Eikonal Phase Retrieval: unleashing the potential of fourth-generation sources for enhanced propagation-based tomography on biological samples.

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 that would otherwise remain hidden under excessive noise. Until now, 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 linearization 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. 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 that efficiently performs the phase retrieval task over the entire near-field range, producing images of superior quality for mixed attenuation objects. Our tests on data with shorter propagation distances show that the artifacts, which our algorithm effectively addresses, are present already in more standard third-generation synchrotron setups. This highlights the potential broad applicability of the Eikonal Phase Retrieval method.