Recent progress in nanofabrication, namely of multilayer optics, and the construction of coherent hard x-ray sources has enabled high resolution x-ray microscopy with large numerical aperture optics for small focal spot sizes. Sub-10 nm and even sub-5 nm focal spot sizes have already been achieved using multilayer optics such as multilayer Laue lenses and multilayer zone plates. However these optics can not be described by the kinematic theory given their extreme aspect-ratio between the depth (thickness) and the layer width. Moreover, the numerical simulation of these optics is challenging, and the absence of an accessible numerical framework inhibits further progress in their design and utilization. Here, we simulate the propagation of x-ray wavefields within and behind optical multilayer elements using a finite-difference propagation method. We show that the method offers high accuracy at reasonable computational cost. We investigate how small focal spot sizes and highest diffraction efficiency of multilayer optics can be achieved, considering volume diffraction effects such as waveguiding and Pendellösung. Finally, we show the simulation of a novel imaging scheme, allowing for a detailed study of image formation and the development of customized phase retrieval schemes.

中文翻译：

---

用于模拟 X 射线多层光学器件的有限差分传播

纳米制造（即多层光学器件）的最新进展以及相干硬 X 射线源的构建使高分辨率 X 射线显微镜成为可能，该显微镜具有用于小焦斑尺寸的大数值孔径光学器件。使用多层光学器件（例如多层劳厄透镜和多层波带板）已经实现了亚 10 纳米甚至亚 5 纳米的焦斑尺寸。然而，考虑到它们在深度（厚度）和层宽之间的极端纵横比，这些光学无法通过运动学理论来描述。此外，这些光学器件的数值模拟具有挑战性，并且缺乏可访问的数值框架阻碍了它们的设计和利用的进一步进展。在这里，我们使用有限差分传播方法模拟 X 射线波场在光学多层元件内部和后面的传播。我们表明该方法以合理的计算成本提供了高精度。我们研究了如何实现多层光学器件的小焦斑尺寸和最高衍射效率，同时考虑到波导和 Pendellösung 等体积衍射效应。最后，我们展示了一种新型成像方案的模拟，允许对图像形成和定制相位检索方案的开发进行详细研究。