Similarity score for screening phase-retrieved maps in X-ray diffraction imaging – characterization in reciprocal space

Abstract

X-ray diffraction imaging (XDI) is utilized for visualizing the structures of non-crystalline particles in material sciences and biology. In the structural analysis, phase-retrieval (PR) algorithms are applied to the diffraction amplitude data alone to reconstruct the electron density map of a specimen particle projected along the direction of the incident X-rays. However, PR calculations may not lead to good convergence because of a lack of diffraction patterns in small-angle regions and Poisson noise in X-ray detection. Therefore, the PR calculation is still a bottleneck for the efficient application of XDI in the structural analyses of non-crystalline particles. For screening maps from hundreds of trial PR calculations, we have been using a score and measuring the similarity between a pair of retrieved maps. Empirically, probable maps approximating the particle structures gave a score smaller than a threshold value, but the reasons for the effectiveness of the score are still unclear. In this study, the score is characterized in terms of the phase differences between the structure factors of the retrieved maps, the usefulness of the score in screening the maps retrieved from experimental diffraction patterns is demonstrated, and the effective resolution of similarity-score-selected maps is discussed.

Redox-induced changes in nanostructures and electron densities of connected Pt–Fe catalysts for fuel cells revealed via in situ coherent X-ray diffraction

“…The ten most probable reconstructions were selected by a principal component analysis 22) with a mean-shift clustering 23) and then the selected projected electron density maps were averaged to produce the final maps. Although the estimation of the effective spatial resolutions of phase-retrieved maps is still a matter of debate, 24) we used the phase retrieval transfer function (PRTF) 25) with the simple, empirical threshold value of e 1/ for the estimation. Figure 2(a) shows the representative CXD patterns of the connected Pt-Fe-alloy catalyst under the initial oxidation (a1), first reduction (a2), second oxidation (a3) and final reduction (a4) atmosphere, respectively.…”