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Single particle diffraction imaging experiments at free-electron lasers (FEL) have a great potential for structure determination of reproducible biological specimens that can not be crystallized. One of the challenges in processing the data from such an experiment is to determine correct orientation of each diffraction pattern from samples randomly injected in the FEL beam. We propose an algorithm (see also O. Yefanov et al., Photon Science - HASYLAB Annual Report 2010) that can solve this problem and can be applied to samples from tens of nanometers to microns in size, measured with sub-nanometer resolution in the presence of noise. This is achieved by the simultaneous analysis of a large number of diffraction patterns corresponding to different orientations of the particles. The algorithms efficiency is demonstrated for two biological samples, an artificial protein structure without any symmetry and a virus with icosahedral symmetry. Both structures are few tens of nanometers in size and consist of more than 100 000 non-hydrogen atoms. More than 10 000 diffraction patterns with Poisson noise were simulated and analyzed for each structure. Our simulations indicate the possibility to achieve resolution of about 3.3 {AA} at 3 {AA} wavelength and incoming flux of 10^{12} photons per pulse focused to 100times 100 nm^2.
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A structural understanding of whole cells in three dimensions at high spatial resolution remains a significant challenge and, in the case of X-rays, has been limited by radiation damage. By alleviating this limitation, cryogenic coherent diffraction imaging (cryo-CDI) could bridge the important resolution gap between optical and electron microscopy in bio-imaging. Here, we report for the first time 3D cryo-CDI of a whole, frozen-hydrated cell - in this case a Neospora caninum tachyzoite - using 8 keV X-rays. Our 3D reconstruction reveals the surface and internal morphology of the cell, including its complex, polarized sub-cellular architecture with a 3D resolution of ~75-100 nm, which is presently limited by the coherent X-ray flux and detector size. Given the imminent improvement in the coherent X-ray flux at the facilities worldwide, our work forecasts the possibility of routine 3D imaging of frozen-hydrated cells with spatial resolutions in the tens of nanometres.
We present here an overview of Coherent X-ray Diffraction Imaging (CXDI) with its application to nanostructures. This imaging approach has become especially important recently due to advent of X-ray Free-Electron Lasers (XFEL) and its applications to the fast developing technique of serial X-ray crystallography. We start with the basic description of coherent scattering on the finite size crystals. The difference between conventional crystallography applied to large samples and coherent scattering on the finite size samples is outlined. The formalism of coherent scattering from a finite size crystal with a strain field is considered. Partially coherent illumination of a crystalline sample is developed. Recent experimental examples demonstrating applications of CXDI to the study of crystalline structures on the nanoscale, including experiments at FELs, are also presented.
Current Flash X-ray single-particle diffraction Imaging (FXI) experiments, which operate on modern X-ray Free Electron Lasers (XFELs), can record millions of interpretable diffraction patterns from individual biomolecules per day. Due to the stochastic nature of the XFELs, those patterns will to a varying degree include scatterings from contaminated samples. Also, the heterogeneity of the sample biomolecules is unavoidable and complicates data processing. Reducing the data volumes and selecting high-quality single-molecule patterns are therefore critical steps in the experimental set-up. In this paper, we present two supervised template-based learning methods for classifying FXI patterns. Our Eigen-Image and Log-Likelihood classifier can find the best-matched template for a single-molecule pattern within a few milliseconds. It is also straightforward to parallelize them so as to fully match the XFEL repetition rate, thereby enabling processing at site.
Coherent X-ray beams with energies $geq 50$ keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction imaging (BCDI). However, the undersampling of the diffraction signal due to Fourier space compression at high X-ray energies renders conventional phase retrieval algorithms unsuitable for three-dimensional reconstruction. To address this problem we utilize a phase retrieval method with a Fourier constraint specifically tailored for undersampled diffraction data measured with coarse-pitched detector pixels that bin the underlying signal. With our approach, we show that it is possible to reconstruct three-dimensional strained crystallites from an undersampled Bragg diffraction data set subject to pixel-area integration without having to physically upsample the diffraction signal. Using simulations and experimental results, we demonstrate that explicit modeling of Fourier space compression during phase retrieval provides a viable means by which to invert high-energy BCDI data, which is otherwise intractable.
In single particle coherent x-ray diffraction imaging experiments, performed at x-ray free-electron lasers (XFELs), samples are exposed to intense x-ray pulses to obtain single-shot diffraction patterns. The high intensity induces electronic dynamics on the femtosecond time scale in the system, which can reduce the contrast of the obtained diffraction patterns and adds an isotropic background. We quantify the degradation of the diffraction pattern from ultrafast electronic damage by performing simulations on a biological sample exposed to x-ray pulses with different parameters. We find that the contrast is substantially reduced and the background is considerably strong only if almost all electrons are removed from their parent atoms. This happens at fluences of at least one order of magnitude larger than provided at currently available XFEL sources.
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