Progress of diffraction enhanced imaging at the Beijing Synchrotron Radiation Facility

A simple framework that allows a new general diffraction enhanced imaging (DEI) equation to be derived is presented. This latter equation may explain all open problems associated with the equation introduced by Chapman and those not explained by the first DEI equation, such as the noise background due to the small-angle scattering reflected by the analyzer. Combing the DEI equation with computed tomography (CT) theory, we propose a new DEI–CT formula that explains qualitatively the contour contrast caused by extinction of the refraction. Two formulae with a new method to extract the refraction angle are also introduced. Within this new theoretical framework the three components of the gradient of the refractive index can be reconstructed.