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

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.