Non-rigid alignment in electron tomography in materials science

Electron tomography is a key technique that enables the visualization of an object in three dimensions with a resolution of about a nanometre. High-quality 3D reconstruction is possible thanks to the latest compressed sensing algorithms and/or better alignment and preprocessing of the 2D projections. Rigid alignment of 2D projections is routine in electron tomography. However, it cannot correct misalignments induced by (i) deformations of the sample due to radiation damage or (ii) drifting of the sample during the acquisition of an image in scanning transmission electron microscope mode. In both cases, those misalignments can give rise to artefacts in the reconstruction. We propose a simple-to-implement non-rigid alignment technique to correct those artefacts. This technique is particularly suited for needle-shaped samples in materials science. It is initiated by a rigid alignment of the projections and it is then followed by several rigid alignments of different parts of the projections. Piecewise linear deformations are applied to each projection to force them to simultaneously satisfy the rigid alignments of the different parts. The efficiency of this technique is demonstrated on three samples, an intermetallic sample with deformation misalignments due to a high electron dose typical to spectroscopic electron tomography, a porous silicon sample with an extremely thin end particularly sensitive to electron beam and another porous silicon sample that was drifting during image acquisitions.