Algorithm for Reconstruction of 3D Images of Nanorice Particles from Diffraction Patterns of Two Particles in Independent Random Orientations with an X-ray Laser

Abstract

Abstract:The method of angular correlations recovers quantities from diffraction patterns of randomly oriented particles, as expected to be measured with an X-ray free electron laser (XFEL), proportional to quadratic functions of the spherical harmonic expansion coefficients of the diffraction volume of a single particle. We have previously shown that it is possible to reconstruct a randomly oriented icosahedral or helical virus from the average over all measured diffraction patterns of such correlations. We point out in this paper that a structure of even simpler particles of 50 Å or so in diameter and consisting of heavier atomic elements (to enhance scattering) that has been used as a test case for reconstructions from XFEL diffraction patterns can also be solved by this technique. Even though there has been earlier work on similar objects (prolate spheroids), one advantage of the present technique is its potential to also work with diffraction patterns not only due to single particles as has been suggested on the basis on nonoverlapping delta functions of angular scattering. Accordingly, we calculated from the diffraction patterns the angular momentum expansions of the pair correlations and triple correlations for general particle images and reconstructed those images in the standard way. Although the images looked pretty much the same, it is not totally clear to us that the angular correlations are exactly the same as different numbers of particles due to the possibility of constructive or destructive interference between the scattered waves from different particles. It is of course known that, for a large number of particles contributing to a diffraction parttern, the correlations converge to that of a single particle. It could be that the lack of perfect agreement between the images reconstructed with one and two particles is due to uncancelling constructive and destructive conditions that are not found in the case of solution scattering.

Reconstruction of 3D Image of Nanorice Particle from Randomly Oriented Single-Shot Experimental Diffraction Patterns Using Angular Correlation Method

“…5. All the above discretized expressions that help reproducing the same results we have here can be conceptually described as continuous forms [13]. From (12), the only unknown is the signs of I l0 (q).…”

X-ray Free-Electron Laser

“…Hanks et al report the two-and three-photon photoionization cross-sections of Li + , Ne 8+ and Ar 16+ under XUV radiation [22], Tyrała et al discuss the state-population narrowing effect on two-photon absorption for intense XFEL pulses [23], while Hatada and Di Cicco describe the modeling of non-equilibrium dynamics and saturable absorption induced by XFEL radiation [24]. Kirrander and Weber discuss the fundamental limits on spatial resolution in ultrafast diffraction with XFELs [25], while Kim et al describe the algorithm for reconstruction of three-dimensional images of rice nanoparticles from the diffraction pattern of two particles in independent random orientations using XFEL [26].…”