Cover illustration: SAXS tensor tomography can probe three-dimensional nanostructure in relatively large volumes, offering the unique chance to correlate spatial nanoscale features over several millimetres [Liebi et al. (2018). Acta Cryst. A74, 12-24]. The image shows a small-angle X-ray scattering pattern (left) from a human bone sample. Around 1 000 000 single SAXS patterns were used to reconstruct the 3D orientation of the mineralized collagen fibrils (right).
The mathematical framework and reconstruction algorithm for small-angle scattering tensor tomography are introduced in detail, as well as strategies which help to reduce the amount of data and therewith the measurement time required. Experimental validation is provided for the application to trabecular bone.
It is demonstrated that, by inputting the reflection data in an incremental fashion starting with low- and medium-resolution reflections, the convergence rate of the hybrid input–output ab initio phasing algorithm can be significantly increased.