  X-ray diffusive dark-field imaging, which allows spatially unresolved
microstructure to be mapped across a sample, is an increasingly popular tool in
an array of settings. Here, we present a new algorithm for phase and dark-field
computed tomography based on the x-ray Fokker-Planck equation. Needing only a
coherent x-ray source, sample, and detector, our propagation-based algorithm
can map the sample density and dark-field/diffusion properties of the sample in
3D. Importantly, incorporating dark-field information in the density
reconstruction process enables a higher spatial resolution reconstruction than
possible with previous propagation-based approaches. Two sample exposures at
each projection angle are sufficient for the successful reconstruction of both
the sample density and dark-field Fokker-Planck diffusion coefficients. We
anticipate that the proposed algorithm may be of benefit in biomedical imaging
and industrial settings.
