Strain engineering is used to obtain desirable materials properties in a range of modern technologies. Direct nanoscale measurement of the three-dimensional strain tensor field within these materials has however been limited by a lack of suitable experimental techniques and data analysis tools. Scanning electron diffraction has emerged as a powerful tool for obtaining two-dimensional maps of strain components perpendicular to the incident electron beam direction. Extension of this method to recover the full three-dimensional strain tensor field has been restricted though by the absence of a formal framework for tensor tomography using such data. Here, we show that it is possible to reconstruct the full non-symmetric strain tensor field as the solution to an ill-posed tensor tomography inverse problem. We then demonstrate the properties of this tomography problem both analytically and computationally, highlighting why incorporating precession to perform scanning precession electron diffraction may be important. We establish a general framework for non-symmetric tensor tomography and demonstrate computationally its applicability for achieving strain tomography with scanning precession electron diffraction data.

中文翻译：

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应变的扫描电子衍射断层扫描

应变工程用于在一系列现代技术中获得理想的材料特性。然而，由于缺乏合适的实验技术和数据分析工具，对这些材料内的三维应变张量场的直接纳米级测量受到限制。扫描电子衍射已成为获得垂直于入射电子束方向的应变分量二维图的有力工具。尽管缺乏使用此类数据的张量断层扫描的正式框架，但扩展该方法以恢复完整的三维应变张量场已受到限制。在这里，我们表明可以重建完整的非对称应变张量场作为不适定张量断层扫描逆问题的解决方案。然后，我们在分析和计算上证明了这个断层扫描问题的特性，强调了为什么结合进动来执行扫描进动电子衍射可能很重要。我们为非对称张量断层扫描建立了一个通用框架，并通过计算证明了其通过扫描进动电子衍射数据实现应变断层扫描的适用性。