  X-ray phase contrast imaging holds great promise for improving the visibility
of light-element materials such as soft tissues and tumors. Single-mask
differential phase contrastnimaging method stands out as a simple and effective
approach to yield differential phase contrast. In this work, we introduce a
novel 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 in retrieved
images. 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. 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.
