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Depth-graded multilayer mirrors for the hard x-ray spectral region: theory and inverse and direct problems

机译：硬X射线光谱区域的深度渐变多层反射镜：理论以及反问题和直接问题

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Abstract: A new approach is proposed for the design of wide band-pass multilayer optical elements for 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. First, assuming the multilayer d-spacing profile to be a monotone function of the depth and the d- spacing gradient to be large enough, we derived the differential equation that describes the change of period necessary to guarantee a given spectral reflectivity profile. Then, a computer code using an algorithm of steepest descent was used to refine numerically the multilayer period profile, each layer thickness being treated as an independent variable. When using the solution to the differential equation as a starting point of the direct problem, a many-fold decrease of computer time could be obtained. At each step, the spectral dependence of reflectivity was accurately computed using a standard matrix method. Simulations of the particular case of constant reflectivity and maximum integrated reflectivity over a wide spectral range are presented. The best choice of material pairs for comprising 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. !28
机译：摘要：提出了一种新的方法来设计用于硬X射线光谱区域的宽带通多层光学元件。该方法基于分析方法和数值方法的组合，解决了反问题，该问题包括推断深度渐变多层涂层的组成轮廓。首先，假设多层d间距轮廓是深度的单调函数，并且d间距梯度足够大，我们导出了描述需要保证给定光谱反射率轮廓的周期变化的微分方程。然后，使用使用最速下降算法的计算机代码对数字化的多层周期轮廓进行数字化细化，将每个层的厚度视为一个自变量。当使用微分方程的解作为直接问题的起点时，可以节省很多时间的计算机时间。在每个步骤中，均使用标准矩阵方法精确计算反射率的光谱依赖性。给出了在宽光谱范围内恒定反射率和最大积分反射率的特殊情况的仿真。从可获得的最大反射率和双层数最少的观点出发，讨论了用于构成深度渐变多层结构的材料对的最佳选择。研究了与常规周期镜不同的深度渐变多层镜的功能。 ！28

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