arXiv subjects

Peter Moeck

Publications and source records attributed to Peter Moeck.

At least 19 recordsLinked to original sources

arXiv2025

Posterior corrections for systematic distortions in atomic-resolution images from hexagonal crystals

Digital images from crystals, as projected from the third spatial dimension and recorded in atomic resolution with any kind of real-world microscope, feature necessarily broken symmetries of the translation-periodicity-restricted Euclidean plane. The symmetry breakings are due to both the imaging process and the real structure of the imaged crystal, with the former cause typically dominating. A posterior algorithmic reduction of the symmetry breaking in such images constitutes, thus, often a correction for many of the distortions that were introduced by the imaging processes. Numerically quantified restorations of such symmetries can, therefore, be used to demonstrate the efficacy of a newly implemented posterior correction method for atomic-resolution images from hexagonal crystals. Recently developed information theory based methods are here shown to be suitable for this purpose. Thirteen experimental atomic-resolution images from graphite and monolayer molybdenite (MoS2), as respectively obtained by scanning tunneling microscopy, atomic force microscopy in the torsional resonance mode, and aberration-corrected parallel illumination transmission electron microscopy served as test cases in our larger (in its totality so far unpublished) study, from which we quote here. The source code of the software that was used for our distortion corrections and the whole report on that study are freely available on GitHub.

cond-mat.mtrl-sci↗

arXiv2024

Histropy: A Computer Program for Quantifications of Histograms of 2D Gray-scale Images

The computer program "Histropy" is an interactive Python program for the quantification of selected features of two-dimensional (2D) images/patterns (in either JPG/JPEG, PNG, GIF, BMP, or baseline TIF/TIFF formats) using calculations based on the pixel intensities in this data, their histograms, and user-selected sections of those histograms. The histograms of these images display pixel-intensity values along the x-axis (of a 2D Cartesian plot), with the frequency of each intensity value within the image represented along the y-axis. The images need to be of 8-bit or 16-bit information depth and can be of arbitrary size. Histropy generates an image's histogram surrounded by a graphical user interface that allows one to select any range of image-pixel intensity levels, i.e. sections along the histograms' x-axis, using either the computer mouse or numerical text entries. The program subsequently calculates the (so-called Monkey Model) Shannon entropy and root-mean-square contrast for the selected section and displays them as part of what we call a "histogram-workspace-plot." To support the visual identification of small peaks in the histograms, the user can switch between a linear and log-base-10 display scale for the y-axis of the histograms. Pixel intensity data from different images can be overlaid onto the same histogram-workspace-plot for visual comparisons. The visual outputs of the program can be saved as histogram-workspace-plots in the PNG format for future usage. The source code of the program and a brief user manual are published in the supporting materials as well as on GitHub. Instead of taking only 2D images as inputs, the program's functionality could be extended by a few lines of code to other potential uses employing data tables with one or two dimensions in the CSV format.

cs.GR↗

arXiv2023

Genuine Plane Symmetries versus Pseudosymmetries in two Crystal Patterns of Graphic Artwork

The reader is informed about a method for the objective identification of the plane symmetry group of a "noisy" crystal pattern. Without giving numerical details, this information theory based method is applied to two beautiful pieces of graphic art. The plane symmetry group identifications distinguish between genuine symmetries and pseudosymmetries as a byproduct. Pieces of graphic/geometric artworks are ideal for the further refinement of the new method because they are macroscopic and their '"noise content" is chiefly due to the handiwork and employed creative procedures of individual artists. As different graphic techniques/procedures were employed in the creation of the classified crystal patterns, one may glean insights on how well a particular technique or procedure supports the realization of a crystallographic symmetry group in a graphic work of art.

physics.comp-ph↗

arXiv2023

Information-theoretic symmetry classifications of crystal patterns in the presence of noise and strong Fedorov type pseudosymmetries for an optimal subsequent crystallographic processing of these patterns

Statistically sound crystallographic symmetry classifications are obtained with information theory based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic images with very strong Fedorov type pseudosymmetries and varying amounts of noise serve as examples. The correct distinctions between genuine symmetries and their Fedorov type pseudosymmetry counterparts failed only for the noisiest image of the series where an inconsistent combination of plane symmetry group and projected Laue class was obtained. Contrary to traditional crystallographic symmetry classifications with an image processing program such as CRISP, the classification process does not need to be supervised by a human being. This enables crystallographic symmetry classification of digital images that are more or less periodic in two dimensions (2D) as recorded with sufficient spatial resolution from a wide range of samples with different types of scanning probe microscopes. Alternatives to the employed objective classification methods as proposed by members of the computational symmetry community and machine learning proponents are briefly discussed in an appendix and are found to be wanting because they ignore Fedorov type pseudosymmetries completely. The information theory based methods are more accurate than visual classifications at first sight by most human experts.

eess.IV↗

arXiv2022

A Computer Program for Objective Point Symmetry Classifications of Pseudosymmetric Electron Diffraction Spot Patterns

A Python program for calculating the metrics necessary to perform information-theory based symmetry classifications and quantifications of transmission electron diffraction spot patterns is introduced. It is the first of its kind, in that it implements objectivity into crystallographic symmetry classifications and quantifications of approximate zone axis patterns from crystals. The equations by which the program operates as well as the required inputs are given. The results of the program's analysis of an experimental transmission electron diffraction spot pattern from a crystal with a pseudo-hexagonal lattice metric and a rectangular-centered Bravias lattice is used as an example. The program will eventually be appended to allow analysis of the other hierarchical translational pseudo-symmetry and Bravais lattice type combinations. Crystallographic Rsym values of traditional classifications into projected point symmetry groups are provided alongside information-theoretic results of the new program's analysis for comparison purposes.

cond-mat.mtrl-sci↗

arXiv2022

Objective crystallographic symmetry classifications of a noisy crystal pattern with strong Fedorov type pseudosymmetries and its optimal image-quality enhancement

Statistically sound crystallographic symmetry classifications are obtained with information theory based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic patterns with strong Fedorov type pseudosymmetries and varying amounts of noise serve as examples. Contrary to traditional crystallographic symmetry classifications with an image processing program such as CRISP, the classification process does not need to be supervised by a human being and is free of any subjectively set thresholds in the geometric model selection process. This enables crystallographic symmetry classification of digital images that are more or less periodic in two dimensions (2D), a.k.a. crystal patterns, as recorded with sufficient structural resolution from a wide range of crystalline samples with different types of scanning probe and transmission electron microscopes. Correct symmetry classifications enable the optimal crystallographic processing of such images. That processing consists in the averaging over all asymmetric units in all unit cells in the selected image area and significantly enhances both the signal to noise ratio and the structural resolution of a microscopic study of a crystal. For sufficiently complex crystal patterns, the information-theoretic symmetry classification methods are more accurate than both visual classifications by human experts and the recommendations of one of the popular crystallographic image processing programs of electron crystallography.

cond-mat.mtrl-sci↗

arXiv2022

Objective Point Symmetry Classifications/Quantifications of an Electron Diffraction Spot Pattern with Pseudo-Hexagonal Metric

The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the analysis of an experimental electron diffraction spot pattern, for the first time. Digital input data are considered in this approach to consist of the pixel-wise sums of approximately Gaussian distributed noise and an unknown underlying signal that is strictly 2D periodic. Structural defects within the crystals or on the crystal surfaces, instrumental image recording noise, slight deviations from zero-crystal-tilt conditions in transmission electron microscopy, inhomogeneous staining in structural biology studies of intrinsic membrane protein complexes in lipid bilayers, and small inaccuracies in the algorithmic processing of the digital data all contribute to a single generalized noise term. The plane symmetry group and projected Laue class(or 2D Bravais lattice type) that is anchored to the least broken symmetries are identified as genuine in the presence of generalized noise. More severely broken symmetries that are not anchored to the least broken symmetries are identified as pseudo-symmetries. Our point symmetry quantification study of an electron diffraction spot pattern is highly topical because a new contrast mechanism for 4D scanning transmission electron microscopy was recently demonstrated by other authors. The usage of objective symmetry quantifications is bound to become the preeminent condition of the establishment of that contrast mode as an industry-wide standard.

cond-mat.mtrl-sci↗

arXiv2022

Information-theoretic point symmetry classifications/quantifications of an electron diffraction spot pattern from a crystal with strong translational pseudosymmetry

The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the analysis of an experimental selected-area transmission electron diffraction spot pattern. The extracted lattice parameters of this crystal are within experimental error bars consistent with a metric tensor that suggests the presence of hexagonal translation symmetry. The point symmetry of the combined low, medium, and high resolution spots is, however, no higher than 2mm. The likelihood of this electron diffraction pattern belonging to a rectangular-centered crystal rather than a hexagonal crystal is quantified on the basis of its information-theoretic point group symmetry classifications. Presumably due to a slight misorientation away from the exact [001] zone axis combined with the curvature of the Ewald sphere and a real structure that includes intergrowth of quadruple NbO and triple BaNbO3 blocks of varying sizes and orientations, the group of highest resolution spots, i.e. d-spacings between 0.125 to 0.085 nm, feature point symmetry .m. only. The crystallographic Rsym values of traditional classifications into the point groups that are compatible with the experimentally obtained primitive lattice parameters are provided for comparison purposes. As it is common practice in diffraction based crystallography, point symmetry classification and quantification results for the group of highest resolution spots are provided separately from their counterparts for the combined low, medium, and high resolution spots.

cond-mat.mtrl-sci↗

arXiv2021

Towards more reasonable identifications of the symmetries in noisy digital images from periodic and aperiodic crystals

A geometric form of information theory allows for reasonable, i.e. probabilistic, evidence-ranking based, and generalized noise-level dependent, classifications of the crystallographic and quasicrystallographic symmetries in noisy digital images. Such classifications are based solely on the image pixel intensity values, justifiable assumptions about the aggregate distribution of generalized noise in the images, asymptotic extrapolations to zero-noise images, and rational symmetry model selections with maximized predictive accuracy in the presence of both symmetry-inclusion relations and pseudo-symmetries. Preferring a well developed geometric form of information theory over a theoretically possible geometric-Bayesian approach for these classifications is the only subjective choice made. Using digital data planes and assuming approximately Gaussian distributed generalized noise, reasonable crystallographic and quasicrystallographic symmetry classifications can be made for noisy images from both scanning probe and transmission electron microscopes. A binary type classification of structurally very similar mate-rials into either a quasicrystal or one of its rational/crystalline approximants based on the approximate point symmetries in their noisy digital images is proposed here for the first time.

physics.data-an↗

arXiv2021

On classification approaches for crystallographic symmetries of noisy 2D periodic patterns

The classifications approaches for the crystallographic symmetries of patterns that are more or less periodic in two dimensions are critically reviewed and their relative performance qualitatively evaluated. The information theory based approach of the author utilizes digital images and turns out to be the only one that allows for fully objective classifications of the crystallographic symmetries, i.e. Bravais lattice type, Laue class, and plane symmetry group, of noisy real-world images. His information theory based crystallographic symmetry classifications utilize geometric bias-corrected sums of squared residuals, i.e. pertinent first order information, and enable the most meaningful crystallographic averaging in the spatial frequency domain, which suppresses generalized noise much more effectively than traditional Fourier filtering. Taking account of the fact that it is fundamentally unsound to assign an abstract mathematical concept such as a single symmetry type, class, or group with 100 % certainty to a more or less 2D periodic record of a noisy real-world imaging experiment that involved a real-world sample, the information theory based approach to crystallographic symmetry classifications delivers probabilistic classifications. Recent applications of deep convolutional neural networks to classifications of crystallographic translation symmetries in 2D and crystals in three dimensions are discussed as these machines deliver probabilistic classifications by non-analytical means.

cond-mat.mtrl-sci↗

arXiv2020

Objective, Probabilistic, and Generalized Noise Level Dependent Classifications of sets of more or less 2D Periodic Images into Plane Symmetry Groups

Crystallographic symmetry classifications from real-world images with periodicities in two dimensions (2D) are of interest to crystallographers and practitioners of computer vision studies alike. Currently, these classifications are typically made by both communities in a subjective manner that relies on arbitrary thresholds for judgments, and are reported under the pretense of being definitive, which is impossible. Moreover, the computer vision community tends to use direct space methods to make such classifications instead of more powerful and computationally efficient Fourier space methods. This is because the proper functioning of those methods requires more periodic repeats of a unit cell motif than are commonly present in images analyzed by the computer vision community. We demonstrate a novel approach to plane symmetry group classifications that is enabled by Kenichi Kanatani's Geometric Akaike Information Criterion and associated Geometric Akaike weights. Our approach leverages the advantages of working in Fourier space, is well suited for handling the hierarchic nature of crystallographic symmetries, and yields probabilistic results that are generalized noise level dependent. The latter feature means crystallographic symmetry classifications can be updated when less noisy image data and more accurate processing algorithms become available. We demonstrate the ability of our approach to objectively estimate the plane symmetry and pseudosymmetries of sets of synthetic 2D-periodic images with varying amounts of red-green-blue and spread noise. Additionally, we suggest a simple solution to the problem of too few periodic repeats in an input image for practical application of Fourier space methods. In doing so, we effectively solve the decades-old and heretofore intractable problem from computer vision of symmetry detection and classification from images in the presence of noise.

cs.CV↗

arXiv2020

Crystallographic image processing for scanning probe microscopy

Scanning probe microscopy (SPM) images of regularly arranged spatially periodic objects can be processed crystallographically. The resulting information may be used to remove from the SPM image distortions that are due to a less than perfect imaging process. The combined effects of these distortions result in a point spread function that gives a quantitative measure of the performance of the microscope for a certain set of experimental conditions. On the basis of highly symmetric calibration samples, the point spread function of the microscope may be extracted and utilized for the correction of SPM images of unknowns that were recorded under essentially the same experimental conditions. We concentrate in this paper on more theoretical aspects of our method. A blunt scanning tunneling microscopy (STM) tip that consists of multiple mini-tips with electron orbital dimensions may be symmetrized on the basis of prior knowledge on the plane symmetry of a two-dimensional periodic array. This is illustrated with the crystallographic processing of a STM image of a regular array of fluorinated cobalt phthalocyanine molecules on graphite and backed up conceptually by simple simulations.

cond-mat.mtrl-sci↗

arXiv2020

Advances in Crystallographic Image Processing for Scanning Probe Microscopy

This book chapter reviews progress in crystallographic image processing (CIP) for scanning probe microscopy (SPM) that has occurred since our description of the technique was first put into open access in this book series in the year 2010. The signal to noise ratio in all kinds of experimental images of more or less regular 2D periodic arrays is significantly enhanced by CIP and the technique is independent of the type of recording device. In the SPM imaging context, CIP can be understood as an a posteriori sharpening of the effective experimental scanning probe tip by computational means. It is now possible to remove multiple scanning probe mini-tip effects in images from 2D periodic arrays of physical objects that either self-assembled or were created artificially. Accepted within the scientific community is by now also the fact that SPM tips can change their shape and fine structure during the operation of a microscope and, thereby, obfuscate the recorded images in systematic ways. CIP restores much of the smeared out information in such images. The adaptation of a geometric Akaike Information Criterion from the robotics and computer vision community to the unambiguous detection of 2D translation symmetries enabled much of our recent progress. In the main body of this book chapter, we discuss this adaptation and briefly illustrate its utility on an example.

cond-mat.mtrl-sci↗

arXiv2020

Clarifying multiple-tip effects on Scanning Tunneling Microscopy imaging of 2D periodic objects and crystallographic averaging in the spatial frequency domain

Crystallographic image processing (CIP) techniques may be utilized in scanning probe microscopy (SPM) to glean information that has been obscured by signals from multiple probe tips. This may be of particular importance for scanning tunneling microscopy (STM) and requires images from a sample that is periodic in two dimensions. The image-forming current for multiple tips in STM is derived in a more straightforward manner than prior approaches. The Fourier spectrum of the current for p4mm Bloch surface wave functions and a pair of delta function tips reveals the tip-separation dependence of various types of image obscurations. In particular our analyses predict that quantum interference should be visible on a macroscopic scale in the form of bands quite distinct from the basket-weave patterns a purely classical model would create at the same periodic double STM tip separations. A surface wave function that models the essential character of highly (0001) oriented pyrolytic graphite (technically known as HOPG) is introduced and used for a similar tip-separation analysis. Using a bonding H_2 tip wave function with significant spatial extent instead of this pair of infinitesimal Dirac delta function tips does not affect these outcomes in any observable way. This is explained by Pierre Curie's well known symmetry principle. Classical simulations of multiple tip effects in STM images may be understood as modeling multiple tip effects in images that were recorded with other types of SPMs). Our analysis clarifies why CIP and crystallographic averaging work well in removing the effects of a blunt SPM tip (that consist of multiple mini-tips) from the recorded 2D periodic images and also outlines the limitations of this image processing techniques for certain spatial separations of STM mini-tips.

cond-mat.mtrl-sci↗

arXiv2019

3D printing in the context of Science, Technology, Engineering, and Mathematics education at the college/university level

An overview concerning 3D printing (a.k.a. additive manufacturing) within the context of Science, Technology, Engineering, and Mathematics (STEM) education at the college/university level is provided. The vast majority of quoted papers report self-made models for which faculty members and their students have created the necessary 3D print files themselves by various routes. The prediction by the Gartner consulting company that it will take more than ten years from July 2014 onwards for Classroom 3D Printing to reach its Plateau of Productivity in one of their hallmark Visibility versus Time (Hype Cycle) graphs is critically assessed. The bibliography of this book chapter sums up the state-of-the art in 3D printing for STEM (including nano-science and nano-engineering) education at the college level approximately four years after Gartner's prediction. Current methodologies and best practices of college-level Classroom 3D printing are described in the main section of this review. Detailed information is given mainly for those papers in which the authors of this book chapter are authors and co-authors. A straightforward route from crystallographic information framework files (CIFs) at a very large open-access database to 3D print files for atomic-level crystal and molecule structure models is described here in some detail. Because the development of methodologies and best practices are typical activities of the penultimate stage of a Hype Cycle, we conclude that (i) Gartner's prediction underestimates the creativity, resourcefulness, and commitment of college educators to their students and that (ii) Classroom 3D Printing will be a widespread reality significantly earlier than the middle of the next decade (at least in the USA as more than one half of the relevant/quoted papers originated there). An appendix provides a brief technical review of contemporary 3D printing techniques.

physics.ed-ph↗

arXiv2018

Towards generalized noise-level dependent crystallographic symmetry classifications of more or less periodic crystal patterns

Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e. in all real world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review.

physics.app-ph↗

arXiv2008

Structural identification of cubic iron-oxide nanocrystal mixtures: X-ray powder diffraction versus quasi-kinematic transmission electron microscopy

Two novel (and proprietary) strategies for the structural identification of a nanocrystal from either a single high-resolution (HR) transmission electron microscopy (TEM) image or a single precession electron diffraction pattern are proposed and their advantages discussed in comparison to structural fingerprinting from powder X-ray diffraction patterns. Simulations for cubic magnetite and maghemite nanocrystals are used as examples. This is an expanded and updated version of a conference paper that has been published in Suppl. Proc. of TMS 2008, 137th Annual Meeting & Exhibition, Volume 1, Materials Processing and Properties, pp. 25-32.

cond-mat.mtrl-sci↗

arXiv2007

Structural fingerprinting in the transmission electron microscope: Overview and opportunities to implement enhanced strategies for nanocrystal identification

This paper illustrates the prospective need for structural fingerprinting methods for nanocrystals. A review of the existing fingerprinting methods for crystal structures by means of transmission electron microscopy which work for a single setting of the specimen goniometer is given. Suggestions are made on how some of these methods could be enhanced when nanocrystals and novel instrumentation are involved, i.e. when either the kinematic or quasi-kinematic scattering approximations are sufficiently well satisfied. A novel strategy for lattice-fringe fingerprinting of nanocrystals from Fourier transforms of high-resolution phase contrast transmission electron microscopy images is briefly outlined. Nanocrystal structure specific limitations to the application of this strategy are discussed. An appeal is made to share the structural data of nanocrystals freely over the internet and infrastructure that would allow this sharing is mentioned. A shorter version of this paper has been accepted for publication in a special issue on the Structure of Nanocrystals of the Zeitschrift fuer Kristallographie, International journal for structural, physical, and chemical aspects of crystalline materials.

cond-mat.mtrl-sci↗