Validation study of small-angle X-ray scattering tensor tomography

Small-angle scattering tensor tomography (SASTT) is a recently developed technique able to tomographically reconstruct the 3D reciprocal space from voxels within a bulk volume. SASTT extends the concept of X-ray computed tomography, which typically reconstructs scalar values, by reconstructing a tensor per voxel, which represents the local nanostructure 3D organization. In this study, the nanostructure orientation in a human trabecular-bone sample obtained by SASTT was validated by sectioning the sample and using 3D scanning small-angle X-ray scattering (3D sSAXS) to measure and analyze the orientation from single voxels within each thin section. Besides the presence of cutting artefacts from the slicing process, the nanostructure orientations obtained with the two independent methods were in good agreement, as quantified with the absolute value of the dot product calculated between the nanostructure main orientations obtained in each voxel. The average dot product per voxel over the full sample containing over 10 000 voxels was 0.84, and in six slices, in which fewer cutting artefacts were observed, the dot product increased to 0.91. In addition, SAXS tensor tomography not only yields orientation information but can also reconstruct the full 3D reciprocal-space map. It is shown that the measured anisotropic scattering for individual voxels was reproduced from the SASTT reconstruction in each voxel of the 3D sample. The scattering curves along different 3D directions are validated with data from single voxels, demonstrating SASTT's potential for a separate analysis of nanostructure orientation and structural information from the angle-dependent intensity distribution.