Single-pulse phase-contrast imaging at free-electron lasers in the hard X-ray regime

Dual-beam X-ray nano-holotomography

Nanotomography with hard X-rays is a widely used technique for high-resolution imaging, providing insights into the structure and composition of various materials. In recent years, tomographic approaches based on simultaneous illuminations of the same sample region from different angles by multiple beams have been developed at micrometre image resolution. Transferring these techniques to the nanoscale is challenging due to the loss in photon flux by focusing the X-ray beam. We present an approach for multi-beam nanotomography using a dual-beam Fresnel zone plate (dFZP) in a near-field holography setup. The dFZP generates two nano-focused beams that overlap in the sample plane, enabling the simultaneous acquisition of two projections from slightly different angles. This first proof-of-principle implementation of the dual-beam setup allows for the efficient removal of ring artifacts and noise using machine-learning approaches. The results open new possibilities for full-field multi-beam nanotomography and pave the way for future advancements in fast holotomography and artifact-reduction techniques.

Artifact-suppressing reconstruction of strongly interacting objects in X-ray near-field holography without a spatial support constraint

The phase problem is a well known ill-posed reconstruction problem of coherent lens-less microscopic imaging, where only the squared magnitude of a complex wavefront is measured by a detector while the phase information of the wave field is lost. To retrieve the lost information, common algorithms rely either on multiple data acquisitions under varying measurement conditions or on the application of strong constraints such as a spatial support. In X-ray near-field holography, however, these methods are rendered impractical in the setting of time sensitive in situ and operando measurements. In this paper, we will forego the spatial support constraint and propose a projected gradient descent (PGD) based reconstruction scheme in combination with proper preprocessing and regularization that significantly reduces artifacts for refractive reconstructions from only a single acquired hologram without a spatial support constraint. We demonstrate the feasibility and robustness of our approach on different data sets obtained at the nano imaging endstation of P05 at PETRA III (DESY, Hamburg) operated by Helmholtz-Zentrum Hereon.

Jetting bubbles observed by x-ray holography at a free-electron laser: internal structure and the effect of non-axisymmetric boundary conditions

In this work, we study the jetting dynamics of individual cavitation bubbles using x-ray holographic imaging and high-speed optical shadowgraphy. The bubbles are induced by a focused infrared laser pulse in water near the surface of a flat, circular glass plate, and later probed with ultrashort x-ray pulses produced by an x-ray free-electron laser (XFEL). The holographic imaging can reveal essential information of the bubble interior that would otherwise not be accessible in the optical regime due to obscuration or diffraction. The influence of asymmetric boundary conditions on the jet's characteristics is analysed for cases where the axial symmetry is perturbed and curved liquid filaments can form inside the cavity. The x-ray images demonstrate that when oblique jets impact the rigid boundary, they produce a non-axisymmetric splash which grows from a moving stagnation point. Additionally, the images reveal the formation of complex gas/liquid structures inside the jetting bubbles that are invisible to standard optical microscopy. The experimental results are analysed with the assistance of full three-dimensional numerical simulations of the Navier-Stokes equations in their compressible formulation, which allow a deeper understanding of the distinctive features observed in the x-ray holographic images. In particular, the effects of varying the dimensionless stand-off distances measured from the initial bubble location to the surface of the solid plate and also to its nearest edge are addressed using both experiments and simulations. A relation between the jet tilting angle and the dimensionless bubble position asymmetry is derived. The present study provides new insights into bubble jetting and demonstrates the potential of x-ray holography for future investigations in this field.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00348-023-03759-9.

Online dynamic flat-field correction for MHz microscopy data at European XFEL

The high pulse intensity and repetition rate of the European X-ray Free-Electron Laser (EuXFEL) provide superior temporal resolution compared with other X-ray sources. In combination with MHz X-ray microscopy techniques, it offers a unique opportunity to achieve superior contrast and spatial resolution in applications demanding high temporal resolution. In both live visualization and offline data analysis for microscopy experiments, baseline normalization is essential for further processing steps such as phase retrieval and modal decomposition. In addition, access to normalized projections during data acquisition can play an important role in decision-making and improve the quality of the data. However, the stochastic nature of X-ray free-electron laser sources hinders the use of standard flat-field normalization methods during MHz X-ray microscopy experiments. Here, an online (i.e. near real-time) dynamic flat-field correction method based on principal component analysis of dynamically evolving flat-field images is presented. The method is used for the normalization of individual X-ray projections and has been implemented as a near real-time analysis tool at the Single Particles, Clusters, and Biomolecules and Serial Femtosecond Crystallography (SPB/SFX) instrument of EuXFEL.

Hard X-ray full-field nanoimaging using a direct photon-counting detector

Full-field X-ray nanoimaging is a widely used tool in a broad range of scientific areas. In particular, for low-absorbing biological or medical samples, phase contrast methods have to be considered. Three well established phase contrast methods at the nanoscale are transmission X-ray microscopy with Zernike phase contrast, near-field holography and near-field ptychography. The high spatial resolution, however, often comes with the drawback of a lower signal-to-noise ratio and significantly longer scan times, compared with microimaging. In order to tackle these challenges a single-photon-counting detector has been implemented at the nanoimaging endstation of the beamline P05 at PETRA III (DESY, Hamburg) operated by Helmholtz-Zentrum Hereon. Thanks to the long sample-to-detector distance available, spatial resolutions of below 100 nm were reached in all three presented nanoimaging techniques. This work shows that a single-photon-counting detector in combination with a long sample-to-detector distance allows one to increase the time resolution for in situ nanoimaging, while keeping a high signal-to-noise level.

Invited article: X-ray phase contrast imaging in inertial confinement fusion and high energy density research

X-ray phase contrast imaging (XPCI) provides enhanced image contrast beyond absorption-based x-ray imaging alone due to refraction and diffraction from gradients in the object material density. It is sensitive to small variations in density, such as internal voids, cracks, grains, defects, and material flow, as well as to stronger density variations such as from a shock wave. Beyond its initial use in biology and materials science, XPCI is now routinely used in inertial confinement fusion (ICF) and high energy density (HED) research, first to characterize ICF capsules and targets, and later applied in dynamic experiments, where coherent x-ray sources, ultrafast x-ray pulses, and high temporal and spatial resolution are required. In this Review article, XPCI image formation theory is presented, its diverse use in ICF and HED research is discussed, the unique requirements for ultrafast XPCI imaging are given, as well as current challenges and issues in its use.

Direct LiF imaging diagnostics on refractive X-ray focusing at the EuXFEL High Energy Density instrument

The application of fluorescent crystal media in wide-range X-ray detectors provides an opportunity to directly image the spatial distribution of ultra-intense X-ray beams including investigation of the focal spot of free-electron lasers. Here the capabilities of the micro- and nano-focusing X-ray refractive optics available at the High Energy Density instrument of the European XFEL are reported, as measured in situ by means of a LiF fluorescent detector placed into and around the beam caustic. The intensity distribution of the beam focused down to several hundred nanometers was imaged at 9 keV photon energy. A deviation from the parabolic surface in a stack of nanofocusing Be compound refractive lenses (CRLs) was found to affect the resulting intensity distribution within the beam. Comparison of experimental patterns in the far field with patterns calculated for different CRL lens imperfections allowed the overall inhomogeneity in the CRL stack to be estimated. The precise determination of the focal spot size and shape on a sub-micrometer level is essential for a number of high energy density studies requiring either a pin-size backlighting spot or extreme intensities for X-ray heating.

Multi-frame, ultrafast, x-ray microscope for imaging shockwave dynamics

Inertial confinement fusion (ICF) holds increasing promise as a potential source of abundant, clean energy, but has been impeded by defects such as micro-voids in the ablator layer of the fuel capsules. It is critical to understand how these micro-voids interact with the laser-driven shock waves that compress the fuel pellet. At the Matter in Extreme Conditions (MEC) instrument at the Linac Coherent Light Source (LCLS), we utilized an x-ray pulse train with ns separation, an x-ray microscope, and an ultrafast x-ray imaging (UXI) detector to image shock wave interactions with micro-voids. To minimize the high- and low-frequency variations of the captured images, we incorporated principal component analysis (PCA) and image alignment for flat-field correction. After applying these techniques we generated phase and attenuation maps from a 2D hydrodynamic radiation code (xRAGE), which were used to simulate XPCI images that we qualitatively compare with experimental images, providing a one-to-one comparison for benchmarking material performance. Moreover, we implement a transport-of-intensity (TIE) based method to obtain the average projected mass density (areal density) of our experimental images, yielding insight into how defect-bearing ablator materials alter microstructural feature evolution, material compression, and shock wave propagation on ICF-relevant time scales.

Single-exposure X-ray phase imaging microscopy with a grating interferometer

The advent of hard X-ray free-electron lasers enables nanoscopic X-ray imaging with sub-picosecond temporal resolution. X-ray grating interferometry offers a phase-sensitive full-field imaging technique where the phase retrieval can be carried out from a single exposure alone. Thus, the method is attractive for imaging applications at X-ray free-electron lasers where intrinsic pulse-to-pulse fluctuations pose a major challenge. In this work, the single-exposure phase imaging capabilities of grating interferometry are characterized by an implementation at the I13-1 beamline of Diamond Light Source (Oxfordshire, UK). For comparison purposes, propagation-based phase contrast imaging was also performed at the same instrument. The characterization is carried out in terms of the quantitativeness and the contrast-to-noise ratio of the phase reconstructions as well as via the achievable spatial resolution. By using a statistical image reconstruction scheme, previous limitations of grating interferometry regarding the spatial resolution can be mitigated as well as the experimental applicability of the technique.

Simultaneous imaging and diffraction in the dynamic diamond anvil cell

The ability to visualize a sample undergoing a pressure-induced phase transition allows for the determination of kinetic parameters, such as the nucleation and growth rates of the high-pressure phase. For samples that are opaque to visible light (such as metallic systems), it is necessary to rely on x-ray imaging methods for sample visualization. Here, we present an experimental platform developed at beamline P02.2 at the PETRA III synchrotron radiation source, which is capable of performing simultaneous x-ray imaging and diffraction of samples that are dynamically compressed in piezo-driven diamond anvil cells. This setup utilizes a partially coherent monochromatic x-ray beam to perform lensless phase contrast imaging, which can be carried out using either a parallel- or focused-beam configuration. The capabilities of this platform are illustrated by experiments on dynamically compressed Ga and Ar. Melting and solidification were identified based on the observation of solid/liquid phase boundaries in the x-ray images and corresponding changes in the x-ray diffraction patterns collected during the transition, with significant edge enhancement observed in the x-ray images collected using the focused-beam. These results highlight the suitability of this technique for a variety of purposes, including melt curve determination.

Shot-to-shot flat-field correction at X-ray free-electron lasers

X-ray free-electron lasers (XFELs) provide high-brilliance pulses, which offer unique opportunities for coherent X-ray imaging techniques, such as in-line holography. One of the fundamental steps to process in-line holographic data is flat-field correction, which mitigates imaging artifacts and, in turn, enables phase reconstructions. However, conventional flat-field correction approaches cannot correct single XFEL pulses due to the stochastic nature of the self-amplified spontaneous emission (SASE), the mechanism responsible for the high brilliance of XFELs. Here, we demonstrate on simulated and megahertz imaging data, measured at the European XFEL, the possibility of overcoming such a limitation by using two different methods based on principal component analysis and deep learning. These methods retrieve flat-field corrected images from individual frames by separating the sample and flat-field signal contributions; thus, enabling advanced phase-retrieval reconstructions. We anticipate that the proposed methods can be implemented in a real-time processing pipeline, which will enable online data analysis and phase reconstructions of coherent full-field imaging techniques such as in-line holography at XFELs.

Methods of Coherent X-Ray Diffraction Imaging

Abstract

Methods of coherent X-ray diffraction imaging of the spatial structure of noncrystalline objects and nanocrystals (nanostructures) are considered. Particular attention is paid to the methods of scanning-based coherent diffraction imaging (ptychography), visualization based on coherent surface scattering with application of correlation spectroscopy approaches, and specific features of visualization using X-ray free-electron laser radiation. The corresponding data in the literature are analyzed to demonstrate the state of the art of the methods of coherent diffraction imaging and fields of their application.

The High Energy Density Scientific Instrument at the European XFEL

The European XFEL delivers up to 27000 intense (>1012 photons) pulses per second, of ultrashort (≤50 fs) and transversely coherent X-ray radiation, at a maximum repetition rate of 4.5 MHz. Its unique X-ray beam parameters enable groundbreaking experiments in matter at extreme conditions at the High Energy Density (HED) scientific instrument. The performance of the HED instrument during its first two years of operation, its scientific remit, as well as ongoing installations towards full operation are presented. Scientific goals of HED include the investigation of extreme states of matter created by intense laser pulses, diamond anvil cells, or pulsed magnets, and ultrafast X-ray methods that allow their diagnosis using self-amplified spontaneous emission between 5 and 25 keV, coupled with X-ray monochromators and optional seeded beam operation. The HED instrument provides two target chambers, X-ray spectrometers for emission and scattering, X-ray detectors, and a timing tool to correct for residual timing jitter between laser and X-ray pulses.

Pump-probe X-ray holographic imaging of laser-induced cavitation bubbles with femtosecond FEL pulses

Cavitation bubbles can be seeded from a plasma following optical breakdown, by focusing an intense laser in water. The fast dynamics are associated with extreme states of gas and liquid, especially in the nascent state. This offers a unique setting to probe water and water vapor far-from equilibrium. However, current optical techniques cannot quantify these early states due to contrast and resolution limitations. X-ray holography with single X-ray free-electron laser pulses has now enabled a quasi-instantaneous high resolution structural probe with contrast proportional to the electron density of the object. In this work, we demonstrate cone-beam holographic flash imaging of laser-induced cavitation bubbles in water with nanofocused X-ray free-electron laser pulses. We quantify the spatial and temporal pressure distribution of the shockwave surrounding the expanding cavitation bubble at time delays shortly after seeding and compare the results to numerical simulations.

Nanosecond timing and synchronization scheme for holographic pump-probe studies at the MID instrument at European XFEL

Single-pulse holographic imaging at XFEL sources with 1012 photons delivered in pulses shorter than 100 fs reveal new quantitative insights into fast phenomena. Here, a timing and synchronization scheme for stroboscopic imaging and quantitative analysis of fast phenomena on time scales (sub-ns) and length-scales (≲100 nm) inaccessible by visible light is reported. A fully electronic delay-and-trigger system has been implemented at the MID station at the European XFEL, and applied to the study of emerging laser-driven cavitation bubbles in water. Synchronization and timing precision have been characterized to be better than 1 ns.

Materials Imaging and Dynamics (MID) instrument at the European X-ray Free-Electron Laser Facility

The Materials Imaging and Dynamics (MID) instrument at the European X-ray Free-Electron Laser (EuXFEL) facility is described. EuXFEL is the first hard X-ray free-electron laser operating in the MHz repetition range which provides novel science opportunities. The aim of MID is to enable studies of nano-structured materials, liquids, and soft- and hard-condensed matter using the bright X-ray beams generated by EuXFEL. Particular emphasis is on studies of structure and dynamics in materials by coherent scattering and imaging using hard X-rays. Commission of MID started at the end of 2018 and first experiments were performed in 2019.

Single-pulse phase-contrast imaging at free-electron lasers in the hard X-ray regime

X-ray free-electron lasers (XFELs) have opened up unprecedented opportunities for time-resolved nano-scale imaging with X-rays. Near-field propagation-based imaging, and in particular near-field holography (NFH) in its high-resolution implementation in cone-beam geometry, can offer full-field views of a specimen's dynamics captured by single XFEL pulses. To exploit this capability, for example in optical-pump/X-ray-probe imaging schemes, the stochastic nature of the self-amplified spontaneous emission pulses, i.e. the dynamics of the beam itself, presents a major challenge. In this work, a concept is presented to address the fluctuating illumination wavefronts by sampling the configuration space of SASE pulses before an actual recording, followed by a principal component analysis. This scheme is implemented at the MID (Materials Imaging and Dynamics) instrument of the European XFEL and time-resolved NFH is performed using aberration-corrected nano-focusing compound refractive lenses. Specifically, the dynamics of a micro-fluidic water-jet, which is commonly used as sample delivery system at XFELs, is imaged. The jet exhibits rich dynamics of droplet formation in the break-up regime. Moreover, pump-probe imaging is demonstrated using an infrared pulsed laser to induce cavitation and explosion of the jet.