Universal and quantitative statistical approach to retrieve X-ray directional dark-field using a single exposure

We present a novel single-exposure method for retrieving both the magnitude and directionality of X-ray dark-field signals through local statistical analysis of structured illumination patterns. Unlike conventional multi-shot or phase-stepping approaches, our technique operates from a single acquisition without any prior knowledge of the modulation structure. By evaluating the local loss of modulation variance along multiple orientations within sliding windows, we reconstruct the spatially resolved anisotropic scattering field with high angular precision. The method is universally compatible with diverse modulator geometries, including random, aperiodic, and periodic patterns, and does not rely on binary or intensity-based modulation. Experimental validation on carbon-fiber phantoms shows excellent agreement between the retrieved scattering orientations and independent small-angle X-ray scattering measurements. This universal, model-free, framework enables rapid and quantitative characterization of anisotropic microstructures in both biomedical and materials imaging.