X-ray free-electron lasers are being used to determine the three-dimensional structure of objects from random snapshots. The two apparently very different Bayesian algorithms capable of performing this at ultra-low signal are fundamentally the same.

The advent of X-ray free-electron lasers promises the possibility to determine the structure of individual particles such as microcrystallites, viruses and biomolecules from single-shot diffraction snapshots obtained before the particle is destroyed by the intense femtosecond pulse. This program requires the ability to determine the orientation of the particle giving rise to each snapshot at signal levels as low as ~10−2 photons per pixel. Two apparently different approaches have recently demonstrated this capability. Here we show they represent different implementations of the same fundamental approach, and identify the primary factors limiting their performance.