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Three-dimensional atomic resolution imaging using transmission electron microscopes is a unique capability that requires challenging experiments. Linear electron tomography methods are limited by the missing wedge effect, requiring a high tilt range. Multislice ptychography can achieve deep sub-{\AA}ngstrom resolution in the transverse direction, but the depth resolution is limited to 2 to 3 nanometers. In this paper, we propose and demonstrate an end-to-end approach to reconstructing the electrostatic potential volume of the sample directly from the 4D-STEM datasets. End-to-end multi-slice ptychographic tomography recovers several slices at each tomography tilt angle and compensates for the missing wedge effect. The algorithm is initially tested in simulation with a Pt@$\mathrm{Al_2O_3}$ core-shell nanoparticle, where both heavy and light atoms are recovered in 3D from an unaligned 4D-STEM tilt series with a restricted tilt range of 90 degrees. We also demonstrate the algorithm experimentally, recovering a Te nanoparticle with sub-{\AA}ngstrom resolution.

Resolving single atoms in large-scale volumes has been a goal for atomic resolution microscopy for a long time. Electron microscopy has come close to this goal using a combination of advanced electron optics and computational imaging algorithms. However, atomic-resolution 3D imaging in volumes larger than the depth of field limit of the electron optics has so far been out of reach. Electron ptychography, a computational imaging method allowing to solve the multiple-scattering problem from position- and momentum-resolved measurements, provides the opportunity to surpass this limit. Here, we experimentally demonstrate atomic resolution three-dimensional phase-contrast imaging in a volume surpassing the depth of field limits using multi-slice ptychographic electron tomography. We reconstruct tilt-series 4D-STEM measurements of a Co3O4 nanocube, yielding 1.75 {\AA} resolution in a reconstructed volume of (18.2nm)^3., Comment: 15 pages

We describe the development, operation, and application of the 4D Camera -- a 576 by 576 pixel active pixel sensor for scanning/transmission electron microscopy which operates at 87,000 Hz. The detector generates data at approximately 480 Gbit/s which is captured by dedicated receiver computers with a parallelized software infrastructure that has been implemented to process the resulting 10 - 700 Gigabyte-sized raw datasets. The back illuminated detector provides the ability to detect single electron events at accelerating voltages from 30 - 300 keV. Through electron counting, the resulting sparse data sets are reduced in size by 10 - 300x compared to the raw data, and open-source sparsity-based processing algorithms offer rapid data analysis. The high frame rate allows for large and complex 4D-STEM experiments to be accomplished with typical STEM scanning parameters.

Four-dimensional scanning transmission electron microscopy (4D-STEM) has recently gained widespread attention for its ability to image atomic electric fields with sub-{\AA}ngstrom spatial resolution. These electric field maps represent the integrated effect of the nucleus, core electrons and valence electrons, and separating their contributions is non-trivial. In this paper, we utilized simultaneously acquired 4D-STEM center of mass (CoM) images and annular dark field (ADF) images to determine the electron charge density in monolayer MoS2. We find that both the core electrons and the valence electrons contribute to the derived electron charge density. However, due to blurring by the probe shape, the valence electron contribution forms a nearly featureless background while most of the spatial modulation comes from the core electrons. Our findings highlight the importance of probe shape in interpreting charge densities derived from 4D STEM.

Transmission electron microscopy (TEM) is a potent technique for the determination of three-dimensional atomic scale structure of samples in structural biology and materials science. In structural biology, three-dimensional structures of proteins are routinely determined using phase-contrast single-particle cryo-electron microscopy from thousands of identical proteins, and reconstructions have reached atomic resolution for specific proteins. In materials science, three-dimensional atomic structures of complex nanomaterials have been determined using a combination of annular dark field (ADF) scanning transmission electron microscopic (STEM) tomography and subpixel localization of atomic peaks, in a method termed atomic electron tomography (AET). However, neither of these methods can determine the three-dimensional atomic structure of heterogeneous nanomaterials containing light elements. Here, we perform mixed-state electron ptychography from 34.5 million diffraction patterns to reconstruct a high-resolution tilt series of a double wall-carbon nanotube (DW-CNT), encapsulating a complex $\mathrm{ZrTe}$ sandwich structure. Class averaging of the resulting reconstructions and subpixel localization of the atomic peaks in the reconstructed volume reveals the complex three-dimensional atomic structure of the core-shell heterostructure with 17 picometer precision. From these measurements, we solve the full $\mathrm{Zr_{11}Te_{50}}$ structure, which contains a previously unobserved $\mathrm{ZrTe_{2}}$ phase in the core. The experimental realization of ptychographic atomic electron tomography (PAET) will allow for structural determination of a wide range of nanomaterials which are beam-sensitive or contain light elements., Comment: 17 pages 3 figures in main text, 7 figures in supplementary materials

The arrival of direct electron detectors (DED) with high frame-rates in the field of scanning transmission electron microscopy has enabled many experimental techniques that require collection of a full diffraction pattern at each scan position, a field which is subsumed under the name four dimensional-scanning transmission electron microscopy (4D-STEM). DED frame rates approaching 100 kHz require data transmission rates and data storage capabilities that exceed commonly available computing infrastructure. Current commercial DEDs allow the user to make compromises in pixel bit depth, detector binning or windowing to reduce the per-frame file size and allow higher frame rates. This change in detector specifications requires decisions to be made before data acquisition that may reduce or lose information that could have been advantageous during data analysis. The 4D Camera, a DED with 87 kHz frame-rate developed at Lawrence Berkeley National Laboratory, reduces the raw data to a linear-index encoded electron event representation (EER). Here we show with experimental data from the 4D Camera that linear-index encoded EER and its direct use in 4D-STEM phase contrast imaging methods enables real-time, interactive phase-contrast from large-area 4D-STEM datasets. We detail the computational complexity advantages of the EER and the necessary computational steps to achieve real-time interactive ptychography and center-of-mass differential phase contrast using commonly available hardware accelerators., Comment: 11 pages

Scanning transmission electron microscopy (STEM) is an extremely versatile method for studying materials on the atomic scale. Many STEM experiments are supported or validated with electron scattering simulations. However, using the conventional multislice algorithm to perform these simulations can require extremely large calculation times, particularly for experiments with millions of probe positions as each probe position must be simulated independently. Recently, the PRISM algorithm was developed to reduce calculation times for large STEM simulations. Here, we introduce a new method for STEM simulation: partitioning of the STEM probe into "beamlets," given by a natural neighbor interpolation of the parent beams. This idea is compatible with PRISM simulations and can lead to even larger improvements in simulation time, as well requiring significantly less computer RAM. We have performed various simulations to demonstrate the advantages and disadvantages of partitioned PRISM STEM simulations. We find that this new algorithm is particularly useful for 4D-STEM simulations of large fields of view. We also provide a reference implementation of the multislice, PRISM and partitioned PRISM algorithms., Comment: 15 pages, 7 figures

Orchestrating parametric fitting of multicomponent spectra at scale is an essential yet underappreciated task in high-throughput quantification of materials and chemical composition. To automate the annotation process for spectroscopic and diffraction data collected in counts of hundreds to thousands, we present a systematic approach compatible with high-performance computing infrastructures using the MapReduce model and task-based parallelization. We implement the approach in software and demonstrate linear computational scaling with respect to spectral components using multidimensional experimental materials characterization datasets from photoemission spectroscopy and powder electron diffraction as benchmarks. Our approach enables efficient generation of high-quality data annotation and online spectral analysis and is applicable to a variety of analytical techniques in materials science and chemistry as a building block for closed-loop experimental systems.

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., Comment: 27 pages, 6 figures in main manuscript. 6 pages, 5 figures in supplementary. All computer code for electron microscopy simulation and reconstruction included in directory anc. Submitted to Microscopy & Microanalysis

Three-dimensional phase contrast imaging of multiply-scattering samples in X-ray and electron microscopy is extremely challenging, due to small numerical apertures, the unavailability of wavefront shaping optics, and the highly nonlinear inversion required from intensity-only measurements. In this work, we present a new algorithm using the scattering matrix formalism to solve the scattering from a non-crystalline medium from scanning diffraction measurements, and recover the illumination aberrations. Our method will enable 3D imaging and materials characterization at high resolution for a wide range of materials.

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 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, from data wrangling to calibration to analysis to 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 have also implemented 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, helps to move the developing standards for data and computational methods in electron microscopy, and invite the community to contribute to this ongoing, fully open-source project., Comment: 32 pages, 18 figures

Electron ptychography has seen a recent surge of interest for phase sensitive imaging at atomic or near-atomic resolution. However, applications are so far mainly limited to radiation-hard samples because the required doses are too high for imaging biological samples at high resolution. We propose the use of non-convex, Bayesian optimization to overcome this problem and reduce the dose required for successful reconstruction by two orders of magnitude compared to previous experiments. We suggest to use this method for imaging single biological macromolecules at cryogenic temperatures and demonstrate 2D single-particle reconstructions from simulated data with a resolution of 7.9 \AA$\,$ at a dose of 20 $e^- / \AA^2$. When averaging over only 15 low-dose datasets, a resolution of 4 \AA$\,$ is possible for large macromolecular complexes. With its independence from microscope transfer function, direct recovery of phase contrast and better scaling of signal-to-noise ratio, cryo-electron ptychography may become a promising alternative to Zernike phase-contrast microscopy.