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.

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.

Precision and accuracy of quantitative scanning transmission electron microscopy (STEM) methods such as ptychography, and the mapping of electric, magnetic, and strain fields depend on the dose. Reasonable acquisition time requires high beam current and the ability to quantitatively detect both large and minute changes in signal. A new hybrid pixel array detector (PAD), the second-generation Electron Microscope Pixel Array Detector (EMPAD-G2), addresses this challenge by advancing the technology of a previous generation PAD, the EMPAD. The EMPAD-G2 images continuously at a frame-rates up to 10 kHz with a dynamic range that spans from low-noise detection of single electrons to electron beam currents exceeding 180 pA per pixel, even at electron energies of 300 keV. The EMPAD-G2 enables rapid collection of high-quality STEM data that simultaneously contain full diffraction information from unsaturated bright-field disks to usable Kikuchi bands and higher-order Laue zones. Test results from 80 to 300 keV are presented, as are first experimental results demonstrating ptychographic reconstructions, strain and polarization maps. We introduce a new information metric, the maximum usable imaging speed (MUIS), to identify when a detector becomes electron-starved, saturated or its pixel count is mismatched with the beam current.

Scanning transmission X-ray microscopy is a powerful method for mapping chemical phases in nano-materials. The point spread function (PSF) of a conventional zone-plate-based microscope limits the achievable spatial resolution and also results in spatially resolved spectra that do not accurately reflect the spatial heterogeneity of the samples when the scale of the detail approaches the probe size. X-ray ptychography, a coherent-scattering-based imaging scheme that effectively removes the probe from the image data, returns accurate spectra from regions smaller than the probe size. We show through simulation how the long tails on the PSF of an x-ray optic can cause spectral distortion near a boundary between two spectrally distinct regions. The resulting apparent point spectra can appear mixed, with the species on one side of the boundary seeming to be present on the other even at a distance from the boundary equal to several times the spatial resolution. We further demonstrate the effect experimentally and show that ptychographic microscopy can return the expected spectra from a model system, whereas conventional microscopy does not.

A reformulated implementation of single-sideband ptychography enables analysis and display of live detector data streams in 4D scanning transmission electron microscopy (STEM) using the LiberTEM open-source platform. This is combined with live first moment and further virtual STEM detector analysis. Processing of both real experimental and simulated data shows the characteristics of this method when data are processed progressively, as opposed to the usual offline processing of a complete data set. In particular, the single-sideband method is compared with other techniques such as the enhanced ptychographic engine in order to ascertain its capability for structural imaging at increased specimen thickness. Qualitatively interpretable live results are obtained also if the sample is moved, or magnification is changed during the analysis. This allows live optimization of instrument as well as specimen parameters during the analysis. The methodology is especially expected to improve contrast- and dose-efficient in situ imaging of weakly scattering specimens, where fast live feedback during the experiment is required.

A new closed cell is presented for in situ X-ray ptychography which allows studies under gas flow and at elevated temperature. In order to gain complementary information by transmission and scanning electron microscopy, the cell makes use of a Protochips E-chipTM which contains a small, thin electron transparent window and allows heating. Two gold-based systems, 50 nm gold particles and nanoporous gold as a relevant catalyst sample, were used for studying the feasibility of the cell. Measurements showing a resolution around 40 nm have been achieved under a flow of synthetic air and during heating up to temperatures of 933 K. An elevated temperature exhibited little influence on image quality and resolution. With this study, the potential of in situ hard X-ray ptychography for investigating annealing processes of real catalyst samples is demonstrated. Furthermore, the possibility to use the same sample holder for ex situ electron microscopy before and after the in situ study underlines the unique possibilities available with this combination of electron microscopy and X-ray microscopy on the same sample.

We present a deterministic approach to the ptychographic retrieval of the wave at the exit surface of a specimen of condensed matter illuminated by X-rays. The method is based on the solution of an overdetermined set of linear equations, and is robust to measurement noise. The set of linear equations is efficiently solved using the conjugate gradient least-squares method implemented using fast Fourier transforms. The method is demonstrated using a data set obtained from a gold–chromium nanostructured test object. It is shown that the transmission function retrieved by this linear method is quantitatively comparable with established methods of ptychography, with a large decrease in computational time, and is thus a good candidate for real-time reconstruction.