Reconstruction of missing low-angle scattering in two-dimensional diffraction signal

TL;DR

This paper introduces an iterative algorithm that reconstructs missing low-angle scattering data in 2D diffraction patterns, enabling more accurate structural analysis from incomplete experimental data.

Contribution

The authors develop a novel Fourier-Abel transform-based iterative method that reconstructs missing low-angle signals with minimal prior structural knowledge.

Findings

Accurately reconstructs missing low-angle scattering in simulated data.

Successfully applies the method to experimental diffraction patterns of CF3I.

Enhances real-space structural retrieval from incomplete diffraction data.

Abstract

Anisotropic two-dimensional diffraction signals encode additional structural information, including atom-pair angular distributions, beyond conventional isotropic scattering. However, experimental constraints such as beam stops result in missing low-angle scattering data, which limits accurate real-space reconstruction. We develop an iterative algorithm to recover the missing low-angle signal in two-dimensional diffraction patterns. The method transforms between momentum-transfer and real-space domains using coupled Fourier and Abel transforms, while enforcing real-space support constraints to suppress reconstruction artifacts. Importantly, the algorithm requires only minimal a priori knowledge of the molecular structure, namely the approximate shortest and longest internuclear distances. We demonstrate accurate reconstruction of the missing signal using both simulated data and experimental diffraction patterns from laser-aligned trifluoroiodomethane (CF3I) molecules, enabling improved real-space structural retrieval from incomplete diffraction data. Our results remove a fundamental experimental limitation in ultrafast diffraction and establish a general route toward complete structural retrieval from incomplete scattering data.