radial profile of the density, lead to a radial profile of
the disc ionisation. Svoboda et al. (2012) showed on a single example that
assuming a radially-structured ionisation profile of the disc can cause an
artificial increase of the radial-emissivity parameter. We further investigate
how the X-ray spectra are modified and quantify this effect for a wide range of
parameters. Computations are carried out with the current state-of-the-art
models for relativistic reflection. We simulated spectra using the response
files of the micro-calorimeter X-IFU, which is planned to be on board of
Athena. We assumed typical parameters for X-ray bright Seyfert-1 galaxies and
considered two scenarios for the disc ionisation: 1) a radial profile for the
disc ionisation, 2) a constant disc ionisation. We found that steep emissivity
profiles can be indeed achieved due to the radial profile of the disc
ionisation, which becomes more important for the cases where the corona is
located at low heights above the black hole and this effect may be even more
prominent than the geometrical effects. We also found that the cases with high
inner disc ionisation, rapidly decreasing with radius, may result in an
inaccurate black hole spin measurements.
