@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{DittmannBallesZabler2018,
  author    = {Dittmann, Jonas and Balles, Andreas and Zabler, Simon},
  title     = {Optimization based evaluation of grating interferometric phase stepping series and analysis of mechanical setup instabilities},
  series = {Journal of Imaging},
  volume    = {4},
  journal   = {Journal of Imaging},
  number    = {6},
  issn      = {2313-433X},
  doi       = {10.3390/jimaging4060077},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-197723},
  pages     = {77},
  year      = {2018},
  abstract  = {The diffraction contrast modalities accessible by X-ray grating interferometers are not imaged directly but have to be inferred from sine-like signal variations occurring in a series of images acquired at varying relative positions of the interferometer's gratings. The absolute spatial translations involved in the acquisition of these phase stepping series usually lie in the range of only a few hundred nanometers, wherefore positioning errors as small as 10 nm will already translate into signal uncertainties of 1-10\% in the final images if not accounted for. Classically, the relative grating positions in the phase stepping series are considered input parameters to the analysis and are, for the Fast Fourier Transform that is typically employed, required to be equidistantly distributed over multiples of the gratings' period. In the following, a fast converging optimization scheme is presented simultaneously determining the phase stepping curves' parameters as well as the actually performed motions of the stepped grating, including also erroneous rotational motions which are commonly neglected. While the correction of solely the translational errors along the stepping direction is found to be sufficient with regard to the reduction of image artifacts, the possibility to also detect minute rotations about all axes proves to be a valuable tool for system calibration and monitoring. The simplicity of the provided algorithm, in particular when only considering translational errors, makes it well suitable as a standard evaluation procedure also for large image series.},
  language  = {en}
}