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.

3D and Multimodal X-Ray Microscopy Reveals the Impact of Voids in CIGS Solar Cells.

Small voids in the absorber layer of thin-film solar cells are generally suspected to impair photovoltaic performance. They have been studied on Cu(In,Ga)Se2 cells with conventional laboratory techniques, albeit limited to surface characterization and often affected by sample-preparation artifacts. Here, synchrotron imaging is performed on a fully operational as-deposited solar cell containing a few tens of voids. By measuring operando current and X-ray excited optical luminescence, the local electrical and optical performance in the proximity of the voids are estimated, and via ptychographic tomography, the depth in the absorber of the voids is quantified. Besides, the complex network of material-deficit structures between the absorber and the top electrode is highlighted. Despite certain local impairments, the massive presence of voids in the absorber suggests they only have a limited detrimental impact on performance.

Development of a Bioreactor-Coupled Flow-Cell Setup for 3D In Situ Nanotomography of Mg Alloy Biodegradation.

Functional materials feature hierarchical microstructures that define their unique set of properties. The prediction and tailoring of these require a multiscale knowledge of the mechanistic interaction of microstructure and property. An important material in this respect is biodegradable magnesium alloys used for implant applications. To correlate the relationship between the microstructure and the nonlinear degradation process, high-resolution in situ three-dimensional (3D) imaging experiments must be performed. For this purpose, a novel experimental flow cell is presented which allows for the in situ 3D-nano imaging of the biodegradation process of materials with nominal resolutions below 100 nm using nanofocused hard X-ray radiation from a synchrotron source. The flow cell setup can operate under adjustable physiological and hydrodynamic conditions. As a model material, the biodegradation of thin Mg-4Ag wires in simulated body fluid under physiological conditions and a flow rate of 1 mL/min is studied. The use of two full-field nanotomographic imaging techniques, namely transmission X-ray microscopy and near-field holotomography, is compared, revealing holotomography as the superior imaging technique for this purpose. Additionally, the importance of maintaining physiological conditions is highlighted by the preliminary results. Supporting measurements using electron microscopy to investigate the chemical composition of the samples after degradation are performed.

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.

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.

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.

Erratum: Ossig, C., et al. Four-Fold Multi-Modal X-ray Microscopy Measurements of a Cu(In, Ga)Se2 Solar Cell. Materials 2021, 14, 228.

In the original version of our article [...].

Combined scanning small-angle X-ray scattering and holography probes multiple length scales in cell nuclei.

X-rays are emerging as a complementary probe to visible-light photons and electrons for imaging biological cells. By exploiting their small wavelength and high penetration depth, it is possible to image whole, intact cells and resolve subcellular structures at nanometer resolution. A variety of X-ray methods for cell imaging have been devised for probing different properties of biological matter, opening up various opportunities for fully exploiting different views of the same sample. Here, a combined approach is employed to study cell nuclei of NIH-3T3 fibroblasts. Scanning small-angle X-ray scattering is combined with X-ray holography to quantify length scales, aggregation state, and projected electron and mass densities of the nuclear material. Only by joining all this information is it possible to spatially localize nucleoli, heterochromatin and euchromatin, and physically characterize them. It is thus shown that for complex biological systems, like the cell nucleus, combined imaging approaches are highly valuable.

Three-dimensional imaging of xylem at cell wall level through near field nano holotomography.

Detailed imaging of the three-dimensionally complex architecture of xylary plants is important for studying biological and mechanical functions of woody plants. Apart from common two-dimensional microscopy, X-ray micro-computed tomography has been established as a three-dimensional (3D) imaging method for studying the hydraulic function of wooden plants. However, this X-ray imaging method can barely reach the resolution needed to see the minute structures (e.g. pit membrane). To complement the xylem structure with 3D views at the nanoscale level, X-ray near-field nano-holotomography (NFH) was applied to analyze the wood species Pinus sylvestris and Fagus sylvatica. The demanded small specimens required focused ion beam (FIB) application. The FIB milling, however, influenced the image quality through gallium implantation on the cell-wall surfaces. The measurements indicated that NFH is appropriate for imaging wood at nanometric resolution. With a 26 nm voxel pitch, the structure of the cell-wall surface in Pinus sylvestris could be visualized in genuine detail. In wood of Fagus sylvatica, the structure of a pit pair, including the pit membrane, between two neighboring fibrous cells could be traced tomographically.

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.

Four-Fold Multi-Modal X-ray Microscopy Measurements of a Cu(In,Ga)Se2 Solar Cell.

Inhomogeneities and defects often limit the overall performance of thin-film solar cells. Therefore, sophisticated microscopy approaches are sought to characterize performance and defects at the nanoscale. Here, we demonstrate, for the first time, the simultaneous assessment of composition, structure, and performance in four-fold multi-modality. Using scanning X-ray microscopy of a Cu(In,Ga)Se2 (CIGS) solar cell, we measured the elemental distribution of the key absorber elements, the electrical and optical response, and the phase shift of the coherent X-rays with nanoscale resolution. We found structural features in the absorber layer-interpreted as voids-that correlate with poor electrical performance and point towards defects that limit the overall solar cell efficiency.

Hard X-ray nano-holotomography with a Fresnel zone plate.

X-ray phase contrast nanotomography enables imaging of a wide range of samples with high spatial resolution in 3D. Near-field holography, as one of the major phase contrast techniques, is often implemented using X-ray optics such as Kirkpatrick-Baez mirrors, waveguides and compound refractive lenses. However, these optics are often tailor-made for a specific beamline and challenging to implement and align. Here, we present a near-field holography setup based on Fresnel zone plates which is fast and easy to align and provides a smooth illumination and flat field. The imaging quality of different types of Fresnel zone plates is compared in terms of the flat-field quality, the achievable resolution and exposure efficiency i.e. the photons arriving at the detector. Overall, this setup is capable of imaging different types of samples at high spatial resolution of below 100 nm in 3D with access to the quantitative phase information.

A phase-retrieval toolbox for X-ray holography and tomography.

Propagation-based phase-contrast X-ray imaging is by now a well established imaging technique, which - as a full-field technique - is particularly useful for tomography applications. Since it can be implemented with synchrotron radiation and at laboratory micro-focus sources, it covers a wide range of applications. A limiting factor in its development has been the phase-retrieval step, which was often performed using methods with a limited regime of applicability, typically based on linearization. In this work, a much larger set of algorithms, which covers a wide range of cases (experimental parameters, objects and constraints), is compiled into a single toolbox - the HoloTomoToolbox - which is made publicly available. Importantly, the unified structure of the implemented phase-retrieval functions facilitates their use and performance test on different experimental data.

Evaluation of the Weighted Mean X-ray Energy for an Imaging System Via Propagation-Based Phase-Contrast Imaging.

For imaging events of extremely short duration, like shock waves or explosions, it is necessary to be able to image the object with a single-shot exposure. A suitable setup is given by a laser-induced X-ray source such as the one that can be found at GSI (Helmholtzzentrum für Schwerionenforschung GmbH) in Darmstadt (Society for Heavy Ion Research), Germany. There, it is possible to direct a pulse from the high-energy laser Petawatt High Energy Laser for Heavy Ion eXperiments (PHELIX) on a tungsten wire to generate a picosecond polychromatic X-ray pulse, called backlighter. For grating-based single-shot phase-contrast imaging of shock waves or exploding wires, it is important to know the weighted mean energy of the X-ray spectrum for choosing a suitable setup. In propagation-based phase-contrast imaging the knowledge of the weighted mean energy is necessary to be able to reconstruct quantitative phase images of unknown objects. Hence, we developed a method to evaluate the weighted mean energy of the X-ray backlighter spectrum using propagation-based phase-contrast images. In a first step wave-field simulations are performed to verify the results. Furthermore, our evaluation is cross-checked with monochromatic synchrotron measurements with known energy at Diamond Light Source (DLS, Didcot, UK) for proof of concepts.

The optical stretcher as a tool for single-particle X-ray imaging and diffraction.

For almost half a century, optical tweezers have successfully been used to micromanipulate micrometre and sub-micrometre-sized particles. However, in recent years it has been shown experimentally that, compared with single-beam traps, the use of two opposing and divergent laser beams can be more suitable in studying the elastic properties of biological cells and vesicles. Such a configuration is termed an optical stretcher due to its capability of applying high deforming forces on biological objects such as cells. In this article the experimental capabilities of an optical stretcher as a potential sample delivery system for X-ray diffraction and imaging studies at synchrotrons and X-ray free-electron laser (FEL) facilites are demonstrated. To highlight the potential of the optical stretcher its micromanipulation capabilities have been used to image polymer beads and label biological cells. Even in a non-optimized configuration based on a commercially available optical stretcher system, X-ray holograms could be recorded from different views on a biological cell and the three-dimensional phase of the cell could be reconstructed. The capability of the setup to deform cells at higher laser intensities in combination with, for example, X-ray diffraction studies could furthermore lead to interesting studies that couple structural parameters to elastic properties. By means of high-throughput screening, the optical stretcher could become a useful tool in X-ray studies employing synchrotron radiation, and, at a later stage, femtosecond X-ray pulses delivered by X-ray free-electron lasers.

Coherence-resolution relationship in holographic and coherent diffractive imaging.

We study by numerical simulation how spatial coherence affects the reconstruction quality of images in coherent diffractive x-ray imaging. Using a conceptually simple, but computationally demanding approach, we have simulated diffraction data recorded under partial coherence, and then use the data for iterative reconstruction algorithms using a support constraint. By comparison of experimental regimes and parameters, we observe a significantly higher robustness against partially coherent illumination in the near-field compared to the far-field setting.

Divide and update: towards single-shot object and probe retrieval for near-field holography.

We present a phase reconstruction scheme for X-ray near-field holographic imaging based on a separability constraint for probe and object. In order to achieve this, we have devised an algorithm which requires only two measurements - with and without an object in the beam. This scheme is advantageous if the standard flat-field correction fails and a full ptychographic dataset can not be acquired, since either object or probe are dynamic. The scheme is validated by numerical simulations and by a proof-of-concept experiment using highly focused undulator radiation of the beamline ID16a of the European Synchrotron Radiation Facility (ESRF).

Reconstructing mode mixtures in the optical near-field.

We propose a reconstruction scheme for hard x-ray inline holography, a variant of propagation imaging, which is compatible with imaging conditions of partial (spatial) coherence. This is a relevant extension of current full-field phase contrast imaging, which requires full coherence. By the ability to reconstruct the coherent modes of the illumination (probe), as demonstrated here, the requirements of coherence filtering could be relaxed in many experimentally relevant settings. The proposed scheme is built on the mixed-state approach introduced in [Nature494, 68 (2013)], combined with multi-plane detection of extended wavefields [Opt. Commun.199, 65 (2001), Opt. Express22, 16571 (2014)]. Notably, the diversity necessary for the reconstruction is generated by acquiring measurements at different defocus positions of the detector. We show that we can recover the coherent mode structure and occupancy numbers of the partial coherent probe. Practically relevant quantities as the transversal coherence length can be computed from the reconstruction in a straightforward way.

The fluence-resolution relationship in holographic and coherent diffractive imaging.

This work presents a numerical study of the fluence-resolution behaviour for two coherent lensless X-ray imaging techniques. To this end the fluence-resolution relationship of inline near-field holography and far-field coherent diffractive imaging are compared in numerical experiments. To achieve this, the phase reconstruction is carried out using iterative phase-retrieval algorithms on simulated noisy data. Using the incident photon fluence on the specimen as the control parameter, the achievable resolution for two example phantoms (cell and bitmap) is studied. The results indicate the superior performance of holography compared with coherent diffractive imaging, for the same fluence and phase-reconstruction procedure.