Michael A. Jackson

DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D

This paper presents a software environment for processing, segmenting, quantifying, representing and manipulating digital microstructure data. The paper discusses the approach to building a generalized representation strategy for digital microstructures and the barriers encountered when trying to integrate a set of existing software tools to create an expandable codebase.

A Model Based Iterative Reconstruction Algorithm For High Angle Annular Dark Field-Scanning Transmission Electron Microscope (HAADF-STEM) Tomography

High angle annular dark field (HAADF)-scanning transmission electron microscope (STEM) data is increasingly being used in the physical sciences to research materials in 3D because it reduces the effects of Bragg diffraction seen in bright field TEM data. Typically, tomographic reconstructions are performed by directly applying either filtered back projection (FBP) or the simultaneous iterative reconstruction technique (SIRT) to the data. Since HAADF-STEM tomography is a limited angle tomography modality with low signal to noise ratio, these methods can result in significant artifacts in the reconstructed volume. In this paper, we develop a model based iterative reconstruction algorithm for HAADF-STEM tomography. We combine a model for image formation in HAADF-STEM tomography along with a prior model to formulate the tomographic reconstruction as a maximum a posteriori probability (MAP) estimation problem. Our formulation also accounts for certain missing measurements by treating them as nuisance parameters in the MAP estimation framework. We adapt the iterative coordinate descent algorithm to develop an efficient method to minimize the corresponding MAP cost function. Reconstructions of simulated as well as experimental data sets show results that are superior to FBP and SIRT reconstructions, significantly suppressing artifacts and enhancing contrast.

Introduction and comparison of new EBSD post-processing methodologies

Electron Backscatter Diffraction (EBSD) provides a useful means for characterizing microstructure. However, it can be difficult to obtain index-able diffraction patterns from some samples. This can lead to noisy maps reconstructed from the scan data. Various post-processing methodologies have been developed to improve the scan data generally based on correlating non-indexed or mis-indexed points with the orientations obtained at neighboring points in the scan grid. Two new approaches are introduced (1) a re-scanning approach using local pattern averaging and (2) using the multiple solutions obtained by the triplet indexing method. These methodologies are applied to samples with noise introduced into the patterns artificially and by the operational settings of the EBSD camera. They are also applied to a heavily deformed and a fine-grained sample. In all cases, both techniques provide an improvement in the resulting scan data, the local pattern averaging providing the most improvement of the two. However, the local pattern averaging is most helpful when the noise in the patterns is due to the camera operating conditions as opposed to inherent challenges in the sample itself. A byproduct of this study was insight into the validity of various indexing success rate metrics. A metric based given by the fraction of points with CI values greater than some tolerance value (0.1 in this case) was confirmed to provide an accurate assessment of the indexing success rate.

A Dictionary Approach to Electron Backscatter Diffraction Indexing.

We propose a framework for indexing of grain and subgrain structures in electron backscatter diffraction patterns of polycrystalline materials. We discretize the domain of a dynamical forward model onto a dense grid of orientations, producing a dictionary of patterns. For each measured pattern, we identify the most similar patterns in the dictionary, and identify boundaries, detect anomalies, and index crystal orientations. The statistical distribution of these closest matches is used in an unsupervised binary decision tree (DT) classifier to identify grain boundaries and anomalous regions. The DT classifies a pattern as an anomaly if it has an abnormally low similarity to any pattern in the dictionary. It classifies a pixel as being near a grain boundary if the highly ranked patterns in the dictionary differ significantly over the pixels neighborhood. Indexing is accomplished by computing the mean orientation of the closest matches to each pattern. The mean orientation is estimated using a maximum likelihood approach that models the orientation distribution as a mixture of Von Mises-Fisher distributions over the quaternionic three sphere. The proposed dictionary matching approach permits segmentation, anomaly detection, and indexing to be performed in a unified manner with the additional benefit of uncertainty quantification.

Model-Based Iterative Reconstruction for Bright-Field Electron Tomography

Bright-Field (BF) electron tomography (ET) has been widely used in the life sciences for 3-D imaging of biological specimens. However, while BF-ET is popular in the life sciences, 3-D BF-ET imaging has been avoided in the physical sciences due to measurement anomalies from crystalline samples caused by dynamical diffraction effects such as Bragg scatter. In practice, these measurement anomalies cause undesirable artifacts in 3-D reconstructions computed using filtered back-projection (FBP). Alternatively, model-based iterative reconstruction (MBIR) is a powerful framework for tomographic reconstruction that combines a forward model for the measurement system and a prior model for the object to obtain reconstructions by minimizing a single cost function. In this paper, we present an MBIR algorithm for BF-ET reconstruction from crystalline materials that can account for the presence of anomalous measurements. We propose a new forward model for the acquisition system which accounts for the presence of anomalous measurements and combine it with a prior model for the object to obtain the MBIR cost function. We then propose a fast algorithm based on majorization-minimization to find a minimum of the corresponding cost function. Results on simulated as well as real data show that our method can dramatically improve reconstruction quality as compared to FBP and conventional MBIR without anomaly modeling.

Consistent representations of and conversions between 3D rotations

In materials science the orientation of a crystal lattice is described by means of a rotation relative to an external reference frame. A number of rotation representations are in use, including Euler angles, rotation matrices, unit quaternions, Rodrigues–Frank vectors and homochoric vectors. Each representation has distinct advantages and disadvantages with respect to the ease of use for calculations and data visualization. It is therefore convenient to be able to easily convert from one representation to another. However, historically, each representation has been implemented using a set of often tacit conventions; separate research groups would implement different sets of conventions, thereby making the comparison of methods and results difficult and confusing. This tutorial article aims to resolve these ambiguities and provide a consistent set of conventions and conversions between common rotational representations, complete with worked examples and a discussion of the trade-offs necessary to resolve all ambiguities. Additionally, an open source Fortran-90 library of conversion routines for the different representations is made available to the community.

h5ebsd: an archival data format for electron back-scatter diffraction data sets

We present an archival format for electron back-scatter diffraction (EBSD) data based on the HDF5 scientific file format. We discuss the differences between archival and data work flow file formats, and present details of the archival file layout for the implementation of h5ebsd, a vendor-neutral EBSD-HDF5 format. Information on sample and external reference frames can be included in the archival file, so that the data is internally consistent and complete. We describe how the format can be extended to include additional experimental modalities, and present some thoughts on the interactions between working files and archival files. The complete file specification as well as an example h5ebsd formatted data set are made available to the reader.

Bayesian tomographic reconstruction for high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM)

HAADF-STEM data is increasingly being used in the physical sciences to study materials in 3D because it is free from the diffraction effects seen in Bright Field STEM data and satisfies the projection requirement for tomography. Typically, reconstruction is performed using Filtered Back Projection (FBP) or the SIRT algorithm. In this paper, we develop a Bayesian reconstruction algorithm for HAADF-STEM tomography which models the image formation, the noise characteristics of the measurement, and the inherent smoothness in the object. Reconstructions of polystyrene functionalized Titanium dioxide nano particle assemblies show results that are qualitatively superior to FBP and SIRT reconstructions, significantly suppressing artifacts and enhancing contrast.

MXA: a customizable HDF5-based data format for multi-dimensional data sets

A new digital file format is proposed for the long-term archival storage of experimental data sets generated by serial sectioning instruments. The format is known as the multi-dimensional eXtensible Archive (MXA) format and is based on the public domain Hierarchical Data Format (HDF5). The MXA data model, its description by means of an eXtensible Markup Language (XML) file with associated Document Type Definition (DTD) are described in detail. The public domain MXA package is available through a dedicated web site (mxa.web.cmu.edu), along with implementation details and example data files.

A phantom-based forward projection approach in support of model-based iterative reconstructions for HAADF-STEM tomography

We introduce a forward model for the computation of high angle annular dark field (HAADF) images of nano-crystalline spherical particles and apply it to image simulations for assemblies of nano-spheres of Al, Cu, and Au with a range of sizes, as well as an artificial bi-sphere, consisting of solid hemispheres of Al and Cu or Al and Au. Comparison of computed intensity profiles with experimental observations on Al spheres at different microscope accelerating voltages provides confidence in the forward model. Simulated tomographic tilt series for both HAADF and bright field (BF) images are then used to illustrate that the model-based iterative reconstruction (MBIR) approach is capable of reconstructing sphere configurations of mixed atomic number, with the correct relative reconstructed intensity ratio proportional to the square of the atomic number ratio.