Beyond the crystallization paradigm: Structure determination from diffraction patterns from ensembles of randomly oriented particles

We amplify on the principles of the method we have recently proposed for recovering an oversampled diffraction pattern of a single particle from measured diffraction patterns from multiple particles in orientations related by rotation about an axis parallel to the incident radiation. We propose an alternative method of phasing a reference resolution ring by means of a non-negativity constraint on the diffraction intensities, point out the need for caution about enantiomeric ambiguities in the reconstruction of a diffraction pattern from its angular correlations, and show that converged correlations may be deduced by appropriate averaging of even very noisy data.