Speckle-Based X-Ray Dark-Field Tomography of an Attenuating Object

Spatial resolution in standard phase-contrast X-ray imaging is limited by the finite number and size of detector pixels. This limits the size of features that can be seen directly in projection images or tomographic reconstructions. Dark-field imaging allows information regarding such features to be obtained, as the reconstructed image is a measure of the position-dependent small-angle X-ray scattering of incident rays from the unresolved microstructure. In this paper we utilize an intrinsic speckle-tracking-based X-ray imaging technique to obtain the effective dark-field signal from a wood sample. This effective dark-field signal is extracted using a Fokker-Planck type formalism, which models the deformations of illuminating reference-beam speckles due to both coherent and diffusive scatter from the sample. We here assume that (a) small-angle scattering fans at the exit surface of the sample are rotationally symmetric, and (b) the object has both attenuating and refractive properties. The associated inverse problem, of extracting the effective dark-field signal, is numerically stabilised using a \weighted determinants" approach. Effective dark-field projection images are presented, as well as the dark-field tomographic reconstructions obtained using Fokker-Planck implicit speckle-tracking.