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

Comparison of wavefront sensing and ablation imprinting for FEL focus diagnostics at FLASH2

Extreme ultraviolet (EUV) photon beam characterization techniques, Hartmann wavefront sensing and single shot ablation imprinting, were compared along the caustic of a tightly focused free-electron laser (FEL) beam at beamline FL24 of FLASH2, the Free-electron LASer in Hamburg at DESY. The transverse coherence of the EUV FEL was determined by a Young's double pinhole experiment and used in a back-propagation algorithm which includes partial coherence to calculate the beam intensity profiles along the caustic from the wavefront measurements. A very good agreement of the profile structure and size is observed for different wavelengths between the back-propagated profiles, an indirect technique, and ablation imprints. As a result, the Hartmann wavefront sensor including its software MrBeam is a very useful, single shot pulse resolved and fast tool for non-invasive determination of focal spot size and shape and also for beam profiles along the caustic.

FURION: modeling of FEL pulses propagation in dispersive soft X-ray beamline systems

Modern X-ray free-electron lasers (XFELs) can generate pulses with durations ranging from femtoseconds to attoseconds. The numerical evaluation of ultra-short XFEL pulses through beamline systems is a critical process of beamline system design. However, the bandwidth of such ultra-short XFEL pulses is often non-negligible, and the propagation cannot be simply approximated using the central wavelength, especially in dispersive beamline systems. We developed a numerical model which is called Fourier optics based Ultrashort x-Ray pulse propagatION tool (FURION). This model can not only be used to simulate dispersive beamline systems but also to evaluate non-dispersive beamline systems. The FURION model utilizes Fresnel integral and angular spectrum integral to perform ultra-short XFEL pulse propagation in free space. We also present the method for XFEL pulse propagation through different types of dispersive gratings, which are commonly used in soft X-ray beamline systems. By using FURION, a start-to-end simulation of the FEL-1 beamline system at Shenzhen superconducting soft X-ray free electron laser (S3FEL) is carried out. This model can also be used to evaluate gratings-based spectrometers, beam splitters, pulse compressors, and pulse stretchers. This work provides valuable insights into the start-to-end simulation of X-ray beamline systems.

A phenomenological model of the X-ray pulse statistics of a high-repetition-rate X-ray free-electron laser

Many coherent imaging applications that utilize ultrafast X-ray free-electron laser (XFEL) radiation pulses are highly sensitive to fluctuations in the shot-to-shot statistical properties of the source. Understanding and modelling these fluctuations are key to successful experiment planning and necessary to maximize the potential of XFEL facilities. Current models of XFEL radiation and their shot-to-shot statistics are based on theoretical descriptions of the source and are limited in their ability to capture the shot-to-shot intensity fluctuations observed experimentally. The lack of accurate temporal statistics in simulations that utilize these models is a significant barrier to optimizing and interpreting data from XFEL coherent diffraction experiments. Presented here is a phenomenological model of XFEL radiation that is capable of capturing the shot-to-shot statistics observed experimentally using a simple time-dependent approximation of the pulse wavefront. The model is applied to reproduce non-stationary shot-to-shot intensity fluctuations observed at the European XFEL, whilst accurately representing the single-shot properties predicted by FEL theory. Compared with previous models, this approach provides a simple, robust and computationally inexpensive method of generating statistical representations of XFEL radiation.

Spatiotemporal response of concave VLS grating to ultra-short X-ray pulses

In soft X-ray free-electron laser (FEL) beamlines, variable-line-spacing (VLS) gratings are often used as dispersive components of monochromators and spectrometers due to their combined dispersion and focusing properties. X-ray FEL pulses passing through the VLS grating can result in not only transverse focusing but also spatiotemporal coupling effects, such as pulse front tilt, pulse front rotation, and pulse stretching. In this paper, we present a theoretical study of the spatiotemporal response of concave VLS gratings to ultra-short X-ray pulses. The theoretical analysis indicates that the tilt angle of the non-zero diffraction orders varies with the propagation distance, and disappears at the focus, where the focal lengths and pulse stretching differ for different diffraction orders. The model demonstrates the pulse duration after the concave VLS grating is the convolution of the initial pulse duration and the stretching term induced by dispersion, while the beam size at the focus in x dimension is the convolution of the geometric scaling beam size and the dispersion term. This work provides a mathematical explanation for the spatiotemporal response of concave VLS grating to ultra-short X-ray pulses and offers valuable insights into the design of FEL grating monochromators, spectrometers, pulse compressors, and pulse stretchers.

The soft X-ray monochromator at the SASE3 beamline of the European XFEL: from design to operation

The SASE3 soft X-ray beamline at the European XFEL has been designed and built to provide experiments with a pink or monochromatic beam in the photon energy range 250-3000 eV. Here, the focus is monochromatic operation of the SASE3 beamline, and the design and performance of the SASE3 grating monochromator are reported. The unique capability of a free-electron laser source to produce short femtosecond pulses of a high degree of coherence challenges the monochromator design by demanding control of both photon energy and temporal resolution. The aim to transport close to transform-limited pulses poses very high demands on the optics quality, in particular on the grating. The current realization of the SASE3 monochromator is discussed in comparison with optimal design performance. At present, the monochromator operates with two gratings: the low-resolution grating is optimized for time-resolved experiments and allows for moderate resolving power of about 2000-5000 along with pulse stretching of a few to a few tens of femtoseconds RMS, and the high-resolution grating reaches a resolving power of 10 000 at the cost of larger pulse stretching.

Effects of radiation damage and inelastic scattering on single-particle imaging of hydrated proteins with an X-ray Free-Electron Laser

We present a computational case study of X-ray single-particle imaging of hydrated proteins on an example of 2-Nitrogenase-Iron protein covered with water layers of various thickness, using a start-to-end simulation platform and experimental parameters of the SPB/SFX instrument at the European X-ray Free-Electron Laser facility. The simulations identify an optimal thickness of the water layer at which the effective resolution for imaging the hydrated sample becomes significantly higher than for the non-hydrated sample. This effect is lost when the water layer becomes too thick. Even though the detailed results presented pertain to the specific sample studied, the trends which we identify should also hold in a general case. We expect these findings will guide future single-particle imaging experiments using hydrated proteins.

Resolution of a bent-crystal spectrometer for X-ray free-electron laser pulses: diamond versus silicon

The resolution function of a bent-crystal spectrometer for pulses of an X-ray free-electron laser is evaluated. Under appropriate conditions, the energy resolution reaches the ratio of the lattice spacing to the crystal thickness.

The resolution function of a spectrometer based on a strongly bent single crystal (bending radius of 10 cm or less) is evaluated. It is shown that the resolution is controlled by two parameters: (i) the ratio of the lattice spacing of the chosen reflection to the crystal thickness and (ii) a single parameter comprising crystal thickness, its bending radius, distance to a detector, and anisotropic elastic constants of the chosen crystal. The results allow the optimization of the parameters of bent-crystal spectrometers for the hard X-ray free-electron laser sources.

Towards novel probes for valence charges via X-ray optical wave mixing

We present a combined theoretical and experimental study of X-ray optical wave mixing. This class of nonlinear phenomena combines the strengths of spectroscopic techniques from the optical domain, with the high-resolution capabilities of X-rays. In particular, the spectroscopic sensitivity of these phenomena can be exploited to selectively probe valence dynamics. Specifically, we focus on the effect of X-ray parametric down-conversion. We present a theoretical description of the process, from which we deduce the observable nonlinear response of valence charges. Subsequently, we simulate scattering patterns for realistic conditions and identify characteristic signatures of the nonlinear conversion. For the observation of this signature, we present a dedicated experimental setup and results of a detailed investigation. However, we do not find evidence of the nonlinear effect. This finding stands in strong contradiction to previous claims of proof-of-principle demonstrations. Nevertheless, we are optimistic to employ related X-ray optical wave mixing processes on the basis of the methods presented here for probing valence dynamics in the future.

Impact of real mirror profiles inside a split-and-delay unit on the spatial intensity profile in pump/probe experiments at the European XFEL

For the High-Energy-Density (HED) beamline at the SASE2 undulator of the European XFEL, a hard X-ray split-and-delay unit (SDU) has been built enabling time-resolved pump/probe experiments with photon energies between 5 keV and 24 keV. The optical layout of the SDU is based on geometrical wavefront splitting and multilayer Bragg mirrors. Maximum delays between Δτ = ±1 ps at 24 keV and Δτ = ±23 ps at 5 keV will be possible. Time-dependent wavefront propagation simulations were performed by means of the Synchrotron Radiation Workshop (SRW) software in order to investigate the impact of the optical layout, including diffraction on the beam splitter and recombiner edges and the three-dimensional topography of all eight mirrors, on the spatio-temporal properties of the XFEL pulses. The radiation is generated from noise by the code FAST which simulates the self-amplified spontaneous emission (SASE) process. A fast Fourier transformation evaluation of the disturbed interference pattern yields for ideal mirror surfaces a coherence time of τc = 0.23 fs and deduces one of τc = 0.21 fs for the real mirrors, thus with an error of Δτ = 0.02 fs which is smaller than the deviation resulting from shot-to-shot fluctuations of SASE2 pulses. The wavefronts are focused by means of compound refractive lenses in order to achieve fluences of a few hundred mJ mm-2 within a spot width of 20 µm (FWHM) diameter. Coherence effects and optics imperfections increase the peak intensity between 200 and 400% for pulse delays within the coherence time. Additionally, the influence of two off-set mirrors in the HED beamline are discussed. Further, we show the fluence distribution for Δz = ±3 mm around the focal spot along the optical axis. The simulations show that the topographies of the mirrors of the SDU are good enough to support X-ray pump/X-ray probe experiments.

Dynamic coherent diffractive imaging using unsupervised identification of spatiotemporal constraints

Dynamic coherent diffractive imaging (CDI) reveals the fine details of structural, chemical, and biological processes occurring at the nanoscale but imposes strict constraints on the object distribution and illumination. Ptychographic CDI relaxes these constraints by exploiting redundant information in data obtained from overlapping regions of an object, but its time resolution is inherently limited. We have extended ptychographic redundancy into the spatiotemporal domain in dynamic CDI, automatically identifying redundant information in time-series coherent diffraction data obtained from dynamic systems. Simulated synchrotron experiments show that high spatiotemporal resolution is achieved without a priori knowledge of the object or its dynamics.

Wavefront Sensing for Evaluation of Extreme Ultraviolet Microscopy

Wavefront analysis is a fast and reliable technique for the alignment and characterization of optics in the visible, but also in the extreme ultraviolet (EUV) and X-ray regions. However, the technique poses a number of challenges when used for optical systems with numerical apertures (NA) > 0.1. A high-numerical-aperture Hartmann wavefront sensor was employed at the free electron laser FLASH for the characterization of a Schwarzschild objective. These are widely used in EUV to achieve very small foci, particularly for photolithography. For this purpose, Schwarzschild objectives require highly precise alignment. The phase measurements acquired with the wavefront sensor were analyzed employing two different methods, namely, the classical calculation of centroid positions and Fourier demodulation. Results from both approaches agree in terms of wavefront maps with negligible degree of discrepancy.

Soft X-ray diffraction patterns measured by a LiF detector with sub-micrometre resolution and an ultimate dynamic range

The unique diagnostic possibilities of X-ray diffraction, small X-ray scattering and phase-contrast imaging techniques applied with high-intensity coherent X-ray synchrotron and X-ray free-electron laser radiation can only be fully realized if a sufficient dynamic range and/or spatial resolution of the detector is available. In this work, it is demonstrated that the use of lithium fluoride (LiF) as a photoluminescence (PL) imaging detector allows measuring of an X-ray diffraction image with a dynamic range of ∼10⁷ within the sub-micrometre spatial resolution. At the PETRA III facility, the diffraction pattern created behind a circular aperture with a diameter of 5 µm irradiated by a beam with a photon energy of 500 eV was recorded on a LiF crystal. In the diffraction pattern, the accumulated dose was varied from 1.7 × 10⁵ J cm^-3 in the central maximum to 2 × 10^-2 J cm^-3 in the 16th maximum of diffraction fringes. The period of the last fringe was measured with 0.8 µm width. The PL response of the LiF crystal being used as a detector on the irradiation dose of 500 eV photons was evaluated. For the particular model of laser-scanning confocal microscope Carl Zeiss LSM700, used for the readout of the PL signal, the calibration dependencies on the intensity of photopumping (excitation) radiation (λ = 488 nm) and the gain have been obtained.

X-ray diffraction from strongly bent crystals and spectroscopy of X-ray free-electron laser pulses

The use of strongly bent crystals in spectrometers for pulses of a hard X-ray free-electron laser is explored theoretically. Diffraction is calculated in both dynamical and kinematical theories. It is shown that diffraction can be treated kinematically when the bending radius is small compared with the critical radius given by the ratio of the Bragg-case extinction length for the actual reflection to the Darwin width of this reflection. As a result, the spectral resolution is limited by the crystal thickness, rather than the extinction length, and can become better than the resolution of a planar dynamically diffracting crystal. As an example, it is demonstrated that spectra of the 12 keV pulses can be resolved in the 440 reflection from a 20 µm-thick diamond crystal bent to a radius of 10 cm.

The SASE1 X-ray beam transport system

SASE1 is the first beamline of the European XFEL that became operational in 2017. It consists of the SASE1 undulator system, the beam transport system, and the two scientific experiment stations: Single Particles, Clusters, and Biomolecules and Serial Femtosecond Crystallography (SPB/SFX), and Femtosecond X-ray Experiments (FXE). The beam transport system comprises mirrors to offset and guide the beam to the instruments and a set of X-ray optical components to align, manipulate and diagnose the beam. The SASE1 beam transport system is described here in its initial configuration, and results and experiences from the first year of user operation are reported.

Wavefront-propagation simulations supporting the design of a time-delay compensating monochromator beamline at FLASH2

Wavefront-propagation simulations have been performed to complete the design of a monochromator beamline for FLASH2, the variable-gap undulator line at the soft X-ray free-electron laser in Hamburg (FLASH). Prior to propagation through the beamline optical elements, the parameters of the photon source were generated using the GENESIS code which includes the free-electron laser experimental data. Threshold tolerances for the misalignment of mirror angles are calculated and, since diffraction effects were included in the simulations, the minimum quality with respect to the slope errors required for the optics is determined.

Installation and commissioning of the European XFEL beam transport in the first two beamlines from a metrology point of view

The European XFEL is a large x-ray free-electron laser facility under construction in the Hamburg area of Germany. It is designed to provide a transversally fully coherent x-ray radiation with outstanding characteristics: high repetition rate (up to 2700 pulses with a 0.6 ms long pulse train at 10 Hz, for a total of 27 000 pulses/s), short wavelength (down to 0.05 nm), short pulse (in the femtosecond scale), and high average brilliance [1.6 × 10²⁵ photons/s/(mm²/mrad²)/0.1% bandwidth]. Five main beamlines are foreseen, with three fully financed and installed, called SASEs (from "self-amplified spontaneous-emission"): SASE1 (hard x-rays, 3-25 KeV), SASE2 (hard x-rays, 3 to possibly 60 KeV with the use of a third harmonic), and SASE3 (soft x-rays, 0.3-3 KeV). For each beamline, two separate scientific instruments will be served using the beam alternately in 24-h, 7-day shifts. The installation and commissioning of the European XFEL beamlines are proceeding rapidly. So far, the hard x-ray SASE1 beamline and the soft x-ray SASE3 beamline, both injected with the same electron beam, have been installed and fully commissioned. SASE1 already delivers beam to the corresponding stations and has been open for external users since September 2017. The SASE3 beamline was successfully commissioned in February 2018, and the simultaneous operation of SASE3 and SASE1 was also demonstrated. In the meantime, the SASE2 beamline is being equipped and will be commissioned starting October 2018. We present the last results in the SASE1 and SASE3 beam transport, taking consideration in particular of the metrology carried out before the installation, the installation itself, and the final commissioning. The different stages were crucial to have good quality optical beam and fast commissioning to proceed with the delivery to experiments and users.

Advanced high resolution x-ray diagnostic for HEDP experiments

High resolution X-ray imaging is crucial for many high energy density physics (HEDP) experiments. Recently developed techniques to improve resolution have, however, come at the cost of a decreased field of view. In this paper, an innovative experimental detector for X-ray imaging in the context of HEDP experiments with high spatial resolution, as well as a large field of view, is presented. The platform is based on coupling an X-ray backligther source with a Lithium Fluoride detector, characterized by its large dynamic range. A spatial resolution of 2 µm over a field of view greater than 2 mm² is reported. The platform was benchmarked with both an X-ray free electron laser (XFEL) and an X-ray source produced by a short pulse laser. First, using a non-coherent short pulse laser-produced backlighter, reduced penumbra blurring, as a result of the large size of the X-ray source, is shown. Secondly, we demonstrate phase contrast imaging with a fully coherent monochromatic XFEL beam. Modeling of the absorption and phase contrast transmission of X-ray radiation passing through various targets is presented.

Sirepo: an open-source cloud-based software interface for X-ray source and optics simulations

Sirepo, a browser-based GUI for X-ray source and optics simulations, is presented. Such calculations can be performed using SRW (Synchrotron Radiation Workshop), which is a physical optics computer code, allowing simulation of entire experimental beamlines using the concept of a `virtual beamline' with accurate treatment of synchrotron radiation generation and propagation through the X-ray optical system. SRW is interfaced with Sirepo by means of a Python application programming interface. Sirepo supports most of the optical elements currently used at beamlines, including recent developments in SRW. In particular, support is provided for the simulation of state-of-the-art X-ray beamlines, exploiting the high coherence and brightness of modern light source facilities. New scientific visualization and reporting capabilities have been recently implemented within Sirepo, as well as automatic determination of electron beam and undulator parameters. Publicly available community databases can be dynamically queried for error-free access to material characteristics. These computational tools can be used for the development and commissioning of new X-ray beamlines and for testing feasibility and optimization of experiments. The same interface can guide simulation on a local computer, a remote server or a high-performance cluster. Sirepo is available online and also within the NSLS-II firewall, with a growing number of users at other light source facilities. Our open source code is available on GitHub.

Finite difference methods for stationary and time-dependent X-ray propagation

We have generalized finite-difference (FD) simulations for time-dependent field propagation problems, in particular in view of ultra-short x-ray pulse propagation and dispersion. To this end, we first derive the stationary paraxial (parabolic) wave equation for the scalar field envelope in a more general manner than typically found in the literature. We then present an efficient FD implementation of propagators for different dimensionality for stationary field propagation, before we treat time-dependent problems by spectral decomposition, and suitable numerical sampling. We prove the validity of the numerical approach by comparison to analytical theory, using simple tractable propagation problems. Finally, we apply the framework to the problem of modal dispersion in X-ray waveguide. We show that X-ray waveguides can be considered as non-dispersive optical elements down to sub-femtosecond pulse width. Only when considering resonant absorption close to an X-ray absorption edge, we observe pronounced dispersion effects for experimentally achievable pulse widths. All code used for the work is made available as supplemental material.

Start-to-end simulation of single-particle imaging using ultra-short pulses at the European X-ray Free-Electron Laser

Single-particle imaging with X-ray free-electron lasers (XFELs) has the potential to provide structural information at atomic resolution for non-crystalline biomolecules. This potential exists because ultra-short intense pulses can produce interpretable diffraction data notwithstanding radiation damage. This paper explores the impact of pulse duration on the interpretability of diffraction data using comprehensive and realistic simulations of an imaging experiment at the European X-ray Free-Electron Laser. It is found that the optimal pulse duration for molecules with a few thousand atoms at 5 keV lies between 3 and 9 fs.

CCP-FEL: a collection of computer programs for free-electron laser research

The latest virtual special issue ofJournal of Applied Crystallography(http://journals.iucr.org/special_issues/2016/ccpfel) collects software for free-electron laser research and presents tools for a range of topics such as simulation of experiments, online monitoring of data collection, selection of hits, diagnostics of data quality, data management, data analysis and structure determination for both nanocrystallography and single-particle diffractive imaging. This article provides an introduction to the special issue.

A comprehensive simulation framework for imaging single particles and biomolecules at the European X-ray Free-Electron Laser

The advent of newer, brighter, and more coherent X-ray sources, such as X-ray Free-Electron Lasers (XFELs), represents a tremendous growth in the potential to apply coherent X-rays to determine the structure of materials from the micron-scale down to the Angstrom-scale. There is a significant need for a multi-physics simulation framework to perform source-to-detector simulations for a single particle imaging experiment, including (i) the multidimensional simulation of the X-ray source; (ii) simulation of the wave-optics propagation of the coherent XFEL beams; (iii) atomistic modelling of photon-material interactions; (iv) simulation of the time-dependent diffraction process, including incoherent scattering; (v) assembling noisy and incomplete diffraction intensities into a three-dimensional data set using the Expansion-Maximisation-Compression (EMC) algorithm and (vi) phase retrieval to obtain structural information. We demonstrate the framework by simulating a single-particle experiment for a nitrogenase iron protein using parameters of the SPB/SFX instrument of the European XFEL. This exercise demonstrably yields interpretable consequences for structure determination that are crucial yet currently unavailable for experiment design.