A theoretical framework is proposed for simultaneous reconstruction of the three-dimensional grain shapes, intragranular strain and orientation fields inside polycrystals from near-field X-ray diffraction images, using box beam illumination. The approach, named Iterative Tensor Field (ITF) reconstruction, uses a tensor field representation and a kinematical forward simulation model to reproduce the measured diffraction signal from individual grains. The framework establishes a link between the local deformation components inside the grains and the intensities of the diffraction signal in the measured images by forming a local linear problem. This is solved using a large scale linear optimisation method in every main iteration of the underlying non-linear problem. The optimisation enforces smooth gradients and the objective function may include regularisation constraints of static equilibrium or input from a Crystal Plasticity FEM simulation. The method has modest computational requirements and enables efficient scanning of millimetre or sub-millimetre sized specimens. Results on experimental data measured on a Gum metal specimen are presented, which demonstrate convergence and the feasibility of the approach. The mathematical formulation, data representation and challenges in the reconstruction and validation are discussed. The physical aspects of the contrast phenomenon, the deformation sensitivity of the technique, and potential means of error assessment are described. A number of alternative concepts for a polycrystalline deformation model and potential solvers are also presented.

提出了一个理论框架，利用箱形光束照明，从近场X射线衍射图像中同时重建多晶内部的三维晶粒形状，晶内应变和取向场。该方法称为迭代张量场（ITF）重建，它使用张量场表示和运动学前向仿真模型从单个晶粒中再现测量的衍射信号。该框架通过形成局部线性问题，在晶粒内部的局部变形分量与测量图像中的衍射信号强度之间建立了联系。在基础非线性问题的每个主要迭代中，使用大规模线性优化方法可以解决此问题。该优化强制执行平滑的梯度，并且目标函数可能包括静态平衡的正则化约束条件或来自Crystal Plasticity FEM仿真的输入。该方法具有适度的计算要求，并且能够有效扫描毫米或亚毫米大小的样本。给出了在口香糖金属样品上测量的实验数据的结果，这些结果证明了该方法的收敛性和可行性。讨论了数学公式，数据表示以及重建和验证中的挑战。描述了对比度现象的物理方面，技术的变形敏感性以及错误评估的潜在手段。还介绍了用于多晶变形模型和势能求解器的许多替代概念。