Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons, Part II: Differential Holographic Tomography.

It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the in-molecule Fresnel diffraction can be significant due to the intrinsically shallow depth of focus. These facts suggest that the three-dimensional reconstruction of such structures from defocus image series collected at multiple rotational orientations of a molecule can be effectively performed for each atom separately, using the incoherent first Born approximation. The corresponding reconstruction method, termed here Differential Holographic Tomography, is developed theoretically and demonstrated computationally on several numerical models of biological molecules. It is shown that the method is capable of accurate reconstruction of the locations of atoms in a molecule from TEM data collected at a small number of random orientations of the molecule, with one or more defocus images per orientation. Possible applications to cryogenic electron microscopy and other areas are briefly discussed.

Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons.

The relative roles of multiple electron scattering and in-molecule Fresnel diffraction in atomic-resolution transmission electron microscopy of small molecules are discussed. It is argued that, while multiple scattering tends to have only a moderate effect, the in-molecule Fresnel diffraction can be significant due to the shallow depth of focus in high-resolution electron microscopy. When the depth of focus is smaller than the size of molecule along the trajectory of the electrons, the projection approximation breaks down and pairs of images at orientations of the molecule rotated by 180 degrees are not the same. Put another way, it matters which way the electrons traverse the specimen. In such cases, diffraction tomography based on the first Born or first Rytov approximation represents a more suitable method for the reconstruction of the three-dimensional distribution of the electrostatic potential, compared to conventional computed tomography which intrinsically relies on the validity of the projection approximation. A simplified method for diffraction tomography based on the approximation of Fresnel diffraction by the transport of intensity equation is proposed and tested on numerically simulated examples.

On real-valued SDE and nonnegative-valued SDE population models with demographic variability.

Population dynamics with demographic variability is frequently studied using discrete random variables with continuous-time Markov chain (CTMC) models. An approximation of a CTMC model using continuous random variables can be derived in a straightforward manner by applying standard methods based on the reaction rates in the CTMC model. This leads to a system of Itô stochastic differential equations (SDEs) which generally have the form [Formula: see text] where [Formula: see text] is the population vector of random variables, [Formula: see text] is the drift vector, and G is the diffusion matrix. In some problems, the derived SDE model may not have real-valued or nonnegative solutions for all time. For such problems, the SDE model may be declared infeasible. In this investigation, new systems of SDEs are derived with real-valued solutions and with nonnegative solutions. To derive real-valued SDE models, reaction rates are assumed to be nonnegative for all time with negative reaction rates assigned probability zero. This biologically realistic assumption leads to the derivation of real-valued SDE population models. However, small but negative values may still arise for a real-valued SDE model. This is due to the magnitudes of certain problem-dependent diffusion coefficients when population sizes are near zero. A slight modification of the diffusion coefficients when population sizes are near zero ensures that a real-valued SDE model has a nonnegative solution, yet maintains the integrity of the SDE model when sizes are not near zero. Several population dynamic problems are examined to illustrate the methodology.

The Standardization of Outpatient Procedure (STOP) Narcotics after anorectal surgery: a prospective non-inferiority study to reduce opioid use.

BACKGROUND: Prescription of opioid medication after ambulatory anorectal surgery may be excessive and lead to opioid misuse. The purpose of this study was to evaluate the efficacy of a multi-modality opioid-sparing approach to control postoperative pain and reduce opioid prescriptions after outpatient anorectal surgery. METHODS: A prospective non-inferiority pre- and post-intervention study was completed at three academic hospitals. Patients included were 18-75 years of age who had outpatient anorectal surgeries. The Standardization of Outpatient Procedure (STOP) Narcotics intervention was implemented, which is a multi-pronged analgesia bundle integrating patient education, health care provider education, and intra-/postoperative analgesia focused on multi-modal pain control strategies and opioid-reduced prescriptions. The primary outcome was patient-reported average pain in the first 7 postoperative days. Secondary outcomes included patient-reported quality of pain management, medication utilization, prescription refills and medication disposal. RESULTS: Ninety-three patients had outpatient anorectal surgery (42 pre-intervention and 51 post-intervention). No difference was seen in average postoperative pain in the pre- vs. post-intervention groups (2.8 vs. 2.6 on an 11-point scale, p = 0.33) or patient-reported quality of pain control (good/very good in 57% vs. 63%, p = 0.58). The median oral morphine equivalents (OME) prescribed was significantly less [112.5 (IQR 50-150) pre-intervention vs. 50 (IQR 50-50) post-intervention, p < 0.001]. In the post-intervention group, only 45% of patients filled their opioid prescription and median opioid use was 12.5 OME (2.5 pills). CONCLUSIONS: While pain control after anorectal surgery must consider the individual patient's needs, a standardized pain care bundle significantly decreased opioid prescribing without an increase in patient-reported postoperative pain.

Separate seasons of infection and reproduction can lead to multi-year population cycles.

Many host-pathogen systems are characterized by a temporal order of disease transmission and host reproduction. For example, this can be due to pathogens infecting certain life cycle stages of insect hosts; transmission occurring during the aggregation of migratory birds; or plant diseases spreading between planting seasons. We develop a simple discrete-time epidemic model with density-dependent transmission and disease affecting host fecundity and survival. The model shows sustained multi-annual cycles in host population abundance and disease prevalence, both in the presence and absence of density dependence in host reproduction, for large horizontal transmissibility, imperfect vertical transmission, high virulence, and high reproductive capability. The multi-annual cycles emerge as invariant curves in a Neimark-Sacker bifurcation. They are caused by a carry-over effect, because the reproductive fitness of an individual can be reduced by virulent effects due to infection in an earlier season. As the infection process is density-dependent but shows an effect only in a later season, this produces delayed density dependence typical for second-order oscillations. The temporal separation between the infection and reproduction season is crucial in driving the cycles; if these processes occur simultaneously as in differential equation models, there are no sustained oscillations. Our model highlights the destabilizing effects of inter-seasonal feedbacks and is one of the simplest epidemic models that can generate population cycles.

Optimal control of a vectored plant disease model for a crop with continuous replanting.

Vector-transmitted diseases of plants have had devastating effects on agricultural production worldwide, resulting in drastic reductions in yield for crops such as cotton, soybean, tomato, and cassava. Plant-vector-virus models with continuous replanting are investigated in terms of the effects of selection of cuttings, roguing, and insecticide use on disease prevalence in plants. Previous models are extended to include two replanting strategies: frequencyreplanting and abundance-replanting. In frequency-replanting, replanting of infected cuttings depends on the selection frequency parameter ε, whereas in abundance-replanting, replanting depends on plant abundance via a selection rate parameter also denoted as ε. The two models are analysed and new thresholds for disease elimination are defined for each model. Parameter values for cassava, whiteflies, and African cassava mosaic virus serve as a case study. A numerical sensitivity analysis illustrates how the equilibrium densities of healthy and infected plants vary with parameter values. Optimal control theory is used to investigate the effects of roguing and insecticide use with a goal of maximizing the healthy plants that are harvested. Differences in the control strategies in the two models are seen for large values of ε. Also, the combined strategy of roguing and insecticide use performs better than a single control.

Phonon Spectroscopy at Atomic Resolution.

Advances in source monochromation in transmission electron microscopy have opened up new possibilities for investigations of condensed matter using the phonon-loss sector of the energy-loss spectrum. Here, we explore the spatial variations of the spectrum as an atomic-sized probe is scanned across a thin flake of hexagonal boron nitride. We demonstrate that phonon spectral mapping of atomic structure is possible. These results are consistent with a model for the quantum excitation of phonons and confirm that Z-contrast imaging is based on inelastic scattering associated with phonon excitation.

Large angle illumination enabling accurate structure reconstruction from thick samples in scanning transmission electron microscopy.

Most reconstructions of the electrostatic potential of a specimen at atomic resolution assume a thin and weakly scattering sample, restricting accurate quantification to specimens only tens of Ångströms thick. We demonstrate that using large-angle-illumination scanning transmission electron microscopy (STEM)-a probe forming aperture with convergence angle larger than about 50 mrad-allows us to better meet the weak phase object approximation and thereby accurately reconstruct the electrostatic potential in samples thicker than the order of 100 Å.

A quantum mechanical exploration of phonon energy-loss spectroscopy using electrons in the aloof beam geometry.

Phonon energy-loss spectroscopy using electrons has both high resolution and low resolution components, associated with short- and long-range interactions, respectively. In this paper, we discuss how these two contributions arise from a fundamental quantum mechanical perspective. Starting from a correlated model for the atomic motion we show how short range 'impact' scattering and long range 'dipole' scattering arises. The latter dominates in aloof beam imaging, an imaging geometry in which radiation damage can be avoided.

Structure Retrieval at Atomic Resolution in the Presence of Multiple Scattering of the Electron Probe.

The projected electrostatic potential of a thick crystal is reconstructed at atomic resolution from experimental scanning transmission electron microscopy data recorded using a new generation fast-readout electron camera. This practical and deterministic inversion of the equations encapsulating multiple scattering that were written down by Bethe in 1928 removes the restriction of established methods to ultrathin (≲50 Å) samples. Instruments already coming on line can overcome the remaining resolution-limiting effects in this method due to finite probe-forming aperture size, spatial incoherence, and residual lens aberrations.

Legionella longbeachae detected in an industrial cooling tower linked to a legionellosis outbreak, New Zealand, 2015; possible waterborne transmission?

A legionellosis outbreak at an industrial site was investigated to identify and control the source. Cases were identified from disease notifications, workplace illness records, and from clinicians. Cases were interviewed for symptoms and risk factors and tested for legionellosis. Implicated environmental sources were sampled and tested for legionella. We identified six cases with Legionnaires' disease and seven with Pontiac fever; all had been exposed to aerosols from the cooling towers on the site. Nine cases had evidence of infection with either Legionella pneumophila serogroup (sg) 1 or Legionella longbeachae sg1; these organisms were also isolated from the cooling towers. There was 100% DNA sequence homology between cooling tower and clinical isolates of L. pneumophila sg1 using sequence-based typing analysis; no clinical L. longbeachae isolates were available to compare with environmental isolates. Routine monitoring of the towers prior to the outbreak failed to detect any legionella. Data from this outbreak indicate that L. pneumophila sg1 transmission occurred from the cooling towers; in addition, L. longbeachae transmission was suggested but remains unproven. L. longbeachae detection in cooling towers has not been previously reported in association with legionellosis outbreaks. Waterborne transmission should not be discounted in investigations for the source of L. longbeachae infection.

Atomic resolution elemental mapping using energy-filtered imaging scanning transmission electron microscopy with chromatic aberration correction.

This paper addresses a novel approach to atomic resolution elemental mapping, demonstrating a method that produces elemental maps with a similar resolution to the established method of electron energy-loss spectroscopy in scanning transmission electron microscopy. Dubbed energy-filtered imaging scanning transmission electron microscopy (EFISTEM) this mode of imaging is, by the quantum mechanical principle of reciprocity, equivalent to tilting the probe in energy-filtered transmission electron microscopy (EFTEM) through a cone and incoherently averaging the results. In this paper we present a proof-of-principle EFISTEM experimental study on strontium titanate. The present approach, made possible by chromatic aberration correction, has the advantage that it provides elemental maps which are immune to spatial incoherence in the electron source, coherent aberrations in the probe-forming lens and probe jitter. The veracity of the experiment is supported by quantum mechanical image simulations, which provide an insight into the image-forming process. Elemental maps obtained in EFTEM suffer from the effect known as preservation of elastic contrast, which, for example, can lead to a given atomic species appearing to be in atomic columns where it is not to be found. EFISTEM very substantially reduces the preservation of elastic contrast and yields images which show stability of contrast with changing thickness. The experimental application is demonstrated in a proof-of-principle study on strontium titanate.

Accuracy and precision of thickness determination from position-averaged convergent beam electron diffraction patterns using a single-parameter metric.

Position-averaged convergent beam electron diffraction patterns are formed by averaging the transmission diffraction pattern while scanning an atomically-fine electron probe across a sample. Visual comparison between experimental and simulated patterns is increasingly being used for sample thickness determination. We explore automating the comparison via a simple sum square difference metric. The thickness determination is shown to be accurate (i.e. the best-guess deduced thickness generally concurs with the true thickness), though factors such as noise, mistilt and inelastic scattering reduce the precision (i.e. increase the uncertainty range). Notably, the precision tends to be higher for smaller probe-forming aperture angles.

Simulation in elemental mapping using aberration-corrected electron microscopy.

Elemental mapping at the atomic scale in aberration-corrected electron microscopes is becoming increasingly widely used. In this paper we describe the essential role of simulation in understanding the underlying physics and thus in correctly interpreting these maps, both qualitatively and quantitatively.

A new method to detect and correct sample tilt in scanning transmission electron microscopy bright-field imaging.

Important properties of functional materials, such as ferroelectric shifts and octahedral distortions, are associated with displacements of the positions of lighter atoms in the unit cell. Annular bright-field scanning transmission electron microscopy is a good experimental method for investigating such phenomena due to its ability to image light and heavy atoms simultaneously. To map atomic positions at the required accuracy precise angular alignment of the sample with the microscope optical axis is necessary, since misalignment (tilt) of the specimen contributes to errors in position measurements of lighter elements in annular bright-field imaging. In this paper it is shown that it is possible to detect tilt with the aid of images recorded using a central bright-field detector placed within the inner radius of the annular bright-field detector. For a probe focus near the middle of the specimen the central bright-field image becomes especially sensitive to tilt and we demonstrate experimentally that misalignment can be detected with a precision of less than a milliradian, as we also confirm in simulation. Coma in the probe, an aberration that can be misidentified as tilt of the specimen, is also investigated and it is shown how the effects of coma and tilt can be differentiated. The effects of tilt may be offset to a large extent by shifting the diffraction plane detector an amount equivalent to the specimen tilt and we provide an experimental proof of principle of this using a segmented detector system.

Composition measurement in substitutionally disordered materials by atomic resolution energy dispersive X-ray spectroscopy in scanning transmission electron microscopy.

The increasing use of energy dispersive X-ray spectroscopy in atomic resolution scanning transmission electron microscopy invites the question of whether its success in precision composition determination at lower magnifications can be replicated in the atomic resolution regime. In this paper, we explore, through simulation, the prospects for composition measurement via the model system of AlxGa1-xAs, discussing the approximations used in the modelling, the variability in the signal due to changes in configuration at constant composition, and the ability to distinguish between different compositions. Results are presented in such a way that the number of X-ray counts, and thus the expected variation due to counting statistics, can be gauged for a range of operating conditions.

Quantitative STEM Imaging of Order-Disorder Phenomena in Double Perovskite Thin Films.

Using aberration-corrected high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM), we investigate ordering phenomena in epitaxial thin films of the double perovskite Sr_{2}CrReO_{6}. Experimental and simulated imaging and diffraction are used to identify antiphase domains in the films. Image simulation provides insight into the effects of atomic-scale ordering along the beam direction on HAADF-STEM intensity. We show that probe channeling results in ±20% variation in intensity for a given composition, allowing 3D ordering information to be probed using quantitative STEM.

Influence of experimental conditions on atom column visibility in energy dispersive X-ray spectroscopy.

Here we report the influence of key experimental parameters on atomically resolved energy dispersive X-ray spectroscopy (EDX). In particular, we examine the role of the probe forming convergence semi-angle, sample thickness, lattice spacing, and dwell/collection time. We show that an optimum specimen-dependent probe forming convergence angle exists to maximize the signal-to-noise ratio of the atomically resolved signal in EDX mapping. Furthermore, we highlight that it can be important to select an appropriate dwell time to efficiently process the X-ray signal. These practical considerations provide insight for experimental parameters in atomic resolution energy dispersive X-ray analysis.

Practical aspects of diffractive imaging using an atomic-scale coherent electron probe.

Four-dimensional scanning transmission electron microscopy (4D-STEM) is a technique where a full two-dimensional convergent beam electron diffraction (CBED) pattern is acquired at every STEM pixel scanned. Capturing the full diffraction pattern provides a rich dataset that potentially contains more information about the specimen than is contained in conventional imaging modes using conventional integrating detectors. Using 4D datasets in STEM from two specimens, monolayer MoS2 and bulk SrTiO3, we demonstrate multiple STEM imaging modes on a quantitative absolute intensity scale, including phase reconstruction of the transmission function via differential phase contrast imaging. Practical issues about sampling (i.e. number of detector pixels), signal-to-noise enhancement and data reduction of large 4D-STEM datasets are emphasized.

Quantitative atomic resolution elemental mapping via absolute-scale energy dispersive X-ray spectroscopy.

Quantitative agreement on an absolute scale is demonstrated between experiment and simulation for two-dimensional, atomic-resolution elemental mapping via energy dispersive X-ray spectroscopy. This requires all experimental parameters to be carefully characterized. The agreement is good, but some discrepancies remain. The most likely contributing factors are identified and discussed. Previous predictions that increasing the probe forming aperture helps to suppress the channelling enhancement in the average signal are confirmed experimentally. It is emphasized that simple column-by-column analysis requires a choice of sample thickness that compromises between being thick enough to yield a good signal-to-noise ratio while being thin enough that the overwhelming majority of the EDX signal derives from the column on which the probe is placed, despite strong electron scattering effects.