Transport-of-intensity model for single-mask x-ray differential phase contrast imaging

X-ray phase contrast imaging holds great promise for improving the visibility of light-element materials such as soft tissues and tumors. The single-mask differential phase contrast imaging method stands out as a simple and effective approach to yield differential phase contrast. In this work, we introduce a model for a single-mask phase imaging system based on the transport-of-intensity equation. Our model provides an accessible understanding of signal and contrast formation in single-mask x-ray phase imaging, offering a clear perspective on the image formation process, for example, the origin of alternate bright and dark fringes in phase contrast intensity images. Aided by our model, we present an efficient retrieval method that yields differential phase contrast imagery in a single acquisition step. Our model gives insight into the contrast generation and its dependence on the system geometry and imaging parameters in both the initial intensity image as well as retrieved images. The model validity as well as the proposed retrieval method are demonstrated via both experimental results on a system developed in house as well as Monte Carlo simulations. In conclusion, our work not only provides a model for an intuitive visualization of image formation but also offers a method to optimize differential phase imaging setups, holding tremendous promise for advancing medical diagnostics and other applications.