Reverse projection retrieval in edge illumination x-ray phase contrast computed tomography

Edge illumination (EI) x-ray phase contrast computed tomography (CT) can provide three-dimensional distributions of the real and imaginary parts of the complex refractive index (n = 1-delta + i beta) of the sample. Phase retrieval, i.e. the separation of attenuation and refraction data from projections that contain a combination of both, is a key step in the image reconstruction process. In EI-based x-ray phase contrast CT, this is conventionally performed on the basis of two projections acquired in opposite illumination configurations (i.e. with different positions of the pre-sample mask) at each CT angle. Displacing the pre-sample mask at each projection makes the scan susceptible to motor-induced misalignment and prevents a continuous sample rotation. We present an alternative method for the retrieval of attenuation and refraction data that does not require repositioning the pre-sample mask. The method is based on the reverse projection relation published by Zhu et al (2010 Proc. Natl Acad. Sci. USA 107 13576-81) for grating interferometry-based x-ray phase contrast CT. We use this relation to derive a simplified acquisition strategy that allows acquiring data with a continuous sample rotation, which can reduce scan time when combined with a fast read-out detector. Besides discussing the theory and the necessary alignment of the experimental setup, we present tomograms obtained with reverse projection retrieval and demonstrate their agreement with those obtained with the conventional EI retrieval.