Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging

X-ray diffraction enhanced imaging based on synchrotron radiation has extremely high sensitivity of weakly absorbing low-Z samples in medical and biological fields. This letter is dedicated to a direct reconstruction algorithm for directional-derivative projections of computed tomography of diffraction enhanced imaging. It is a one-step algorithm and does not require any restoration processing compared with the current two-step methods. The actual values of the sample's refractive index decrement can be estimated from its reconstruction images directly. The algorithm is proven by the actual experiment at the Beijing Synchrotron Radiation Facility and the reconstructed images are described finally.