Theoretical and computational advances in small-angle x-ray tensor tomography

Abstract: The relationships between microscopic and macroscopic structures is a central topic of materials physics. Small-angle x-ray scattering (SAXS) is a powerful experimental technique for probing and mapping variations in electron density, given by the reciprocal space map, down to the nanometer scale in two dimensions. SAXS tensor tomography combines this mapping with tomographic techniques to yield a three-dimenisonal reconstruction of the reciprocal space map. The development of an improved method for SAXS tensor tomographic reconstruction using a basis of real spherical harmonics has yielded faster and more accurate reconstructions with a more detailed representations of the reciprocal space map. The reconstructed reciprocal space maps yielded by RUSHTT can be further analyzed to quantify their degree of symmetry, and retrieve complex features such as multiple orientations within a single volume element. Moreover, the development of a mathematical framework for SAXS tensor tomography using spherical harmonics in terms of integral geometry has furthered understanding of the method’s possibilities and constraints.