Effect of the surface roughness on X ray absorption by mirrors operating at extremely small grazing angles

This study theoretically analyzes an increase in X ray absorption by a grazing incidence mirror due to its surface roughness. We demonstrate that the increase in absorption can be several hundred times larger than predicted by the Nevot Croce formula. As a result, absorption enhances by several times compared to a perfectly smooth mirror despite the extremely small grazing angle of an incident X ray beam a fraction of the critical angle of the total external reflection and the high quality of the reflecting surface the roughness height was 0.5 nm in modeling . The main contribution to the absorption increase was dictated by the mid scale roughness waviness of the virgin substrate surface, whose quality thus defines an absorption enhancement. The approach was applied to the analysis of two real mirrors used in a synchrotron BESSY I and a European X ray free electron laser XFEL beamline. The modern surface finishing technology of elastic emission machining provides extremely low substrate waviness, guaranteeing the negligible effect of the surface roughness on the absorption increas