Tensor Tomography of Dark Field Scatter using X-ray Interferometry with Bi-prisms

X-ray grating-based differential phase-contrast imaging is able to obtain excellent soft-tissue contrast of phase, attenuation, and small angle scatter. In this work we model the performance of an X-ray interferometer wherein the phase gratings are replaced with a single Fresnel micro-bi-prism. Our goal is to develop imaging systems based on bi-prism interferometry with improved polychromatic performance. In our investigation we obtain an analytical expression for the irradiance distribution of the bi-prism. The localized regions of fringe visibility within the irradiance distribution are non-periodic. Following the work of Pfeiffer et al., we then develop a method for reconstructing scattering directions that can be used to obtain a three-dimensional tensor field. This will eventually be used in modified bi-prism-based differential phase-contrast imaging to obtain tissue properties through mathematical reconstruction of tensor tomographic data.