Two-dimensional ultra-small angle X-ray scattering with grating interferometry

Abstract

It was recently established that the pixel-wise ultra-small angle x-ray distribution can be retrieved with grating interferometry. However, in these one dimensional approaches the contrast was limited to the direction orthogonal to the structure of the line gratings. Here, we demonstrate that sensitivity in two contrast directions can be achieved by using two pairs of crossed line gratings and by adapting scan procedures and data analysis accordingly. We demonstrate the retrieval of two-dimensional scattering distributions with grating interferometry, thus overcoming the previously reported limit of seven obtainable, complementary contrasts. In addition, we give further evidence for the superiority of the signal-to-noise ratio for the dark-field contrast, if a deconvolution-based instead of the standard analysis is utilized.

Near-field speckle-scanning-based x-ray imaging

“…The concept was first introduced by Yashiro et al in [45] and [46] using a grating interferometer, wherein the scattering effect of the sample is treated as a local point spread function whose estimated width mirrors the local scattering strength. Later on, Modregger et al [47,48] also used a grating interferometer but, this time, combined with numerical deconvolution to be able to extract the higher moments of the scattering distribution. In this section, we introduce by equivalence the recovery of the ultrasmallangle x-ray scattering distribution using near-field speckle scans similar to the ones recorded and used in the previous section.…”

State of the Art of X-ray Speckle-Based Phase-Contrast and Dark-Field Imaging

“…Although this approach gives a large number of contrast channels, some of which are not accessible with the other reconstruction methods, and has been shown to have improved angular sensitivity [158,159], the cumbersome and computationally expensive reconstruction procedure has so far impeded its wider implementation for speckle-based imaging.…”

“…The reconstruction approach relies on recovering the optical transfer function using iterative methods like the Richardson-Lucy deconvolution [160,161]. The moments of the scattering distribution carry different information about the sample [158,159]. The zeroth moment is equivalent to the transmission through the specimen, while the first order moments can be interpreted as the differential phase signals in the two directions.…”

“…This was inspired by an analogue reconstruction process introduced for 1D and 2D grating interferometry [158,159]. In general, the sample interference pattern can be expressed as the convolution of the reference signal without the sample in the beam and the optical transfer function of the specimen, equivalent to the sample scattering distribution.…”

Object Initialization For Ptychographic Scans With Reduced Overlap

“…Object initialization for ptychographic iteration refers to the utilization of a low resolution estimation of the object's complex wave field, which is constructed from the diffraction pattern D j (q) measured at scan position R j via moment analysis. The moments of the diffraction patterns M uv with the integers u and v can be calculated by [8,9] M uv (R j ) = dq (q x ) u (q y ) v D j (q)…”