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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.

This work proposes an innovative approach to improve Bragg coherent diffraction imaging (BCDI) microscopy applied to time evolving crystals and/or non-homogeneous crystalline strain fields, identified as two major limitations of BCDI microscopy. Speckle BCDI (spBCDI), introduced here, rests on the ability of a strongly non-uniform illumination to induce a convolution of the three-dimensional (3D) frequency content associated with the finite-size crystal and a kernel acting perpendicularly to the illumination beam. In the framework of Bragg diffraction geometry, this convolution is beneficial as it encodes some 3D information about the sample in a single two-dimensional (2D) measurement, i.e., in the detector plane. With this approach, we demonstrate that we can drastically reduce the sampling frequency along the rocking curve direction and still obtain data sets with enough information to be inverted by a traditional phase retrieval algorithm. Numerical simulations, performed for a highly distorted crystal, show that spBCDI allows a gain in the sampling ratio ranging between 4 and 20 along the rocking curve scan, for a speckle illumination with individual speckle size of 50 nm. Furthermore, spBCDI allows working at low intensity levels, leading to an additional gain for the total scanning time. Reductions of a factor of about 32 were numerically observed. Thus, measurements in the 0.3 s time scale at 4th generation synchrotrons become feasible, with a remarkable performance for the imaging of strongly distorted crystals. Practical details on the implementation of the method are also discussed., Comment: 17 pages, 11 figures