Atomic structure imaging beyond conventional resolution limits in the transmission electron microscope

Diffusion distribution model for damage mitigation in scanning transmission electron microscopy

Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent reports suggest that certain types of damage can be modelled as a diffusion process and that the accumulation effects of this process must be kept low in order to reduce damage. We therefore develop an explicit mathematical formulation of spatiotemporal diffusion processes in STEM that take into account both instrument and sample parameters. Furthermore, our framework can aid the design of Diffusion Controlled Sampling (DCS) strategies using optimally selected probe positions in STEM, that constrain the cumulative diffusion distribution. Numerical simulations highlight the variability of the cumulative diffusion distribution for different experimental STEM configurations. These analytical and numerical frameworks can subsequently be used for careful design of 2- and 4-dimensional STEM experiments where beam damage is minimised.

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.

Morphological variations to a ptychographic algorithm

Ptychography is a technique widely used in microscopy for achieving high-resolution imaging. This method relies on computational processing of images gathered from diffraction patterns produced by several partial illuminations of a sample. We numerically studied the effect of using different shapes for illuminating the aforementioned sample: convex shapes, such as circles and regular polygons, and unconnected shapes that resemble a QR code. Our results suggest that the use of unconnected shapes seems to outperform convex shapes in terms of convergence and, in some cases, accuracy.

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.

Electron Ptychographic Diffractive Imaging of Boron Atoms in LaB6 Crystals

Ptychographic diffractive imaging has the potential for structural determination of materials without the constraints of relatively small, isolated samples required for conventional coherent diffractive imaging. The increased illumination diversity introduced using multiple measurements (overlapped probe positions) also provides higher sensitivity to phase changes in weakly scattering samples. The resolution of a ptychographic reconstruction is ultimately determined by the diffraction limit for the wavelength of the radiation used. However, in practical experiments using electrons either the maximum collection angle of the detector used to record the data or the partial coherence of the source impose lower resolution limits. Nonetheless for medium energy electrons this suggests a potential sub 0.1 nm spatial resolution limit, comparable to that obtained using aberration corrected instruments. However, simultaneous visualization of light and heavier atoms in specimens using ptychography at sub 0.1 nm resolution presents a significant challenge. Here, we demonstrate a ptychographic reconstruction of a LaB₆ crystal in which light B atoms were clearly resolved together with the heavy La atoms in the reconstructed phase. The technique used is general and can also be applied to non-crystalline and extended crystalline samples. As such it offers an alternative future basis for imaging the atomic structure of materials, particularly those containing low atomic number elements.

Solving ptychography with a convex relaxation

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that currently solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the ptychographic reconstruction algorithm that is currently in widespread use.

Exceeding conventional resolution limits in high-resolution transmission electron microscopy using tilted illumination and exit-wave restoration

Tilted illumination exit-wave restoration is compared for two aberration-corrected instruments at different accelerating voltages. The experimental progress of this technique is also reviewed and the significance of off-axial aberrations examined. Finally, the importance of higher order aberration compensation combined with careful correction of the lower order aberrations is highlighted.