Optimal mapping of x-ray laser diffraction patterns into three dimensions using routing algorithms.

Coherent diffractive imaging with x-ray free-electron lasers (XFEL) promises high-resolution structure determination of noncrystalline objects. Randomly oriented particles are exposed to XFEL pulses for acquisition of two-dimensional (2D) diffraction snapshots. The knowledge of their orientations enables 3D imaging by multiview reconstruction, combining 2D diffraction snapshots in different orientations. Here we introduce a globally optimal algorithm that can infer these orientations. We apply it to experimental XFEL data of nanoparticles and so determine their 3D electron density.