Applying the Fokker-Planck equation to grating-based x-ray phase and dark-field imaging
Applying the Fokker-Planck equation to grating-based x-ray phase and dark-field imaging
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DOI：
10.1038/s41598-019-52283-6
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发表时间：
2019-11-25
影响因子：
4.6
通讯作者：
Paganin, David M.
中科院分区：
文献类型：
--
作者：
Morgan, Kaye S.;Paganin, David M.
X射线成像通常依赖于衰减来提供对比度。近年来，增加了两种互补的模式;（a）相位对比，其可以捕获使用衰减难以看到的低密度样品，以及（B）暗场X射线成像，其揭示亚像素样品结构的存在。这三种模式可以使用晶体分析仪，光栅干涉仪或通过观察直接分辨的网格，光栅或斑点图案来访问。光栅和基于网格的方法通过测量照明中的特征由于样本的存在而横向移位多远来提取差分相位信号。暗场信号通过测量结构化照明的可见度如何降低来提取，这通常是由于样本中存在子像素结构。暗场信号的强度可以取决于光栅周期、像素尺寸和设置距离，并且附加的暗场信号贡献可以被看作是强相位效应或其他因素的结果。在本文中，我们表明，有限差分形式的福克-普朗克方程可以应用于描述的漂移（相位信号）和扩散（暗场信号）的周期性或结构化的照明用于相位衬度X射线成像与光栅，为了更好地理解任何衰减，相位和暗场X射线信号之间的串扰。在未来的工作中，这种数学描述可以被用来作为新的方法的基础上恢复相位和暗场信息的逆问题。
X-ray imaging has conventionally relied upon attenuation to provide contrast. In recent years, two complementary modalities have been added; (a) phase contrast, which can capture low-density samples that are difficult to see using attenuation, and (b) dark-field x-ray imaging, which reveals the presence of sub-pixel sample structures. These three modalities can be accessed using a crystal analyser, a grating interferometer or by looking at a directly-resolved grid, grating or speckle pattern. Grating and grid-based methods extract a differential phase signal by measuring how far a feature in the illumination has been shifted transversely due to the presence of a sample. The dark-field signal is extracted by measuring how the visibility of the structured illumination is decreased, typically due to the presence of sub-pixel structures in a sample. The strength of the dark-field signal may depend on the grating period, the pixel size and the set-up distances, and additional dark-field signal contributions may be seen as a result of strong phase effects or other factors. In this paper we show that the finite-difference form of the Fokker-Planck equation can be applied to describe the drift (phase signal) and diffusion (dark-field signal) of the periodic or structured illumination used in phase contrast x-ray imaging with gratings, in order to better understand any cross-talk between attenuation, phase and dark-field x-ray signals. In future work, this mathematical description could be used as a basis for new approaches to the inverse problem of recovering both phase and dark-field information.