Phase retrieval from crystalline diffraction averaged over several different unit cells

Joe P. J. Chen, Rick A. Kirian, Kenneth R. Beyerlein, Richard J. Bean, Henry N. Chapman, Philip J. Bones, Rick P. Millane

Abstract: In protein nanocrystallography using x-ray lasers, diffraction is measured from an ensemble of very small crystals. The measured diffraction data can sometimes be processed to estimate the continuous Fourier transform intensity of the contents within the unit cell that makes up the crystals. However, in most cases the intensity data are averaged over a number of different kinds of unit cell that can occur in the ensemble. We investigate the properties of this problem and describe two algorithms to reconstruct the electron density of these unit cells from the averaged x-ray diffraction intensity data. The algorithms are evaluated by simulation.