An Efficient Electron Ptychography Method for Retrieving the Object Spectrum from Only a Few Iterations.

We present an efficient approach for electron ptychography based on a mathematical relationship that differs from that underlying the established algorithms of the ptychography iterative engine or the noniterative algorithms like the Wigner-distribution-deconvolution or the single-side-band method. Three variables are handled in this method-the transfer function of the objective lens, the object spectrum, and the diffraction wave whose phase is unknown. In the case of an aberration-corrected electron microscope, one is able to obtain a well-estimated transfer function of the lens. After reducing the number of three variables down to two, we construct an iterative loop between the object spectrum and the diffraction wave, which retrieves the object spectrum within a small number of iterations. We tested this object spectrum retrieval method on both a calculated and an experimental 4D-STEM datasets. By applying this method, we explore the influence of sampling, dose, and the size of illumination aperture on the reconstructed phase images.

Integrated Differential Phase Contrast (IDPC)-STEM Utilizing a Multi-Sector Detector for Imaging Thick Samples.

The integrated differential phase contrast (IDPC) method is useful for generating the potential map of a thin sample. We evaluate theoretically the potential of IDPC imaging for thick samples by varying the focus at different sample thicknesses. Our calculations show that high defocus values result in enhanced anisotropy of the contrast transfer function (CTF) and uninterpretable images, if a quadrant detector is applied. We further show that applying a multi-sector detector can result in an almost isotropic CTF. By sector number-dependent calculations for both Cc/C3-corrected and C3-corrected scanning transmission electron microscopy (STEM), we show that the increase of detector sectors not only removes the anisotropy of the CTF, but also improves image contrast and resolution. For a proof-of-principle IDPC-STEM (uncorrected) experiment, we realize the functionality of a 12-sector detector from a physical quadrant detector and demonstrate the improvement in contrast and resolution on the example of InGaN/GaN quantum well structure.

Computationally Efficient Handling of Partially Coherent Electron Sources in (S)TEM Image Simulations via Matrix Diagonalization.

We introduce a novel method to improve the computational efficiency for (S)TEM image simulation by employing matrix diagonalization of the mixed envelope function (MEF). The MEF is derived by taking the finite size and the energy spread of the effective electron source into account, and is a component of the transmission cross-coefficient that accounts for the correlation between partially coherent waves. Since the MEF is a four-dimensional array and its application in image calculations is time-consuming, we reduce the computation time by using its eigenvectors. By incorporating the aperture function into the matrix diagonalization, only a small number of eigenvectors are required to approximate the original matrix with high accuracy. The diagonalization enables for each eigenvector the calculation of the corresponding image by employing the coherent model. The individual images are weighted by the corresponding eigenvalues and then summed up, resulting in the total partially coherent image.

Mrs Movers & Shakers.

Y. Shirley Meng, University of California, San Diego, has earned the 2020 Faraday Medal from the Royal Society of Chemistry. The Faraday Medal is awarded annually by the Electrochemistry Group of the Royal Society of Chemistry to an electrochemist working outside of the UK and Ireland in recognition of their outstanding original contributions and innovation as a mid-career researcher in any field of electrochemistry.

Chromatic Aberration Correction for Atomic Resolution TEM Imaging from 20 to 80 kV.

Atomic resolution in transmission electron microscopy of thin and light-atom materials requires a rigorous reduction of the beam energy to reduce knockon damage. However, at the same time, the chromatic aberration deteriorates the resolution of the TEM image dramatically. Within the framework of the SALVE project, we introduce a newly developed C_{c}/C_{s} corrector that is capable of correcting both the chromatic and the spherical aberration in the range of accelerating voltages from 20 to 80 kV. The corrector allows correcting axial aberrations up to fifth order as well as the dominating off-axial aberrations. Over the entire voltage range, optimum phase-contrast imaging conditions for weak signals from light atoms can be adjusted for an optical aperture of at least 55 mrad. The information transfer within this aperture is no longer limited by chromatic aberrations. We demonstrate the performance of the microscope using the examples of 30 kV phase-contrast TEM images of graphene and molybdenum disulfide, showing unprecedented contrast and resolution that matches image calculations.

Minimum-dose phase-contrast tomography by successive numerical optical sectioning employing the aberration-corrected STEM and a pixelated detector.

Aberration correction combined with a pixelated detector enable atomic-resolution phase-contrast imaging in the scanning transmission electron microscope (STEM) using all elastically scattered electrons within the illumination cone. The review describes this possibility in detail revisiting the image formation in the STEM on a fundamental quantum-mechanical treatment of electron scattering within the object and the effect of the lenses on the electron wave. Describing electron scattering by means of scattering amplitudes enables a straightforward derivation of a) the reciprocity theorem, b) the optical theorem of electron scattering, and c) the precise formulation of the image intensity distribution in the STEM for different modes of operation. The second part of the review describes in detail a novel method for obtaining pure phase-contrast images in the STEM using the integrated differential phase-contrast (IDPC) procedure. The incorporation of a chromatic (Cc) and spherically (Cs) corrected objective lens and a pixelated detector in the STEM combined with numerical through-focusing enables optical sectioning with atomic 3D resolution of thick objects with about the same dose as that for a 2D object, at least in principle. Numerical simulations of the IDPC transfer function and the point spread function for the focal plane and several reconstructed defocused planes demonstrate the feasibility of the method.

The contributions of Otto Scherzer (1909-1982) to the development of the electron microscope.

Otto Scherzer was one of the pioneers of theoretical electron optics. He was coauthor of the first comprehensive book on electron optics and was the first to understand that round electron lenses could not be combined to correct aberrations, as is the case in light optics. He subsequently was the first to describe several alternative means to correct spherical and chromatic aberration of electron lenses. These ideas were put into practice by his laboratory and students at Darmstadt and their successors, leading to the fully corrected electron microscopes now in operation.

Lattice contrast in the core-loss EFTEM signal of graphene.

The realization of chromatic aberration correction enables energy-filtered transmission electron microscopy (EFTEM) at atomic resolution even for large energy windows. Previous works have demonstrated lattice contrast from ionization-edge signals such as the L2,3 edges of silicon or titanium. However, the direct interpretation as chemical information was found to be hampered by contributions from elastic contrast with dynamic scattering, especially for thick samples. Here we demonstrate that even for thin samples with light atoms, the interpretation of the ionization-edge signal is complicated by inversions from bright-atom to dark-atom contrast. Our EFTEM experiments for graphene show lattice contrast in the carbon K-edge signal, and we find bright-atom and dark-atom contrast for different defoci.

Historical aspects of aberration correction.

A brief history of the development of direct aberration correction in electron microscopy is outlined starting from the famous Scherzer theorem established in 1936. Aberration correction is the long story of many seemingly fruitless efforts to improve the resolution of electron microscopes by compensating for the unavoidable resolution-limiting aberrations of round electron lenses over a period of 50 years. The successful breakthrough, in 1997, can be considered as a quantum step in electron microscopy because it provides genuine atomic resolution approaching the size of the radius of the hydrogen atom. The additional realization of monochromators, aberration-free imaging energy filters and spectrometers has been leading to a new generation of analytical electron microscopes providing elemental and electronic information about the object on an atomic scale.

First application of Cc-corrected imaging for high-resolution and energy-filtered TEM.

Contrast-transfer calculations indicate that C(c) correction should be highly beneficial for high-resolution and energy-filtered transmission electron microscopy. A prototype of an electron optical system capable of correcting spherical and chromatic aberration has been used to verify these calculations. A strong improvement in resolution at an acceleration voltage of 80 kV has been measured. Our first C(c)-corrected energy-filtered experiments examining a (LaAlO(3))(0.3)(Sr(2)AlTaO(6))(0.7)/LaCoO(3) interface demonstrated a significant gain for the spatial resolution in elemental maps of La.

Efficient linear phase contrast in scanning transmission electron microscopy with matched illumination and detector interferometry.

The ability to image light elements in soft matter at atomic resolution enables unprecedented insight into the structure and properties of molecular heterostructures and beam-sensitive nanomaterials. In this study, we introduce a scanning transmission electron microscopy technique combining a pre-specimen phase plate designed to produce a probe with structured phase with a high-speed direct electron detector to generate nearly linear contrast images with high efficiency. We demonstrate this method by using both experiment and simulation to simultaneously image the atomic-scale structure of weakly scattering amorphous carbon and strongly scattering gold nanoparticles. Our method demonstrates strong contrast for both materials, making it a promising candidate for structural determination of heterogeneous soft/hard matter samples even at low electron doses comparable to traditional phase-contrast transmission electron microscopy. Simulated images demonstrate the extension of this technique to the challenging problem of structural determination of biological material at the surface of inorganic crystals.

Future trends in aberration-corrected electron microscopy.

The attainable specimen resolution is determined by the instrumental resolution limit d(i) and by radiation damage. Solid objects such as metals are primarily damaged by atom displacement resulting from knock-on collisions of the incident electrons with the atomic nuclei. The instrumental resolution improves appreciably by means of aberration correction. To achieve atomic resolution at voltages below approximately 100 kV and a large number of equally resolved image points, we propose an achromatic electron-optical aplanat, which is free of chromatic aberration, spherical aberration and total off-axial coma. Its anisotropic component is eliminated either by a dual objective lens consisting of two separate windings with opposite directions of their currents or by skew octopoles employed in the TEAM corrector. We obtain optimum imaging conditions by operating the aberration-corrected electron microscope at voltages below the knock-on threshold for atom displacement and by shifting the phase of the non-scattered wave by pi/2 or that of the scattered wave by -pi/2. In this negative contrast mode, the phase contrast and the scattering contrast add up with the same sign. The realization of a low-voltage aberration-corrected phase transmission electron microscope for the visualization of radiation-sensitive objects is the aim of the proposed SALVE (Sub-A Low-Voltage Electron microscope) project. This microscope will employ a coma-free objective lens, an obstruction-free phase plate and a novel corrector compensating for the spherical and chromatic aberrations.

Electrostatic correction of the chromatic and of the spherical aberration of charged-particle lenses (part II).

A doubly symmetric electrostatic corrector which compensates for the axial chromatic and the axial third-order aberration of charged-particle lenses is outlined. Due to the double symmetry the corrector does not introduce linear off-axis aberrations and yields in combination with a round objective lens an electron-optical aplanat. The principle of the electrostatic correction of the axial chromatic aberration is explained in mathematical terms. The geometry of the electrodes of a suitable corrector is optimized with respect to the chromatic correction, the maximum strength of the electric field, and the residual higher-order aberrations which limit the resolution. The resulting aplanat achieves a resolution limit of about 2 nm for an image field with a diameter of 1500 nm. The required stabilities of the electric power supplies are discussed in detail.