In grating-based x-ray phase sensitive imaging, dark-field contrast refers to the extinction of the interference fringes due to small-angle scattering. For configurations where the sample is placed before the beamsplitter grating, the dark-field contrast has been quantified with theoretical wave propagation models. Yet when the grating is placed before the sample, the dark-field contrast has only been modeled in the geometric optics regime. Here we attempt to quantify the dark-field effect in the grating-before-sample geometry with first-principle wave calculations and understand the associated particle-size selectivity. We obtain an expression for the dark-field effect in terms of the sample material's complex refractive index, which can be verified experimentally without fitting parameters. A dark-field computed tomography experiment shows that the particle-size selectivity can be used to differentiate materials of identical x-ray absorption.
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