  Small-angle scattering tensor tomography is a technique for studying
anisotropic nanostructures of millimeter-sized samples in a volume-resolved
manner. It requires the acquisition of data through repeated tomographic
rotations about an axis which is subjected to a series of tilts. The tilt that
can be achieved with a typical setup is geometrically constrained, which leads
to limits in the set of directions from which the different parts of the
reciprocal-space map can be probed. Here, we characterize the impact of this
limitation on reconstructions in terms of the missing wedge problem of
tomography, by treating the problem of tensor tomography as the reconstruction
of a three-dimensional field of functions on the unit sphere, represented by a
grid of Gaussian radial basis functions. We then devise an acquisition scheme
to obtain complete data by remounting the sample, which we apply to a sample of
human trabecular bone. Performing tensor tomographic reconstructions of limited
data sets as well as the complete data set, we further investigate and validate
the missing wedge understanding of data incompleteness by investigating
reconstruction errors due to data incompleteness across both real and
reciprocal space. Finally, we carry out an analysis of orientations and derived
scalar quantities, to quantify the impact of this missing wedge problem on a
typical tensor tomographic analysis. We conclude that the effects of data
incompleteness are consistent with the predicted impact of the missing wedge
problem, and that the impact on tensor tomographic analysis is appreciable but
limited, especially if precautions are taken. In particular, there is only
limited impact on the means and relative anisotropies of the reconstructed
reciprocal space maps.
