Reconstruction of scalar and vectorial components in X-ray dark-field tomography

Grating-based X-ray dark-field imaging is a novel technique for obtaining image contrast for object structures at size scales below setup resolution. Such an approach appears particularly beneficial for medical imaging and nondestructive testing. It has already been shown that the dark-field signal depends on the direction of observation. However, up to now, algorithms for fully recovering the orientation dependence in a tomographic volume are still unexplored. In this publication, we propose a reconstruction method for grating-based X-ray dark-field tomography, which models the orientation-dependent signal as an additional observable from a standard tomographic scan. In detail, we extend the tomographic volume to a tensorial set of voxel data, containing the local orientation and contributions to dark-field scattering. In our experiments, we present the first results of several test specimens exhibiting a heterogeneous composition in microstructure, which demonstrates the diagnostic potential of the method.