Low-dose cryo electron ptychography via non-convex Bayesian optimization

Ghostbuster: A phase retrieval diffraction tomography algorithm for cryo-EM

Ewald sphere curvature correction, which extends beyond the projection approximation, stretches the shallow depth of field in cryo-EM reconstructions of thick particles. Here we show that even for previously assumed thin particles, reconstruction artifacts which we refer to as ghosts can appear. By retrieving the lost phases of the electron exitwaves and accounting for the first Born approximation scattering within the particle, we show that these ghosts can be effectively eliminated. Our simulations demonstrate how such ghostbusting can improve reconstructions as compared to existing state-of-the-art software. Like ptychographic cryo-EM, our Ghostbuster algorithm uses phase retrieval to improve reconstructions, but unlike the former, we do not need to modify the existing data acquisition pipelines.

Local-orbital ptychography for ultrahigh-resolution imaging

Technical advances paired with developments in methodology have enabled electron microscopy to reach atomic resolution. Further improving the information limit in microscopic imaging requires further improvements in methodology. Here we report a ptychographic method that describes the object as the sum of discrete atomic-orbital-like functions (for example, Gaussian functions) and the probe in terms of aberration functions. Using this method, we realize an improved information limit of microscopic imaging, reaching down to 14 pm. High-quality probes and objects contribute to superior signal-to-noise ratios at low electron doses, allowing for relaxation of the sample thickness restriction to 50 nm for dense materials. Additionally, our method has the capability to decompose the total phase into element components, revealing that the information limit is element dependent. With enhanced spatial resolution, signal-to-noise ratio and thickness threshold compared with conventional ptychography methods, our local-orbital ptychography may find applications in atomic-resolution imaging of metals, ceramics, electronic devices or beam-sensitive material.

Aberration Correction for Large-Angle Illumination Scanning Transmission Electron Microscopy by Using Iterative Electron Ptychography Algorithms

Modern aberration correctors in the scanning transmission electron microscope (STEM) have dramatically improved the attainable spatial resolution and enabled atomical structure and spectroscopic analysis even at low acceleration voltages (≤80 kV). For a large-angle illumination, achieving successful aberration correction to high angles is challenging with an aberration corrector, which limits further improvements in applications such as super-resolution, three-dimensional atomic depth resolution, or atomic surface morphology analyses. Electron ptychography based on four-dimensional STEM can provide a postprocessing strategy to overcome the current technological limitations. In this work, we have demonstrated that aberration correction for large-angle illumination is feasible by pushing the capabilities of regularized ptychographic iterative engine algorithms to reconstruct 4D data sets acquired using a relatively low-efficiency complementary metal oxide semiconductor camera. We report super resolution (0.71 Å) with large-angle illumination (50-60 mrad) and under 60 kV accelerating voltage.

Achieving sub-0.5-angstrom-resolution ptychography in an uncorrected electron microscope

Subangstrom resolution has long been limited to aberration-corrected electron microscopy, where it is a powerful tool for understanding the atomic structure and properties of matter. Here, we demonstrate electron ptychography in an uncorrected scanning transmission electron microscope (STEM) with deep subangstrom spatial resolution down to 0.44 angstroms, exceeding the conventional resolution of aberration-corrected tools and rivaling their highest ptychographic resolutions​. Our approach, which we demonstrate on twisted two-dimensional materials in a widely available commercial microscope, far surpasses prior ptychographic resolutions (1 to 5 angstroms) of uncorrected STEMs. We further show how geometric aberrations can create optimized, structured beams for dose-efficient electron ptychography. Our results demonstrate that expensive aberration correctors are no longer required for deep subangstrom resolution.

Design of Electrostatic Aberration Correctors for Scanning Transmission Electron Microscopy

In a scanning transmission electron microscope (STEM), producing a high-resolution image generally requires an electron beam focused to the smallest point possible. However, the magnetic lenses used to focus the beam are unavoidably imperfect, introducing aberrations that limit resolution. Modern STEMs overcome this by using hardware aberration correctors comprised of many multipole elements, but these devices are complex, expensive, and can be difficult to tune. We demonstrate a design for an electrostatic phase plate that can act as an aberration corrector. The corrector is comprised of annular segments, each of which is an independent two-terminal device that can apply a constant or ramped phase shift to a portion of the electron beam. We show the improvement in image resolution using an electrostatic corrector. Engineering criteria impose that much of the beam within the probe-forming aperture be blocked by support bars, leading to large probe tails for the corrected probe that sample the specimen beyond the central lobe. We also show how this device can be used to create other STEM beam profiles such as vortex beams and probes with a high degree of phase diversity, which improve information transfer in ptychographic reconstructions.

Cryo-electron ptychography: Applications and potential in biological characterisation

There is a clear need for developments in characterisation techniques that provide detailed information about structure-function relationships in biology. Using electron microscopy to achieve high resolution while maintaining a broad field of view remains a challenge, particularly for radiation-sensitive specimens where the signal-to-noise ratio required to maintain structural integrity is limited by low electron fluence. In this review, we explore the potential of cryogenic electron ptychography as an alternative method for characterising biological systems under low-fluence conditions. Using this method with increased information content from multiple sampled regions of interest potentially allows 3D reconstruction with far fewer particles than required in conventional cryo-electron microscopy. This is important for achieving higher resolution in systems where distributions of homogeneous single particles are difficult to obtain. We discuss the progress, limitations, and potential areas for future development of this approach for both single particle analysis and applications to heterogeneous large objects.

Solving complex nanostructures with ptychographic atomic electron tomography

Transmission electron microscopy (TEM) is essential for determining atomic scale structures in structural biology and materials science. In structural biology, three-dimensional structures of proteins are routinely determined from thousands of identical particles using phase-contrast TEM. In materials science, three-dimensional atomic structures of complex nanomaterials have been determined using 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 ptychographic electron tomography from 34.5 million diffraction patterns to reconstruct an atomic resolution tilt series of a double wall-carbon nanotube (DW-CNT) encapsulating a complex ZrTe sandwich structure. Class averaging the resulting tilt series images and subpixel localization of the atomic peaks reveals a Zr11Te50 structure containing a previously unobserved ZrTe2 phase in the core. The experimental realization of atomic resolution ptychographic electron tomography will allow for the structural determination of a wide range of beam-sensitive nanomaterials containing light elements.

In Situ and Emerging Transmission Electron Microscopy for Catalysis Research

Catalysts are the primary facilitator in many dynamic processes. Therefore, a thorough understanding of these processes has vast implications for a myriad of energy systems. The scanning/transmission electron microscope (S/TEM) is a powerful tool not only for atomic-scale characterization but also in situ catalytic experimentation. Techniques such as liquid and gas phase electron microscopy allow the observation of catalysts in an environment conducive to catalytic reactions. Correlated algorithms can greatly improve microscopy data processing and expand multidimensional data handling. Furthermore, new techniques including 4D-STEM, atomic electron tomography, cryogenic electron microscopy, and monochromated electron energy loss spectroscopy (EELS) push the boundaries of our comprehension of catalyst behavior. In this review, we discuss the existing and emergent techniques for observing catalysts using S/TEM. Challenges and opportunities highlighted aim to inspire and accelerate the use of electron microscopy to further investigate the complex interplay of catalytic systems.

Deep reinforcement learning for data-driven adaptive scanning in ptychography

We present a method that lowers the dose required for an electron ptychographic reconstruction by adaptively scanning the specimen, thereby providing the required spatial information redundancy in the regions of highest importance. The proposed method is built upon a deep learning model that is trained by reinforcement learning, using prior knowledge of the specimen structure from training data sets. We show that using adaptive scanning for electron ptychography outperforms alternative low-dose ptychography experiments in terms of reconstruction resolution and quality.

Cryogenic electron ptychographic single particle analysis with wide bandwidth information transfer

Advances in cryogenic transmission electron microscopy have revolutionised the determination of many macromolecular structures at atomic or near-atomic resolution. This method is based on conventional defocused phase contrast imaging. However, it has limitations of weaker contrast for small biological molecules embedded in vitreous ice, in comparison with cryo-ptychography, which shows increased contrast. Here we report a single-particle analysis based on the use of ptychographic reconstruction data, demonstrating that three dimensional reconstructions with a wide information transfer bandwidth can be recovered by Fourier domain synthesis. Our work suggests future applications in otherwise challenging single particle analyses, including small macromolecules and heterogeneous or flexible particles. In addition structure determination in situ within cells without the requirement for protein purification and expression may be possible.

PtyLab.m/py/jl: a cross-platform, open-source inverse modeling toolbox for conventional and Fourier ptychography

Conventional (CP) and Fourier (FP) ptychography have emerged as versatile quantitative phase imaging techniques. While the main application cases for each technique are different, namely lens-less short wavelength imaging for CP and lens-based visible light imaging for FP, both methods share a common algorithmic ground. CP and FP have in part independently evolved to include experimentally robust forward models and inversion techniques. This separation has resulted in a plethora of algorithmic extensions, some of which have not crossed the boundary from one modality to the other. Here, we present an open source, cross-platform software, called PtyLab, enabling both CP and FP data analysis in a unified framework. With this framework, we aim to facilitate and accelerate cross-pollination between the two techniques. Moreover, the availability in Matlab, Python, and Julia will set a low barrier to enter each field.

An integrated constrained gradient descent (iCGD) protocol to correct scan-positional errors for electron ptychography with high accuracy and precision

Correcting scan-positional errors is critical in achieving electron ptychography with both high resolution and high precision. This is a demanding and challenging task due to the sheer number of parameters that need to be optimized. For atomic-resolution ptychographic reconstructions, we found classical refining methods for scan positions not satisfactory due to the inherent entanglement between the object and scan positions, which can produce systematic errors in the results. Here, we propose a new protocol consisting of a series of constrained gradient descent (CGD) methods to achieve better recovery of scan positions. The central idea of these CGD methods is to utilize a priori knowledge about the nature of STEM experiments and add necessary constraints to isolate different types of scan positional errors during the iterative reconstruction process. Each constraint will be introduced with the help of simulated 4D-STEM datasets with known positional errors. Then the integrated constrained gradient decent (iCGD) protocol will be demonstrated using an experimental 4D-STEM dataset of the 1H-MoS₂ monolayer. We will show that the iCGD protocol can effectively address the errors of scan positions across the spectrum and help to achieve electron ptychography with high accuracy and precision.

Automatic Differentiation for Inverse Problems in X-ray Imaging and Microscopy

Computational techniques allow breaking the limits of traditional imaging methods, such as time restrictions, resolution, and optics flaws. While simple computational methods can be enough for highly controlled microscope setups or just for previews, an increased level of complexity is instead required for advanced setups, acquisition modalities or where uncertainty is high; the need for complex computational methods clashes with rapid design and execution. In all these cases, Automatic Differentiation, one of the subtopics of Artificial Intelligence, may offer a functional solution, but only if a GPU implementation is available. In this paper, we show how a framework built to solve just one optimisation problem can be employed for many different X-ray imaging inverse problems.

Optical ptychography for biomedical imaging: recent progress and future directions [Invited]

Ptychography is an enabling microscopy technique for both fundamental and applied sciences. In the past decade, it has become an indispensable imaging tool in most X-ray synchrotrons and national laboratories worldwide. However, ptychography's limited resolution and throughput in the visible light regime have prevented its wide adoption in biomedical research. Recent developments in this technique have resolved these issues and offer turnkey solutions for high-throughput optical imaging with minimum hardware modifications. The demonstrated imaging throughput is now greater than that of a high-end whole slide scanner. In this review, we discuss the basic principle of ptychography and summarize the main milestones of its development. Different ptychographic implementations are categorized into four groups based on their lensless/lens-based configurations and coded-illumination/coded-detection operations. We also highlight the related biomedical applications, including digital pathology, drug screening, urinalysis, blood analysis, cytometric analysis, rare cell screening, cell culture monitoring, cell and tissue imaging in 2D and 3D, polarimetric analysis, among others. Ptychography for high-throughput optical imaging, currently in its early stages, will continue to improve in performance and expand in its applications. We conclude this review article by pointing out several directions for its future development.

SIM-STEM Lab: Incorporating Compressed Sensing Theory for Fast STEM Simulation

Recently it has been shown that precise dose control and an increase in the overall acquisition speed of atomic resolution scanning transmission electron microscope (STEM) images can be achieved by acquiring only a small fraction of the pixels in the image experimentally and then reconstructing the full image using an inpainting algorithm. In this paper, we apply the same inpainting approach (a form of compressed sensing) to simulated, sub-sampled atomic resolution STEM images. We find that it is possible to significantly sub-sample the area that is simulated, the number of g-vectors contributing the image, and the number of frozen phonon configurations contributing to the final image while still producing an acceptable fit to a fully sampled simulation. Here we discuss the parameters that we use and how the resulting simulations can be quantifiably compared to the full simulations. As with any Compressed Sensing methodology, care must be taken to ensure that isolated events are not excluded from the process, but the observed increase in simulation speed provides significant opportunities for real time simulations, image classification and analytics to be performed as a supplement to experiments on a microscope to be developed in the future.

Three-dimensional electron ptychography of organic-inorganic hybrid nanostructures

Three dimensional scaffolded DNA origami with inorganic nanoparticles has been used to create tailored multidimensional nanostructures. However, the image contrast of DNA is poorer than those of the heavy nanoparticles in conventional transmission electron microscopy at high defocus so that the biological and non-biological components in 3D scaffolds cannot be simultaneously resolved using tomography of samples in a native state. We demonstrate the use of electron ptychography to recover high contrast phase information from all components in a DNA origami scaffold without staining. We further quantitatively evaluate the enhancement of contrast in comparison with conventional transmission electron microscopy. In addition, We show that for ptychography post-reconstruction focusing simplifies the workflow and reduces electron dose and beam damage.

The authors demonstrate electron ptychographic computed tomography by simultaneously recording high contrast data from both the organic- and inorganic components in a 3D DNA-origami framework hybrid nanostructure.

Automatic parameter selection for electron ptychography via Bayesian optimization

Electron ptychography provides new opportunities to resolve atomic structures with deep sub-angstrom spatial resolution and to study electron-beam sensitive materials with high dose efficiency. In practice, obtaining accurate ptychography images requires simultaneously optimizing multiple parameters that are often selected based on trial-and-error, resulting in low-throughput experiments and preventing wider adoption. Here, we develop an automatic parameter selection framework to circumvent this problem using Bayesian optimization with Gaussian processes. With minimal prior knowledge, the workflow efficiently produces ptychographic reconstructions that are superior to those processed by experienced experts. The method also facilitates better experimental designs by exploring optimized experimental parameters from simulated data.

Accurate and Robust Calibration of the Uniform Affine Transformation Between Scan-Camera Coordinates for Atom-Resolved In-Focus 4D-STEM Datasets

Accurate geometrical calibration between the scan coordinates and the camera coordinates is critical in four-dimensional scanning transmission electron microscopy (4D-STEM) for both quantitative imaging and ptychographic reconstructions. For atomic-resolved, in-focus 4D-STEM datasets, we propose a hybrid method incorporating two sub-routines, namely a J-matrix method and a Fourier method, which can calibrate the uniform affine transformation between the scan-camera coordinates using raw data, without a priori knowledge of the crystal structure of the specimen. The hybrid method is found robust against scan distortions and residual probe aberrations. It is also effective even when defects are present in the specimen, or the specimen becomes relatively thick. We will demonstrate that a successful geometrical calibration with the hybrid method will lead to a more reliable recovery of both the specimen and the electron probe in a ptychographic reconstruction. We will also show that, although the elimination of local scan position errors still requires an iterative approach, the rate of convergence can be improved, and the residual errors can be further reduced if the hybrid method can be firstly applied for initial calibration. The code is made available as a simple-to-use tool to correct affine transformations of the scan-camera coordinates in 4D-STEM experiments.

Shaping of Electron Beams Using Sculpted Thin Films

Electron beam shaping by sculpted thin films relies on electron-matter interactions and the wave nature of electrons. It can be used to study physical phenomena of special electron beams and to develop technological applications in electron microscopy that offer new and improved measurement techniques and increased resolution in different imaging modes. In this Perspective, we review recent applications of sculpted thin films for electron orbital angular momentum sorting, improvements in phase contrast transmission electron microscopy, and aberration correction. For the latter, we also present new results of our work toward correction of the spherical aberration of Lorentz scanning transmission electron microscopes and suggest a method to correct chromatic aberration using thin films. This review provides practical insight for researchers in the field and motivates future progress in electron microscopy.

Making the Most of your Electrons: Challenges and Opportunities in Characterizing Hybrid Interfaces with STEM

Inspired by the unique architectures composed of hard and soft materials in natural and biological systems, synthetic hybrid structures and associated soft-hard interfaces have recently evoked significant interest. Soft matter is typically dominated by fluctuations even at room temperature, while hard matter (which often serves as the substrate or anchor for the soft component) is governed by rigid mechanical behavior. This dichotomy offers considerable opportunities to leverage the disparate properties offered by these components across a wide spectrum spanning from basic science to engineering insights with significant technological overtones. Such hybrid structures, which include polymer nanocomposites, DNA functionalized nanoparticle superlattices and metal organic frameworks to name a few, have delivered promising insights into the areas of catalysis, environmental remediation, optoelectronics, medicine, and beyond. The interfacial structure between these hard and soft phases exists across a variety of length scales and often strongly influence the functionality of hybrid systems. While scanning/transmission electron microscopy (S/TEM) has proven to be a valuable tool for acquiring intricate molecular and nanoscale details of these interfaces, the unusual nature of hybrid composites presents a suite of challenges that make assessing or establishing the classical structure-property relationships especially difficult. These include challenges associated with preparing electron-transparent samples and obtaining sufficient contrast to resolve the interface between dissimilar materials given the dose sensitivity of soft materials. We discuss each of these challenges and supplement a review of recent developments in the field with additional experimental investigations and simulations to present solutions for attaining a nano or atomic-level understanding of these interfaces. These solutions present a host of opportunities for investigating and understanding the role interfaces play in this unique class of functional materials.

Single-particle cryo-EM: alternative schemes to improve dose efficiency

Imaging of biomolecules by ionizing radiation, such as electrons, causes radiation damage which introduces structural and compositional changes of the specimen. The total number of high-energy electrons per surface area that can be used for imaging in cryogenic electron microscopy (cryo-EM) is severely restricted due to radiation damage, resulting in low signal-to-noise ratios (SNR). High resolution details are dampened by the transfer function of the microscope and detector, and are the first to be lost as radiation damage alters the individual molecules which are presumed to be identical during averaging. As a consequence, radiation damage puts a limit on the particle size and sample heterogeneity with which electron microscopy (EM) can deal. Since a transmission EM (TEM) image is formed from the scattering process of the electron by the specimen interaction potential, radiation damage is inevitable. However, we can aim to maximize the information transfer for a given dose and increase the SNR by finding alternatives to the conventional phase-contrast cryo-EM techniques. Here some alternative transmission electron microscopy techniques are reviewed, including phase plate, multi-pass transmission electron microscopy, off-axis holography, ptychography and a quantum sorter. Their prospects for providing more or complementary structural information within the limited lifetime of the sample are discussed.

Efficient large field of view electron phase imaging using near-field electron ptychography with a diffuser

Most implementations of ptychography on the electron microscope operate in scanning transmission (STEM) mode, where a small focussed probe beam is rapidly scanned across the sample. In this paper we introduce a different approach based on near-field ptychography, where the focussed beam is replaced by a wide-field, structured illumination, realised through a purpose-designed etched Silicon Nitride window. We show that fields of view as large as 100 μm² can be imaged using the new approach, and that quantitative electron phase images can be reconstructed from as few as nine near-field diffraction pattern measurements.

A data reduction and compression description for high throughput time-resolved electron microscopy

Fast, direct electron detectors have significantly improved the spatio-temporal resolution of electron microscopy movies. Preserving both spatial and temporal resolution in extended observations, however, requires storing prohibitively large amounts of data. Here, we describe an efficient and flexible data reduction and compression scheme (ReCoDe) that retains both spatial and temporal resolution by preserving individual electron events. Running ReCoDe on a workstation we demonstrate on-the-fly reduction and compression of raw data streaming off a detector at 3 GB/s, for hours of uninterrupted data collection. The output was 100-fold smaller than the raw data and saved directly onto network-attached storage drives over a 10 GbE connection. We discuss calibration techniques that support electron detection and counting (e.g., estimate electron backscattering rates, false positive rates, and data compressibility), and novel data analysis methods enabled by ReCoDe (e.g., recalibration of data post acquisition, and accurate estimation of coincidence loss).

The use of electron detectors with high spatio-temporal resolution is limited by the large amounts of data generated. Here, the authors describe ReCoDe, a data reduction and compression scheme, that preserves individual electron events, and enable on-the-fly reduction and compression of raw data.

Contrast transfer and noise considerations in focused-probe electron ptychography

Electron ptychography is a 4-D STEM phase-contrast imaging technique with applications to light-element and beam-sensitive materials. Although the electron dose (electrons incident per unit area on the sample) is the primary figure of merit for imaging beam-sensitive materials, it is also necessary to consider the contrast transfer properties of the imaging technique. Here, we explore the contrast transfer properties of electron ptychography. The contrast transfer of focused-probe, non-iterative electron ptychography using the single-side-band (SSB) method is demonstrated experimentally. The band-pass nature of the phase-contrast transfer function (PCTF) for SSB ptychography places strict limitations on the probe convergence semi-angles required to resolve specific sample features with high contrast. The PCTF of the extended ptychographic iterative engine (ePIE) is broader than that for SSB ptychography, although when both high and low spatial frequencies are transferred, band-pass filtering is required to remove image artefacts. Normalisation of the transfer function with respect to the noise level shows that the transfer window is increased while avoiding noise amplification. Avoiding algorithms containing deconvolution steps may also increase the dose-efficiency of ptychographic phase reconstructions.

Practical implementation of high-resolution electron ptychography and comparison with off-axis electron holography

Ptychography is a coherent diffractive imaging technique that can determine how an electron wave is transmitted through an object by probing it in many small overlapping regions and processing the diffraction data obtained at each point. The resulting electron transmission model describes both phase and amplitude changes to the electron wave. Ptychography has been adopted in transmission electron microscopy in recent years following advances in high-speed direct electron detectors and computer algorithms which now make the technique suitable for practical applications. Its ability to retrieve quantitative phase information at high spatial resolution makes it a plausible alternative or complement to electron holography. Furthermore, unlike off-axis electron holography, it can provide phase information without an electron bi-prism assembly or the requirement of a minimally structured region adjacent to the region of interest in the object. However, it does require a well-calibrated scanning transmission electron microscope and a well-managed workflow to manage the calibration, data acquisition and reconstruction process to yield a practical technique. Here we detail this workflow and highlight how this is greatly assisted by acquisition management software. Through experimental data and modelling we also explore the similarities and differences between high-resolution ptychography and electron holography. Both techniques show a dependence of the recovered phase on the crystalline orientation of the material which is attributable to dynamical scattering. However, the exact nature of the variation differs reflecting fundamental expectations, but nonetheless equally useful information is obtained from electron holography and the ptychographically determined object transmission function.

Mixed-state electron ptychography enables sub-angstrom resolution imaging with picometer precision at low dose

Both high resolution and high precision are required to quantitatively determine the atomic structure of complex nanostructured materials. However, for conventional imaging methods in scanning transmission electron microscopy (STEM), atomic resolution with picometer precision cannot usually be achieved for weakly-scattering samples or radiation-sensitive materials, such as 2D materials. Here, we demonstrate low-dose, sub-angstrom resolution imaging with picometer precision using mixed-state electron ptychography. We show that correctly accounting for the partial coherence of the electron beam is a prerequisite for high-quality structural reconstructions due to the intrinsic partial coherence of the electron beam. The mixed-state reconstruction gains importance especially when simultaneously pursuing high resolution, high precision and large field-of-view imaging. Compared with conventional atomic-resolution STEM imaging techniques, the mixed-state ptychographic approach simultaneously provides a four-times-faster acquisition, with double the information limit at the same dose, or up to a fifty-fold reduction in dose at the same resolution.

With conventional scanning transmission electron microscopy, some sensitive materials are difficult to image with atomic resolution. The authors present a method of mixed-state electron ptychography that enables picometer precision with fast acquisition and low dosage.

Low-dose phase retrieval of biological specimens using cryo-electron ptychography

Cryo-electron microscopy is an essential tool for high-resolution structural studies of biological systems. This method relies on the use of phase contrast imaging at high defocus to improve information transfer at low spatial frequencies at the expense of higher spatial frequencies. Here we demonstrate that electron ptychography can recover the phase of the specimen with continuous information transfer across a wide range of the spatial frequency spectrum, with improved transfer at lower spatial frequencies, and as such is more efficient for phase recovery than conventional phase contrast imaging. We further show that the method can be used to study frozen-hydrated specimens of rotavirus double-layered particles and HIV-1 virus-like particles under low-dose conditions (5.7 e/Å2) and heterogeneous objects in an Adenovirus-infected cell over large fields of view (1.14 × 1.14 μm), thus making it suitable for studies of many biologically important structures.

Serial protein crystallography in an electron microscope

Serial X-ray crystallography at free-electron lasers allows to solve biomolecular structures from sub-micron-sized crystals. However, beam time at these facilities is scarce, and involved sample delivery techniques are required. On the other hand, rotation electron diffraction (MicroED) has shown great potential as an alternative means for protein nano-crystallography. Here, we present a method for serial electron diffraction of protein nanocrystals combining the benefits of both approaches. In a scanning transmission electron microscope, crystals randomly dispersed on a sample grid are automatically mapped, and a diffraction pattern at fixed orientation is recorded from each at a high acquisition rate. Dose fractionation ensures minimal radiation damage effects. We demonstrate the method by solving the structure of granulovirus occlusion bodies and lysozyme to resolutions of 1.55 Å and 1.80 Å, respectively. Our method promises to provide rapid structure determination for many classes of materials with minimal sample consumption, using readily available instrumentation.

Emerging Electron Microscopy Techniques for Probing Functional Interfaces in Energy Materials

Interfaces play a fundamental role in many areas of chemistry. However, their localized nature requires characterization techniques with high spatial resolution in order to fully understand their structure and properties. State-of-the-art atomic resolution or in situ scanning transmission electron microscopy and electron energy-loss spectroscopy are indispensable tools for characterizing the local structure and chemistry of materials with single-atom resolution, but they are not able to measure many properties that dictate function, such as vibrational modes or charge transfer, and are limited to room-temperature samples containing no liquids. Here, we outline emerging electron microscopy techniques that are allowing these limitations to be overcome and highlight several recent studies that were enabled by these techniques. We then provide a vision for how these techniques can be paired with each other and with in situ methods to deliver new insights into the static and dynamic behavior of functional interfaces.

Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond

Scanning transmission electron microscopy (STEM) is widely used for imaging, diffraction, and spectroscopy of materials down to atomic resolution. Recent advances in detector technology and computational methods have enabled many experiments that record a full image of the STEM probe for many probe positions, either in diffraction space or real space. In this paper, we review the use of these four-dimensional STEM experiments for virtual diffraction imaging, phase, orientation and strain mapping, measurements of medium-range order, thickness and tilt of samples, and phase contrast imaging methods, including differential phase contrast, ptychography, and others.

Atomic Resolution Defocused Electron Ptychography at Low Dose with a Fast, Direct Electron Detector

Electron ptychography has recently attracted considerable interest for high resolution phase-sensitive imaging. However, to date studies have been mainly limited to radiation resistant samples as the electron dose required to record a ptychographic dataset is too high for use with beam-sensitive materials. Here we report defocused electron ptychography using a fast, direct-counting detector to reconstruct the transmission function, which is in turn related to the electrostatic potential of a two-dimensional material at atomic resolution under various low dose conditions.

Electron beam damage of perfluorosulfonic acid studied by soft X-ray spectromicroscopy

Scanning transmission X-ray microscopy (STXM) was used to study chemical changes to perfluorosulfonic acid (PFSA) spun cast thin films as a function of dose imparted by exposure of a 200 kV electron beam in a Transmission Electron Microscope (TEM). The relationship between electron beam fluence and absorbed dose was calibrated using a modified version of a protocol based on the positive to negative lithography transition in PMMA [Leontowich et al, J. Synchrotron Rad. 19 (2012) 976]. STXM was used to characterize and quantify the chemical changes caused by electron irradiation of PFSA under several different conditions. The critical dose for CF₂-CF₂ amorphization was used to explore the effects of the sample environment on electron beam damage. Use of a silicon nitride substrate was found to increase the CF₂-CF₂ amorphization critical dose by ∼x2 from that for free-standing PFSA films. Freestanding PFSA and PMMA films were damaged by 200 kV electrons at ∼100 K and then the damage was measured by STXM at 300 K (RT). The lithography cross-over dose for PMMA was found to be ∼2x higher when the PMMA thin film was electron irradiated at 120 K rather than at 300 K. The critical dose for CF₂-CF₂ amorphization in PFSA irradiated at 120 K followed by warming and delayed measurement by STXM at 300 K was found to be ∼2x larger than at 300 K. To place these results in the context of the use of electron microscopy to study PFSA ionomer in fuel cell systems, an exposure of 300 e^-/nm² at 300 K (which corresponds to an absorbed dose of ∼20 MGy) amorphizes ∼10% of the CF₂-CF₂ bonds in PFSA. At this dose level, the spatial resolution for TEM imaging of PFSA is limited to 3.5 nm by radiation damage, if one is using a direct electron detector with DQE = 1. This work recommends caution about 2D and 3D morphological information of PFSA materials based on TEM studies which use fluences higher than 300 e^-/nm².

Singular Value Decomposition Method To Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance: II. Estimating Uncertainty

This paper is a continuation of the method introduced by Srivastava and Freed (2017) that is a new method based on truncated singular value decomposition (TSVD) for obtaining physical results from experimental signals without any need for Tikhonov regularization or other similar methods that require a regularization parameter. We show here how to estimate the uncertainty in the SVD-generated solutions. The uncertainty in the solution may be obtained by finding the minimum and maximum values over which the solution remains converged. These are obtained from the optimum range of singular value contributions, where the width of this region depends on the solution point location (e.g., distance) and the signal-to-noise ratio (SNR) of the signal. The uncertainty levels typically found are very small with substantial SNR of the (denoised) signal, emphasizing the reliability of the method. With poorer SNR, the method is still satisfactory but with greater uncertainty, as expected. Pulsed dipolar electron spin resonance spectroscopy experiments are used as an example, but this TSVD approach is general and thus applicable to any similar experimental method wherein singular matrix inversion is needed to obtain the physically relevant result. We show that the Srivastava-Freed TSVD method along with the estimate of uncertainty can be effectively applied to pulsed dipolar electron spin resonance signals with SNR > 30, and even for a weak signal (e.g., SNR ≈ 3) reliable results are obtained by this method, provided the signal is first denoised using wavelet transforms (WavPDS).

Probing Light Atoms at Subnanometer Resolution: Realization of Scanning Transmission Electron Microscope Holography

Atomic resolution imaging of light elements in electron-transparent materials has long been a challenge. Biomolecular materials, for example, are rapidly altered by incident electrons. We demonstrate a scanning transmission electron microscopy (STEM) technique, called STEM holography, capable of efficient structural analysis of beam-sensitive nanomaterials. STEM holography measures the absolute phase and amplitude of electrons passed through a specimen via interference with a vacuum reference wave. We use an amplitude-dividing nanofabricated grating to prepare multiple beams focused at the sample. We configure the postspecimen microscope imaging system to overlap the beams, forming an interference pattern. We record and analyze the pattern at each 2D-raster-scan-position, reconstructing the complex object wave. As a demonstration, we image gold nanoparticles on an amorphous carbon substrate at 2.4 Å resolution. STEM holography offers higher contrast of the carbon while maintaining gold atomic lattice resolution compared to high angle annular dark field STEM.

A streaming multi-GPU implementation of image simulation algorithms for scanning transmission electron microscopy

Simulation of atomic-resolution image formation in scanning transmission electron microscopy can require significant computation times using traditional methods. A recently developed method, termed plane-wave reciprocal-space interpolated scattering matrix (PRISM), demonstrates potential for significant acceleration of such simulations with negligible loss of accuracy. Here, we present a software package called Prismatic for parallelized simulation of image formation in scanning transmission electron microscopy (STEM) using both the PRISM and multislice methods. By distributing the workload between multiple CUDA-enabled GPUs and multicore processors, accelerations as high as 1000 × for PRISM and 15 × for multislice are achieved relative to traditional multislice implementations using a single 4-GPU machine. We demonstrate a potentially important application of Prismatic, using it to compute images for atomic electron tomography at sufficient speeds to include in the reconstruction pipeline. Prismatic is freely available both as an open-source CUDA/C++ package with a graphical user interface and as a Python package, PyPrismatic.