3D reconstruction algorithm for cone-beam differential phase contrast computed tomography

Differential phase contrast computed tomography (DPC-CT) is a novel x-ray inspection method. It reconstructs the refraction index decrement rather than the attenuation coefficient, and can subsequently be applied to inspect weakly absorbing samples. Recently, DPC-CT is implemented, using conventional x-ray tube instead of synchrotron radiation source. In this paper, the reconstruction problem for cone-beam DPC-CT was studied. Some mathematical assumptions were made and a FDK-type algorithm was applied to reconstruct the refractive index decrement distribution of the samples directly from phase contrast projection images. Despite the approximation of our algorithm, it has great features for simplicity of computation and for relatively small errors. The efficacy and shortcoming of the algorithm is presented by its application to a mathematical phantom.