  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.
