X-ray holographic imaging of hydrated biological cells in solution

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.

Fast algorithms for nonlinear and constrained phase retrieval in near-field X-ray holography based on Tikhonov regularization

Based on phase retrieval, lensless coherent imaging and in particular holography offers quantitative phase and amplitude images. This is of particular importance for spectral ranges where suitable lenses are challenging, such as for hard x-rays. Here, we propose a phase retrieval approach for inline x-ray holography based on Tikhonov regularization applied to the full nonlinear forward model of image formation. The approach can be seen as a nonlinear generalization of the well-established contrast transfer function (CTF) reconstruction method. While similar methods have been proposed before, the current work achieves nonlinear, constrained phase retrieval at competitive computation times. We thus enable high-throughput imaging of optically strong objects beyond the scope of CTF. Using different examples of inline holograms obtained from illumination by a x-ray waveguide-source, we demonstrate superior image quality even for samples which do not obey the assumption of a weakly varying phase. Since the presented approach does not rely on linearization, we expect it to be well suited also for other probes such as visible light or electrons, which often exhibit strong phase interaction.

Coherent Diffractive Imaging with Diffractive Optics

We present a novel approach to x-ray microscopy based on a multilayer zone plate which is positioned behind a sample similar to an objective lens. However, unlike transmission x-ray microscopy, we do not content ourselves with a sharp intensity image; instead, we incorporate the multilayer zone plate transfer function directly in an iterative phase retrieval scheme to exploit the large diffraction angles of the small layers. The presence of multiple diffraction orders, which is conventionally a nuisance, now comes as an advantage for the reconstruction and photon efficiency. In a first experiment, we achieve sub-10-nm resolution and a quantitative phase contrast.

Observation on the Droplet Ranging from 2 to 16 μm in Cloud Droplet Size Distribution Based on Digital Holography

Cloud droplets size distribution (DSD) is one of the significant characteristics for liquid clouds. It plays an important role for the aerosol–droplet–cloud mechanism and variation in cloud microphysics. However, the minuscule sampling space is insufficient for the observation of whole DSD when using high-magnification optical systems. In this paper, we propose an observation method for cloud droplets ranging from 2 to 16 μm, by which the balance relationship between sampling space and optical magnification is realized. The method combines an in-line digital holographic interferometer (DHI) with the optical magnification of 5.89× and spatial stitching technique. The minimum size in DSD is extended to 2 μm, which improves the integrity of size distribution. Simultaneously, the stability of DSD is enhanced by increasing the tenfold sampling volume of cloud droplets. The comparative experiment between the in-line DHI and fog monitor demonstrates that the DSD obtained by this method is reliable, which can be used for the analysis of microphysical parameters. In the Beijing Aerosol and Cloud Interaction Chamber (BACIC), the observation results show that the size of cloud droplets follows the Gamma distribution, which is consistent with the theoretical DSD. The results of cloud microphysical parameters indicate that each pair of parameters has a positive correlation, and then the validity of observation method is confirmed. Additionally, the high-concentration aerosol condition significantly mitigates the effect of random turbulence and enhances the robustness of the microphysical parameter data.

Dose-efficient multimodal microscopy of human tissue at a hard X-ray nanoprobe beamline

X-ray fluorescence microscopy performed at nanofocusing synchrotron beamlines produces quantitative elemental distribution maps at unprecedented resolution (down to a few tens of nanometres), at the expense of relatively long measuring times and high absorbed doses. In this work, a method was implemented in which fast low-dose in-line holography was used to produce quantitative electron density maps at the mesoscale prior to nanoscale X-ray fluorescence acquisition. These maps ensure more efficient fluorescence scans and the reduction of the total absorbed dose, often relevant for radiation-sensitive (e.g. biological) samples. This multimodal microscopy approach was demonstrated on human sural nerve tissue. The two imaging modes provide complementary information at a comparable resolution, ultimately limited by the focal spot size. The experimental setup presented allows the user to swap between them in a flexible and reproducible fashion, as well as to easily adapt the scanning parameters during an experiment to fine-tune resolution and field of view.

Three-dimensional virtual histology of the human hippocampus based on phase-contrast computed tomography

We demonstrate multiscale phase-contrast X-ray computed tomography (CT) of postmortem human brain tissue. Large tissue volumes can be covered by parallel-beam CT and combined with subcellular detail for selected regions scanned at high magnification. This has been repeated identically for a larger number of individuals, including both Alzheimer’s-diseased patients and a control group. Optimized phase retrieval, followed by automated segmentation based on machine learning, as well as feature identification and classification based on optimal transport theory, indicates a pathway from healthy to pathological structure without prior hypothesis. This study provides a blueprint for studying the cytoarchitecture of the human brain and its alterations associated with neurodegenerative diseases.

We have studied the three-dimensional (3D) cytoarchitecture of the human hippocampus in neuropathologically healthy and Alzheimer’s disease (AD) individuals, based on phase-contrast X-ray computed tomography of postmortem human tissue punch biopsies. In view of recent findings suggesting a nuclear origin of AD, we target in particular the nuclear structure of the dentate gyrus (DG) granule cells. Tissue samples of 20 individuals were scanned and evaluated using a highly automated approach of measurement and analysis, combining multiscale recordings, optimized phase retrieval, segmentation by machine learning, representation of structural properties in a feature space, and classification based on the theory of optimal transport. Accordingly, we find that the prototypical transformation between a structure representing healthy granule cells and the pathological state involves a decrease in the volume of granule cell nuclei, as well as an increase in the electron density and its spatial heterogeneity. The latter can be explained by a higher ratio of heterochromatin to euchromatin. Similarly, many other structural properties can be derived from the data, reflecting both the natural polydispersity of the hippocampal cytoarchitecture between different individuals in the physiological context and the structural effects associated with AD pathology.

Degradation Analysis of Thin Mg-xAg Wires Using X-ray Near-Field Holotomography

Magnesium–silver alloys are of high interest for the use as temporary bone implants due to their antibacterial properties in addition to biocompatibility and biodegradability. Thin wires in particular can be used for scaffolding, but the determination of their degradation rate and homogeneity using traditional methods is difficult. Therefore, we have employed 3D imaging using X-ray near-field holotomography with sub-micrometer resolution to study the degradation of thin (250 μm diameter) Mg-2Ag and Mg-6Ag wires. The wires were studied in two states, recrystallized and solution annealed to assess the influence of Ag content and precipitates on the degradation. Imaging was employed after degradation in Dulbecco’s modified Eagle’s medium and 10% fetal bovine serum after 1 to 7 days. At 3 days of immersion the degradation rates of both alloys in both states were similar, but at 7 days higher silver content and solution annealing lead to decreased degradation rates. The opposite was observed for the pitting factor. Overall, the standard deviation of the determined parameters was high, owing to the relatively small field of view during imaging and high degradation inhomogeneity of the samples. Nevertheless, Mg-6Ag in the solution annealed state emerges as a potential material for thin wire manufacturing for implants.

High-resolution achromatic X-ray optical systems for broad-band imaging and for focusing attosecond pulses

Achromatic focusing systems for hard X-rays are examined which consist of a refractive lens paired with a diffractive lens. Compared with previous analyses, we take into account the behaviour of thick refractive lenses, such as compound refractive lenses and waveguide gradient index refractive lenses, in which both the focal length and the position of the principal planes vary with wavelength. Achromatic systems formed by the combination of such a thick refractive lens with a multilayer Laue lens are found that can operate at a focusing resolution of about 3 nm, over a relative bandwidth of about 1%. With the appropriate distance between the refractive and diffractive lenses, apochromatic systems can also be found, which operate over relative bandwidth greater than 10%. These systems can be used to focus short pulses without distorting them in time by more than several attoseconds. Such systems are suitable for high-flux scanning microscopy and for creating high intensities from attosecond X-ray pulses.

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.

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.

Observation of electron-induced characteristic x-ray and bremsstrahlung radiation from a waveguide cavity

We demonstrate x-ray generation based on direct emission of spontaneous x-rays into waveguide modes. Photons are generated by electron impact onto a structured anode target, which is formed as an x-ray waveguide or waveguide array. Both emission of characteristic radiation and bremsstrahlung are affected by the changes in mode density induced by the waveguide structure. We investigate how the excited modal pattern depends on the positions of the metal atoms and the distance of the focused electron beam with respect to the waveguide exit side. We compare the results to synchrotron-excited fluorescence. We then discuss how x-ray generation in waveguides can be used to increase the brilliance and directional emission of tabletop x-ray sources, with a corresponding increase in the spatial coherence. On the basis of the Purcell effect, we lastly show that the gain of emission into waveguide modes is governed by the quality factor of the waveguide.

X-Ray Structural Analysis of Single Adult Cardiomyocytes: Tomographic Imaging and Microdiffraction

We present a multiscale imaging approach to characterize the structure of isolated adult murine cardiomyocytes based on a combination of full-field three-dimensional coherent x-ray imaging and scanning x-ray diffraction. Using these modalities, we probe the structure from the molecular to the cellular scale. Holographic projection images on freeze-dried cells have been recorded using highly coherent and divergent x-ray waveguide radiation. Phase retrieval and tomographic reconstruction then yield the three-dimensional electron density distribution with a voxel size below 50 nm. In the reconstruction volume, myofibrils, sarcomeric organization, and mitochondria can be visualized and quantified within a single cell without sectioning. Next, we use microfocusing optics by compound refractive lenses to probe the diffraction signal of the actomyosin lattice. Comparison between recordings of chemically fixed and untreated, living cells indicate that the characteristic lattice distances shrink by ∼10% upon fixation.

3d phase-contrast nanotomography of unstained human skin biopsies may identify morphological differences in the dermis and epidermis between subjects

BACKGROUND

Enteric neuropathy is described in most patients with gastrointestinal dysmotility and may be found together with reduced intraepidermal nerve fiber density (IENFD). The aim of this pilot study was to assess whether three-dimensional (3d) imaging of skin biopsies could be used to examine various tissue components in patients with gastrointestinal dysmotility.

MATERIAL AND METHODS

Four dysmotility patients of different etiology and two healthy volunteers were included. From each subject, two 3-mm punch skin biopsies were stained with antibodies against protein gene product 9.5 or evaluated as a whole with two X-ray phase-contrast computed tomography (CT) setups, a laboratory µCT setup and a dedicated synchrotron radiation nanoCT end-station.

RESULTS

Two patients had reduced IENFD, and two normal IENFD, compared with controls. µCT and X-ray phase-contrast holographic nanotomography scanned whole tissue specimens, with optional high-resolution scans revealing delicate structures, without differentiation of various fibers and cells. Irregular architecture of dermal fibers was observed in the patient with Ehlers-Danlos syndrome and the patient with idiopathic dysmotility showed an abundance of mesenchymal ground substance.

CONCLUSIONS

3d phase-contrast tomographic imaging may be useful to illustrate traits of connective tissue dysfunction in various organs and to demonstrate whether disorganized dermal fibers could explain organ dysfunction.

Nanotomographic evaluation of precipitate structure evolution in a Mg-Zn-Zr alloy during plastic deformation

Magnesium and its alloys attract increasingly wide attention in various fields, ranging from transport to medical solutions, due to their outstanding structural and degradation properties. These properties can be tailored through alloying and thermo-mechanical processing, which is often complex and multi-step, thus requiring in-depth analysis. In this work, we demonstrate the capability of synchrotron-based nanotomographic X-ray imaging methods, namely holotomography and transmission X-ray microscopy, for the quantitative 3D analysis of the evolution of intermetallic precipitate (particle) morphology and distribution in magnesium alloy Mg–5.78Zn–0.44Zr subjected to a complex multi-step processing. A rich history of variation of the intermetallic particle structure in the processed alloy provided a testbed for challenging the analytical capabilities of the imaging modalities studied. The main features of the evolving precipitate structure revealed earlier by traditional light and electron microscopy methods were confirmed by the 3D techniques of synchrotron-based X-ray imaging. We further demonstrated that synchrotron-based X-ray imaging enabled uncovering finer details of the variation of particle morphology and number density at various stages of processing—above and beyond the information provided by visible light and electron microscopy.

Micro-liquid enclosure array and its semi-automated assembling system for x-ray free-electron laser diffractive imaging of samples in solution

We developed micro-liquid enclosure arrays (MLEAs) for holding solution samples in coherent diffractive imaging (CDI) using x-ray free-electron lasers (XFELs). Hundreds of fully isolated micro-liquid enclosures are arranged in a single MLEA chip for efficient measurement, where each enclosure is destroyed after exposure to a single XFEL pulse. A semi-automated MLEA assembling system was also developed to enclose solution samples into MLEAs efficiently at high precision. We performed XFEL-based CDI experiments using MLEAs and imaged in-solution structures of self-assembled gold nanoparticles. The sample hit rate can be optimized by adjusting solution concentration, and we achieved a single-particle hit rate of 31%, which is not far from the theoretical upper limit of 37% derived from the Poisson statistics. MELAs allow us to perform CDI measurement under controlled solution conditions and will help reveal the nanostructures and dynamics of particles in solution.

Near, far, wherever you are: simulations on the dose efficiency of holographic and ptychographic coherent imaging

Different studies in X-ray microscopy have arrived at conflicting conclusions about the dose efficiency of imaging modes involving the recording of intensity distributions in the near (Fresnel regime) or far (Fraunhofer regime) field downstream of a specimen. A numerical study is presented on the dose efficiency of near-field holography, near-field ptychography and far-field ptychography, where ptychography involves multiple overlapping finite-sized illumination positions. Unlike what has been reported for coherent diffraction imaging, which involves recording a single far-field diffraction pattern, it is found that all three methods offer similar image quality when using the same fluence on the specimen, with far-field ptychography offering slightly better spatial resolution and a lower mean error. These results support the concept that (if the experiment and image reconstruction are done properly) the sample can be near or far; wherever you are, photon fluence on the specimen sets one limit to spatial resolution.

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.

A beamline-compatible STED microscope for combined visible-light and X-ray studies of biological matter

A dedicated stimulated emission depletion (STED) microscope had been designed and implemented into the Göttingen Instrument for Nano-Imaging with X-rays (GINIX) at the synchrotron beamline P10 of the PETRA III storage ring (DESY, Hamburg). The microscope was installed on the same optical table used for X-ray holography and scanning small-angle X-ray scattering (SAXS). Scanning SAXS was implemented with the Kirkpatrick-Baez (KB) nano-focusing optics of GINIX, while X-ray holography used a combined KB and X-ray waveguide optical system for full-field projection recordings at a defocus position of the object. The STED optical axis was aligned (anti-)parallel to the focused synchrotron beam and was laterally displaced from the KB focus. This close proximity between the STED and the X-ray probe enabled in situ combined recordings on the same biological cell, tissue or any other biomolecular sample, using the same environment and mounting. Here, the instrumentation and experimental details of this correlative microscopy approach are described, as first published in our preceding work [Bernhardt et al. (2018), Nat. Commun. 9, 3641], and the capabilities of correlative STED microscopy, X-ray holography and scanning SAXS are illustrated by presenting additional datasets on cardiac tissue cells with labeled actin cytoskeleton.

Contrast enhancement for visualizing neuronal cytoarchitecture by propagation-based x-ray phase-contrast tomography

Knowledge of the three-dimensional (3d) neuronal cytoarchitecture is an important factor in order to understand the connection between tissue structure and function or to visualize pathological changes in neurodegenerative diseases or tumor development. The gold standard in neuropathology is histology, a technique which provides insights into the cellular organization based on sectioning of the sample. Conventional histology, however, misses the complete 3d information as only individual two-dimensional slices through the object are available. In this work, we use propagation-based phase-contrast x-ray tomography to perform 3d virtual histology on cerebellar tissue from mice. This technique enables us to non-invasively visualize the entire 3d density distribution of the examined samples at isotropic (sub-)cellular resolution. One central challenge, however, of the technique is the fact that contrast for important structural features can be easily lost due to small electron density differences, notably between the cells and surrounding tissue. Here, we evaluate the influence of different embedding media, which are intermediate steps in sample preparation for classical histology, on contrast formation and examine the applicability of the different sample preparations both at a synchrotron-based holotomography setup as well as a laboratory source.

Multiscale x-ray phase-contrast tomography in a mouse model of transient focal cerebral ischemia

Cerebral ischemia is associated with a lack of oxygen and high-energy phosphates within the brain tissue, leading to irreversible cell injury. Visualizing these cellular injuries has long been a focus of experimental stroke research with application of immunohistochemistry as one of the standard approaches. It is, however, a destructive imaging technique with non-isotropic resolution, as only the two-dimensional tissue structure of a thin brain section is visualized using optical microscopy and specific stainings. Herein, we extend the structural analysis of mouse brain tissue after cerebral ischemia to the third dimension via microfocus computed tomography (µ-CT). Contrast of the weakly absorbing unstained brain tissue is enhanced by phase contrast. We show that recordings at two different magnifications and fields of view can be combined as a single approach for visualization of the associated structural alterations at isotropic resolution, from the level of the whole organ down to single cells.

Perspective: Towards single shot time-resolved microscopy using short wavelength table-top light sources

Time-resolved imaging allows revealing the interaction mechanisms in the microcosm of both inorganic and biological objects. While X-ray microscopy has proven its advantages for resolving objects beyond what can be achieved using optical microscopes, dynamic studies using full-field imaging at the nanometer scale are still in their infancy. In this perspective, we present the current state of the art techniques for full-field imaging in the extreme-ultraviolet- and soft X-ray-regime which are suitable for single exposure applications as they are paramount for studying dynamics in nanoscale systems. We evaluate the performance of currently available table-top sources, with special emphasis on applications, photon flux, and coherence. Examples for applications of single shot imaging in physics, biology, and industrial applications are discussed.

Correlative microscopy approach for biology using X-ray holography, X-ray scanning diffraction and STED microscopy

We present a correlative microscopy approach for biology based on holographic X-ray imaging, X-ray scanning diffraction, and stimulated emission depletion (STED) microscopy. All modalities are combined into the same synchrotron endstation. In this way, labeled and unlabeled structures in cells are visualized in a complementary manner. We map out the fluorescently labeled actin cytoskeleton in heart tissue cells and superimpose the data with phase maps from X-ray holography. Furthermore, an array of local far-field diffraction patterns is recorded in the regime of small-angle X-ray scattering (scanning SAXS), which can be interpreted in terms of biomolecular shape and spatial correlations of all contributing scattering constituents. We find that principal directions of anisotropic diffraction patterns coincide to a certain degree with the actin fiber directions and that actin stands out in the phase maps from holographic recordings. In situ STED recordings are proposed to formulate models for diffraction data based on co-localization constraints.

A comparison of absorption and phase contrast for X-ray imaging of biological cells

X-ray imaging allows biological cells to be examined at a higher resolution than possible with visible light and without some of the preparation difficulties associated with electron microscopy of thick samples. The most used and developed technique is absorption contrast imaging in the water window which exploits the contrast between carbon and oxygen at an energy of around 500 eV. A variety of phase contrast techniques are also being developed. In general these operate at a higher energy, enabling thicker cells to be examined and, in some cases, can be combined with X-ray fluorescence imaging to locate specific metals. The various methods are based on the differences between the complex refractive indices of the cellular components and the surrounding cytosol or nucleosol, the fluids present in the cellular cytoplasm and nucleus. The refractive indices can be calculated from the atomic composition and density of the components. These in turn can be obtained from published measurements using techniques such as chemical analysis, scanning electron microscopy and X-ray imaging at selected energies. As examples, the refractive indices of heterochromatin, inner mitochondrial membranes, the neutral core of lipid droplets, starch granules, cytosol and nucleosol are calculated. The refractive index calculations enable the required doses and fluences to be obtained to provide images with sufficient statistical significance, for X-ray energies between 200 and 4000 eV. The statistical significance (e.g. the Rose criterion) for various requirements is discussed. The calculations reveal why some cellular components are more visible by absorption contrast and why much greater exposure times are required to see some cellular components. A comparison of phase contrast as a function of photon energy with absorption contrast in the water window is provided and it is shown that much higher doses are generally required for the phase contrast measurements. This particularly applies to those components with a high carbon content but with a mass density similar to the surrounding cytosol or nucleosol. The results provide guidance for the most appropriate conditions for X-ray imaging of individual cellular components within cells of various thicknesses.

X-ray computed tomography and its potential in ecological research: A review of studies and optimization of specimen preparation

Imaging techniques are a cornerstone of contemporary biology. Over the last decades, advances in microscale imaging techniques have allowed fascinating new insights into cell and tissue morphology and internal anatomy of organisms across kingdoms. However, most studies so far provided snapshots of given reference taxa, describing organs and tissues under "idealized" conditions. Surprisingly, there is an almost complete lack of studies investigating how an organism's internal morphology changes in response to environmental drivers. Consequently, ecology as a scientific discipline has so far almost neglected the possibilities arising from modern microscale imaging techniques. Here, we provide an overview of recent developments of X-ray computed tomography as an affordable, simple method of high spatial resolution, allowing insights into three-dimensional anatomy both in vivo and ex vivo. We review ecological studies using this technique to investigate the three-dimensional internal structure of organisms. In addition, we provide practical comparisons between different preparation techniques for maximum contrast and tissue differentiation. In particular, we consider the novel modality of phase contrast by self-interference of the X-ray wave behind an object (i.e., phase contrast by free space propagation). Using the cricket Acheta domesticus (L.) as model organism, we found that the combination of FAE fixative and iodine staining provided the best results across different tissues. The drying technique also affected contrast and prevented artifacts in specific cases. Overall, we found that for the interests of ecological studies, X-ray computed tomography is useful when the tissue or structure of interest has sufficient contrast that allows for an automatic or semiautomatic segmentation. In particular, we show that reconstruction schemes which exploit phase contrast can yield enhanced image quality. Combined with suitable specimen preparation and automated analysis, X-ray CT can therefore become a promising quantitative 3D imaging technique to study organisms' responses to environmental drivers, in both ecology and evolution.

First point-spread function and x-ray phase-contrast imaging results with an 88-mm diameter single crystal

In this study, we report initial demonstrations of the use of single crystals in indirect x-ray imaging with a benchtop implementation of propagation-based x-ray phase-contrast imaging. Based on single Gaussian peak fits to the x-ray images, we observed a four times smaller system point-spread function (PSF) with the 50-µm thick single crystal scintillators than with the reference polycrystalline phosphor/scintillator. Fiber-optic plate depth-of-focus and Al reflective-coating aspects are also elucidated. Guided by the results from the 25-mm diameter crystal samples, we report additionally the first results with a unique 88-mm diameter single crystal bonded to a fiber optic plate and coupled to the large format CCD. Both PSF and x-ray phase-contrast imaging data are quantified and presented.

Phase recovery and holographic image reconstruction using deep learning in neural networks

Phase recovery from intensity-only measurements forms the heart of coherent imaging techniques and holography. In this study, we demonstrate that a neural network can learn to perform phase recovery and holographic image reconstruction after appropriate training. This deep learning-based approach provides an entirely new framework to conduct holographic imaging by rapidly eliminating twin-image and self-interference-related spatial artifacts. This neural network-based method is fast to compute and reconstructs phase and amplitude images of the objects using only one hologram, requiring fewer measurements in addition to being computationally faster. We validated this method by reconstructing the phase and amplitude images of various samples, including blood and Pap smears and tissue sections. These results highlight that challenging problems in imaging science can be overcome through machine learning, providing new avenues to design powerful computational imaging systems.

Live cell X-ray imaging of autophagic vacuoles formation and chromatin dynamics in fission yeast

Seeing physiological processes at the nanoscale in living organisms without labeling is an ultimate goal in life sciences. Using X-ray ptychography, we explored in situ the dynamics of unstained, living fission yeast Schizosaccharomyces pombe cells in natural, aqueous environment at the nanoscale. In contrast to previous X-ray imaging studies on biological matter, in this work the eukaryotic cells were alive even after several ptychographic X-ray scans, which allowed us to visualize the chromatin motion as well as the autophagic cell death induced by the ionizing radiation. The accumulated radiation of the sequential scans allowed for the determination of a characteristic dose of autophagic vacuole formation and the lethal dose for fission yeast. The presented results demonstrate a practical method that opens another way of looking at living biological specimens and processes in a time-resolved label-free setting.

Imaging of Biological Materials and Cells by X-ray Scattering and Diffraction

Cells and biological materials are large objects in comparison to the size of internal components such as organelles and proteins. An understanding of the functions of these nanoscale elements is key to elucidating cellular function. In this review, we describe the advances in X-ray scattering and diffraction techniques for imaging biological systems at the nanoscale. We present a number of principal technological advances in X-ray optics and development of sample environments. We identify radiation damage as one of the most severe challenges in the field, thus rendering the dose an important parameter when putting different X-ray methods in perspective. Furthermore, we describe different successful approaches, including scanning and full-field techniques, along with prominent examples. Finally, we present a few recent studies that combined several techniques in one experiment in order to collect highly complementary data for a multidimensional sample characterization.

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).

Four dimensional material movies: High speed phase-contrast tomography by backprojection along dynamically curved paths

We present an approach towards four dimensional (4d) movies of materials, showing dynamic processes within the entire 3d structure. The method is based on tomographic reconstruction on dynamically curved paths using a motion model estimated by optical flow techniques, considerably reducing the typical motion artefacts of dynamic tomography. At the same time we exploit x-ray phase contrast based on free propagation to enhance the signal from micron scale structure recorded with illumination times down to a millisecond (ms). The concept is demonstrated by observing the burning process of a match stick in 4d, using high speed synchrotron phase contrast x-ray tomography recordings. The resulting movies reveal the structural changes of the wood cells during the combustion.

Goos-Hänchen effect observed for focused x-ray beams under resonant mode excitation

We have coupled a nano-focused synchrotron beam into a planar x-ray waveguide structure through a thinned cladding, using the resonant beam coupling (RBC) geometry, which is well established for coupling of macroscopic x-ray beams into x-ray waveguides. By reducing the beam size and using specially designed waveguide structures with multiple guiding layers, we can observe two reflected beams of similar amplitudes upon resonant mode excitation. At the same time, the second reflected beam is shifted along the surface by several millimeters, constituting a exceptionally large Goos-Hänchen effect. We evidence this effect based on its characteristic far-field patterns resulting from interference of the multiple reflected beams. The experimental results are in perfect agreement with finite-difference simulations.

Three-dimensional single-cell imaging with X-ray waveguides in the holographic regime

X-ray tomography at the level of single biological cells is possible in a low-dose regime, based on full-field holographic recordings, with phase contrast originating from free-space wave propagation. Building upon recent progress in cellular imaging based on the illumination by quasi-point sources provided by X-ray waveguides, here this approach is extended in several ways. First, the phase-retrieval algorithms are extended by an optimized deterministic inversion, based on a multi-distance recording. Second, different advanced forms of iterative phase retrieval are used, operational for single-distance and multi-distance recordings. Results are compared for several different preparations of macrophage cells, for different staining and labelling. As a result, it is shown that phase retrieval is no longer a bottleneck for holographic imaging of cells, and how advanced schemes can be implemented to cope also with high noise and inconsistencies in the data.

Reconstruction of the near-field distribution in an X-ray waveguide array

Iterative phase retrieval has been used to reconstruct the near-field distribution behind tailored X-ray waveguide arrays, by inversion of the measured far-field pattern recorded under fully coherent conditions. It is thereby shown that multi-waveguide interference can be exploited to control the near-field distribution behind the waveguide exit. This can, for example, serve to create a secondary quasi-focal spot outside the waveguide structure. For this proof of concept, an array of seven planar Ni/C waveguides are used, with precisely varied guiding layer thickness and cladding layer thickness, as fabricated by high-precision magnetron sputtering systems. The controlled thickness variations in the range of 0.2 nm results in a desired phase shift of the different waveguide beams. Two kinds of samples, a one-dimensional waveguide array and periodic waveguide multilayers, were fabricated, each consisting of seven C layers as guiding layers and eight Ni layers as cladding layers. These are shown to yield distinctly different near-field patterns.

Combined scanning X-ray diffraction and holographic imaging of cardiomyocytes

This article presents scanning small-angle X-ray scattering (SAXS) experiments on the actomyosin assemblies in freeze-dried neo-natal rat cardiac muscle cells. By scanning the cells through a sub-micrometre focused beam, the local structure and filament orientation can be probed and quantified. To this end, SAXS data were recorded and analyzed directly in reciprocal space to generate maps of different structural parameters (scanning SAXS). The scanning SAXS experiments were complemented by full-field holographic imaging of the projected electron density, following a slight rearrangement of the instrumental setup. It is shown that X-ray holography is ideally suited to complete missing scattering data at low momentum transfer in the structure factor, extending the covered range of spatial frequencies by two orders of magnitude. Regions of interest for scanning can be easily selected on the basis of the electron density maps. Finally, the combination of scanning SAXS and holography allows for a direct verification of possible radiation-induced structural changes in the cell.

The fluence-resolution relationship in holographic and coherent diffractive imaging

In this work the fluence efficiency of two coherent X-ray imaging techniques is studied by numerical experiments. The techniques surveyed are near-field holography and far-field diffraction 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.

Contrast-transfer-function phase retrieval based on compressed sensing

We report on a new contrast-transfer-function (CTF) phase-retrieval method based on the alternating direction method of multipliers (ADMMs), which allows us to exploit any compressed sensing regularization scheme reflecting the sparsity of the investigated object. The proposed iterative algorithm retrieves accurate phase maps from highly noisy single-distance projection microscopy data and is characterized by a stable convergence, not bounded to the prior knowledge of the object support or to the initialization strategy. Experiments on simulated and real datasets show that ADMM-CTF yields reconstructions with a substantial lower amount of artifacts and enhanced signal-to-noise ratio compared to the standard analytical inversion.

Probe reconstruction for holographic X-ray imaging

In X-ray holographic near-field imaging the resolution and image quality depend sensitively on the beam. Artifacts are often encountered due to the strong focusing required to reach high resolution. Here, two schemes for reconstructing the complex-valued and extended wavefront of X-ray nano-probes, primarily in the planes relevant for imaging (i.e. focus, sample and detection plane), are presented and compared. Firstly, near-field ptychography is used, based on scanning a test pattern laterally as well as longitudinally along the optical axis. Secondly, any test pattern is dispensed of and the wavefront reconstructed only from data recorded for different longitudinal translations of the detector. For this purpose, an optimized multi-plane projection algorithm is presented, which can cope with the numerically very challenging setting of a divergent wavefront emanating from a hard X-ray nanoprobe. The results of both schemes are in very good agreement. The probe retrieval can be used as a tool for optics alignment, in particular at X-ray nanoprobe beamlines. Combining probe retrieval and object reconstruction is also shown to improve the image quality of holographic near-field imaging.

Three-dimensional mouse brain cytoarchitecture revealed by laboratory-based x-ray phase-contrast tomography

Studies of brain cytoarchitecture in mammals are routinely performed by serial sectioning of the specimen and staining of the sections. The procedure is labor-intensive and the 3D architecture can only be determined after aligning individual 2D sections, leading to a reconstructed volume with non-isotropic resolution. Propagation-based x-ray phase-contrast tomography offers a unique potential for high-resolution 3D imaging of intact biological specimen due to the high penetration depth and potential resolution. We here show that even compact laboratory CT at an optimized liquid-metal jet microfocus source combined with suitable phase-retrieval algorithms and a novel tissue preparation can provide cellular and subcellular resolution in millimeter sized samples of mouse brain. We removed water and lipids from entire mouse brains and measured the remaining dry tissue matrix in air, lowering absorption but increasing phase contrast. We present single-cell resolution images of mouse brain cytoarchitecture and show that axons can be revealed in myelinated fiber bundles. In contrast to optical 3D techniques our approach does neither require staining of cells nor tissue clearing, procedures that are increasingly difficult to apply with increasing sample and brain sizes. The approach thus opens a novel route for high-resolution high-throughput studies of brain architecture in mammals.

μCT of ex-vivo stained mouse hearts and embryos enables a precise match between 3D virtual histology, classical histology and immunochemistry

The small size of the adult and developing mouse heart poses a great challenge for imaging in preclinical research. The aim of the study was to establish a phosphotungstic acid (PTA) ex-vivo staining approach that efficiently enhances the x-ray attenuation of soft-tissue to allow high resolution 3D visualization of mouse hearts by synchrotron radiation based μCT (SRμCT) and classical μCT. We demonstrate that SRμCT of PTA stained mouse hearts ex-vivo allows imaging of the cardiac atrium, ventricles, myocardium especially its fibre structure and vessel walls in great detail and furthermore enables the depiction of growth and anatomical changes during distinct developmental stages of hearts in mouse embryos. Our x-ray based virtual histology approach is not limited to SRμCT as it does not require monochromatic and/or coherent x-ray sources and even more importantly can be combined with conventional histological procedures. Furthermore, it permits volumetric measurements as we show for the assessment of the plaque volumes in the aortic valve region of mice from an ApoE-/- mouse model. Subsequent, Masson-Goldner trichrome staining of paraffin sections of PTA stained samples revealed intact collagen and muscle fibres and positive staining of CD31 on endothelial cells by immunohistochemistry illustrates that our approach does not prevent immunochemistry analysis. The feasibility to scan hearts already embedded in paraffin ensured a 100% correlation between virtual cut sections of the CT data sets and histological heart sections of the same sample and may allow in future guiding the cutting process to specific regions of interest. In summary, since our CT based virtual histology approach is a powerful tool for the 3D depiction of morphological alterations in hearts and embryos in high resolution and can be combined with classical histological analysis it may be used in preclinical research to unravel structural alterations of various heart diseases.

Mesoscale imaging with cryo-light and X-rays: Larger than molecular machines, smaller than a cell

In the context of cell biology, the term mesoscale describes length scales ranging from that of an individual cell, down to the size of the molecular machines. In this spatial regime, small building blocks self-organise to form large, functional structures. A comprehensive set of rules governing mesoscale self-organisation has not been established, making the prediction of many cell behaviours difficult, if not impossible. Our knowledge of mesoscale biology comes from experimental data, in particular, imaging. Here, we explore the application of soft X-ray tomography (SXT) to imaging the mesoscale, and describe the structural insights this technology can generate. We also discuss how SXT imaging is complemented by the addition of correlative fluorescence data measured from the same cell. This combination of two discrete imaging modalities produces a 3D view of the cell that blends high-resolution structural information with precise molecular localisation data.

How many photons are needed to reconstruct random objects in coherent X-ray diffractive imaging?

This paper presents an investigation of the reconstructibility of coherent X-ray diffractive imaging diffraction patterns for a class of binary random `bitmap' objects. Combining analytical results and numerical simulations, the critical fluence per bitmap pixel is determined, for arbitrary contrast values (absorption level and phase shift), both for the optical near- and far-field. This work extends previous investigations based on information theory, enabling a comparison of the amount of information carried by single photons in different diffraction regimes. The experimental results show an order-of-magnitude agreement.

Following DNA Compaction During the Cell Cycle by X-ray Nanodiffraction

X-ray imaging of intact biological cells is emerging as a complementary method to visible light or electron microscopy. Owing to the high penetration depth and small wavelength of X-rays, it is possible to resolve subcellular structures at a resolution of a few nanometers. Here, we apply scanning X-ray nanodiffraction in combination with time-lapse bright-field microscopy to nuclei of 3T3 fibroblasts and thus relate the observed structures to specific phases in the cell division cycle. We scan the sample at a step size of 250 nm and analyze the individual diffraction patterns according to a generalized Porod's law. Thus, we obtain information on the aggregation state of the nuclear DNA at a real space resolution on the order of the step size and in parallel structural information on the order of few nanometers. We are able to distinguish nucleoli, heterochromatin, and euchromatin in the nuclei and follow the compaction and decompaction during the cell division cycle.

Holographic imaging with a hard x-ray nanoprobe: ptychographic versus conventional phase retrieval

We have performed near-field x-ray imaging with simultaneous object and probe reconstruction. By an advanced ptychographic algorithm based on longitudinal and lateral translations, full-field images of nanoscale objects are reconstructed with quantitative contrast values, along with the extended wavefronts used to illuminate the objects. The imaging scheme makes idealizing assumptions on the probe obsolete, and efficiently disentangles phase shifts related to the object from the imperfections in the illumination. We validate this approach by comparison to the conventional reconstruction scheme without simultaneous probe retrieval, based on the contrast transfer function algorithm. To this end, a set of semiconductor nanowires with controlled chemical composition (InP core, insulating SiO₂ layer, and indium tin oxide cover) is imaged using the quasi-point source illumination realized by the hard x-ray nanofocus (26  nm×39  nm spot size) of the ID16A Nano-Imaging beamline at the European Synchrotron Radiation Facility.

Miniaturized beamsplitters realized by X-ray waveguides

This paper reports on the fabrication and characterization of X-ray waveguide beamsplitters. The waveguide channels were manufactured by electron-beam lithography, reactive ion etching and wafer bonding techniques, with an empty (air) channel forming the guiding layer and silicon the cladding material. A focused synchrotron beam is efficiently coupled into the input channel. The beam is guided and split into two channels with a controlled (and tunable) distance at the exit of the waveguide chip. After free-space propagation and diffraction broadening, the two beams interfere and form a double-slit interference pattern in the far-field. From the recorded far-field, the near-field was reconstructed by a phase retrieval algorithm (error reduction), which was found to be extremely reliable for the two-channel setting. By numerical propagation methods, the reconstructed field was then propagated along the optical axis, to investigate the formation of the interference pattern from the two overlapping beams. Interestingly, phase vortices were observed and analysed.

Using sparsity information for iterative phase retrieval in x-ray propagation imaging

For iterative phase retrieval algorithms in near field x-ray propagation imaging experiments with a single distance measurement, it is indispensable to have a strong constraint based on a priori information about the specimen; for example, information about the specimen's support. Recently, Loock and Plonka proposed to use the a priori information that the exit wave is sparsely represented in a certain directional representation system, a so-called shearlet system. In this work, we extend this approach to complex-valued signals by applying the new shearlet constraint to amplitude and phase separately. Further, we demonstrate its applicability to experimental data.

X-rays Reveal the Internal Structure of Keratin Bundles in Whole Cells

In recent years, X-ray imaging of biological cells has emerged as a complementary alternative to fluorescence and electron microscopy. Different techniques were established and successfully applied to macromolecular assemblies and structures in cells. However, while the resolution is reaching the nanometer scale, the dose is increasing. It is essential to develop strategies to overcome or reduce radiation damage. Here we approach this intrinsic problem by combing two different X-ray techniques, namely ptychography and nanodiffraction, in one experiment and on the same sample. We acquire low dose ptychography overview images of whole cells at a resolution of 65 nm. We subsequently record high-resolution nanodiffraction data from regions of interest. By comparing images from the two modalities, we can exclude strong effects of radiation damage on the specimen. From the diffraction data we retrieve quantitative structural information from intracellular bundles of keratin intermediate filaments such as a filament radius of 5 nm, hexagonal geometric arrangement with an interfilament distance of 14 nm and bundle diameters on the order of 70 nm. Thus, we present an appealing combined approach to answer a broad range of questions in soft-matter physics, biophysics and biology.

Impact of noise in holography with extended references in the low signal regime

Signal-to-noise ratio is a key factor in lensless imaging, particularly for low diffraction signal experiments in the single shot regime. We present our recent study of the noise impact on holography with extended references. Experimental data have been measured in single shot acquisition using an intense coherent soft X-ray high harmonic source. The impact of hardware and software noise under various detection conditions is discussed. A final comparison between single shot and multi-shot regimes is given.

Regularized Newton methods for x-ray phase contrast and general imaging problems

Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear image formation from a given object to the observations is often available, explicit inversion formulas are typically not known. Moreover, the measured data might be insufficient for stable image reconstruction, in which case it has to be complemented by suitable a priori information. In this work, regularized Newton methods are presented as a general framework for the solution of such ill-posed nonlinear imaging problems. For a proof of principle, the approach is applied to x-ray phase contrast imaging in the near-field propagation regime. Simultaneous recovery of the phase- and amplitude from a single near-field diffraction pattern without homogeneity constraints is demonstrated for the first time. The presented methods further permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval and tomographic inversion. We demonstrate the potential of this approach by three-dimensional imaging of a colloidal crystal at 95nm isotropic resolution.

Signal-to-noise criterion for free-propagation imaging techniques at free-electron lasers and synchrotrons

We propose a signal-to-noise criterion which predicts whether a feature of a given size and scattering strength, placed inside a larger object, can be retrieved with two common X-ray imaging techniques: coherent diffraction imaging and projection microscopy. This criterion, based on how efficiently these techniques detect the scattered photons and validated through simulations, shows in general that projection microscopy can resolve smaller phase differences and features than coherent diffraction imaging. Our criterion can be used to design optimized imaging experiments and perform feasibility studies for sensitive biological materials in free-electron lasers, where the number of photons per pulse is limited, or in synchrotron experiments, for both techniques.