Quantitative x-ray dark-field computed tomography

The basic principles of x-ray image formation in radiology have remained essentially unchanged since Röntgen first discovered x-rays over a hundred years ago. The conventional approach relies on x-ray attenuation as the sole source of contrast and draws exclusively on ray or geometrical optics to describe and interpret image formation. Phase-contrast or coherent scatter imaging techniques, which can be understood using wave optics rather than ray optics, offer ways to augment or complement the conventional approach by incorporating the wave-optical interaction of x-rays with the specimen. With a recently developed approach based on x-ray optical gratings, advanced phase-contrast and dark-field scatter imaging modalities are now in reach for routine medical imaging and non-destructive testing applications. To quantitatively assess the new potential of particularly the grating-based dark-field imaging modality, we here introduce a mathematical formalism together with a material-dependent parameter, the so-called linear diffusion coefficient and show that this description can yield quantitative dark-field computed tomography (QDFCT) images of experimental test phantoms.