Diffraction imaging of single particles and biomolecules

Theory predicts that with a very short and very intense X-ray pulse, the image of a single diffraction pattern may be recorded from a large macromolecule, a virus, or a nanocluster of proteins without the need for a crystal. A three-dimensional data set can be assembled from such images when many copies of the molecule are exposed to the beam one by one in random orientations. We outline a method for structure reconstruction from such a data set in which no independent information is available about the orientation of the images. The basic requirement for reconstruction and/or signal averaging is the ability to tell whether two noisy diffraction patterns represent the same view of the sample or two different views. With this knowledge, averaging techniques can be used to enhance the signal and extend the resolution in a redundant data set. Based on statistical properties of the diffraction pattern, we present an analytical solution to the classification problem. The solution connects the number of incident X-ray photons with the particle size and the achievable resolution. The results are surprising in that they show that classification can be done with less than one photon per pixel in the limiting resolution shell, assuming Poisson-type photon noise in the image. The results can also be used to provide criteria for improvements in other image classification procedures, e.g., those used in electron tomography or diffraction.