Geometric reconstruction methods for electron tomography

TL;DR

This paper reviews geometric reconstruction algorithms for electron tomography that address missing data and diffraction effects, improving 3D nanostructure imaging by incorporating geometric priors to reduce tilt requirements.

Contribution

It introduces and discusses new algorithms from geometric and discrete tomography that utilize prior knowledge to enhance electron tomography reconstructions.

Findings

Algorithms effectively reduce missing wedge artefacts.

Incorporating geometric priors decreases the number of required tilt angles.

Successful reconstruction of an InAs nanowire demonstrates method effectiveness.

Abstract

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and nonlinear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full $180^\circ$ tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire.