On the origin of contrast in edge illumination X-ray phase-contrast imaging

Edge illumination (EI) has emerged as an X-ray phase-contrast imaging (XPCi) modality which could present significant advantages in terms of translation to clinical and laboratory applications. In this paper, we model its signal through the use of the "transport of intensity" equation. The validity conditions for this approach and its relationship with previous theoretical models for EI XPCi are discussed. The proposed model enables a simple estimation of the different contributions to the signal, which is shown to complement previously obtained results. In particular, it allows taking into account the effect of both slowly and rapidly varying refraction angles, corresponding to large and small object features. The derived framework is then used to investigate the effect on the signal of the smoothness of the mask edges, of the blurring from the source size and of the width of the object edge.