Design of X-ray supermirrors

A new approach is proposed for the design of wide band-pass multilayer optical elements operating in the hard X-ray spectral region. The method, based on the combination of analytical and numerical methods, solves the inverse problem consisting of inferring the composition profile of a depth-graded multilayer coating. The key feature of our approach consists in using an analytical expression for the depth-distribution of the period as initial solution for direct computer calculations. This allows a global minimization of the merit function and a many-fold decrease of the computer run time. Simulations of two particular cases are presented: a constant reflectivity over a wide spectral range and a complicated reflectivity profile. The best choice of material pairs for composing a depth-graded multilayer structure is discussed from the viewpoint of maximum achievable reflectivity and least number of bi-layers. Features of depth-graded multilayer mirrors, which are distinctive from conventional periodic mirrors, are examined. The factors influencing the optical quality of broad-band multilayers are also considered.