  The evolution of synchrotrons towards higher brilliance beams has increased
the possible sample-to-detector propagation distances for which the source
confusion circle does not lead to geometrical blurring. This makes it possible
to push near-field propagation driven phase contrast enhancement to the limit,
revealing low contrast features which would otherwise remain hidden under an
excessive noise. Until today this possibility was hindered, in many objects of
scientific interest, by the simultaneous presence of strong phase gradient
regions and low contrast features. The strong gradients, when enhanced with the
now possible long propagation distances, induce such strong phase effects that
the linearisation assumptions of current state-of-the-art single-distance phase
retrieval filters are broken, and the resulting image quality is jeopardized.
Here, we introduce a new iterative phase-retrieval algorithm and compare it
with the Paganin phase-retrieval algorithm, in both the monochromatic and
polychromatic cases, obtaining superior image quality. In the polychromatic
case the comparison was done with an extrapolated Paganin algorithm obtained by
reintroducing, into our phase retrieval algorithm, the linearization
approximations underlying the Paganin forward model. Our work provides an
innovative algorithm which efficiently performs the phase retrieval task over
the entire near-field range, producing images of exceptional quality for mixed
attenuation objects.
