Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Three-dimensional phase and intensity reconstruction from coherent modulation imaging measurements

Coherent modulation imaging is a lensless imaging technique, where a complex-valued image can be recovered from a single diffraction pattern using the iterative algorithm. Although mostly applied in two dimensions, it can be tomographically combined to produce three-dimensional (3D) images. Here we present a 3D reconstruction procedure for the sample's phase and intensity from coherent modulation imaging measurements. Pre-processing methods to remove illumination probe, inherent ambiguities in phase reconstruction results, and intensity fluctuation are given. With the projections extracted by our method, standard tomographic reconstruction frameworks can be used to recover accurate quantitative 3D phase and intensity images. Numerical simulations and optical experiments validate our method.

Spatiotemporal coherent modulation imaging for dynamic quantitative phase and amplitude microscopy

The single-shot capability of coherent modulation imaging (CMI) makes it have great potential in the investigation of dynamic processes. Its main disadvantage is the relatively low signal-to-noise ratio (SNR) which affects the spatial resolution and reconstruction accuracy. Here, we propose the improvement of a general spatiotemporal CMI method for imaging of dynamic processes. By making use of the redundant information in time-series reconstructions, the spatiotemporal CMI can achieve robust and fast reconstruction with higher SNR and spatial resolution. The method is validated by numerical simulations and optical experiments. We combine the CMI module with an optical microscope to achieve quantitative phase and amplitude reconstruction of dynamic biological processes. With the reconstructed complex field, we also demonstrate the 3D digital refocusing ability of the CMI microscope. With further development, we expect the spatiotemporal CMI method can be applied to study a range of dynamic phenomena.

Modulator refinement algorithm for coherent modulation imaging

Coherent modulation imaging (CMI) has been shown to be an effective lensless diffraction approach to imaging general extended samples with fast algorithmic convergence and high robustness to data imperfection. In the reported phasing algorithms of CMI, an exact knowledge of modulator is used as a priori. Extra characterization of the modulator is thus required before the CMI experiments are conducted and this can be cumbersome. Here we propose a modulator refinement algorithm that allows for modulator refinement in the same iterative process of image reconstruction. We demonstrate the method for both near-field and far-field geometries in simulations and for a far-field experiment. A relaxed requirement on exactly knowing the modulator would turn CMI into a standalone technique and make it much easier to implement, thus open up its wider applications in biology and materials science.

High-quality reconstruction of coherent modulation imaging using weak cascade modulators

Coherent modulation imaging (CMI) has been shown to be an effective lensless diffraction approach to imaging general extended samples with fast algorithmic convergence and high robustness to data imperfection. Being a single-shot technique, CMI holds a high potential for imaging dynamics with ultrafast pulses like the ones from free-electron lasers. In the reported work, strong modulators have been suggested for CMI to have the optimal performance, which may be an obstacle for the wide adoption of the method. Here we show that with our improved reconstruction algorithm the requirements on the modulation depth and feature size of a modulator can be relaxed. Furthermore, we demonstrate that when cascade configuration is used, the modulators can be even weaker while providing lower image errors in reconstruction than the case of a single modulator. Detailed numerical studies in both far-field and near-field experiment geometry are given via simulation. A relaxed requirement on modulators in CMI could pave the way for its wide use in biology and materials science.

Quantitative nanotomography of amorphous and polycrystalline samples using coherent X-ray diffraction

This article presents a combined approach where quantitative forward-scattering coherent diffraction imaging (CDI) is supported by crystal diffraction using 8.1 keV synchrotron X-ray radiation. The method allows the determination of the morphology, mass density and crystallinity of an isolated microscopic specimen. This approach is tested on three homogeneous samples made of different materials with different degrees of crystallinity. The mass density and morphology are revealed using three-dimensional coherent diffraction imaging with a resolution better than 36 nm. The crystallinity is extracted from the diffraction profiles measured simultaneously with coherent diffraction patterns. The presented approach extends CDI to structural characterization of samples when crystallinity aspects are of interest.

X-ray nanotomography of coccolithophores reveals that coccolith mass and segment number correlate with grid size

Coccolithophores of the Noëlaerhabdaceae family are covered by imbricated coccoliths, each composed of multiple calcite crystals radially distributed around the periphery of a grid. The factors that determine coccolith size remain obscure. Here, we used synchrotron-based three-dimensional Coherent X-ray Diffraction Imaging to study coccoliths of 7 species of Gephyrocapsa, Emiliania and Reticulofenestra with a resolution close to 30 nm. Segmentation of 45 coccoliths revealed remarkable size, mass and segment number variations, even within single coccospheres. In particular, we observed that coccolith mass correlates with grid perimeter which scales linearly with crystal number. Our results indirectly support the idea that coccolith mass is determined in the coccolith vesicle by the size of the organic base plate scale (OBPS) around which R-unit nucleation occurs every 110–120 nm. The curvation of coccoliths allows inference of a positive correlation between cell nucleus, OBPS and coccolith sizes.

Coccolithophores are one of the most abundant phytoplankton and calcifying organisms, well-known to produce intricate calcareous exoskeletons made of coccoliths. Here the authors show, by using X-ray nanotomography, the dependence of the grid size on the calcite nucleation site number and on the mass of coccoliths.

Three-dimensional X-ray diffraction imaging of dislocations in polycrystalline metals under tensile loading

The nucleation and propagation of dislocations is an ubiquitous process that accompanies the plastic deformation of materials. Consequently, following the first visualization of dislocations over 50 years ago with the advent of the first transmission electron microscopes, significant effort has been invested in tailoring material response through defect engineering and control. To accomplish this more effectively, the ability to identify and characterize defect structure and strain following external stimulus is vital. Here, using X-ray Bragg coherent diffraction imaging, we describe the first direct 3D X-ray imaging of the strain field surrounding a line defect within a grain of free-standing nanocrystalline material following tensile loading. By integrating the observed 3D structure into an atomistic model, we show that the measured strain field corresponds to a screw dislocation.

Identifying atomic defects during deformation is crucial to understand material response but remains challenging in three dimensions. Here, the authors couple X-ray Bragg coherent diffraction imaging and atomistic simulations to correlate a strain field to a screw dislocation in a single copper grain.

Single-particle XFEL 3D reconstruction of ribosome-size particles based on Fourier slice matching: requirements to reach subnanometer resolution

Three-dimensional (3D) structures of biomolecules provide insight into their functions. Using X-ray free-electron laser (XFEL) scattering experiments, it was possible to observe biomolecules that are difficult to crystallize, under conditions that are similar to their natural environment. However, resolving 3D structure from XFEL data is not without its challenges. For example, strong beam intensity is required to obtain sufficient diffraction signal and the beam incidence angles to the molecule need to be estimated for diffraction patterns with significant noise. Therefore, it is important to quantitatively assess how the experimental conditions such as the amount of data and their quality affect the expected resolution of the resulting 3D models. In this study, as an example, the restoration of 3D structure of ribosome from two-dimensional diffraction patterns created by simulation is shown. Tests are performed using the diffraction patterns simulated for different beam intensities and using different numbers of these patterns. Guidelines for selecting parameters for slice-matching 3D reconstruction procedures are established. Also, the minimum requirements for XFEL experimental conditions to obtain diffraction patterns for reconstructing molecular structures to a high-resolution of a few nanometers are discussed.

Atmospheric coherent X-ray diffraction imaging for in situ structural analysis at SPring-8 Hyogo beamline BL24XU

Coherent X-ray diffraction imaging (CXDI) is a promising technique for non-destructive structural analysis of micrometre-sized non-crystalline samples at nanometre resolutions. This article describes an atmospheric CXDI system developed at SPring-8 Hyogo beamline BL24XU for in situ structural analysis and designed for experiments at a photon energy of 8 keV. This relatively high X-ray energy enables experiments to be conducted under ambient atmospheric conditions, which is advantageous for the visualization of samples in native states. The illumination condition with pinhole-slit optics is optimized according to wave propagation calculations based on the Fresnel-Kirchhoff diffraction formula so that the sample is irradiated by X-rays with a plane wavefront and high photon flux of ∼1 × 10¹⁰ photons/16 µmø(FWHM)/s. This work demonstrates the imaging performance of the atmospheric CXDI system by visualizing internal voids of sub-micrometre-sized colloidal gold particles at a resolution of 29.1 nm. A CXDI experiment with a single macroporous silica particle under controlled humidity was also performed by installing a home-made humidity control device in the system. The in situ observation of changes in diffraction patterns according to humidity variation and reconstruction of projected electron-density maps at 5.2% RH (relative humidity) and 82.6% RH at resolutions of 133 and 217 nm, respectively, were accomplished.

Three-Dimensional Integrated X-ray Diffraction Imaging of a Native Strain in Multi-Layered WSe2

Emerging two-dimensional (2-D) materials such as transition-metal dichalcogenides show great promise as viable alternatives for semiconductor and optoelectronic devices that progress beyond silicon. Performance variability, reliability, and stochasticity in the measured transport properties represent some of the major challenges in such devices. Native strain arising from interfacial effects due to the presence of a substrate is believed to be a major contributing factor. A full three-dimensional (3-D) mapping of such native nanoscopic strain over micron length scales is highly desirable for gaining a fundamental understanding of interfacial effects but has largely remained elusive. Here, we employ coherent X-ray diffraction imaging to directly image and visualize in 3-D the native strain along the (002) direction in a typical multilayered (∼100-350 layers) 2-D dichalcogenide material (WSe₂) on silicon substrate. We observe significant localized strains of ∼0.2% along the out-of-plane direction. Experimentally informed continuum models built from X-ray reconstructions trace the origin of these strains to localized nonuniform contact with the substrate (accentuated by nanometer scale asperities, i.e., surface roughness or contaminants); the mechanically exfoliated stresses and strains are localized to the contact region with the maximum strain near surface asperities being more or less independent of the number of layers. Machine-learned multimillion atomistic models show that the strain effects gain in prominence as we approach a few- to single-monolayer limit. First-principles calculations show a significant band gap shift of up to 125 meV per percent of strain. Finally, we measure the performance of multiple WSe₂ transistors fabricated on the same flake; a significant variability in threshold voltage and the "off" current setting is observed among the various devices, which is attributed in part to substrate-induced localized strain. Our integrated approach has broad implications for the direct imaging and quantification of interfacial effects in devices based on layered materials or heterostructures.

Three-dimensional reconstruction for coherent diffraction patterns obtained by XFEL

The three-dimensional (3D) structural analysis of single particles using an X-ray free-electron laser (XFEL) is a new structural biology technique that enables observations of molecules that are difficult to crystallize, such as flexible biomolecular complexes and living tissue in the state close to physiological conditions. In order to restore the 3D structure from the diffraction patterns obtained by the XFEL, computational algorithms are necessary as the orientation of the incident beam with respect to the sample needs to be estimated. A program package for XFEL single-particle analysis based on the Xmipp software package, that is commonly used for image processing in 3D cryo-electron microscopy, has been developed. The reconstruction program has been tested using diffraction patterns of an aerosol nanoparticle obtained by tomographic coherent X-ray diffraction microscopy.

Calculation of two-dimensional scattering patterns for oriented systems

A versatile procedure to calculate two-dimensional scattering patterns of oriented systems is presented. The systems are represented by a set of dummy atoms with different scattering length densities, which allows the construction of very complex shapes either for single particles or for sets of particles. By the use of oriented pair distance distribution functions it is possible to perform a fast calculation of the scattering intensity from the oriented system in a given direction in the scattering vector (q) space and generate the two-dimensional scattering pattern on a givenqplane. Several examples of the calculations are presented, demonstrating the method and its applicability. The presented results open new possibilities for the analysis of scattering patters obtained from oriented systems.

Fundamental properties of high-quality carbon nanofoam: from low to high density

Highly uniform samples of carbon nanofoam from hydrothermal sucrose carbonization were studied by helium ion microscopy (HIM), X-ray photoelectron spectroscopy (XPS), and Raman spectroscopy. Foams with different densities were produced by changing the process temperature in the autoclave reactor. This work illustrates how the geometrical structure, electron core levels, and the vibrational signatures change when the density of the foams is varied. We find that the low-density foams have very uniform structure consisting of micropearls with ≈2-3 μm average diameter. Higher density foams contain larger-sized micropearls (≈6-9 μm diameter) which often coalesced to form nonspherical μm-sized units. Both, low- and high-density foams are comprised of predominantly sp²-type carbon. The higher density foams, however, show an advanced graphitization degree and a stronger sp³-type electronic contribution, related to the inclusion of sp³ connections in their surface network.

Single-pulse enhanced coherent diffraction imaging of bacteria with an X-ray free-electron laser

High-resolution imaging offers one of the most promising approaches for exploring and understanding the structure and function of biomaterials and biological systems. X-ray free-electron lasers (XFELs) combined with coherent diffraction imaging can theoretically provide high-resolution spatial information regarding biological materials using a single XFEL pulse. Currently, the application of this method suffers from the low scattering cross-section of biomaterials and X-ray damage to the sample. However, XFELs can provide pulses of such short duration that the data can be collected using the “diffract and destroy” approach before the effects of radiation damage on the data become significant. These experiments combine the use of enhanced coherent diffraction imaging with single-shot XFEL radiation to investigate the cellular architecture of Staphylococcus aureus with and without labeling by gold (Au) nanoclusters. The resolution of the images reconstructed from these diffraction patterns were twice as high or more for gold-labeled samples, demonstrating that this enhancement method provides a promising approach for the high-resolution imaging of biomaterials and biological systems.

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.

Quantitative X-ray phase contrast waveguide imaging of bacterial endospores

Quantitative X-ray phase contrast imaging uniquely offers quantitative imaging information in terms of electron density maps allowing for mass and mass density determinations of soft biological samples (‘weighing with light’). Here, it was carried out using coherent X-ray waveguide illumination, yielding values of the mass and mass density of freeze-dried bacterial endospores (Bacillus spp.).

Quantitative waveguide-based X-ray phase contrast imaging has been carried out on the level of single, unstained, unsliced and freeze-dried bacterial cells of Bacillus thuringiensis and Bacillus subtilis using hard X-rays of 7.9 keV photon energy. The cells have been prepared in the metabolically dormant state of an endospore. The quantitative phase maps obtained by iterative phase retrieval using a modified hybrid input–output algorithm allow for mass and mass density determinations on the level of single individual endospores but include also large field of view investigations. Additionally, a direct reconstruction based on the contrast transfer function is investigated, and the two approaches are compared. Depending on the field of view and method, a resolution down to 65 nm was achieved at a maximum applied dose of below 5 × 10⁵ Gy. Masses in the range of about ∼110–190 (20) fg for isolated endospores have been obtained.

Coherent X-ray diffraction imaging and characterization of strain in silicon-on-insulator nanostructures

Coherent X-ray diffraction imaging (CDI) has emerged in the last decade as a promising high resolution lens-less imaging approach for the characterization of various samples. It has made significant technical progress through developments in source, algorithm and imaging methodologies thus enabling important scientific breakthroughs in a broad range of disciplines. In this report, we will introduce the principles of forward scattering CDI and Bragg geometry CDI (BCDI), with an emphasis on the latter. BCDI exploits the ultra-high sensitivity of the diffraction pattern to the distortions of crystalline lattice. Its ability of imaging strain on the nanometer scale in three dimensions is highly novel. We will present the latest progress on the application of BCDI in investigating the strain relaxation behavior in nanoscale patterned strained silicon-on-insulator (sSOI) materials, aiming to understand and engineer strain for the design and implementation of new generation semiconductor devices.

Cryogenic x-ray diffraction microscopy utilizing high-pressure cryopreservation

We present cryo x-ray diffraction microscopy of high-pressure-cryofixed bacteria and report high-convergence imaging with multiple image reconstructions. Hydrated D. radiodurans cells were cryofixed at 200 MPa pressure into ∼10-μm-thick water layers and their unstained, hydrated cellular environments were imaged by phasing diffraction patterns, reaching sub-30-nm resolutions with hard x-rays. Comparisons were made with conventional ambient-pressure-cryofixed samples, with respect to both coherent small-angle x-ray scattering and the image reconstruction. The results show a correlation between the level of background ice signal and phasing convergence, suggesting that phasing difficulties with frozen-hydrated specimens may be caused by high-background ice scattering.

Three-dimensional coherent diffractive imaging on non-periodic specimens at the ESRF beamline ID10

The progress of tomographic coherent diffractive imaging with hard X-rays at the ID10 beamline of the European Synchrotron Radiation Facility is presented. The performance of the instrument is demonstrated by imaging a cluster of Fe2P magnetic nanorods at 59 nm 3D resolution by phasing a diffraction volume measured at 8 keV photon energy. The result obtained shows progress in three-dimensional imaging of non-crystalline samples in air with hard X-rays.

Molecular imaging using X-ray free-electron lasers

The opening of hard X-ray free-electron laser facilities, such as the Linac Coherent Light Source (LCLS) at SLAC National Accelerator Laboratory in the United States, has ushered in a new era in structural determination. With X-ray pulse durations down to 10 fs or shorter, and up to 10(13) transversely coherent photons per pulse in a narrow spectral bandwidth, focused irradiances of 10(18) to 10(21) W cm(-2) or higher can be produced at X-ray energies ranging from 500 eV to 10 keV. New techniques for determining the structure of systems that cannot be crystallized and for studying the time-resolved behavior of irreversible reactions at femtosecond timescales are now available.

High-energy ultra-small-angle X-ray scattering instrument at the Advanced Photon Source

This paper reports recent tests performed on the Bonse–Hart-type ultra-small-angle X-ray scattering (USAXS) instrument at the Advanced Photon Source with higher-order reflection optics – Si(440) instead of Si(220) – and with X-ray energies greater than 20 keV. The results obtained demonstrate the feasibility of high-energy operation with narrower crystal reflectivity curves, which provides access to a scatteringqrange from ∼2 × 10−5to 1.8 Å−1and up to 12 decades in the associated sample-dependent scattering intensity range. The corresponding size range of the scattering features spans about five decades – from less than 10 Å to ∼15 µm. These tests have indicated that mechanical upgrades are required to ensure the alignment capability and operational stability of this instrument for general user operations because of the tighter angular-resolution constraints of the higher-order crystal optics.

Experimental characterization of the coherence properties of hard x-ray sources

The experimental characterization of the coherence properties of hard X-ray sources is reported and discussed. The source is described by its Mutual Optical Intensity (MOI). The coherent-mode decomposition is applied to the MOI described by a Gaussian-Schell model. The method allows for a direct, quantitative characterization of the degree of coherence of both synchrotron and laboratory sources. The latter represents the first example of characterizing a low coherence hard x-ray source.

Transmission and emission x-ray microscopy: operation modes, contrast mechanisms and applications

Advances in microscopy techniques based on x-rays have opened unprecedented opportunities in terms of spatial resolution, combined with chemical and morphology sensitivity, to analyze solid, soft and liquid matter. The advent of ultrabright third and fourth generation photon sources and the continuous development of x-ray optics and detectors has pushed the limits of imaging and spectroscopic analysis to structures as small as a few tens of nanometers. Specific interactions of x-rays with matter provide elemental and chemical sensitivity that have made x-ray spectromicroscopy techniques a very attractive tool, complementary to other microscopies, for characterization in all actual research fields. The x-ray penetration power meets the demand to examine samples too thick for electron microscopes implementing 3D imaging and recently also 4D imaging which adds time resolution as well. Implementation of a variety of phase contrast techniques enhances the structural sensitivity, especially for the hard x-ray regime. Implementation of lensless or diffraction imaging helps to enhance the lateral resolution of x-ray imaging to the wavelength dependent diffraction limit.

Data preparation and evaluation techniques for x-ray diffraction microscopy

The post-experiment processing of X-ray Diffraction Microscopy data is often time-consuming and difficult. This is mostly due to the fact that even if a preliminary result has been reconstructed, there is no definitive answer as to whether or not a better result with more consistently retrieved phases can still be obtained. We show here that the first step in data analysis, the assembly of two-dimensional diffraction patterns from a large set of raw diffraction data, is crucial to obtaining reconstructions of highest possible consistency. We have developed software that automates this process and results in consistently accurate diffraction patterns. We have furthermore derived some criteria of validity for a tool commonly used to assess the consistency of reconstructions, the phase retrieval transfer function, and suggest a modified version that has improved utility for judging reconstruction quality.

Fresnel coherent diffraction tomography

Tomographic coherent imaging requires the reconstruction of a series of two-dimensional projections of the object. We show that using the solution for the image of one projection as the starting point for the reconstruction of the next projection offers a reliable and rapid approach to the image reconstruction. The method is demonstrated on simulated and experimental data. This technique also simplifies reconstructions using data with curved incident wavefronts.

Three-dimensional electron density mapping of shape-controlled nanoparticle by focused hard X-ray diffraction microscopy

Coherent diffraction microscopy using highly focused hard X-ray beams allows us to three-dimensionally observe thick objects with a high spatial resolution, also providing us with unique structural information, i.e., electron density distribution, not obtained by X-ray tomography with lenses, atom probe microscopy, or electron tomography. We measured high-contrast coherent X-ray diffraction patterns of a shape-controlled Au/Ag nanoparticle and successfully reconstructed a projection and a three-dimensional image of the nanoparticle with a single pixel (or a voxel) size of 4.2 nm in each dimension. The small pits on the surface and a hollow interior were clearly visible. The Au-rich regions were identified based on the electron density distribution, which provided insight into the formation of Au/Ag nanoboxes.

Three-dimensional imaging of strain in a single ZnO nanorod

Nanoscale structures can be highly strained because of confinement effects and the strong influence of their external boundaries. This results in dramatically different electronic, magnetic and optical material properties of considerable utility. Third-generation synchrotron-based coherent X-ray diffraction has emerged as a non-destructive tool for three-dimensional (3D) imaging of strain and defects in crystals that are smaller than the coherence volume, typically a few cubic micrometres, of the available beams that have sufficient flux to reveal the material's structure. Until now, measurements have been possible only at a single Bragg point of a given crystal because of the limited ability to maintain alignment; it has therefore been possible to determine only one component of displacement and not the full strain tensor. Here we report key advances in our fabrication and experimental techniques, which have enabled diffraction patterns to be obtained from six Bragg reflections of the same ZnO nanocrystal for the first time. All three Cartesian components of the ion displacement field, and in turn the full nine-component strain tensor, have thereby been imaged in three dimensions.

Use of a complex constraint in coherent diffractive imaging

We demonstrate use of a complex constraint based on the interaction of x-rays with matter for reconstructing images from coherent X-ray diffraction. We show the complementary information provided by the phase and magnitude of the reconstructed wavefield greatly improves the quality of the resulting estimate of the transmission function of an object without the need for a priori information about the object composition.

Diffractive imaging using partially coherent x rays

The measured spatial coherence characteristics of the illumination used in a diffractive imaging experiment are incorporated in an algorithm that reconstructs the complex transmission function of an object from experimental x-ray diffraction data using 1.4 keV x rays. Conventional coherent diffractive imaging, which assumes full spatial coherence, is a limiting case of our approach. Even in cases in which the deviation from full spatial coherence is small, we demonstrate a significant improvement in the quality of wave field reconstructions. Our formulation is applicable to x-ray and electron diffraction imaging techniques provided that the spatial coherence properties of the illumination are known or can be measured.

Cryogenic X-ray diffraction microscopy for biological samples

X-ray diffraction microscopy (XDM) is well suited for nondestructive, high-resolution biological imaging, especially for thick samples, with the high penetration power of x rays and without limitations imposed by a lens. We developed nonvacuum, cryogenic (cryo-) XDM with hard x rays at 8 keV and report the first frozen-hydrated imaging by XDM. By preserving samples in amorphous ice, the risk of artifacts associated with dehydration or chemical fixation is avoided, ensuring the imaging condition closest to their natural state. The reconstruction shows internal structures of intact D. radiodurans bacteria in their natural contrast.

Ultrahigh-resolution soft-x-ray microscopy with zone plates in high orders of diffraction

We present an x-ray optical approach to overcome the current limitations in spatial resolution of x-ray microscopes. Our new BESSY full-field x-ray microscope operates with an energy resolution up to E/DeltaE=10(4). We demonstrate that under these conditions it is possible to employ high orders of diffraction for imaging. Using the third order of diffraction of a zone plate objective with 25 nm outermost zone width, 14 nm lines and spaces of a multilayer test structure were clearly resolved. We believe that high-order imaging paves the way towards sub-10-nm real space x-ray imaging.

Extracting coherent modes from partially coherent wavefields

A method for numerically recovering the coherent modes and their occupancies from a known mutual optical intensity function is described. As an example, the technique is applied to previously published experimental data from an x-ray undulator source. The data are found to be described by three coherent modes, and the functional forms and relative occupancies of these modes are recovered.

Astigmatic phase retrieval: an experimental demonstration

We present the first experimental demonstration of the astigmatic phase retrieval technique, in which the diffracted wavefield is distorted by cylindrical curvature in two orthogonal directions. A charge-one vortex, a charge-two vortex, and a simple test image are all correctly reconstructed.

An assessment of the resolution limitation due to radiation-damage in x-ray diffraction microscopy

X-ray diffraction microscopy (XDM) is a new form of x-ray imaging that is being practiced at several third-generation synchrotron-radiation x-ray facilities. Nine years have elapsed since the technique was first introduced and it has made rapid progress in demonstrating high-resolution three-dimensional imaging and promises few-nm resolution with much larger samples than can be imaged in the transmission electron microscope. Both life- and materials-science applications of XDM are intended, and it is expected that the principal limitation to resolution will be radiation damage for life science and the coherent power of available x-ray sources for material science. In this paper we address the question of the role of radiation damage. We use a statistical analysis based on the so-called "dose fractionation theorem" of Hegerl and Hoppe to calculate the dose needed to make an image of a single life-science sample by XDM with a given resolution. We find that for simply-shaped objects the needed dose scales with the inverse fourth power of the resolution and present experimental evidence to support this finding. To determine the maximum tolerable dose we have assembled a number of data taken from the literature plus some measurements of our own which cover ranges of resolution that are not well covered otherwise. The conclusion of this study is that, based on the natural contrast between protein and water and "Rose-criterion" image quality, one should be able to image a frozen-hydrated biological sample using XDM at a resolution of about 10 nm.