Review and Experimental Verification of X-ray Dark-field Signal Interpretations with Respect to Quantitative Isotropic and Anisotropic Dark-field Computed Tomography

Talbot(-Lau) interferometric x-ray and neutron dark-field imaging has, over the past decade, gained substantial interest for its ability to provide insights into a sample's microstructure below the imaging resolution by means of ultra small angle scattering effects. Quantitative interpretations of such images depend on models of the signal origination process that relate the observable image contrast to underlying physical processes. A review of such models is given here and their relation to the wave optical derivations by Yashiro et al and Lynch et al as well as to small angle scattering is discussed. Fresnel scaling is introduced to explain the characteristic distance dependence observed in cone beam geometries. Moreover, a model describing the anisotropic signals of fibrous objects is derived. The Yashiro-Lynch model is experimentally verified both in radiographic and tomographic imaging in a monochromatic synchrotron setting, considering both the effects of material and positional dependence of the resulting dark-field contrast. The effect of varying sample-detector distance on the dark-field signal is shown to be non-negligible for tomographic imaging, yet can be largely compensated for by symmetric acquisition trajectories. The derived orientation dependence of the dark-field contrast of fibrous materials both with respect to variations in autocorrelation width and scattering cross section is experimentally validated using carbon fiber reinforced rods.