A three‐image algorithm is proposed to retrieve the sample's transmission, refraction and dark‐field information in hard X‐ray grating interferometry. Analytical formulae of the three‐image algorithm are theoretically derived and presented, and evaluated by proof‐of‐principle synchrotron radiation experiments. The results confirm the feasibility of the proposed algorithm. The novelty of the proposed algorithm is that it allows versatile and tunable multimodal X‐ray imaging by substantially relaxing the existing limitations on the lateral grating position. Furthermore, this algorithm can also be adapted for samples with negligible refraction, reducing the number of required sample measurements to two. Furthermore, the noise properties of the retrieved images are investigated in terms of the standard deviations. Theoretical models are presented and verified by synchrotron radiation measurements. It is shown that the noise standard deviations exhibit strong dependence on the lateral grating position, especially in the case of refraction and dark‐field images. Further noise reduction and dose reduction can thus be possible by optimizing the lateral grating position for a selected region of interest. Those results can serve as general guidelines to optimize the data acquisition scheme for specific applications and problems.

中文翻译：

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硬X射线光栅干涉仪中的透射，折射和暗场检索

提出了一种三图像算法来检索硬X射线光栅干涉仪中样品的透射，折射和暗场信息。理论上推导并给出了三​​图像算法的分析公式，并通过原理证明同步辐射实验进行了评估。结果证实了该算法的可行性。所提出算法的新颖之处在于，它可以通过实质上放宽对横向光栅位置的现有限制，实现通用且可调谐的多峰X射线成像。此外，该算法还可以适用于折射率可忽略不计的样本，从而将所需的样本测量数量减少到两个。此外，根据标准偏差对检索图像的噪声特性进行了研究。提出了理论模型，并通过同步加速器辐射测量进行了验证。结果表明，噪声标准偏差对横向光栅位置表现出很大的依赖性，特别是在折射和暗场图像的情况下。因此，通过针对所选感兴趣区域优化横向光栅位置，可以进一步降低噪声和降低剂量。这些结果可以用作一般准则，以针对特定应用和问题优化数据采集方案。因此，通过针对选定的感兴趣区域优化横向光栅位置，可以进一步降低噪声和降低剂量。这些结果可以用作一般准则，以针对特定应用和问题优化数据采集方案。因此，通过针对选定的感兴趣区域优化横向光栅位置，可以进一步降低噪声和降低剂量。这些结果可以用作一般准则，以针对特定应用和问题优化数据采集方案。