The x-ray dark-field signal measured in grating interferometers is anisotropic, depending on both the beam direction and the grating orientation with respect to the sample. We present a novel general closed-form, continuous forward model of the anisotropic dark-field signal. Furthermore, we derive a discretization using spherical harmonics, leading to a large-scale linear inverse problem. We present first experimental results of a wooden sample, demonstrating marked advantages over previous results, in particular, the resolution of multiple scattering directions in one volume element.

• Received 7 June 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.158101