Coherence properties of the high-energy fourth-generation X-ray synchrotron sources

Small-angle scattering of complex fluids in flow

Complex fluids encompass a significant proportion of the materials that we use today from feedstocks such as cellulose fibre dispersions, materials undergoing processing or formulation, through to consumer end products such as shampoo. Such systems exhibit intricate behaviour due to their composition and microstructure, particularly when analysing their texture and response to flow (rheology). In particular, these fluids when flowing may undergo transitions in their nano- to microstructure, potentially aligning with flow fields, breaking and reassembling or reforming, or entirely changing phase. This manifests as macroscopic changes in material properties, such as core-annular flow of concentrated emulsions in pipelines or the favourable texture of liquid soaps. Small-angle scattering provides a unique method for probing underlying changes in fluid nano- to microstructure, from a few angströms to several microns, of complex fluids under flow. In particular, the alignment of rigid components or shape changes of soft components can be explored, along with local inter-particle ordering and global alignment with macroscopic flow fields. This review highlights recent important developments in the study of such complex fluid systems that couple flow or shear conditions with small-angle scattering measurements, and highlights the physical insight obtained by these experiments. Recent results from neutron scattering measurements made using a simple flow cell are presented, offering a facile method to explore alignment of complex fluids in an easily accessible geometry, and contextualised within existing and potential future research questions.

A distributed data processing scheme based on Hadoop for synchrotron radiation experiments

With the development of synchrotron radiation sources and high-frame-rate detectors, the amount of experimental data collected at synchrotron radiation beamlines has increased exponentially. As a result, data processing for synchrotron radiation experiments has entered the era of big data. It is becoming increasingly important for beamlines to have the capability to process large-scale data in parallel to keep up with the rapid growth of data. Currently, there is no set of data processing solutions based on the big data technology framework for beamlines. Apache Hadoop is a widely used distributed system architecture for solving the problem of massive data storage and computation. This paper presents a set of distributed data processing schemes for beamlines with experimental data using Hadoop. The Hadoop Distributed File System is utilized as the distributed file storage system, and Hadoop YARN serves as the resource scheduler for the distributed computing cluster. A distributed data processing pipeline that can carry out massively parallel computation is designed and developed using Hadoop Spark. The entire data processing platform adopts a distributed microservice architecture, which makes the system easy to expand, reduces module coupling and improves reliability.

Mutual optical intensity propagation through non-ideal two-dimensional mirrors

The mutual optical intensity (MOI) model is a partially coherent radiation propagation tool that can sequentially simulate beamline optics and provide beam intensity, local degree of coherence and phase distribution at any location along a beamline. This paper extends the MOI model to non-ideal two-dimensional (2D) optical systems, such as ellipsoidal and toroidal mirrors with 2D figure errors. Simulation results show that one can tune the trade-off between calculation efficiency and accuracy by varying the number of wavefront elements. The focal spot size of an ellipsoidal mirror calculated with 100 × 100 elements gives less than 0.4% deviation from that with 250 × 250 elements, and the computation speed is nearly two orders of magnitude faster. Effects of figure errors on 2D focusing are also demonstrated for a non-ideal ellipsoidal mirror and by comparing the toroidal and ellipsoidal mirrors. Finally, the MOI model is benchmarked against the multi-electron Synchrotron Radiation Workshop (SRW) code showing the model's high accuracy.

X-ray Emission Spectroscopy of Single Protein Crystals Yields Insights into Heme Enzyme Intermediates

Enzyme reactivity is often enhanced by changes in oxidation state, spin state, and metal-ligand covalency of associated metallocofactors. The development of spectroscopic methods for studying these processes coincidentally with structural rearrangements is essential for elucidating metalloenzyme mechanisms. Herein, we demonstrate the feasibility of collecting X-ray emission spectra of metalloenzyme crystals at a third-generation synchrotron source. In particular, we report the development of a von Hamos spectrometer for the collection of Fe Kβ emission optimized for analysis of dilute biological samples. We further showcase its application in crystals of the immunosuppressive heme-dependent enzyme indoleamine 2,3-dioxygenase. Spectra from protein crystals in different states were compared with relevant reference compounds. Complementary density functional calculations assessing covalency support our spectroscopic analysis and identify active site conformations that correlate to high- and low-spin states. These experiments validate the suitability of an X-ray emission approach for determining spin states of previously uncharacterized metalloenzyme reaction intermediates.

FOCUS: fast Monte Carlo approach to coherence of undulator sources

FOCUS (Fast Monte CarlO approach to Coherence of Undulator Sources) is a new GPU-based simulation code to compute the transverse coherence of undulator radiation from ultra-relativistic electrons. The core structure of the code, which is written in the language C++ accelerated with CUDA, combines an analytical description of the emitted electric fields and massively parallel computations on GPUs. The combination is rigorously justified by a statistical description of synchrotron radiation based on a Fourier optics approach. FOCUS is validated by direct comparison with multi-electron Synchrotron Radiation Workshop (SRW) simulations, evidencing a reduction in computation times by up to five orders of magnitude on a consumer laptop. FOCUS is then applied to systematically study the transverse coherence in typical third- and fourth-generation facilities, highlighting peculiar features of undulator sources close to the diffraction limit. FOCUS is aimed at fast evaluation of the transverse coherence of undulator radiation as a function of the electron beam parameters, to support and help prepare more advanced and detailed numerical simulations with traditional codes like SRW.

Physical optics simulations for synchrotron radiation sources

We describe approaches to high-accuracy physical optics calculations used for the development of x-ray beamlines at synchrotron radiation sources, as well as simulation of experiments and processing of experimental data at some of these beamlines. We pay special attention to the treatment of the partial coherence of x rays, a topic of high practical importance for modern low-emittance high-brightness synchrotron radiation facilities. The approaches are based, to a large extent, on the works of Emil Wolf and co-authors, including the basic scalar diffraction theory and the coherent mode decomposition method. The presented simulation examples are related to the case of the novel Coherent Diffractive Imaging beamline that is currently under development at the National Synchrotron Light Source II at the Brookhaven National Laboratory.

Classification of diffraction patterns using a convolutional neural network in single-particle-imaging experiments performed at X-ray free-electron lasers

Single particle imaging (SPI) at X-ray free-electron lasers is particularly well suited to determining the 3D structure of particles at room temperature. For a successful reconstruction, diffraction patterns originating from a single hit must be isolated from a large number of acquired patterns. It is proposed that this task could be formulated as an image-classification problem and solved using convolutional neural network (CNN) architectures. Two CNN configurations are developed: one that maximizes the F1 score and one that emphasizes high recall. The CNNs are also combined with expectation-maximization (EM) selection as well as size filtering. It is observed that the CNN selections have lower contrast in power spectral density functions relative to the EM selection used in previous work. However, the reconstruction of the CNN-based selections gives similar results. Introducing CNNs into SPI experiments allows the reconstruction pipeline to be streamlined, enables researchers to classify patterns on the fly, and, as a consequence, enables them to tightly control the duration of their experiments. Incorporating non-standard artificial-intelligence-based solutions into an existing SPI analysis workflow may be beneficial for the future development of SPI experiments.

Wave-optics simulation software for synchrotron radiation from 4th generation storage rings based on a coherent modes model

The evolution from 3rd to 4th generation of storage rings significantly enhanced the coherence of synchrotron radiation sources, making coherent scattering techniques such as coherent X-ray diffraction imaging (CXDI) and X-ray photon correlation spectroscopy more accessible. In conformance with the design requirements of coherent beamlines at the High Energy Photon Source (HEPS), we have developed wave optics simulation software, the Coherence Analysis Toolbox, based on coherent modes decomposition and a wavefront propagation model. Simulations of beamline performance and a CXDI experiment on the hard X-ray coherent scattering beamline at HEPS were carried out. This software is open source and now available on GitHub.

From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

High spatial coherence and short pulse duration revealed by the Hanbury Brown and Twiss interferometry at the European XFEL

Second-order intensity interferometry was employed to study the spatial and temporal properties of the European X-ray Free-Electron Laser (EuXFEL). Measurements were performed at the soft x-ray Self-Amplified Spontaneous Emission (SASE3) undulator beamline at a photon energy of 1.2 keV in the Self-Amplified Spontaneous Emission (SASE) mode. Two high-power regimes of the SASE3 undulator settings, i.e., linear and quadratic undulator tapering at saturation, were studied in detail and compared with the linear gain regime. The statistical analysis showed an exceptionally high degree of spatial coherence up to 90% for the linear undulator tapering. Analysis of the measured data in spectral and spatial domains provided an average pulse duration of about 10 fs in our measurements. The obtained results will be valuable for the experiments requiring and exploiting short pulse duration and utilizing high coherence properties of the EuXFEL.

Internal resistive heating of non-metallic samples to 3000 K and >60 GPa in the diamond anvil cell

High pressure-temperature experiments provide information on the phase diagrams and physical characteristics of matter at extreme conditions and offer a synthesis pathway for novel materials with useful properties. Experiments recreating the conditions of planetary interiors provide important constraints on the physical properties of constituent phases and are key to developing models of planetary processes and interpreting geophysical observations. The laser-heated diamond anvil cell (DAC) is currently the only technique capable of routinely accessing the Earth's lower-mantle geotherm for experiments on non-metallic samples, but large temperature uncertainties and poor temperature stability limit the accuracy of measured data and prohibits analyses requiring long acquisition times. We have developed a novel internal resistive heating (IRH) technique for the DAC and demonstrate stable heating of non-metallic samples up to 3000 K and 64 GPa, as confirmed by in situ synchrotron x-ray diffraction and simultaneous spectroradiometric temperature measurement. The temperature generated in our IRH-DAC can be precisely controlled and is extremely stable, with less than 20 K variation over several hours without any user intervention, resulting in temperature uncertainties an order of magnitude smaller than those in typical laser-heating experiments. Our IRH-DAC design, with its simple geometry, provides a new and highly accessible tool for investigating materials at extreme conditions. It is well suited for the rapid collection of high-resolution P-V-T data, precise demarcation of phase boundaries, and experiments requiring long acquisition times at high temperature. Our IRH technique is ideally placed to exploit the move toward coherent nano-focused x-ray beams at next-generation synchrotron sources.

An advanced workflow for single-particle imaging with the limited data at an X-ray free-electron laser

An improved analysis for single-particle imaging (SPI) experiments, using the limited data, is presented here. Results are based on a study of bacteriophage PR772 performed at the Atomic, Molecular and Optical Science instrument at the Linac Coherent Light Source as part of the SPI initiative. Existing methods were modified to cope with the shortcomings of the experimental data: inaccessibility of information from half of the detector and a small fraction of single hits. The general SPI analysis workflow was upgraded with the expectation-maximization based classification of diffraction patterns and mode decomposition on the final virus-structure determination step. The presented processing pipeline allowed us to determine the 3D structure of bacteriophage PR772 without symmetry constraints with a spatial resolution of 6.9 nm. The obtained resolution was limited by the scattering intensity during the experiment and the relatively small number of single hits.

Phase analysis for partially coherent light propagating through an optimized aperture in a synchrotron beamline

The mutual optical intensity propagation of partially coherent light through a beamline is calculated for different aperture sizes and positions. The coherence, intensity and phase distribution can be extracted from the mutual optical intensity. The phase distribution depends on the aperture size and position. The results show that the widest flat phase distribution is obtained at the optimized aperture size and position. The aperture plays a more important role for partially coherent light than for incoherent light. The influence of the aperture size and position on the intensity and spot size at the focal plane is also analyzed. A way to obtain a balance between the flat phase distribution area, spot size and intensity for partially coherent light in the beamline is demonstrated.

Hard X-ray ptychography for optics characterization using a partially coherent synchrotron source

Ptychography is a scanning coherent diffraction imaging technique which provides high resolution imaging and complete spatial information of the complex electric field probe and sample transmission function. Its ability to accurately determine the illumination probe has led to its use at modern synchrotrons and free-electron lasers as a wavefront-sensing technique for optics alignment, monitoring and correction. Recent developments in the ptychography reconstruction process now incorporate a modal decomposition of the illuminating probe and relax the restriction of using sources with high spatial coherence. In this article a practical implementation of hard X-ray ptychography from a partially coherent X-ray source with a large number of modes is demonstrated experimentally. A strongly diffracting Siemens star test sample is imaged using the focused beam produced by either a Fresnel zone plate or beryllium compound refractive lens. The recovered probe from each optic is back propagated in order to plot the beam caustic and determine the precise focal size and position. The power distribution of the reconstructed probe modes also allows the quantification of the beams coherence and is compared with the values predicted by a Gaussian-Schell model and the optics exit intensity.

Genuine-field modeling of partially coherent X-ray imaging systems

A genuine representation of the cross-spectral density function as a superposition of mutually uncorrelated, spatially localized modes is applied to model the propagation of spatially partially coherent light beams in X-ray optical systems. Numerical illustrations based on mode propagation with VirtualLab software are presented for imaging systems with ideal and non-ideal grazing-incidence mirrors.