Linear information retrieval method in X-ray grating-based phase contrast imaging and its interchangeability with tomographic reconstruction

Abstract

In X-ray grating-based phase contrast imaging, information retrieval is necessary for quantitative research, especially for phase tomography. However, numerous and repetitive processes have to be performed for tomographic reconstruction. In this paper, we report a novel information retrieval method, which enables retrieving phase and absorption information by means of a linear combination of two mutually conjugate images. Thanks to the distributive law of the multiplication as well as the commutative law and associative law of the addition, the information retrieval can be performed after tomographic reconstruction, thus simplifying the information retrieval procedure dramatically. The theoretical model of this method is established in both parallel beam geometry for Talbot interferometer and fan beam geometry for Talbot-Lau interferometer. Numerical experiments are also performed to confirm the feasibility and validity of the proposed method. In addition, we discuss its possibility in cone beam geometry and its advantages compared with other methods. Moreover, this method can also be employed in other differential phase contrast imaging methods, such as diffraction enhanced imaging, non-interferometric imaging, and edge illumination.