It has been suggested that the extended intensity profiles surrounding Bragg reflections that arise when a series of finite crystals of varying size and shape are illuminated by the intense, coherent illumination of an x-ray free-electron laser may enable the crystal’s unit-cell electron density to be obtained ab initio via well-established iterative phasing algorithms. Such a technique could have a significant impact on the field of biological structure determination since it avoids the need for a priori information from similar known structures, multiple measurements near resonant atomic absorption energies, isomorphic derivative crystals, or atomic-resolution data. Here, we demonstrate this phasing technique on diffraction patterns recorded from artificial two-dimensional microcrystals using the seeded soft x-ray free-electron laser FERMI. We show that the technique is effective when the illuminating wavefront has nonuniform phase and amplitude, and when the diffraction intensities cannot be measured uniformly throughout reciprocal space because of a limited signal-to-noise ratio.

This study explores the capabilities of the Coherent X-ray Imaging Instrument at the Linac Coherent Light Source to image small biological samples. The weak signal from small samples puts a significant demand on the experiment. Aerosolized Omono River virus particles of ∼40 nm in diameter were injected into the submicrometre X-ray focus at a reduced pressure. Diffraction patterns were recorded on two area detectors. The statistical nature of the measurements from many individual particles provided information about the intensity profile of the X-ray beam, phase variations in the wavefront and the size distribution of the injected particles. The results point to a wider than expected size distribution (from ∼35 to ∼300 nm in diameter). This is likely to be owing to nonvolatile contaminants from larger droplets during aerosolization and droplet evaporation. The results suggest that the concentration of nonvolatile contaminants and the ratio between the volumes of the initial droplet and the sample particles is critical in such studies. The maximum beam intensity in the focus was found to be 1.9 × 10¹² photons per µm² per pulse. The full-width of the focus at half-maximum was estimated to be 500 nm (assuming 20% beamline transmission), and this width is larger than expected. Under these conditions, the diffraction signal from a sample-sized particle remained above the average background to a resolution of 4.25 nm. The results suggest that reducing the size of the initial droplets during aerosolization is necessary to bring small particles into the scope of detailed structural studies with X-ray lasers.