Recent progress in the design and the manufacturing of wide bandpass x-ray multilayers has opened up new possibilities in hard x-ray optics, particularly in astrophysics and synchrotron x-ray applications.
In contrast to previous design based on semi-empirical laws or extensive computer calculation, the recent development of an analytical expression has greatly improved the design of aperiodic multilayer mirrors, allowing to generate any given spectral dependence of the reflectivity. In practice, an approximate differential equation is used to derive an in-depth multilayer composition profile whose reflectivity response approaches the desired one. Based on this asymptotic solution, usually sufficiently close to the final solution, the optimum multilayer composition profile is calculated numerically using a classical downhill algorithm.
We have studied the intrinsic characteristics of depth-graded multilayers using the procedure described above, with an emphasis put on the important case of a flat reflectivity response over a large but limited spectral range. The performance of depth-graded multilayer mirrors manufactured at ESRF and characterized at the BM5 beamline are presented. The necessity to account at the design level for deposition process parameters, such as chemical composition and thickness errors, and for the effective optical constants is highlighted.