Convolution reconstruction algorithm for refraction-contrast computed tomography using a Laue-case analyzer for dark-field imaging

We derive a reconstruction algorithm for refraction-contrast computed tomography (CT) using dark-field imaging (DFI) optics, which can extract refraction information by a single shot, from the ray equation in geometrical optics. The proposed algorithm is similar to the convolution reconstruction technique widely used in conventional CT. Thus, this algorithm can be implemented simply while also being fast and stable. To demonstrate its validity, we constructed the imaging system based on DFI optics composed of a transmission Laue-type angular analyzer at the vertical wiggler beamline BL-14C in KEK and performed a preliminary imaging experiment using a physical phantom to successfully obtain the DFI-CT image using the proposed algorithm.