Refraction angle extracting strategy for fan-beam differential phase contrast CT

In this paper, the fan-beam differential phase contrast computed tomography (DPC-CT) reconstruction method is studied. We first present a new vision of how to implement the Reverse-Projection (RP) method to extract the refraction-angle data efficiently in fan-beam geometry, and then provide a Katsevich-type formula for fan-beam DPC-CT reconstruction. The proposed method has two key properties. First, it is essentially a filtered back projection (FBP) reconstruction formula. Second, it can deal with incomplete data sets. The main contributions of this paper lie in the following three aspects: First, the physical principle of the bent-grating based fan-beam DPC imaging is discussed and the RP-method is extended to the fan-beam case. Second, an implementation strategy of Katsevich algorithm for fan-beam DPC-CT is proposed. Third, a semi-quantitative research on the influence of the approximation errors introduced by the RP-method is carried out by using several numerical simulations. It should be pointed out that the RP-method will certainly introduce some errors. The effect of these errors on our reconstruction algorithm is discussed by several numerical simulations.