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.
X-ray mirrors with high focusing performances are in use in both mirror modules for X-ray telescopes and in synchrotron and FEL (Free Electron Laser) beamlines. A degradation of the focus sharpness arises in general from geometrical deformations and
surface roughness, the former usually described by geometrical optics and the latter by physical optics. In general, technological developments are aimed at a very tight focusing, which requires the mirror profile to comply with the nominal shape as much as possible and to keep the roughness at a negligible level. However, a deliberate deformation of the mirror can be made to endow the focus with a desired size and distribution, via piezo actuators as done at the EIS-TIMEX beamline of FERMI@Elettra. The resulting profile can be characterized with a Long Trace Profilometer and correlated with the expected optical quality via a wavefront propagation code. However, if the roughness contribution can be neglected, the computation can be performed via a ray-tracing routine, and, under opportune assumptions, the focal spot profile (the Point Spread Function, PSF) can even be predicted analytically. The advantage of this approach is that the analytical relation can be reversed; i.e, from the desired PSF the required mirror profile can be computed easily, thereby avoiding the use of complex and time-consuming numerical codes. The method can also be suited in the case of spatially inhomogeneous beam intensities, as commonly experienced at Synchrotrons and FELs. In this work we expose the analytical method and the application to the beam shaping problem.
