A mathematical apparatus for solving problems of X‐ray wave propagation through complex optical systems, when the lens thickness can change with jumps, is developed and presented. The developed method is based on the use of the superposition of oriented Gaussian beams, which satisfy the Helmholtz equation with high accuracy. The wave propagation in air and through kinoform and ordinary lenses is considered. Focusing and imaging properties are compared for both types of X‐ray optics. The diffraction effects arising due to thickness jumps in the kinoform lenses and the influence of these jumps on the X‐ray focusing and imaging are investigated. The prospect of using the developed theory for X‐ray optics applications is discussed.

中文翻译：

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硬X射线聚焦和折射光学的高精度计算

当透镜的厚度可以随跳变而变化时，开发并提出了一种解决X射线在复杂光学系统中传播问题的数学装置。所开发的方法是基于使用定向高斯光束的叠加，该高斯光束满足Helmholtz方程的高精度。考虑了空气中的波以及通过kinoform和普通透镜的波传播。比较了两种X射线光学器件的聚焦和成像特性。研究了由于在kinoform透镜中厚度跳变而引起的衍射效应，以及这些跳变对X射线聚焦和成像的影响。讨论了将开发的理论用于X射线光学应用的前景。