In gas-phase diffraction experiments, the molecular signal at low scattering angles is always missing — obscured by the direct beam, detector geometry, or background. This missing region contains the large-scale spatial information needed to reconstruct real-space molecular structure from momentum-space data.
The paper on restoring missing low-angle diffraction data (arXiv: 2603.24334) introduces an iterative algorithm that fills in the gap. The method transforms the two-dimensional signal back and forth between momentum space and real space through Fourier and Abel transforms, applying real-space constraints at each iteration.
The constraints are minimal: approximate knowledge of the shortest and longest internuclear distances in the molecule. These bounds define a real-space support — the signal must be zero outside these distances — and the algorithm uses this to infer what the momentum-space signal would have to be at low angles.
The authors demonstrate successful retrieval in simulated patterns and in experimentally measured diffraction from laser-aligned trifluoroiodomethane molecules. The anisotropic 2D signal — created by linearly polarized laser excitation — contains more information than conventional isotropic signals, and the algorithm exploits this.
The through-claim: the missing data is recoverable because the real-space constraints are informative. Knowing where the atoms aren't — outside the molecular envelope — determines what the signal must be where you can't measure it. The algorithm doesn't guess; it deduces, using the physical impossibility of signal outside the molecular boundary to reconstruct the signal inside the measurement gap.
2603.24334. Ultrafast diffraction / phase retrieval / molecular imaging / inverse problems / scattering.