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Microscopy is the workhorse of the physical and life sciences, producing crisp images of everything from atoms to cells well beyond the capabilities of the human eye. However, the analysis of these images is frequently little more accurate than manual marking. Here, we revolutionize the analysis of microscopy images, extracting all the useful information theoretically contained in a complex microscope image. Using a generic, methodological approach, we extract the information by fitting experimental images with a detailed optical model of the microscope, a method we call parameter extraction from reconstructing images (PERI). As a proof of principle, we demonstrate this approach with a confocal image of colloidal spheres, improving measurements of particle positions and radii by 10–100 times over current methods and attaining the maximum possible accuracy. With this unprecedented accuracy, we measure nanometer-scale colloidal interactions in dense suspensions solely with light microscopy, a previously impossible feat. Our approach is generic and applicable to imaging methods from brightfield to electron microscopy, where we expect accuracies of 1 nm and 0.1 pm, respectively.

We explore new ways of regulating defect behavior in systems of conservation laws. Contrary to usual regularization schemes (such as a vanishing viscosity limit), which attempt to control defects by making them smoother, our schemes result in defects which are more singular, and we thus refer to such schemes as “irregularizations”. In particular, we seek to produce delta shock defects which satisfy a condition of stationarity. We are motivated to pursue such exotic defects by a physical example arising from dislocation dynamics in materials physics, which we describe.

Nonlinear stresses surrounding defect cores in three-dimensional colloidal crystals are experimentally determined at the single-particle level. The mechanical, structural and functional properties of crystals are determined by their defects 1 , 2 , 3 , 4 , and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear 1 , 5 , 6 , 7 , 8 . Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding colloidal crystalline defect cores, and show that the stresses at vacancy cores generate attractive interactions between them. We also directly visualize the softening of crystalline regions surrounding dislocation cores, and find that stress fluctuations in quiescent polycrystals are uniformly distributed rather than localized at grain boundaries, as is the case in strained atomic polycrystals. Nonlinear stress measurements have important implications for strain hardening 9 , yield 1 , 5 and fatigue 10 .

The Open Knowledgebase of Interatomic Models (OpenKIM) project is a framework intended to facilitate access to standardized implementations of interatomic models for molecular simulations along with computational protocols to evaluate them. These protocols includes tests to compute materials properties predicted by models and verification checks to assess their coding integrity. While housing this content in a unified, publicly available environment constitutes a major step forward for the molecular modeling community, it further presents the opportunity to understand the range of validity of interatomic models and their suitability for specific target applications. To this end, OpenKIM includes a computational pipeline that runs tests and verification checks using all available interatomic models contained within the OpenKIM Repository at https://openkim.org. The OpenKIM Processing Pipeline is built on a set of Docker images hosted on distributed, heterogeneous hardware and utilizes open-source software to automatically run test-model and verification check-model pairs and resolve dependencies between them. The design philosophy and implementation choices made in the development of the pipeline are discussed as well as an example of its application to interatomic model selection.

Microscopy is the workhorse of the physical and life sciences, producing crisp images of everything from atoms to cells well beyond the capabilities of the human eye. However, the analysis of these images is frequently little better than automated manual marking. Here, we revolutionize the analysis of microscopy images, extracting all the information theoretically contained in a complex microscope image. Using a generic, methodological approach, we extract the information by fitting experimental images with a detailed optical model of the microscope, a method we call Parameter Extraction from Reconstructing Images (PERI). As a proof of principle, we demonstrate this approach with a confocal image of colloidal spheres, improving measurements of particle positions and radii by 100x over current methods and attaining the maximum possible accuracy. With this unprecedented resolution, we measure nanometer-scale colloidal interactions in dense suspensions solely with light microscopy, a previously impossible feat. Our approach is generic and applicable to imaging methods from brightfield to electron microscopy, where we expect accuracies of 1 nm and 0.1 pm, respectively.

Image registration is the inference of transformations relating noisy and distorted images. It is fundamental in computer vision, experimental physics, and medical imaging. Many algorithms and analyses exist for inferring shift, rotation, and nonlinear transformations between image coordinates. Even in the simplest case of translation, however, all known algorithms are biased and none have achieved the precision limit of the Cramer Rao bound (CRB). Following Bayesian inference, we prove that the standard method of shifting one image to match another cannot reach the CRB. We show that the bias can be cured and the CRB reached if, instead, we use Super Registration: learning an optimal model for the underlying image and shifting that to match the data. Our theory shows that coarse-graining oversampled images can improve registration precision of the standard method. For oversampled data, our method does not yield striking improvements as measured by eye. In these cases, however, we show our new registration method can lead to dramatic improvements in extractable information, for example, inferring \\(10\\times\\) more precise particle positions.

Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with domains of focal conics under constraining boundary conditions yields a set of strict rules, which are similar to the compatibility conditions in a martensitic crystal. Here we present the rules giving compatible conditions for the concentric circle domains found at two-dimensional smectic interfaces with planar boundary conditions. Using configurations generated by numerical simulations, we develop a clustering algorithm to decompose the planar boundaries into domains. The interfaces between different domains agree well with the smectic compatibility conditions. We also discuss generalizations of our approach to describe the full three-dimensional smectic domains, where the variant symmetry group is the Weyl-Poincaré group of Lorentz boosts, translations, rotations, and dilatations.

Automated particle locating algorithms have revolutionized microscopy image analysis, enabling researchers to rapidly locate many particles to within a few pixels in a microscope image. The vast majority of these algorithms operate through heuristic approaches inspired by computer vision, such as identifying particles with a blob detection. While rapid, these algorithms are plagued by biases [4, 15, 24], and many researchers still frequently ignore or understate these biases. In this paper, we examine sources of biases in particle localization. Rather than exhaustively examine all possible sources of bias, we illustrate their scale, the large number of sources, and the difficulty of correcting the biases with a heuristic method. We do this by generating a series of simple images, introducing sources of bias one at a time. Using these images, we examine the performance of two heuristic algorithms throughout the process: a centroid algorithm and a Gaussian fitting algorithm. We contrast the two heuristic methods with a new approach based on reconstructing an image with a generative model to fit the data (Parameter Extraction from Reconstructing Images, or PERI). While the heuristic approaches produce considerable biases even on unrealistically simple images, the reconstruction-based approach accurately measures particle positions even in complex, highly realistic images. We close by reiterating the fundamental reason that a reconstruction-based approach accurately extracts particle positions -- any imperfections in the fit both demonstrate which sources of systematic error are still present and provide a roadmap to incorporating them.

Smectic liquid crystals vividly illustrate the subtle interplay of broken translational and orientational symmetries, by exhibiting defect structures forming geometrically perfect confocal ellipses and hyperbolas. Here, we develop and numerically implement an effective theory to study the dynamics of focal conic domains in smectic-A liquid crystals. We use the information about the smectic's structure and energy density provided by our simulations to develop several novel visualization tools for the focal conics. Our simulations accurately describe both simple and extensional shear, which we compare to experiments, and provide additional insight into the coarsening dynamics of focal conic domains.

The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding colloidal crystalline defect cores, and show that the stresses at vacancy cores generate attractive interactions between them. We also directly visualize the softening of crystalline regions surrounding dislocation cores, and find that stress fluctuations in quiescent polycrystals are uniformly distributed rather than localized at grain boundaries, as is the case in strained atomic polycrystals. Nonlinear stress measurements have important implications for strain hardening, yield, and fatigue.