Promising achievements of resonance inelastic X‐ray scattering and other spectroscopy studies in the range from hard X‐ray to extreme ultraviolet require the development of exact tools for modeling energy characteristics of state‐of‐the‐art optical instruments for bright coherent X‐ray sources, space science, and plasma and superconductor physics. Accurate computations of the absorption and scattering intensity by structured interfaces in short wavelength ranges, i.e. realistic gratings, zone plates and mirrors, including multilayer‐coated, are not widely explored by the existing methods and codes, due to some limitations connected, primarily, with solving difficult problems at very small wavelength‐to‐period (or to correlation length) ratios and accounting for random roughness statistics. In this work, absorption integrals and scattering factors are derived from a rigorous solution of the vector Helmholtz equations based on the boundary integral equations and the Monte Carlo method. Then, using explicit formulae (in quadratures), the author finds the absorption and scattering intensity of one‐ and bi‐periodic gratings and mirrors, which may have random roughnesses. Examples of space and spectral power distributions for gratings and mirrors working in X‐rays are compared with those derived using the usual indirect approach and well known approximations.

中文翻译：

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X射线中结构化界面的吸收和散射

从硬X射线到极紫外的共振非弹性X射线散射和其他光谱学研究取得了令人鼓舞的成就，这需要开发精确的工具来建模用于明亮相干X射线的最新光学仪器的能量特性来源，空间科学以及等离子和超导体物理学。在短波长范围内，即结构化界面对吸收和散射强度的准确计算由于存在一些局限性，主要是在很小的波长周期内（或相关长度上）解决难题，因此，现有方法和规范并未广泛地探索现实的光栅，波带片和反射镜，包括多层涂层的光栅比率并考虑随机粗糙度统计信息。在这项工作中，基于边界积分方程和蒙特卡洛方法，从矢量亥姆霍兹方程的严格解中得出了吸收积分和散射因子。然后，作者使用显式（正交），求出一周期和二周期光栅和反射镜的吸收和散射强度，它们可能具有随机粗糙度。