Increasing interest in three-dimensional nanostructures adds impetus to electron microscopy techniques capable of imaging at or below the nanoscale in three dimensions. We present a reconstruction algorithm that takes as input a focal series of four-dimensional scanning transmission electron microscopy (4D-STEM) data. We apply the approach to a lead iridate, Pb$_2$Ir$_2$O$_7$, and yttrium-stabilized zirconia, Y$_{0.095}$Zr$_{0.905}$O$_2$, heterostructure from data acquired with the specimen in a single plan-view orientation, with the epitaxial layers stacked along the beam direction. We demonstrate that Pb–Ir atomic columns are visible in the uppermost layers of the reconstructed volume. We compare this approach to the alternative techniques of depth sectioning using differential phase contrast scanning transmission electron microscopy (DPC-STEM) and multislice ptychographic reconstruction.

A method for three-dimensional reconstruction of objects from defocused images collected at multiple illumination directions in high-resolution transmission electron microscopy is presented. The method effectively corrects for the Ewald sphere curvature by taking into account the in-particle propagation of the electron beam. Numerical simulations demonstrate that the proposed method is capable of accurately reconstructing biological molecules or nanoparticles from high-resolution defocused images under conditions achievable in single-particle electron cryo-microscopy or electron tomography with realistic radiation doses, non-trivial aberrations, multiple scattering, and other experimentally relevant factors. The physics of the method is based on the well-known Diffraction Tomography formalism, but with the phase-retrieval step modified to include a conjugation of the phase (i.e., multiplication of the phase by a negative constant). At each illumination direction, numerically backpropagating the beam with the conjugated phase produces maximum contrast at the location of individual atoms in the molecule or nanoparticle. The resultant algorithm, Conjugated Holographic Reconstruction, can potentially be incorporated into established software tools for single-particle analysis, such as, for example, RELION or FREALIGN, in place of the conventional contrast transfer function correction procedure, in order to account for the Ewald sphere curvature and improve the spatial resolution of the three-dimensional reconstruction.

Recent work has revived interest in the scattering matrix formulation of electron scattering in transmission electron microscopy as a stepping stone toward atomic-resolution structure determination in the presence of multiple scattering. We discuss ways of visualizing the scattering matrix that make its properties clear. Through a simulation-based case study incorporating shot noise, we shown how regularizing on this continuity enables the scattering matrix to be reconstructed from 4D scanning transmission electron microscopy (STEM) measurements from a single defocus value. Intriguingly, for crystalline samples, this process also yields the sample thickness to nanometer accuracy with no a priori knowledge about the sample structure. The reconstruction quality is gauged by using the reconstructed scattering matrix to simulate STEM images at defocus values different from that of the data from which it was reconstructed.

Scanning transmission electron microscopy (STEM) allows for imaging, diffraction, and spectroscopy of materials on length scales ranging from microns to atoms. By using a high-speed, direct electron detector, it is now possible to record a full two-dimensional (2D) image of the diffracted electron beam at each probe position, typically a 2D grid of probe positions. These 4D-STEM datasets are rich in information, including signatures of the local structure, orientation, deformation, electromagnetic fields, and other sample-dependent properties. However, extracting this information requires complex analysis pipelines that include data wrangling, calibration, analysis, and visualization, all while maintaining robustness against imaging distortions and artifacts. In this paper, we present py4DSTEM, an analysis toolkit for measuring material properties from 4D-STEM datasets, written in the Python language and released with an open-source license. We describe the algorithmic steps for dataset calibration and various 4D-STEM property measurements in detail and present results from several experimental datasets. We also implement a simple and universal file format appropriate for electron microscopy data in py4DSTEM, which uses the open-source HDF5 standard. We hope this tool will benefit the research community and help improve the standards for data and computational methods in electron microscopy, and we invite the community to contribute to this ongoing project.

The invention of silicon drift detectors has resulted in an unprecedented improvement in detection efficiency for energy-dispersive X-ray (EDX) spectroscopy in the scanning transmission electron microscope. The result is numerous beautiful atomic-scale maps, which provide insights into the internal structure of a variety of materials. However, the task still remains to understand exactly where the X-ray signal comes from and how accurately it can be quantified. Unfortunately, when crystals are aligned with a low-order zone axis parallel to the incident beam direction, as is necessary for atomic-resolution imaging, the electron beam channels. When the beam becomes localized in this way, the relationship between the concentration of a particular element and its spectroscopic X-ray signal is generally nonlinear. Here, we discuss the combined effect of both spatial integration and sample tilt for ameliorating the effects of channeling and improving the accuracy of EDX quantification. Both simulations and experimental results will be presented for a perovskite-based oxide interface. We examine how the scattering and spreading of the electron beam can lead to erroneous interpretation of interface compositions, and what approaches can be made to improve our understanding of the underlying atomic structure.

Multiple electron scattering and the nonintuitive nature of image formation with coherent radiation complicate the interpretation of conventional transmission electron microscopy images. Precession of the illuminating beam in transmission electron microscopy (TEM) can lead to more robust and interpretable images with some penalty to image contrast, a technique known as dynamic hollow-cone illumination TEM. We demonstrate direct and robust imaging of light and heavy atoms in a crystalline environment with this technique. This method is similar to the annular bright-field technique in scanning transmission electron microscopy, via the principle of reciprocity. Dynamic hollow-cone illumination TEM is challenging in practice due to sensitivity to the misalignment of the precession axis, microscope objective aperture, and crystal zone axis.