Contrast transfer function (CTF) is a vital function in transmission electron microscopy (TEM). It expresses to what extent amplitudes converted from the phase changes of the diffracted waves contribute to the TEM image, including the effects of lens aberrations. Simulation is very helpful to understand the application of the function thoroughly. In this work, we develop the CTFscope as a component in the Landyne software suite, to calculate the CTF with temporal and spatial dumping envelopes for conventional TEM and to extend it to various aberrations (up to fifth order) for aberration-corrected (AC)-TEM. It also includes effects on the CTF and imaging due to the objective aperture and image drift for tutorial purposes. The CTFscope has a user-friendly graphical interface for simulation, visualization, saving, and loading of the microscopy conditions and results. It can be used to explore instrumental performance information due to optical aberrations, effects on the resolution of a TEM and AC-TEM, and for teaching electron microscopy courses.

Current progress in programmable electrostatic phase plates raises questions about their usefulness for specific applications. Here, we explore different designs for such phase plates with the specific goal of correcting spherical aberration in the transmission electron microscope (TEM). We numerically investigate whether a phase plate could provide down to 1 Ångström spatial resolution on a conventional uncorrected TEM. Different design aspects (fill factor, pixel pattern, symmetry) were evaluated to understand their effect on the electron probe size and current density. Some proposed designs show a probe size ($d_{50}$) down to 0.66 Å, proving that it should be possible to correct spherical aberration well past the 1 Å limit using a programmable phase plate consisting of an array of electrostatic phase-shifting elements.

This article introduces a training simulator for electron beam alignment using Ronchigrams. The interactive web application, www.ronchigram.com, is an advanced educational tool aimed at making scanning transmission electron microscopy (STEM) more accessible and open. For experienced microscopists, the tool offers on-hand quantification of simulated Ronchigrams and their resolution limits.

Aberration correction in the analytical transmission electron microscope is most closely associated with improvements in high-resolution imaging. In this paper, the combination of that technology with new system designs, which optimize both electron optics and x-ray detection, is shown to provide more than a tenfold increase in performance over the last 25 years.

The selection of the correct convergence angle is essential for achieving the highest resolution imaging in scanning transmission electron microscopy (STEM). The use of poor heuristics, such as Rayleigh's quarter-phase rule, to assess probe quality and uncertainties in the measurement of the aberration function results in the incorrect selection of convergence angles and lower resolution. Here, we show that the Strehl ratio provides an accurate and efficient way to calculate criteria for evaluating the probe size for STEM. A convolutional neural network trained on the Strehl ratio is shown to outperform experienced microscopists at selecting a convergence angle from a single electron Ronchigram using simulated datasets. Generating tens of thousands of simulated Ronchigram examples, the network is trained to select convergence angles yielding probes on average 85% nearer to optimal size at millisecond speeds (0.02% of human assessment time). Qualitative assessment on experimental Ronchigrams with intentionally introduced aberrations suggests that trends in the optimal convergence angle size are well modeled but high accuracy requires a high number of training datasets. This near-immediate assessment of Ronchigrams using the Strehl ratio and machine learning highlights a viable path toward the rapid, automated alignment of aberration-corrected electron microscopes.

This article introduces an intuitive understanding of electron Ronchigrams and how they are affected by aberrations. This is accomplished through a portable web application, http://Ronchigram.com. The history of the Ronchigram, the physics which define it, and its visual features are reviewed in the context of aberration-corrected scanning transmission electron microscopy.

The resolution of high-resolution transmission electron microscopes (TEM) has been improved down to subangstrom levels by correcting the spherical aberration (Cs) of the objective lens, and the information limit is thus determined mainly by partial temporal coherence. As a traditional Young’s fringe test does not reveal the true information limit for an ultra-high-resolution electron microscope, new methods to evaluate temporal coherence have been proposed based on a tilted-beam diffractogram. However, the diffractogram analysis cannot be applied when the nonlinear contribution becomes significant. Therefore, we have proposed a method based on the three-dimensional (3D) Fourier transform (FT) of through-focus TEM images, and evaluated the performance of some Cs-corrected TEMs at lower voltages. In this report, we generalize the 3D FT analysis and derive the 3D transmission cross-coefficient. The profound difference of the 3D FT analysis from the diffractogram analysis is its capability to extract linear image information from the image intensity, and further to evaluate two linear image contributions separately on the Ewald sphere envelopes. Therefore, contrary to the diffractogram analysis the 3D FT analysis can work with a strong scattering object. This is the necessary condition if we want to directly observe the linear image transfer down to a few tens of picometer.

This paper presents a proposal for reducing the final probe size of focused electron/ion beam columns that are operated in a high primary beam current mode where relatively large final apertures are used, typically required in applications such as electron beam lithography, focused ion beams, and electron beam spectroscopy. An annular aperture together with a lens corrector unit is used to replace the conventional final hole-aperture, creating an annular ring-shaped primary beam. The corrector unit is designed to eliminate the first- and second-order geometric aberrations of the objective lens, and for the same probe current, the final geometric aberration limited spot size is predicted to be around a factor of 50 times smaller than that of the corresponding conventional hole-aperture beam. Direct ray tracing simulation is used to illustrate how a three-stage core lens corrector can be used to eliminate the first- and second-order geometric aberrations of an electric Einzel objective lens.

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.

Helium accumulation negatively impacts structural materials used in neutron-irradiated environments, such as fission and fusion reactors. Next-generation fission and fusion reactors will require structural materials, such as steels, that are resistant to large neutron doses yet see service temperatures in the range most affected by helium embrittlement. Previous work has indicated the difficulty of experimentally differentiating nanometer-sized cavities such as helium bubbles from the Ti–Y–O rich nanoclusters (NCs) in radiation-tolerant nanostructured ferritic alloys (NFAs). Because the NCs are expected to sequester helium away from grain boundaries and reduce embrittlement, experimental methods to study simultaneously the NC and bubble populations are needed. In this study, aberration-corrected scanning transmission electron microscopy (STEM) results combining high-collection-efficiency X-ray spectrum images (SIs), multivariate statistical analysis (MVSA), and Fresnel-contrast bright-field STEM imaging, have been used for such a purpose. Fresnel-contrast imaging, with careful attention to TEM-STEM reciprocity, differentiates bubbles from NCs. MVSA of X-ray SIs unambiguously identifies NCs. Therefore, combined Fresnel-contrast STEM and X-ray SI is an effective STEM-based method to characterize helium-bearing NFAs.

One of the difficulties in analyzing atomic resolution electron microscope images is that the sample thickness is usually unknown or has to be fitted from parameters that are not precisely known. An accurate measure of thickness, ideally on a column-by-column basis, parameter free, and with single atom accuracy, would be of great value for many applications, such as matching to simulations. Here we propose such a quantification method for annular dark field scanning transmission electron microscopy by using the single electron intensity level of the detector. This method has the advantage that we can routinely quantify annular dark field images operating at both low and high beam currents, and under high dynamic range conditions, which is useful for the quantification of ultra-thin or light-element materials. To facilitate atom counting at the atomic scale we use the mean intensity in an annular dark field image averaged over a primitive cell, with no free parameters to be fitted. To illustrate the potential of our method, we demonstrate counting the number of Al (or N) atoms in a wurtzite-type aluminum nitride single crystal at each primitive cell over the range of 3–99 atoms.

The advent of aberration correction for transmission electron microscopy has transformed atomic resolution imaging into a nearly routine technique for structural analysis. Now an emerging frontier in electron microscopy is the development of in situ capabilities to observe reactions at atomic resolution in real time and within realistic environments. Here we present a new in situ gas cell holder that is designed for compatibility with a wide variety of sample type (i.e., dimpled 3-mm discs, standard mesh grids, various types of focused ion beam lamellae attached to half grids). Its capabilities include localized heating and precise control of the gas pressure and composition while simultaneously allowing atomic resolution imaging at ambient pressure. The results show that 0.25-nm lattice fringes are directly visible for nanoparticles imaged at ambient pressure with gas path lengths up to 20 μm. Additionally, we quantitatively demonstrate that while the attainable contrast and resolution decrease with increasing pressure and gas path length, resolutions better than 0.2 nm should be accessible at ambient pressure with gas path lengths less than the 15 μm utilized for these experiments.

TEAM I is the final product of the Transmission Electron Aberration-corrected Microscope (TEAM) Project, a collaborative project funded by the Department of Energy with the goal of designing and building a platform for a next generation aberration-corrected electron microscope capable of image resolution of up to 50 pm. The TEAM instrument incorporates a number of new technologies, including spherical- and chromatic-aberration correction, an all-piezo-electric sample stage and an active-pixel direct electron detector. This article describes the functionality of this advanced instrumentation, its response to changes in environment or operating conditions, and its stability during daily operation within the National Center for Electron Microscopy user facility.

Aberration correction, after a 50 year incubation period of developing ideas and techniques while awaiting enabling technology, has transformed electron microscopy during the first dozen years of the 21st century. Some of the conditions that accompanied this transformation, the required complexity and its effect on the way microscopy is pursued, recent results that promise to change the field, and directions for the future are briefly described.

The high beam current and subangstrom resolution of aberration-corrected scanning transmission electron microscopes has enabled electron energy loss spectroscopy (EELS) mapping with atomic resolution. These spectral maps are often dose limited and spatially oversampled, leading to low counts/channel and are thus highly sensitive to errors in background estimation. However, by taking advantage of redundancy in the dataset map, one can improve background estimation and increase chemical sensitivity. We consider two such approaches—linear combination of power laws and local background averaging—that reduce background error and improve signal extraction. Principal component analysis (PCA) can also be used to analyze spectrum images, but the poor peak-to-background ratio in EELS can lead to serious artifacts if raw EELS data are PCA filtered. We identify common artifacts and discuss alternative approaches. These algorithms are implemented within the Cornell Spectrum Imager, an open source software package for spectroscopic analysis.

The increasing use of environmental transmission electron microscopy (ETEM) in materials science provides exciting new possibilities for investigating chemical reactions and understanding both the interaction of fast electrons with gas molecules and the effect of the presence of gas on high-resolution imaging. A gaseous atmosphere in the pole-piece gap of the objective lens of the microscope alters both the incoming electron wave prior to interaction with the sample and the outgoing wave below the sample. Whereas conventional TEM samples are usually thin (below 100 nm), the gas in the environmental cell fills the entire gap between the pole pieces and is thus not spatially localized. By using an FEI Titan environmental transmission electron microscope equipped with a monochromator and an aberration corrector on the objective lens, we have investigated the effects on imaging and spectroscopy caused by the presence of the gas.

The twin interface structure in twinning superlattice InP nanowires with zincblende structure has been investigated using electron exit wavefunction restoration from focal series images recorded on an aberration-corrected transmission electron microscope. By comparing the exit wavefunction phase with simulations from model structures, it was possible to determine the twin structure to be the ortho type with preserved In-P bonding order across the interface. The bending of the thin nanowires away from the intended ⟨110⟩ axis could be estimated locally from the calculated diffraction pattern, and this parameter was successfully taken into account in the simulations.

Aberration correction reduces the depth of field in scanning transmission electron microscopy (STEM) and thus allows three-dimensional (3D) imaging by depth sectioning. This imaging mode offers the potential for sub-Ångstrom lateral resolution and nanometer-scale depth sensitivity. For biological samples, which may be many microns across and where high lateral resolution may not always be needed, optimizing the depth resolution even at the expense of lateral resolution may be desired, aiming to image through thick specimens. Although there has been extensive work examining and optimizing the probe formation in two dimensions, there is less known about the probe shape along the optical axis. Here the probe shape is examined in three dimensions in an attempt to better understand the depth resolution in this mode. Examples are presented of how aberrations change the probe shape in three dimensions, and it is found that off-axial aberrations may need to be considered for focal series of large areas. It is shown that oversized or annular apertures theoretically improve the vertical resolution for 3D imaging of nanoparticles. When imaging nanoparticles of several nanometer size, regular STEM can thereby be optimized such that the vertical full-width at half-maximum approaches that of the aberration-corrected STEM with a standard aperture.