Considerations towards quantitative X-ray and neutron tensor tomography: on the validity of linear approximations of dark-field anisotropy

Abstract: The validity of two approximative linear tensor models to be used for grating based X-ray or neutron dark-field tensor tomography is investigated in a simulation study. While the dark-field contrast originating from anisotropic microscopic mass distributions has, in a previous study, been confirmed to be in general a non-linear function of two orientations (optical axis and axis of interferometer sensitivity), linear approximations with a reduced parameter space (considering only one of the orientation dependencies) are highly preferable with respect to tomographic volume reconstruction from projections. By regarding isolated volume elements and systematically exploring the full range of possible anisotropies, direct correspondences are drawn between the respective tensors characterizing the complete model used for signal synthesization and the reduced linear models used for reconstruction. The tensors' dominant orientations are found to agree to a typical accuracy of 1{\deg}, with their eigenspectra exhibiting fuzzy, yet almost linear relations among each other. Although modeling only either of two orientation dependencies for the purpose of tensor reconstruction, the data acquisition scheme must nevertheless adequately address both dependencies.