Retrieval of missing small-angle scattering data in gas-phase diffraction experiments

We report an iterative algorithm to retrieve accurate real space information from gas phase ultrafast diffraction measurements with missing data at low momentum transfer. The algorithm operates in a manner similar to phase retrieval algorithms which transform signals back and forth between the signal domain and the Fourier transform domain and apply constraints to retrieve the missing phase. Our algorithm retrieves missing data that is not accessible experimentally by applying a real-space constraint that requires only an approximate a-priori knowledge of the shortest and longest internuclear distances in the molecule. We demonstrate successful retrieval of the missing data in simulated data and in experimentally measured electron diffraction signals of photo-dissociated iodobenzene molecules.