Abstract
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.
Highlights
High-resolution hard x-ray imaging relies on optics with depths ranging from several micrometers for diffractive optics up to centimeters for reflective or refractive optics
We showed that the finite-difference propagation (FD) approach is well-suited for numerical wavefield propagation through multilayer optics with large aspect-ratios of layer width to depth
The latter phenomenon is well known as Pendellösung from the analytical theory of dynamical diffraction
Summary
High-resolution hard x-ray imaging relies on optics with depths ranging from several micrometers for diffractive optics up to centimeters for reflective or refractive optics. The depths are many orders of magnitude higher than the wavelength λ, resulting from the rather low interaction compared to other spectral ranges, notably visible light This is the case for compound refractive lenses (CRL), reaching sub-50 nm focal sizes [1], waveguide (WG) optics, which most recently reached sub-15 nm resolution in holographic full-field imaging [2], as well as for multilayer optics, with focus sizes below 10 nm [3,4,5] and high focusing efficiencies [6,7].
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