Graetz Jonas
Universität Würzburg, Lehrstuhl für Röntgenmikroskopie, Würzburg, Germany.
Fraunhofer IIS, Magentic Resonance and X-ray Imaging Department, Würzburg, Germany.
Sci Rep. 2021 Sep 16;11(1):18477. doi: 10.1038/s41598-021-97389-y.
Tensor tomography is fundamentally based on the assumption of a both anisotropic and linear contrast mechanism. While the X-ray or neutron dark-field contrast obtained with Talbot(-Lau) interferometers features the required anisotropy, a preceding detailed study of dark-field signal origination however found its specific orientation dependence to be a non-linear function of the underlying anisotropic mass distribution and its orientation, especially challenging the common assumption that dark-field signals are describable by a function over the unit sphere. Here, two approximative linear tensor models with reduced orientation dependence are investigated in a simulation study with regard to their applicability to grating based X-ray or neutron dark-field tensor tomography. By systematically simulating and reconstructing a large sample of isolated volume elements covering the full range of feasible anisotropies and orientations, direct correspondences are drawn between the respective tensors characterizing the physically based dark-field model used for signal synthesization and the mathematically motivated simplified models used for reconstruction. The anisotropy of freely rotating volume elements is thereby confirmed to be, for practical reconstruction purposes, approximable both as a function of the optical axis' orientation or as a function of the interferometer's grating orientation. The eigenvalues of the surrogate models' tensors are found to exhibit fuzzy, yet almost linear relations to those of the synthesization model. Dominant orientations are found to be recoverable with a margin of error on the order of magnitude of 1[Formula: see text]. Although the input data must adequately address the full orientation dependence of dark-field anisotropy, the present results clearly support the general feasibility of quantitative X-ray dark-field tensor tomography within an inherent yet acceptable statistical margin of uncertainty.
张量断层扫描基本上基于各向异性和线性对比度机制的假设。虽然用塔尔博特（-劳）干涉仪获得的X射线或中子暗场对比度具有所需的各向异性，但之前对暗场信号起源的详细研究发现，其特定的方向依赖性是潜在各向异性质量分布及其方向的非线性函数，这尤其挑战了暗场信号可由单位球面上的函数描述这一常见假设。在此，在一项模拟研究中，研究了两种方向依赖性降低的近似线性张量模型，以探讨它们在基于光栅的X射线或中子暗场张量断层扫描中的适用性。通过系统地模拟和重建大量孤立体积元素样本，涵盖可行各向异性和方向的全范围，在表征用于信号合成的基于物理的暗场模型的各个张量与用于重建的数学驱动简化模型之间建立了直接对应关系。由此证实，对于实际重建目的，自由旋转体积元素的各向异性既可以近似为光轴方向的函数，也可以近似为干涉仪光栅方向的函数。发现替代模型张量的特征值与合成模型的特征值呈现模糊但几乎线性的关系。发现主导方向能够以约1[公式：见正文]数量级的误差范围恢复。尽管输入数据必须充分考虑暗场各向异性的全方向依赖性，但目前的结果明确支持了在固有但可接受的统计不确定性范围内进行定量X射线暗场张量断层扫描的总体可行性。
