Phase retrieval for crystalline specimens

The recent availability of ultra-bright and ultra-short X-rays pulses from new sources called x-ray free-electron lasers (XFELs) has introduced a new paradigm in X-ray crystallography. Called "diffraction-before-destruction," this paradigm addresses the main problems that plague crystallography using synchrotron sources. However, the phase problem of coherent diffraction imaging remains: one has to retrieve the phase of the measured diffraction amplitude in order to reconstruct the object. Fibrous and membrane proteins that crystallize in 1D and 2D crystals can now potentially be used for data collection with free-electron lasers. The crystallographic phase problem with such crystalline specimens is eased as the Fourier amplitude can be sampled more finely than at the Bragg sampling along one or two directions. Here we characterise uniqueness of the phase problem for different types of crystalline specimen. Simulated ab initio phase retrieval using iterative projection algorithms for 2D crystals is presented.