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The shape of the angular and spectral reflection curves of depth-graded x-ray multilayer mirrors may be controlled by the proper variation of the layer thicknesses. The determination of the thickness distribution of the layers that gives the best possible approximation to the desired reflection curve profile is a complicated mathematical problem. The present work reports on the application of the needle variations method to the design of graded x-ray multilayer mirrors in both angular and spectral domain.
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Vladimir V. Protopopov, Alexander V. Tikhonravov, Andrei V. Voronov, Michael K. Trubetskov, Gary W. DeBell, "Optimal design of graded x-ray multilayer mirrors in the angular and spectral domains," Proc. SPIE 3766, X-Ray Optics, Instruments, and Missions II, (29 September 1999); https://doi.org/10.1117/12.363645