Phase retrieval in femtosecond X-ray nanocrystallography

Protein X-ray crystallography is a method for determining the 3-dimensional structures of large biological molecules arranged in regular arrays inside a crystal. Samples of the Fourier magnitude of the molecular charge density can be measured from the amplitudes of the scattered X-rays but the determination of the Fourier phases requires chemical modification to the sample and collection of additional data. There is thus a need for a direct digital phasing method that does not require modified specimens. The diffraction from very small crystals allows for a finer sampling of the diffraction amplitude and although highly attenuated, these additional samples offer the possibility of iterative phase retrieval without the use of ancillary experimental data. Following on from a previous study [6], we examine in detail the noise characteristics of finite crystal diffraction and propose a data selection strategy to improve 3-dimensional reconstructions of the molecular charge density using iterative phase retrieval algorithms. Simulation results verify that higher noise levels can indeed be tolerated by employing such a strategy to precondition the data.