Phase retrieval for object and probe using a series of defocus near-field images

Abstract

Full field x-ray propagation imaging can be severely deteriorated by wave front aberrations. Here we present an extension of ptychographic phase retrieval with simultaneous probe and object reconstruction suitable for the near-field diffractive imaging setting. Update equations used to iteratively solve the phase problem from a set of near-field images in view of reconstruction both object and probe are derived. The algorithm is tested based on numerical simulations including photon shot noise. The results indicate that the approach provides an efficient way to overcome restrictive idealizations of the illumination wave in the near-field (propagation) imaging.

X-Ray Near-Field Holography: Beyond Idealized Assumptions of the Probe

“…A detailed description of NFP can be found in earlier publications [14,76]. The preprocessing steps for the NFP are as follows: The holograms were dark field corrected.…”

“…5.1. This is to be compared to established near-field ptychographic schemes, which are based on lateral [13,154] and/or longi- tudinal translations of the object [14,76]. Hence, the standard approaches require sequential recordings and significantly more input data.…”

“…This position scanning is extensive, since an overlap between 60% to 85% is necessary for proper convergence of the ptychographic algorithm [138], depending on experimental modalities. This applies for the far-field [12,139] case of ptychography and its extensions to NFH [65,76]. Ptychography can also account for other non ideal states (e.g.…”

Phase retrieval problems in x-ray physics

“…the approximated source size. In this context, promising algorithms for the simultaneous reconstruction of the empty beam ι 0 and the object function by taking intensity measurements at several distances have been proposed recently [36,64]. Figures 2.7 and 2.8 also illustrate that in order to predict the reconstruction's quality the error value δ max has to be considered in relation to the hologram's contrast.…”

Phase retrieval for object and probe in the optical near-field

“…If longitudinal diversity is of such importance for near-field imaging, what is the purpose of lateral diversity in this context? We have shown that simultaneous phase retrieval of an object and a non-uniform probe is not possible by exclusively using on-axis shifts [82]. We will see that lateral translations of the object are important for a successful reconstruction of the probe -unperturbed by twin image artifacts.…”