Analytical single-shot phase-contrast computed tomography for multi-material samples

We present a novel single-shot technique for quantitative X-ray phase contrast imaging (XPCI) with the edge illumination (EI) method based on the linear joint reconstruction (LJR) approach. Unlike conventional two-step EI approaches that require multiple exposures per projection to separate phase and absorption prior to tomographic reconstruction, our method uses a single exposure per angle of projection and directly reconstructs the sample’s absorption and phase components simultaneously. This is achieved by applying a first-order Taylor expansion to the system’s illumination curve, which linearizes the EI imaging model and transforms it into a convex least-squares problem with a unique analytical solution, eliminating the non-convexity that typically leads to local minima in iterative approaches. As a result, the approach is both fast and robust. We demonstrate the method’s performance on both simulated and experimental datasets, including multi-material plastic rods and an intact mouse brain inside its native skull. The results show that the proposed technique produces high-quality, quantitatively accurate phase and absorption tomograms that are a close match to those obtained with the standard EI method, while considerably reducing data acquisition and computational time. This development enables rapid, reliable XPCI of complex multi-material samples under challenging imaging conditions.