Theoretical study of the influence of small angle scattering on diffraction enhanced imaging

Small angle scattering plays an important role in diffraction enhanced imaging (DEI). The DEI equation proposed by Chapman is accepted and widely used by many applications in medical, biological and material researches. However, in this framework the contribution of the small angle scattering determined by the crystal analyzer is neglected and the extinction contrast caused by the rejection of the small angle scattering by the analyzer is not explicitly expressed. In this contribution we introduce two additional terms in the DEI equation that describe the additional background introduced by the small angle scattering collected by the analyzer crystal and the extinction contrast associated to the rejection of the small angle scattering by the analyzer crystal, respectively. Four kinds of images of the DEI method were considered by using these revised equations and results were presented and discussed.