X射线相衬成像：一些基本原理的广泛概述
X-ray phase-contrast imaging: a broad overview of some fundamentals
摘要：
我们概述了一些基本的成像使用完全相干和部分相干的X射线束，强调相衬成像。我们开始与X射线成像的一些基本概念，包括真空波方程和复杂的标量场的强度和相位的物理意义。介绍了投影近似，以及衰减对比度和相位对比度的概念。我们还概述了通过厚样品或光学元件的X射线传播的多切片方法，以及菲涅耳缩放定理。在介绍了基本原理之后，我们考虑了正问题的几个方面，即模拟相衬X射线图像的形成。与这一正问题相关的几个主题被认为是，包括传输的强度方程，任意线性成像系统，平移不变的线性成像系统，传递函数形式主义，有限的源尺寸引起的模糊，部分相干场的空间-频率模型，和Fokker-Planck方程的近轴X射线成像。在考虑了这些手段建模的X射线相衬图像的形成，然后我们考虑相位恢复相关的逆问题的方面。这涉及如何解码相衬图像以获得关于样本引起的衰减和相移的信息。
英文摘要：
We outline some basics of imaging using both fully-coherent and partially-coherent X-ray beams, with an emphasis on phase-contrast imaging. We open with some of the basic notions of X-ray imaging, including the vacuum wave equations and the physical meaning of the intensity and phase of complex scalar fields. The projection approximation is introduced, together with the concepts of attenuation contrast and phase contrast. We also outline the multi-slice approach to X-ray propagation through thick samples or optical elements, together with the Fresnel scaling theorem. Having introduced the fundamentals, we then consider several aspects of the forward problem, of modelling the formation of phase-contrast X-ray images. Several topics related to this forward problem are considered, including the transport-of-intensity equation, arbitrary linear imaging systems, shift-invariant linear imaging systems, the transfer-function formalism, blurring induced by finite source size, the space-frequency model for partially-coherent fields, and the Fokker-Planck equation for paraxial X-ray imaging. Having considered these means for modelling the formation of X-ray phase-contrast images, we then consider aspects of the associated inverse problem of phase retrieval. This concerns how one may decode phase-contrast images to gain information regarding the sample-induced attenuation and phase shift.
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