arXiv subjects

Christoph Hofer

Publications and source records attributed to Christoph Hofer.

At least 19 recordsLinked to original sources

arXiv2025

Investigating the convergence properties of iterative ptychography for atomic-resolution low-dose imaging

This study investigates the convergence properties of a collection of iterative electron ptychography methods, under low electron doses ($<$ 10$^3$ $e^-/A^2$) and gives particular attention to the impact of the user-defined update strengths. We demonstrate that carefully chosen values for this parameter, ideally smaller than those conventionally met in the literature, are essential for achieving accurate reconstructions of the projected electrostatic potential. Using a 4D dataset of a thin hybrid organic-inorganic formamidinium lead bromide (FAPbBr$_{3}$) sample, we show that convergence is in practice achievable only when the update strengths for both the object and probe are relatively small compared to what is found in literature. Additionally we demonstrate that under low electron doses, the reconstructions initial error increases when the update strength coefficients are reduced below a certain threshold emphasizing the existence of critical values beyond which the algorithms are trapped in local minima. These findings highlight the need for carefully optimized reconstruction parameters in iterative ptychography, especially when working with low electron doses, ensuring both effective convergence and correctness of the result.

cond-mat.mtrl-sci↗

arXiv2025

Improving the low-dose performance of aberration correction in single sideband ptychography

The single sideband (SSB) framework of analytical electron ptychography can account for the presence of residual geometrical aberrations induced by the probe-forming lens. However, the accuracy of this aberration correction method is highly sensitive to noise, in part due to the necessity of phase unwrapping. In this work, we thus propose two strategies to improve aberration correction performance in low-dose conditions: confining phase unwrapping within the sidebands and selecting only well-unwrapped sidebands for calculating aberration coefficients. These strategies are validated through SSB reconstructions of both simulated and experimental 4D-STEM datasets of monolayer tungsten diselenide (WSe2). A comparison of results demonstrates significant improvements in Poisson noise tolerance, making aberration correction more robust and reliable for low-dose imaging.

physics.app-ph↗

arXiv2023

Phase offset method of ptychographic contrast reversal correction

The contrast transfer function of direct ptychography methods such as the single side band (SSB) method are single signed, yet these methods still sometimes exhibit contrast reversals, most often where the projected potentials are strong. In thicker samples central focusing often provides the best ptychographic contrast as this leads to defocus variations within the sample canceling out. However focusing away from the entrance surface is often undesirable as this degrades the annular dark field (ADF) signal. Here we discuss how phase wrap asymptotes in the frequency response of SSB ptychography give rise to contrast reversals, without the need for dynamical scattering, and how these can be counteracted by manipulating the phases such that the asymptotes are either shifted to higher frequencies or damped via amplitude modulation. This is what enables post collection defocus correction of contrast reversals. However, the phase offset method of counteracting contrast reversals we introduce here is generally found to be superior to post collection application of defocus, with greater reliability and generally stronger contrast. Importantly, the phase offset method also works for thin and thick samples where central focusing does not. Finally, the independence of the method from focus is useful for optical sectioning involving ptychography, improving interpretability by better disentangling the effects of strong potentials and focus.

physics.optics↗

arXiv2023

Reliable phase quantification in focused probe electron ptychography of thin materials

Electron ptychography provides highly sensitive, dose efficient phase images which can be corrected for aberrations after the data has been acquired. This is crucial when very precise quantification is required, such as with sensitivity to charge transfer due to bonding. Drift can now be essentially eliminated as a major impediment to focused probe ptychography, which benefits from the availability of easily interpretable simultaneous Z-contrast imaging. However challenges have remained when quantifying the ptychographic phases of atomic sites. The phase response of a single atom has a negative halo which can cause atoms to reduce in phase when brought closer together. When unaccounted for, as in integrating methods of quantification, this effect can completely obscure the effects of charge transfer. Here we provide a new method of quantification that overcomes this challenge, at least for 2D materials, and is robust to experimental parameters such as noise, sample tilt.

cond-mat.mtrl-sci↗

arXiv2023

Detecting charge transfer at defects in 2D materials with electron ptychography

Electronic charge transfer at the atomic scale can reveal fundamental information about chemical bonding, but is far more challenging to directly image than the atomic structure. The charge density is dominated by the atomic nuclei, with bonding causing only a small perturbation. Thus detecting any change due to bonding requires a higher level of sensitivity than imaging structure and the overall charge density. Here we achieve the sensitivity required to detect charge transfer in both pristine and defected monolayer WS\textsubscript{2} using the high dose efficiency of electron ptychography and its ability to correct for lens aberrations. Excellent agreement is achieved with first-principles image simulations including where thermal diffuse scattering is explicitly modeled via finite-temperature molecular dynamics based on density functional theory. The focused-probe ptychography configuration we use also provides the important ability to concurrently collect the annular dark-field signal, which can be unambiguously interpreted in terms of the atomic structure and chemical identity of the atoms, independently of the charge transfer. Our results demonstrate both the power of ptychographic reconstructions and the importance of quantitatively accurate simulations to aid their interpretation.

cond-mat.mtrl-sci↗

arXiv2022

Picometer-precision few-tilt ptychotomography of 2D materials

From ripples to defects, edges and grain boundaries, the 3D atomic structure of 2D materials is critical to their properties. However the damage inflicted by conventional 3D analysis precludes its use with fragile 2D materials, particularly for the analysis of local defects. Here we dramatically increase the potential for precise local 3D atomic structure analysis of 2D materials, with both greatly improved dose efficiency and sensitivity to light elements. We demonstrate light atoms can now be located in complex 2D materials with picometer precision at doses 30 times lower than previously possible. Moreover we demonstrate this using a material, WS$_2$, in which the light S atoms are in fact practically invisible to conventional methods. The key advance is combining the concept of few tilt tomography with highly dose efficient ptychography in scanning transmission electron microscopy. We further demonstrate the method experimentally with the even more challenging and newly discovered 2D CuI, leveraging a new extremely high temporal resolution camera.

physics.app-ph↗

arXiv2021

Event driven 4D STEM acquisition with a Timepix3 detector: microsecond dwell time and faster scans for high precision and low dose applications

Four dimensional scanning transmission electron microscopy (4D STEM) records the scattering of electrons in a material in great detail. The benefits offered by 4D STEM are substantial, with the wealth of data it provides facilitating for instance high precision, high electron dose efficiency phase imaging via center of mass or ptychography based analysis. However the requirement for a 2D image of the scattering to be recorded at each probe position has long placed a severe bottleneck on the speed at which 4D STEM can be performed. Recent advances in camera technology have greatly reduced this bottleneck, with the detection efficiency of direct electron detectors being especially well suited to the technique. However even the fastest frame driven pixelated detectors still significantly limit the scan speed which can be used in 4D STEM, making the resulting data susceptible to drift and hampering its use for low dose beam sensitive applications. Here we report the development of the use of an event driven Timepix3 direct electron camera that allows us to overcome this bottleneck and achieve 4D STEM dwell times down to 100~ns; orders of magnitude faster than what has been possible with frame based readout. We characterise the detector for different acceleration voltages and show that the method is especially well suited for low dose imaging and promises rich datasets without compromising dwell time when compared to conventional STEM imaging.

physics.ins-det↗

arXiv2021

Towards Exotic Layered Materials: 2D Cuprous Iodide

Heterostructures composed of two-dimensional (2D) materials are already opening many new possibilities in such fields of technology as electronics and magnonics, but far more could be achieved if the number and diversity of 2D materials is increased. So far, only a few dozen 2D crystals have been extracted from materials that exhibit a layered phase in ambient conditions, omitting entirely the large number of layered materials that may exist in other temperatures and pressures. Here, we demonstrate how these structures can be stabilized in 2D van der Waals stacks under room temperature via growing them directly in graphene encapsulation by using graphene oxide as the template material. Specifically, we produce an ambient stable 2D structure of copper and iodine, a material that normally only occurs in layered form at elevated temperatures between 645 and 675 K. Our results establish a route to the production of more exotic phases of materials that would otherwise be difficult or impossible to stabilize for experiments in ambient.

cond-mat.mtrl-sci↗

arXiv2021

Aligned Stacking of Nanopatterned 2D materials -- Towards 3D printing at atomic resolution

Two-dimensional materials can be combined by placing individual layers on top of each other, so that they are bound only by their van der Waals interaction. The sequence of layers can be chosen arbitrarily, enabling an essentially atomic-level control of the material and thereby a wide choice of properties along one dimension. However, simultaneous control over the structure in the in-plane directions is so far still rather limited. Here, we combine spatially controlled modifications of 2D materials, using focused electron irradiation or electron beam induced etching, with the layer-by-layer assembly of van der Waals heterostructures. A novel assembly process makes it possible to structure each layer with an arbitrary pattern prior to the assembly into the heterostructure. Moreover, it enables a stacking of the layers with accurate lateral alignment, with an accuracy of currently 10nm, under observation in an electron microscope. Together, this enables the fabrication of almost arbitrary 3D structures with highest spatial resolution.

physics.app-ph↗

arXiv2021

Topological Attention for Time Series Forecasting

The problem of (point) forecasting $ \textit{univariate} $ time series is considered. Most approaches, ranging from traditional statistical methods to recent learning-based techniques with neural networks, directly operate on raw time series observations. As an extension, we study whether $\textit{local topological properties}$, as captured via persistent homology, can serve as a reliable signal that provides complementary information for learning to forecast. To this end, we propose $\textit{topological attention}$, which allows attending to local topological features within a time horizon of historical data. Our approach easily integrates into existing end-to-end trainable forecasting models, such as $\texttt{N-BEATS}$, and in combination with the latter exhibits state-of-the-art performance on the large-scale M4 benchmark dataset of 100,000 diverse time series from different domains. Ablation experiments, as well as a comparison to a broad range of forecasting methods in a setting where only a single time series is available for training, corroborate the beneficial nature of including local topological information through an attention mechanism.

cs.LG↗

arXiv2019

Connectivity-Optimized Representation Learning via Persistent Homology

We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an autoencoder's latent space via a novel type of loss, operating on information from persistent homology. Under mild conditions, this loss is differentiable and we present a theoretical analysis of the properties induced by the loss. We choose one-class learning as our upstream task and demonstrate that the imposed structure enables informed parameter selection for modeling the in-class distribution via kernel density estimators. Evaluated on computer vision data, these one-class models exhibit competitive performance and, in a low sample size regime, outperform other methods by a large margin. Notably, our results indicate that a single autoencoder, trained on auxiliary (unlabeled) data, yields a mapping into latent space that can be reused across datasets for one-class learning.

cs.LG↗

arXiv2019

High-resolution remote thermography using luminescent low-dimensional tin-halide perovskites

While metal-halide perovskites have recently revolutionized research in optoelectronics through a unique combination of performance and synthetic simplicity, their low-dimensional counterparts can further expand the field with hitherto unknown and practically useful optical functionalities. In this context, we present the strong temperature dependence of the photoluminescence (PL) lifetime of low-dimensional, perovskite-like tin-halides, and apply this property to thermal imaging with a high precision of 0.05 °C. The PL lifetimes are governed by the heat-assisted de-trapping of self-trapped excitons, and their values can be varied over several orders of magnitude by adjusting the temperature (up to 20 ns °C-1). Typically, this sensitive range spans up to one hundred centigrade, and it is both compound-specific and shown to be compositionally and structurally tunable from -100 to 110 ° C going from [C(NH2)3]2SnBr4 to Cs4SnBr6 and (C4N2H14I)4SnI6. Finally, through the innovative implementation of cost-effective hardware for fluorescence lifetime imaging (FLI), based on time-of-flight (ToF) technology, these novel thermoluminophores have been used to record thermographic videos with high spatial and thermal resolution.

physics.app-ph↗

arXiv2018

Direct visualization of the 3D structure of silicon impurities in graphene

We directly visualize the three-dimensional (3D) geometry and dynamics of silicon impurities in graphene as well as their dynamics by aberration-corrected scanning transmission electron microscopy. By acquiring images when the sample is tilted, we show that an asymmetry of the atomic position of the heteroatom in the projection reveals the non-planarity of the structure. From a sequence of images, we further demonstrate that the Si atom switches between up- and down- configurations with respect to the graphene plane, with an asymmetric cross-section. We further analyze the 3D structure and dynamics of a silicon tetramer in graphene. Our results clarify the out-of-plane structure of impurities in graphene by direct experimental observation and open a new route to study their dynamics in three dimensions.

physics.app-ph↗

arXiv2018

Revealing the 3D Structure of Graphene Defects

We demonstrate insights into the three-dimensional structure of defects in graphene, in particular grain boundaries, obtained via a new approach from two transmission electron microscopy images recorded at different angles. The structure is obtained through an optimization process where both the atomic positions as well as the simulated imaging parameters are iteratively changed until the best possible match to the experimental images is found. We first demonstrate that this method works using an embedded defect in graphene that allows direct comparison to the computationally predicted three-dimensional shape. We then applied the method to a set of grain boundary structures with misorientation angles nearly spanning the whole available range (2.6-29.8°). The measured height variations at the boundaries reveal a strong correlation with the misorientation angle with lower angles resulting in stronger corrugation and larger kink angles. Our results allow for the first time a direct comparison with theoretical predictions for the corrugation at grain boundaries and we show that the measured kink angles are significantly smaller than the largest predicted ones.

physics.app-ph↗

arXiv2018

Analysis of point defects in graphene using low dose scanning transmission electron microscopy imaging and maximum likelihood reconstruction

Freestanding graphene displays an outstanding resilience to electron irradiation at low electron energies. Point defects in graphene are, however, subject to beam driven dynamics. This means that high resolution micrographs of point defects, which usually require a high electron irradiation dose might not represent the intrinsic defect population. Here, we capture the inital defects formed by ejecting carbon atoms under electron irradiation, by imaging with very low doses and subsequent reconstruction of the frequently occuring defects via a maximum likelihood algorithm.

cond-mat.mes-hall↗

arXiv2018

A parallel multigrid solver for multi-patch Isogeometric Analysis

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are considered, one obtains the approximation power of a high-order method, but the number of degrees of freedom behaves like for a low-order method. One important ingredient to use a discretization with large spline degree, is a robust and preferably parallelizable solver. While numerical evidence shows that multigrid solvers with standard smoothers (like Gauss Seidel) does not perform well if the spline degree is increased, the multigrid solvers proposed by the authors and their co-workers proved to behave optimal both in the grid size and the spline degree. In the present paper, the authors want to show that those solvers are parallelizable and that they scale well in a parallel environment.

math.NA↗

arXiv2018

Discontinuous Galerkin Isogeometric Analysis for segmentations generating overlapping regions

In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g., provided by a Computer Aided Design (CAD) model. Typically, small gap and overlapping regions can appear at the patch interfaces of such multipatch representations. In the current work we consider multipatch representations having only small overlapping regions between the patches. We develop a Discontinuous Galerkin (DG)- IGA method which can be immediately applied to these representations. Our method appropriately connects the fluxes of the one face of the overlapping region with the flux of the opposite face. We provide a theoretical justification of our approach by splitting the whole error into two components: the first is related to the incorrect representation of the patches (consistency error) and the second to the approximation properties of the IGA space. We show bounds for both components of the error. We verify the theoretical error estimates in a series of numerical examples.

math.NA↗

arXiv2018

Automated image acquisition for low-dose STEM at atomic resolution

Beam damage is a major limitation in electron microscopy that becomes increasingly severe at higher resolution. One possible route to circumvent radiation damage, which forms the basis for single-particle electron microscopy and related techniques, is to distribute the dose over many identical copies of an object. For the acquisition of low-dose data, ideally no dose should be applied to the region of interest prior to the acquisition of data. We present an automated approach that can collect large amounts of data efficiently by acquiring images in an user-defined area-of-interest with atomic resolution. We demonstrate that the stage mechanics of the Nion UltraSTEM, combined with an intelligent algorithm to move the sample, allows the automated acquisition of atomically resolved images from micron-sized areas of a graphene substrate. Moving the sample stage automatically in a regular pattern over the area-of-interest enables the collection of data from pristine sample regions without exposing them to the electron beam before recording an image. Therefore, it is possible to obtain data with minimal dose (no prior exposure from focusing), which is only limited by the minimum signal needed for data processing. This enables us to prevent beam induced damage in the sample and to acquire large datasets within a reasonable amount of time.

cond-mat.mtrl-sci↗