Robert Hovden

Robert Hovden, Yi Jiang, Huolin L. Xin et al.

The discrete Fourier transform is among the most routine tools used in high-resolution scanning / transmission electron microscopy (S/TEM). However, when calculating a Fourier transform, periodic boundary conditions are imposed and sharp discontinuities between the edges of an image cause a cross patterned artifact along the reciprocal space axes. This artifact can interfere with the analysis of reciprocal lattice peaks of an atomic resolution image. Here we demonstrate that the recently developed Periodic Plus Smooth Decomposition technique provides a simple, efficient method for reliable removal of artifacts caused by edge discontinuities. In this method, edge artifacts are reduced by subtracting a smooth background that solves Poisson's equation with boundary conditions set by the image's edges. Unlike the traditional windowed Fourier transforms, Periodic Plus Smooth Decomposition maintains sharp reciprocal lattice peaks from the image's entire field of view.

Yi Jiang, Elliot Padgett, Robert Hovden et al.

Electron tomography (ET) has become a standard technique for 3D characterization of materials at the nano-scale. Traditional reconstruction algorithms such as weighted back projection suffer from disruptive artifacts with insufficient projections. Popularized by compressed sensing, sparsity-exploiting algorithms have been applied to experimental ET data and show promise for improving reconstruction quality or reducing the total beam dose applied to a specimen. Nevertheless, theoretical bounds for these methods have been less explored in the context of ET applications. Here, we perform numerical simulations to investigate performance of l_1-norm and total-variation (TV) minimization under various imaging conditions. From 36,100 different simulated structures, our results show specimens with more complex structures generally require more projections for exact reconstruction. However, once sufficient data is acquired, dividing the beam dose over more projections provides no improvements - analogous to the traditional dose-fraction theorem. Moreover, a limited tilt range of +-75 or less can result in distorting artifacts in sparsity-exploiting reconstructions. The influence of optimization parameters on reconstructions is also discussed.