Phase retrieval for near-field X-ray imaging beyond linearisation or compact support

X-ray phase contrast imaging based on free space propagation relies on phase retrieval to obtain sharp images of micro- and nanoscale objects, with widespread applications in material science and biomedical research. For high resolution synchrotron experiments, phase retrieval is largely based on the single step reconstruction using the contrast transfer function approach (CTF), as introduced almost twenty years ago [Cloetens et al., Appl. Phys. Lett. 75, 2912 (1999)]. Notwithstanding its tremendous merits, this scheme makes stringent assumptions on the optical properties of the object, requiring, in particular, a weakly varying phase. In this work, we show how significant the loss in image quality becomes if these assumption are violated, and how phase retrieval can be easily improved by a simple scheme of alternating projections. Importantly, the approach demonstrated here uses the same input data and constraint sets as the conventional CTF-based phase retrieval, and is particularly well suited for the holographic regime. (C) 2018 Author(s).