@phdthesis{GraetzgebDittmann2022,
  author    = {Graetz [geb. Dittmann], Jonas},
  title     = {X-Ray Dark-Field Tensor Tomography : a Hitchhiker's Guide to Tomographic Reconstruction and Talbot Imaging},
  doi       = {10.25972/OPUS-28143},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-281437},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {X-ray dark-field imaging allows to resolve the conflict between the demand for centimeter scaled fields of view and the spatial resolution required for the characterization of fibrous materials structured on the micrometer scale. It draws on the ability of X-ray Talbot interferometers to provide full field images of a sample's ultra small angle scattering properties, bridging a gap of multiple orders of magnitude between the imaging resolution and the contrasted structure scale. The correspondence between shape anisotropy and oriented scattering thereby allows to infer orientations within a sample's microstructure below the imaging resolution. First demonstrations have shown the general feasibility of doing so in a tomographic fashion, based on various heuristic signal models and reconstruction approaches. Here, both a verified model of the signal anisotropy and a reconstruction technique practicable for general imaging geometries and large tensor valued volumes is developed based on in-depth reviews of dark-field imaging and tomographic reconstruction techniques. To this end, a wide interdisciplinary field of imaging and reconstruction methodologies is revisited. To begin with, a novel introduction to the mathematical description of perspective projections provides essential insights into the relations between the tangible real space properties of cone beam imaging geometries and their technically relevant description in terms of homogeneous coordinates and projection matrices. Based on these fundamentals, a novel auto-calibration approach is developed, facilitating the practical determination of perspective imaging geometries with minimal experimental constraints. A corresponding generalized formulation of the widely employed Feldkamp algorithm is given, allowing fast and flexible volume reconstructions from arbitrary tomographic imaging geometries. Iterative reconstruction techniques are likewise introduced for general projection geometries, with a particular focus on the efficient evaluation of the forward problem associated with tomographic imaging. A highly performant 3D generalization of Joseph's classic linearly interpolating ray casting algorithm is developed to this end and compared to typical alternatives. With regard to the anisotropic imaging modality required for tensor tomography, X-ray dark-field contrast is extensively reviewed. Previous literature is brought into a joint context and nomenclature and supplemented by original work completing a consistent picture of the theory of dark-field origination. Key results are explicitly validated by experimental data with a special focus on tomography as well as the properties of anisotropic fibrous scatterers. In order to address the pronounced susceptibility of interferometric images to subtle mechanical imprecisions, an efficient optimization based evaluation strategy for the raw data provided by Talbot interferometers is developed. Finally, the fitness of linear tensor models with respect to the derived anisotropy properties of dark-field contrast is evaluated, and an iterative scheme for the reconstruction of tensor valued volumes from projection images is proposed. The derived methods are efficiently implemented and applied to fiber reinforced plastic samples, imaged at the ID19 imaging beamline of the European Synchrotron Radiation Facility. The results represent unprecedented demonstrations of X-ray dark-field tensor tomography at a field of view of 3-4cm, revealing local fiber orientations of both complex shaped and low-contrast samples at a spatial resolution of 0.1mm in 3D. The results are confirmed by an independent micro CT based fiber analysis.},
  subject      = {Dreidimensionale Rekonstruktion},
  language  = {en}
}
@article{MuellerGraetzBallesetal.2021,
  author    = {M{\"u}ller, Dominik and Graetz, Jonas and Balles, Andreas and Stier, Simon and Hanke, Randolf and Fella, Christian},
  title     = {Laboratory-Based Nano-Computed Tomography and Examples of Its Application in the Field of Materials Research},
  series = {Crystals},
  volume    = {11},
  journal   = {Crystals},
  number    = {6},
  issn      = {2073-4352},
  doi       = {10.3390/cryst11060677},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-241048},
  year      = {2021},
  abstract  = {In a comprehensive study, we demonstrate the performance and typical application scenarios for laboratory-based nano-computed tomography in materials research on various samples. Specifically, we focus on a projection magnification system with a nano focus source. The imaging resolution is quantified with common 2D test structures and validated in 3D applications by means of the Fourier Shell Correlation. As representative application examples from nowadays material research, we show metallization processes in multilayer integrated circuits, aging in lithium battery electrodes, and volumetric of metallic sub-micrometer fillers of composites. Thus, the laboratory system provides the unique possibility to image non-destructively structures in the range of 170-190 nanometers, even for high-density materials.},
  language  = {en}
}
@article{Graetz2021,
  author    = {Graetz, Jonas},
  title     = {Simulation study towards quantitative X-ray and neutron tensor tomography regarding the validity of linear approximations of dark-field anisotropy},
  series = {Scientific Reports},
  volume    = {11},
  journal   = {Scientific Reports},
  doi       = {10.1038/s41598-021-97389-y},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-261844},
  year      = {2021},
  abstract  = {Tensor tomography is fundamentally based on the assumption of a both anisotropic and linear contrast mechanism. While the X-ray or neutron dark-field contrast obtained with Talbot(-Lau) interferometers features the required anisotropy, a preceding detailed study of dark-field signal origination however found its specific orientation dependence to be a non-linear function of the underlying anisotropic mass distribution and its orientation, especially challenging the common assumption that dark-field signals are describable by a function over the unit sphere. Here, two approximative linear tensor models with reduced orientation dependence are investigated in a simulation study with regard to their applicability to grating based X-ray or neutron dark-field tensor tomography. By systematically simulating and reconstructing a large sample of isolated volume elements covering the full range of feasible anisotropies and orientations, direct correspondences are drawn between the respective tensors characterizing the physically based dark-field model used for signal synthesization and the mathematically motivated simplified models used for reconstruction. The anisotropy of freely rotating volume elements is thereby confirmed to be, for practical reconstruction purposes, approximable both as a function of the optical axis' orientation or as a function of the interferometer's grating orientation. The eigenvalues of the surrogate models' tensors are found to exhibit fuzzy, yet almost linear relations to those of the synthesization model. Dominant orientations are found to be recoverable with a margin of error on the order of magnitude of 1 degrees. Although the input data must adequately address the full orientation dependence of dark-field anisotropy, the present results clearly support the general feasibility of quantitative X-ray dark-field tensor tomography within an inherent yet acceptable statistical margin of uncertainty.},
  language  = {en}
}