Three-dimensional electron tomography and recent expansion of its applications in materials science.

Electron tomography (ET) is a powerful tool for elucidating the properties and functionalities of materials. The innovative development of aberration-corrected electron microscopy in the early 21st century and the remarkable progress in the development of detectors, equipment and devices related to ET have resulted in substantial improvements in resolution. However, not only advances in hardware but also remarkable developments in reconstruction algorithms and related three-dimensional (3D) analysis methods have contributed to the resolution improvements. ET has its own problems, including the missing-wedge problem due to the limited tilt-angle range and the need to acquire numerous specimen-tilt images, the latter of which is time-consuming and can potentially damage the specimen. This review paper aims to (i) describe the established basic theories and definitions regarding 3D resolution of ET and practical 3D resolution measurement methods, (ii) discuss various reconstruction algorithms that effectively overcome the aforementioned problems and (iii) describe recent progress in the core of ET applications in materials science with respect to atomic ET, analytical ET and in-situ ET. The aforementioned ET problems have been addressed with each method developed in each field of application. Notably, in terms of aim (ii), recently developed reconstruction algorithms can reduce the number of projection images (specimen-tilt images) needed to attain a certain resolution without violating the Nyquist criterion. This approach is interpreted as a novel non-linear sampling theorem.