In this work, we developed a new theoretical framework using wave optics to explain the working mechanism of the grating based X-ray differential phase contrast imaging (XPCI) interferometer systems consist of more than one phase grating. Under the optical reversibility principle, the wave optics interpretation was simplified into the geometrical optics interpretation, in which the phase grating was treated as a thin lens. Moreover, it was derived that the period of an arrayed source, e.g., the period of a source grating, is always equal to the period of the diffraction fringe formed on the source plane. When a source grating is utilized, the theory indicated that it is better to keep the periods of the two phase gratings different to generate large period diffraction fringes. Experiments were performed to validate these theoretical findings.

中文翻译：

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基于双相光栅的带源光栅的X射线微分相衬成像：理论与验证

在这项工作中，我们开发了一种使用波光学的新理论框架，以解释基于光栅的X射线差分相衬成像（XPCI）干涉仪系统的工作机理，该系统由多个相位光栅组成。在光学可逆性原理下，将波光学解释简化为几何光学解释，其中将相位光栅视为薄透镜。此外，得出的是，排列的源的周期，例如源光栅的周期，总是等于在源平面上形成的衍射条纹的周期。当使用源光栅时，该理论表明，最好使两个相位光栅的周期保持不同，以产生大周期的衍射条纹。进行实验以验证这些理论发现。