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Ultra-intense, ultra-fast X-ray free-electron lasers (XFELs) enable the imaging of single protein molecules under ambient temperature and pressure. A crucial aspect of structure reconstruction involves determining the relative orientations of each diffraction pattern and recovering the missing phase information. In this paper, we introduce a predicted model-aided algorithm for orientation determination and phase retrieval, which has been tested on various simulated datasets and has shown significant improvements in the success rate, accuracy and efficiency of XFEL data reconstruction.

X-ray free-electron lasers (XFELs) can probe chemical and biological reactions as they unfold with unprecedented spatial and temporal resolution. A principal challenge in this pursuit involves the delivery of samples to the X-ray interaction point in such a way that produces data of the highest possible quality and with maximal efficiency. This is hampered by intrinsic constraints posed by the light source and operation within a beamline environment. For liquid samples, the solution typically involves some form of high-speed liquid jet, capable of keeping up with the rate of X-ray pulses. However, conventional jets are not ideal because of radiation-induced explosions of the jet, as well as their cylindrical geometry combined with the X-ray pointing instability of many beamlines which causes the interaction volume to differ for every pulse. This complicates data analysis and contributes to measurement errors. An alternative geometry is a liquid sheet jet which, with its constant thickness over large areas, eliminates the problems related to X-ray pointing. Since liquid sheets can be made very thin, the radiation-induced explosion is reduced, boosting their stability. These are especially attractive for experiments which benefit from small interaction volumes such as fluctuation X-ray scattering and several types of spectroscopy. Although their use has increased for soft X-ray applications in recent years, there has not yet been wide-scale adoption at XFELs. Here, gas-accelerated liquid sheet jet sample injection is demonstrated at the European XFEL SPB/SFX nano focus beamline. Its performance relative to a conventional liquid jet is evaluated and superior performance across several key factors has been found. This includes a thickness profile ranging from hundreds of nanometres to 60 nm, a fourfold increase in background stability and favorable radiation-induced explosion dynamics at high repetition rates up to 1.13 MHz. Its minute thickness also suggests that ultrafast single-particle solution scattering is a possibility.

One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand–maximize–compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.

Free‐electron lasers could enable X‐ray imaging of single biological macromolecules and the study of protein dynamics, paving the way for a powerful new imaging tool in structural biology, but a low signal‐to‐noise ratio and missing regions in the detectors, colloquially termed 'masks', affect data collection and hamper real‐time evaluation of experimental data. In this article, the challenges posed by noise and masks are tackled by introducing a neural network pipeline that aims to restore diffraction intensities. For training and testing of the model, a data set of diffraction patterns was simulated from 10 900 different proteins with molecular weights within the range of 10–100 kDa and collected at a photon energy of 8 keV. The method is compared with a simple low‐pass filtering algorithm based on autocorrelation constraints. The results show an improvement in the mean‐squared error of roughly two orders of magnitude in the presence of masks compared with the noisy data. The algorithm was also tested at increasing mask width, leading to the conclusion that demasking can achieve good results when the mask is smaller than half of the central speckle of the pattern. The results highlight the competitiveness of this model for data processing and the feasibility of restoring diffraction intensities from unknown structures in real time using deep learning methods. Finally, an example is shown of this preprocessing making orientation recovery more reliable, especially for data sets containing very few patterns, using the expansion–maximization–compression algorithm. [ABSTRACT FROM AUTHOR]

Single‐particle X‐ray diffractive imaging (SPI) of small (bio‐)nanoparticles (NPs) requires optimized injectors to collect sufficient diffraction patterns to allow for the reconstruction of the NP structure with high resolution. Typically, aerodynamic lens‐stack injectors are used for NP injection. However, current injectors were developed for larger NPs (>100 nm), and their ability to generate high‐density NP beams suffers with decreasing NP size. Here, an aerodynamic lens‐stack injector with variable geometry and a geometry‐optimization procedure are presented. The optimization for 50 nm gold‐NP (AuNP) injection using a numerical‐simulation infrastructure capable of calculating the carrier‐gas flow and the particle trajectories through the injector is also introduced. The simulations were experimentally validated using spherical AuNPs and sucrose NPs. In addition, the optimized injector was compared with the standard‐installation 'Uppsala injector' for AuNPs. Results for these heavy particles showed a shift in the particle‐beam focus position rather than a change in beam size, which results in a lower gas background for the optimized injector. Optimized aerodynamic lens‐stack injectors will allow one to increase NP beam density, reduce the gas background, discover the limits of current injectors and contribute to structure determination of small NPs using SPI. [ABSTRACT FROM AUTHOR]

With the emergence of X-ray free-electron lasers, it is possible to investigate the structure of nanoscale samples by employing coherent diffractive imaging in the X-ray spectral regime. In this work, we developed a refinement method for structure reconstruction applicable to low-quality coherent diffraction data. The method is based on the gradient search method and considers the missing region of a diffraction pattern and the small number of detected photons. We introduced an initial estimate of the structure in the method to improve the convergence. The present method is applied to an experimental diffraction pattern of an Xe cluster obtained in an X-ray scattering experiment at the SPring-8 Angstrom Compact free-electron LAser (SACLA) facility. It is found that the electron density is successfully reconstructed from the diffraction pattern with a large missing region, with a good initial estimate of the structure. The diffraction pattern calculated from the reconstructed electron density reproduced the observed diffraction pattern well, including the characteristic intensity modulation in each ring. Our refinement method enables structure reconstruction from diffraction patterns under difficulties such as missing areas and low diffraction intensity, and it is potentially applicable to the structure determination of samples that have low scattering power.

The routine atomic resolution structure determination of single particles is expected to have profound implications for probing structure–function relationships in systems ranging from energy-storage materials to biological molecules. Extremely bright ultrashort-pulse X-ray sources – X-ray free-electron lasers (XFELs) – provide X-rays that can be used to probe ensembles of nearly identical nanoscale particles. When combined with coherent diffractive imaging, these objects can be imaged; however, as the resolution of the images approaches the atomic scale, the measured data are increasingly difficult to obtain and, during an X-ray pulse, the number of photons incident on the 2D detector is much smaller than the number of pixels. This latter concern, the signal `sparsity', materially impedes the application of the method. An experimental analog using a conventional X-ray source is demonstrated and yields signal levels comparable with those expected from single biomolecules illuminated by focused XFEL pulses. The analog experiment provides an invaluable cross check on the fidelity of the reconstructed data that is not available during XFEL experiments. Using these experimental data, it is established that a sparsity of order 1.3 × 10−3 photons per pixel per frame can be overcome, lending vital insight to the solution of the atomic resolution XFEL single-particle imaging problem by experimentally demonstrating 3D coherent diffractive imaging from photon-sparse random projections.