The reflected radiation from a black-hole accretion disc illuminated by a corona above is computed using the Monte Carlo radiative transfer code STOKES. The structure of the disc, modelled as a constant density slab, has been computed with the TITAN code for optically thick and hot photo-ionized media.
The resulting simulated spectra locally emitted by the accretion disc are compared to the results obtained by various, published radiative transfer codes. In addition to these, the STOKES code provides also the polarization degree and polarization position angle of the outcoming radiation.
Further, we use the relativistic code KYNSTOKES based on our well-tested relativistic KY package to account for all relativistic effects on radiation near a black hole and to compute the total disc emission for two different coronal geometries. It is then possible to predict X-ray spectral and polarization properties of the inner parts of compact accreting sources and their dependence on various parameters of the system, such as spin of the black hole, ionization of the accretion disc, observer inclination.