  The crystallographic texture is a key organization feature of many technical
and biological materials. In these materials, especially hierarchically
structured ones, the preferential alignment of the nano constituents is heavily
influencing the macroscopic behaviour of the material. In order to study local
crystallographic texture with both high spatial and angular resolution, we
developed Texture tomography (TexTOM). This approach allows to model the
diffraction data of polycrystalline materials by using the full reciprocal
space of the ensemble of crystals and describe the texture in each voxel via a
orientation distribution function. This means, it provides 3D reconstructions
of the local texture by measuring the probabilities of all crystal
orientations. The TexTOM approach addresses limitations associated with
existing models: It correlates the intensities from several Bragg reflections,
thus reduces ambiguities resulting from symmetry. Further, it yields
quantitative probability distributions of local real space crystal orientations
without further assumptions on the sample structure. Finally, its efficient
mathematical formulation enables reconstructions faster than the time-scale of
the experiment. In this manuscript, we present the mathematical model, the
inversion strategy and its current experimental implementation. We show
characterizations of simulated data as well as experimental data obtained from
a synthetic, inorganic model sample, the silica-witherite biomorph. In
conclusion, Tex-TOM provides a versatile framework to reconstruct 3D
quantitative texture information for polycrystalline samples. In this way, it
opens the door for unprecedented insights into the nanostructural makeup of
natural and technical materials.
