Fast reconstruction of tensor tomographic X-ray scattering data for real-time applications

X-ray scattering tensor tomography reveals nanoscale structural orientation in 3D, but its reliance on slow iterative reconstruction limits real-time use. We introduce an extension of a direct reconstruction approach for parallel-beam geometries that computes algebraic filters approximating multiple iterative updates with a single filtering and back-projection step. By explicitly separating the tomographic projector from a view-dependent mixing operator, the method generalizes across tensor representations and modes of (small-angle) X-ray scattering measurement. Simulated and experimental results show that the approach approximates iterative reconstructions while reducing computation time by over an order of magnitude, realizing a reconstruction of a 53x53x53x28 tensor volume in 1 second on commercially available hardware. The resulting speed and stability enable high-throughput analysis and open the door to real-time scattering-based imaging.