Sensing the wavefront of x-ray free-electron lasers using aerosol spheres

Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 105 structural models and 106 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable "shape envelope" among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

Deep learning for laser beam imprinting

Methods of ablation imprints in solid targets are widely used to characterize focused X-ray laser beams due to a remarkable dynamic range and resolving power. A detailed description of intense beam profiles is especially important in high-energy-density physics aiming at nonlinear phenomena. Complex interaction experiments require an enormous number of imprints to be created under all desired conditions making the analysis demanding and requiring a huge amount of human work. Here, for the first time, we present ablation imprinting methods assisted by deep learning approaches. Employing a multi-layer convolutional neural network (U-Net) trained on thousands of manually annotated ablation imprints in poly(methyl methacrylate), we characterize a focused beam of beamline FL24/FLASH2 at the Free-electron laser in Hamburg. The performance of the neural network is subject to a thorough benchmark test and comparison with experienced human analysts. Methods presented in this Paper pave the way towards a virtual analyst automatically processing experimental data from start to end.

Skopi: a simulation package for diffractive imaging of noncrystalline biomolecules

X-ray free-electron lasers (XFELs) have the ability to produce ultra-bright femtosecond X-ray pulses for coherent diffraction imaging of biomolecules. While the development of methods and algorithms for macromolecular crystallography is now mature, XFEL experiments involving aerosolized or solvated biomolecular samples offer new challenges in terms of both experimental design and data processing. Skopi is a simulation package that can generate single-hit diffraction images for reconstruction algorithms, multi-hit diffraction images of aggregated particles for training machine learning classifiers using labeled data, diffraction images of randomly distributed particles for fluctuation X-ray scattering algorithms, and diffraction images of reference and target particles for holographic reconstruction algorithms. Skopi is a resource to aid feasibility studies and advance the development of algorithms for noncrystalline experiments at XFEL facilities.

A Metropolis Monte Carlo algorithm for merging single-particle diffraction intensities

Single-particle imaging with X-ray free-electron lasers depends crucially on algorithms that merge large numbers of weak diffraction patterns despite missing measurements of parameters such as particle orientations. The expand–maximize–compress (EMC) algorithm is highly effective at merging single-particle diffraction patterns with missing orientation values, but most implementations exhaustively sample the space of missing parameters and may become computationally prohibitive as the number of degrees of freedom extends beyond orientation angles. This paper describes how the EMC algorithm can be modified to employ Metropolis Monte Carlo sampling rather than grid sampling, which may be favorable for reconstruction problems with more than three missing parameters. Using simulated data, this variant is compared with the standard EMC algorithm.

Discerning best practices in XFEL-based biological crystallography - standards for nonstandard experiments

Serial femtosecond crystallography (SFX) at X-ray free-electron lasers (XFELs) is a novel tool in structural biology. In contrast to conventional crystallography, SFX relies on merging partial intensities acquired with X-ray beams of often randomly fluctuating properties from a very large number of still diffraction images of generally randomly oriented microcrystals. For this reason, and possibly due to limitations of the still evolving data-analysis programs, XFEL-derived SFX data are typically of a lower quality than 'standard' crystallographic data. In contrast with this, the studies performed at XFELs often aim to investigate issues that require precise high-resolution data, for example to determine structures of intermediates at low occupancy, which often display very small conformational changes. This is a potentially dangerous combination and underscores the need for a critical evaluation of procedures including data-quality standards in XFEL-based structural biology. Here, such concerns are addressed.

High-Throughput 3D Ensemble Characterization of Individual Core-Shell Nanoparticles with X-ray Free Electron Laser Single-Particle Imaging

The structures as building blocks for designing functional nanomaterials have fueled the development of versatile nanoprobes to understand local structures of noncrystalline specimens. Progress in analyzing structures of individual specimens with atomic scale accuracy has been notable recently. In most cases, however, only a limited number of specimens are inspected lacking statistics to represent the systems with structural inhomogeneity. Here, by employing single-particle imaging with X-ray free electron lasers and algorithms for multiple-model 3D imaging, we succeeded in investigating several thousand specimens in a couple of hours and identified intrinsic heterogeneities with 3D structures. Quantitative analysis has unveiled 3D morphology, facet indices, and elastic strain. The 3D elastic energy distribution is further corroborated by molecular dynamics simulations to gain mechanical insight at the atomic level. This work establishes a route to high-throughput characterization of individual specimens in large ensembles, hence overcoming statistical deficiency while providing quantitative information at the nanoscale.

Characterization of megahertz X-ray laser beams by multishot desorption imprints in PMMA

Proper diagnostics of intense free-electron laser (FEL) X-ray pulses is indisputably important for experimental data analysis as well as for the protection of beamline optical elements. New challenges for beam diagnostic methods are introduced by modern FEL facilities capable of delivering powerful pulses at megahertz (MHz) repetition rates. In this paper, we report the first characterization of a defocused MHz 13.5-nm beam generated by the free-electron laser in Hamburg (FLASH) using the method of multi-pulse desorption imprints in poly(methyl methacrylate)(PMMA). The beam fluence profile is reconstructed in a novel and highly accurate way that takes into account the nonlinear response of material removal to total dose delivered by multiple pulses. The algorithm is applied to experimental data of single-shot ablation imprints and multi-shot desorption imprints at both low (10 Hz) and high (1 MHz) repetition rates. Reconstructed response functions show a great agreement with the theoretical desorption response function model.

Pulse-to-pulse wavefront sensing at free-electron lasers using ptychography

The pressing need for knowledge of the detailed wavefront properties of ultra-bright and ultra-short pulses produced by free-electron lasers has spurred the development of several complementary characterization approaches. Here a method based on ptychography is presented that can retrieve high-resolution complex-valued wavefunctions of individual pulses without strong constraints on the illumination or sample object used. The technique is demonstrated within experimental conditions suited for diffraction experiments and exploiting Kirkpatrick-Baez focusing optics. This lensless technique, applicable to many other short-pulse instruments, can achieve diffraction-limited resolution.

The role of transient resonances for ultra-fast imaging of single sucrose nanoclusters

Intense x-ray free-electron laser (XFEL) pulses hold great promise for imaging function in nanoscale and biological systems with atomic resolution. So far, however, the spatial resolution obtained from single shot experiments lags averaging static experiments. Here we report on a combined computational and experimental study about ultrafast diffractive imaging of sucrose clusters which are benchmark organic samples. Our theoretical model matches the experimental data from the water window to the keV x-ray regime. The large-scale dynamic scattering calculations reveal that transient phenomena driven by non-linear x-ray interaction are decisive for ultrafast imaging applications. Our study illuminates the complex interplay of the imaging process with the rapidly changing transient electronic structures in XFEL experiments and shows how computational models allow optimization of the parameters for ultrafast imaging experiments.

X-ray free electron lasers provide high photon flux to explore single particle diffraction imaging of biological samples. Here the authors present dynamic electronic structure calculations and benchmark them to single-particle XFEL diffraction data of sucrose clusters to predict optimal single-shot imaging conditions.

Characterizing the intrinsic properties of individual XFEL pulses via single-particle diffraction

With each single X-ray pulse having its own characteristics, understanding the individual property of each X-ray free-electron laser (XFEL) pulse is essential for its applications in probing and manipulating specimens as well as in diagnosing the lasing performance. Intensive research using XFEL radiation over the last several years has introduced techniques to characterize the femtosecond XFEL pulses, but a simple characterization scheme, while not requiring ad hoc assumptions, to address multiple aspects of XFEL radiation via a single data collection process is scant. Here, it is shown that single-particle diffraction patterns collected using single XFEL pulses can provide information about the incident photon flux and coherence property simultaneously, and the X-ray beam profile is inferred. The proposed scheme is highly adaptable to most experimental configurations, and will become an essential approach to understanding single X-ray pulses.

xcalib: a focal spot calibrator for intense X-ray free-electron laser pulses based on the charge state distributions of light atoms

The xcalib toolkit has been developed to calibrate the beam profile of an X-ray free-electron laser (XFEL) at the focal spot based on the experimental charge state distributions (CSDs) of light atoms. Characterization of the fluence distribution at the focal spot is essential to perform the volume integrations of physical quantities for a quantitative comparison between theoretical and experimental results, especially for fluence-dependent quantities. The use of the CSDs of light atoms is advantageous because CSDs directly reflect experimental conditions at the focal spot, and the properties of light atoms have been well established in both theory and experiment. Theoretical CSDs are obtained using xatom, a toolkit to calculate atomic electronic structure and to simulate ionization dynamics of atoms exposed to intense XFEL pulses, which involves highly excited multiple core-hole states. Employing a simple function with a few parameters, the spatial profile of an XFEL beam is determined by minimizing the difference between theoretical and experimental results. The optimization procedure employing the reinforcement learning technique can automatize and organize calibration procedures which, before, had been performed manually. xcalib has high flexibility, simultaneously combining different optimization methods, sets of charge states, and a wide range of parameter space. Hence, in combination with xatom, xcalib serves as a comprehensive tool to calibrate the fluence profile of a tightly focused XFEL beam in the interaction region.

On-line monitoring of the spatial properties of hard X-ray free-electron lasers based on a grating splitter

X-ray free-electron lasers (XFELs) play an increasingly important role in addressing the new scientific challenges relating to their high brightness, high coherence and femtosecond time structure. As a result of pulse-by-pulse fluctuations, the pulses of an XFEL beam may demonstrate subtle differences in intensity, energy spectrum, coherence, wavefront, etc., and thus on-line monitoring and diagnosis of a single pulse are required for many XFEL experiments. Here a new method is presented, based on a grating splitter and bending-crystal analyser, for single-pulse on-line monitoring of the spatial characteristics including the intensity profile, coherence and wavefront, which was suggested and applied experimentally to the temporal diagnosis of an XFEL single pulse. This simulation testifies that the intensity distribution, coherence and wavefront of the first-order diffracted beam of a grating preserve the properties of the incident beam, by using the coherent mode decomposition of the Gaussian-Schell model and Fourier optics. Indicatively, the first-order diffraction of appropriate gratings can be used as an alternative for on-line monitoring of the spatial properties of a single pulse without any characteristic deformation of the principal diffracted beam. However, an interesting simulation result suggests that the surface roughness of gratings will degrade the spatial characteristics in the case of a partially coherent incident beam. So, there exists a suitable roughness value for non-destructive monitoring of the spatial properties of the downstream beam, which depends on the specific optical path. Here, experiments based on synchrotron radiation X-rays are carried out in order to verify this method in principle. The experimental results are consistent with the theoretical calculations.

Coherent diffractive imaging of single helium nanodroplets with a high harmonic generation source

Coherent diffractive imaging of individual free nanoparticles has opened routes for the in situ analysis of their transient structural, optical, and electronic properties. So far, single-shot single-particle diffraction was assumed to be feasible only at extreme ultraviolet and X-ray free-electron lasers, restricting this research field to large-scale facilities. Here we demonstrate single-shot imaging of isolated helium nanodroplets using extreme ultraviolet pulses from a femtosecond-laser-driven high harmonic source. We obtain bright wide-angle scattering patterns, that allow us to uniquely identify hitherto unresolved prolate shapes of superfluid helium droplets. Our results mark the advent of single-shot gas-phase nanoscopy with lab-based short-wavelength pulses and pave the way to ultrafast coherent diffractive imaging with phase-controlled multicolor fields and attosecond pulses.

Diffraction imaging studies of free individual nanoparticles have so far been restricted to XUV and X-ray free - electron laser facilities. Here the authors demonstrate the possibility of using table-top XUV laser sources to image prolate shapes of superfluid helium droplets.

Experimental strategies for imaging bioparticles with femtosecond hard X-ray pulses

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.

WavePropaGator: interactive framework for X-ray free-electron laser optics design and simulations

This article describes the WavePropaGator (WPG) package, a new interactive software framework for coherent and partially coherent X-ray wavefront propagation simulations. The package has been developed at European XFEL for users at the existing and emerging free-electron laser (FEL) facilities, as well as at the third-generation synchrotron sources and future diffraction-limited storage rings. The WPG addresses the needs of beamline scientists and user groups to facilitate the design, optimization and improvement of X-ray optics to meet their experimental requirements. The package uses the Synchrotron Radiation Workshop (SRW) C/C++ library and its Python binding for numerical wavefront propagation simulations. The framework runs reliably under Linux, Microsoft Windows 7 and Apple Mac OS X and is distributed under an open-source license. The available tools allow for varying source parameters and optics layouts and visualizing the results interactively. The wavefront history structure can be used for tracking changes in every particular wavefront during propagation. The batch propagation mode enables processing of multiple wavefronts in workflow mode. The paper presents a general description of the package and gives some recent application examples, including modeling of full X-ray FEL beamlines and start-to-end simulation of experiments.

Dragonfly: an implementation of the expand-maximize-compress algorithm for single-particle imaging

Single-particle imaging (SPI) with X-ray free-electron lasers has the potential to change fundamentally how biomacromolecules are imaged. The structure would be derived from millions of diffraction patterns, each from a different copy of the macromolecule before it is torn apart by radiation damage. The challenges posed by the resultant data stream are staggering: millions of incomplete, noisy and un-oriented patterns have to be computationally assembled into a three-dimensional intensity map and then phase reconstructed. In this paper, the Dragonfly software package is described, based on a parallel implementation of the expand-maximize-compress reconstruction algorithm that is well suited for this task. Auxiliary modules to simulate SPI data streams are also included to assess the feasibility of proposed SPI experiments at the Linac Coherent Light Source, Stanford, California, USA.

CFEL-ASG Software Suite (CASS): usage for free-electron laser experiments with biological focus

CASS [Foucar et al. (2012). Comput. Phys. Commun.183, 2207-2213] is a well established software suite for experiments performed at any sort of light source. It is based on a modular design and can easily be adapted for use at free-electron laser (FEL) experiments that have a biological focus. This article will list all the additional functionality and enhancements of CASS for use with FEL experiments that have been introduced since the first publication. The article will also highlight some advanced experiments with biological aspects that have been performed.

Characterizing transverse coherence of an ultra-intense focused X-ray free-electron laser by an extended Young's experiment

Characterization of transverse coherence is one of the most critical themes for advanced X-ray sources and their applications in many fields of science. However, for hard X-ray free-electron laser (XFEL) sources there is very little knowledge available on their transverse coherence characteristics, despite their extreme importance. This is because the unique characteristics of the sources, such as the ultra-intense nature of XFEL radiation and the shot-by-shot fluctuations in the intensity distribution, make it difficult to apply conventional techniques. Here, an extended Young's interference experiment using a stream of bimodal gold particles is shown to achieve a direct measurement of the modulus of the complex degree of coherence of XFEL pulses. The use of interference patterns from two differently sized particles enables analysis of the transverse coherence on a single-shot basis without a priori knowledge of the instantaneous intensity ratio at the particles. For a focused X-ray spot as small as 1.8 µm (horizontal) × 1.3 µm (vertical) with an ultrahigh intensity that exceeds 10(18) W cm(-2) from the SPring-8 Ångstrom Compact free-electron LAser (SACLA), the coherence lengths were estimated to be 1.7 ± 0.2 µm (horizontal) and 1.3 ± 0.1 µm (vertical). The ratios between the coherence lengths and the focused beam sizes are almost the same in the horizontal and vertical directions, indicating that the transverse coherence properties of unfocused XFEL pulses are isotropic. The experiment presented here enables measurements free from radiation damage and will be readily applicable to the analysis of the transverse coherence of ultra-intense nanometre-sized focused XFEL beams.

A minimal view of single-particle imaging with X-ray lasers

The ability to serially interrogate single biomolecules with femtosecond X-ray pulses from free-electron lasers has ushered in the possibility of determining the three-dimensional structure of biomolecules without crystallization. However, the complexity of imaging a sample's structure from very many of its noisy and incomplete diffraction data can be daunting. In this review, we introduce a simple analogue of this imaging workflow, use it to describe a structure reconstruction algorithm based on the expectation maximization principle, and consider the effects of extraneous noise. Such a minimal model can aid experiment and algorithm design in future studies.

Wavefront metrology measurements at SACLA by means of X-ray grating interferometry

The knowledge of the X-ray wavefront is of importance for many experiments at synchrotron sources and hard X-ray free-electron lasers. We will report on metrology measurements performed at the SACLA X-ray Free Electron Laser by means of grating interferometry which allows for an at-wavelength, in-situ, and single-shot characterization of the X-ray wavefront. At SACLA the grating interferometry technique was used for the study of the X-ray optics installed upstream of the end station, two off-set mirror systems and a double crystal monochromator. The excellent quality of the optical components was confirmed by the experimental results. Consequently grating interferometry presents the ability to support further technical progresses in X-ray mirror manufacturing and mounting.

Toward unsupervised single-shot diffractive imaging of heterogeneous particles using X-ray free-electron lasers

Single shot diffraction imaging experiments via X-ray free-electron lasers can generate as many as hundreds of thousands of diffraction patterns of scattering objects. Recovering the real space contrast of a scattering object from these patterns currently requires a reconstruction process with user guidance in a number of steps, introducing severe bottlenecks in data processing. We present a series of measures that replace user guidance with algorithms that reconstruct contrasts in an unsupervised fashion. We demonstrate the feasibility of automating the reconstruction process by generating hundreds of contrasts obtained from soot particle diffraction experiments.