  To enhance the reflectivity of X-ray mirrors beyond the critical angle,
multilayer coatings are required. Interface imperfections in the multilayer
growth process are known to cause non-specular scattering and degrade the
mirror optical performance; therefore, it is important to predict the amount of
X-ray scattering from the rough topography of the outer surface of the coating,
which can be directly measured, e.g., with an Atomic Force Microscope (AFM).
This kind of characterization, combined with X-ray reflectivity measurements to
assess the deep multilayer stack structure, can be used to model the layer
roughening during the growth process via a well-known roughness evolution
model. In this work, X-ray scattering measurements are performed and compared
with simulations obtained from the modeled interfacial Power Spectral Densities
(PSDs) and the modeled Crossed Spectral Densities for all the couples of
interfaces. We already used this approach in a previous work for periodic
multilayers; we now show how this method can be extended to graded multilayers.
The upgraded code is validated for both periodic and graded multilayers, with a
good accord between experimental data and model findings. Doing this, different
kind of defects observed in AFM scans are included in the PSD analysis. The
subsequent data-model comparison enables us to recognize them as surface
contamination or interfacial defects that contribute to the X-ray scattering of
the multilayer.
