Transport-of-Intensity Model for Single-Mask X-ray Differential Phase Contrast Imaging

X-ray phase contrast imaging has emerged as a promising technique for enhancing contrast and visibility of light-element materials, including soft tissues and tumors. In this paper, we propose a novel model for a single-mask phase imaging system based on the transport-of-intensity equation. Our model offers an intuitive understanding of signal and contrast formation in single-mask phase imaging systems. We also demonstrate efficient retrieval of attenuation and differential phase contrast with just one intensity image without requiring spectral information or mask/detector movement. The model validity as well as the proposed retrieval method is demonstrated via both experimental results on a system developed in-house as well as with Monte Carlo simulations. Our proposed model overcomes the limitations of existing models by providing an intuitive visualization of the image formation process. It also allows optimizing differential phase imaging geometries for practical applications, further enhancing broader applicability. Furthermore, the general methodology described herein offers insight on deriving transport-of-intensity models for novel X-ray imaging systems with periodic structures in the beam path.