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

Prospects for coherent X-ray diffraction imaging at fourth-generation synchrotron sources

Coherent X-ray diffraction imaging is a lens-less microscopy technique that emerged with the advent of third-generation synchrotrons, modern detectors and computers. It can image isolated micrometre-sized objects with a spatial resolution of a few nanometres. The method is based on the inversion of the speckle pattern in the far field produced by the scattering from the object under coherent illumination. The retrieval of the missing phase is performed using an iterative algorithm that numerically phases the amplitudes from the intensities of speckles measured with sufficient oversampling. Two- and three-dimensional imaging is obtained by simple inverse Fourier transform. This lens-less imaging technique has been applied to various specimens for their structural characterization on the nanoscale. Here, we review the theoretical and experimental elements of the technique, its achievements, and its limitations at third-generation synchrotrons. We also discuss the new opportunities offered by modern fourth-generation synchrotrons and outline the developments necessary to maximize the potential of the technique.

Reduction of artifacts associated with missing data in coherent diffractive imaging

Coherent diffractive imaging experiments often collect incomplete datasets containing regions that lack any measurements. These regions can arise because of beamstops, gaps between detectors, or, in tomography experiments, a missing wedge of data due to a limited sample rotation range. We describe practical and effective approaches to mitigate reconstruction artifacts by bringing uniqueness back to the phase retrieval problem. This is accomplished by looking for a solution that both matches the data and has minimum total variation, which essentially sets the unconstrained modes to reduce oscillations within the reconstruction. Two algorithms are described. The first algorithm assumes that there is an accurate estimate of the phase and can be used for pre- and post-processing. The second algorithm attempts to simultaneously minimize the total variation and recover the phase. We demonstrate the utility of these algorithms with numerical simulations and, experimentally, on a large, three-dimensional dataset.

Self-transformation of solid CaCO3 microspheres into core-shell and hollow hierarchical structures revealed by coherent X-ray diffraction imaging

The self-transformation of solid microspheres into complex core-shell and hollow architectures cannot be explained by classical Ostwald ripening alone. Here, coherent X-ray diffraction imaging and 3D X-ray fluorescence were used to visualize in 3D the formation of hollow microparticles of calcium carbonate in the presence of polystyrene sulfonate (PSS). During the dissolution of the core made from 10-25 nm crystals, the shell developed a global spheroidal shape composed of an innermost layer of 30 nm particles containing high PSS content on which oriented vaterite crystals grew with their c axis mainly oriented along the meridians. The stabilizing role of PSS and the minimization of the intercrystal dipolar energy can explain in combination with Ostwald ripening the formation of these sophisticated structures as encountered in many systems such as ZnO, TiO₂, Fe₂O₃, Co₃O₄, MnO₂, Cu₂O, ZnS, CaCO₃ and Ca₈H₂(PO₄)₆·5H₂O.

Nanoscale imaging of shale fragments with coherent X-ray diffraction

Despite the abundance of shales in the Earth's crust and their industrial and environmental importance, their microscale physical properties are poorly understood, owing to the presence of many structurally related mineral phases and a porous network structure spanning several length scales. Here, the use of coherent X-ray diffraction imaging (CXDI) to study the internal structure of microscopic shale fragments is demonstrated. Simultaneous wide-angle X-ray diffraction (WAXD) measurement facilitated the study of the mineralogy of the shale microparticles. It was possible to identify pyrite nanocrystals as inclusions in the quartz-clay matrix and the volume of closed unconnected pores was estimated. The combined CXDI-WAXD analysis enabled the establishment of a correlation between sample morphology and crystallite shape and size. The results highlight the potential of the combined CXDI-WAXD approach as an upcoming imaging modality for 3D nanoscale studies of shales and other geological formations via serial measurements of microscopic fragments.

PyNX: high-performance computing toolkit for coherent X-ray imaging based on operators

The open-source PyNX toolkit has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical processing units (GPUs) to achieve high-performance computing speeds. The toolkit can be used for coherent diffraction imaging (CDI), ptychography and wavefront propagation, in the far- or near-field regime. Moreover, all imaging operations (propagation, projections, algorithm cycles…) can be implemented in Python as simple mathematical operators, an approach which can be used to easily combine basic algorithms in a tailored chain. Calculations can also be distributed to multiple GPUs, e.g. for large ptychography data sets. Command-line scripts are available for on-line CDI and ptychography analysis, either from raw beamline data sets or using the coherent X-ray imaging data format.

Free log-likelihood as an unbiased metric for coherent diffraction imaging

Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object. The uncertainty of the object support can lead to over-fitting and prevents an unambiguous metric evaluation of solutions. We propose to use a ‘free’ log-likelihood indicator, where a small percentage of points are masked from the reconstruction algorithms, as an unbiased metric to evaluate the validity of computed solutions, independent of the sample studied. We also show how a set of solutions can be analysed through an eigen-decomposition to yield a better estimate of the real object. Example analysis on experimental data is presented both for a test pattern dataset, and the diffraction pattern from a live cyanobacteria cell. The method allows the validation of reconstructions on a wide range of materials (hard condensed or biological), and should be particularly relevant for 4th generation synchrotrons and X-ray free electron lasers, where large, high-throughput datasets require a method for unsupervised data evaluation.

Bimodal Porosity and Stability of a TiO2 Gig-Lox Sponge Infiltrated with Methyl-Ammonium Lead Iodide Perovskite

We created a blend between a TiO2 sponge with bimodal porosity and a Methyl-Ammonium Lead Iodide (MAPbI3) perovskite. The interpenetration of the two materials is effective thanks to the peculiar sponge structure. During the early stages of the growth of the TiO2 sponge, the formation of 5-10 nm-large TiO2 auto-seeds is observed which set the micro-porosity (<5 nm) of the layer, maintained during further growth. In a second stage, the auto-seeds aggregate into hundreds-of-nm-large meso-structures by their mutual shadowing of the grazing Ti flux for local oxidation. This process generates meso-pores (10-100 nm) treading across the growing layer, as accessed by tomographic synchrotron radiation coherent X-ray imaging and environmental ellipsometric porosimetry. The distributions of pore size are extracted before (>47% V) and after MAPbI3 loading, and after blend ageing, unfolding a starting pore filling above 80% in volume. The degradation of the perovskite in the blend follows a standard path towards PbI2 accompanied by the concomitant release of volatile species, with an activation energy of 0.87 eV under humid air. The use of dry nitrogen as environmental condition has a positive impact in increasing this energy by ~0.1 eV that extends the half-life of the material to 7 months under continuous operation at 60 °C.

Implications of disturbed photon-counting statistics of Eiger detectors for X-ray speckle visibility experiments

This paper reports on coherent scattering experiments in the low-count regime with less than one photon per pixel per acquisition on average, conducted with two detectors based on the Eiger single-photon-counting chip. The obtained photon-count distributions show systematic deviations from the expected Poisson-gamma distribution, which result in a strong overestimation of the measured speckle contrast. It is shown that these deviations originate from an artificial increase of double-photon events, which is proportional to the detected intensity and inversely proportional to the exposure time. The observed miscounting effect may have important implications for new coherent scattering experiments emerging with the advent of high-brilliance X-ray sources. Different correction schemes are discussed in order to obtain the correct photon distributions from the data. A successful correction is demonstrated with the measurement of Brownian motion from colloidal particles using X-ray speckle visibility spectroscopy.

Mechanical Competence and Bone Quality Develop During Skeletal Growth

Bone fracture risk is influenced by bone quality, which encompasses bone's composition as well as its multiscale organization and architecture. Aging and disease deteriorate bone quality, leading to reduced mechanical properties and higher fracture incidence. Largely unexplored is how bone quality and mechanical competence progress during longitudinal bone growth. Human femoral cortical bone was acquired from fetal (n = 1), infantile (n = 3), and 2- to 14-year-old cases (n = 4) at the mid-diaphysis. Bone quality was assessed in terms of bone structure, osteocyte characteristics, mineralization, and collagen orientation. The mechanical properties were investigated by measuring tensile deformation at multiple length scales via synchrotron X-ray diffraction. We find dramatic differences in mechanical resistance with age. Specifically, cortical bone in 2- to 14-year-old cases exhibits a 160% greater stiffness and 83% higher strength than fetal/infantile cases. The higher mechanical resistance of the 2- to 14-year-old cases is associated with advantageous bone quality, specifically higher bone volume fraction, better micronscale organization (woven versus lamellar), and higher mean mineralization compared with fetal/infantile cases. Our study reveals that bone quality is superior after remodeling/modeling processes convert the primary woven bone structure to lamellar bone. In this cohort of female children, the microstructural differences at the femoral diaphysis were apparent between the 1- to 2-year-old cases. Indeed, the lamellar bone in 2- to 14-year-old cases had a superior structural organization (collagen and osteocyte characteristics) and composition for resisting deformation and fracture than fetal/infantile bone. Mechanistically, the changes in bone quality during longitudinal bone growth lead to higher fracture resistance because collagen fibrils are better aligned to resist tensile forces, while elevated mean mineralization reinforces the collagen scaffold. Thus, our results reveal inherent weaknesses of the fetal/infantile skeleton signifying its inferior bone quality. These results have implications for pediatric fracture risk, as bone produced at ossification centers during children's longitudinal bone growth could display similarly weak points. © 2019 American Society for Bone and Mineral Research.

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.

Experimental 3D coherent diffractive imaging from photon-sparse random projections

The routine atomic resolution structure determination of single particles is expected to have profound implications for probing structure-function relationships in systems ranging from energy-storage materials to biological molecules. Extremely bright ultrashort-pulse X-ray sources - X-ray free-electron lasers (XFELs) - provide X-rays that can be used to probe ensembles of nearly identical nanoscale particles. When combined with coherent diffractive imaging, these objects can be imaged; however, as the resolution of the images approaches the atomic scale, the measured data are increasingly difficult to obtain and, during an X-ray pulse, the number of photons incident on the 2D detector is much smaller than the number of pixels. This latter concern, the signal 'sparsity', materially impedes the application of the method. An experimental analog using a conventional X-ray source is demonstrated and yields signal levels comparable with those expected from single biomolecules illuminated by focused XFEL pulses. The analog experiment provides an invaluable cross check on the fidelity of the reconstructed data that is not available during XFEL experiments. Using these experimental data, it is established that a sparsity of order 1.3 × 10-3 photons per pixel per frame can be overcome, lending vital insight to the solution of the atomic resolution XFEL single-particle imaging problem by experimentally demonstrating 3D coherent diffractive imaging from photon-sparse random projections.

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.

High-resolution coherent x-ray diffraction imaging of metal-coated polymer microspheres

Coherent x-ray diffraction imaging (CXDI) is becoming an important 3D quantitative microscopy technique, allowing structural investigation of a wide range of delicate mesoscale samples that cannot be imaged by other techniques like electron microscopy. Here we report high-resolution 3D CXDI performed on spherical microcomposites consisting of a polymer core coated with a triple layer of nickel-gold-silica. These composites are of high interest to the microelectronics industry, where they are applied in conducting adhesives as fine-pitch electrical contacts-which requires an exceptional degree of uniformity and reproducibility. Experimental techniques that can assess the state of the composites non-destructively, preferably also while embedded in electronic chips, are thus in high demand. We demonstrate that using CXDI, all four different material components of the composite could be identified, with radii matching well to the nominal specifications of the manufacturer. Moreover, CXDI provided detailed maps of layer thicknesses, roughnesses, and defects such as holes, thus also facilitating cross-layer correlations. The side length of the voxels in the reconstruction, given by the experimental geometry, was 16 nm. The effective resolution enabled resolving even the thinnest coating layer of ∼20  nm nominal width. We discuss critically the influence of the weak phase approximation and the projection approximation on the reconstructed electron density estimates, demonstrating that the latter has to be employed. We conclude that CXDI has excellent potential as a metrology tool for microscale composites.

Lensless Tomographic Imaging of Near Surface Structures of Frozen Hydrated Malaria-Infected Human Erythrocytes by Coherent X-Ray Diffraction Microscopy

Lensless, coherent X-ray diffraction microscopy has been drawing considerable attentions for tomographic imaging of whole human cells. In this study, we performed cryogenic coherent X-ray diffraction imaging of human erythrocytes with and without malaria infection. To shed light on structural features near the surface, “ghost cells” were prepared by the removal of cytoplasm. From two-dimensional images, we found that the surface of erythrocytes after 32 h of infection became much rougher compared to that of healthy, uninfected erythrocytes. The Gaussian roughness of an infected erythrocyte surface (69 nm) is about two times larger than that of an uninfected one (31 nm), reflecting the formation of protein knobs on infected erythrocyte surfaces. Three-dimensional tomography further enables to obtain images of the whole cells with no remarkable radiation damage, whose accuracy was estimated using phase retrieval transfer functions to be as good as 64 nm for uninfected and 80 nm for infected erythrocytes, respectively. Future improvements in phase retrieval algorithm, increase in degree of coherence, and higher flux in combination with complementary X-ray fluorescence are necessary to gain both structural and chemical details of mesoscopic architectures, such as cytoskeletons, membraneous structures, and protein complexes, in frozen hydrated human cells, especially under diseased states.

X-Ray Nanoscopy of a Bulk Heterojunction

Optimizing the morphology of bulk heterojunctions is known to significantly improve the photovoltaic performance of organic solar cells, but available quantitative imaging techniques are few and have severe limitations. We demonstrate X-ray ptychographic coherent diffractive imaging applied to all-organic blends. Specifically, the phase-separated morphology in bulk heterojunction photoactive layers for organic solar cells, prepared from a 50:50 blend of poly(3-hexylthiophene) (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM) and thermally treated for different annealing times is imaged to high resolution. Moreover, using a fast-scanning calorimetry chip setup, the nano-morphological changes caused by repeated thermal annealing applied to the same sample could be monitored. X-ray ptychography resolves to better than 100 nm the phase-segregated domains of electron donor and electron acceptor materials over a large field of view within the active layers. The quantitative phase contrast images further allow us to estimate the local volume fraction of PCBM across the photovoltaically active layers. The volume fraction gradient for different regions provides insight on the PCBM diffusion across the depletion zone surrounding PCBM aggregates. Phase contrast X-ray microscopy is under rapid development, and the results presented here are promising for future studies of organic-organic blends, also under in situ conditions, e.g., for monitoring the structural stability during UV-Vis irradiation.

Strong infrared photoluminescence in highly porous layers of large faceted Si crystalline nanoparticles

Almost all physical processes in solids are influenced by phonons, but their effect is frequently overlooked. In this paper, we investigate the photoluminescence of large silicon nanoparticles (approximately 100 nm size, synthesized by chemical vapor deposition) in the visible to the infrared detection range. We find that upon increasing laser irradiance, an enormous photoluminescence emission band appears in the infrared. Its intensity exhibits a superlinear power dependence, increasing over four orders of magnitude in the investigated pump power range. Particles of different sizes as well as different shapes in porous layers are investigated. The results are discussed taking into account the efficient generation of phonons under high-power pumping, and the reduced capability, porosity dependent, of the silicon nanoparticles to exchange energy with each other and with the substrate. Our findings are relevant for heat management strategies in silicon.

Wavefront metrology for coherent hard X-rays by scanning a microsphere

Characterization of the wavefront of an X-ray beam is of primary importance for all applications where coherence plays a major role. Imaging techniques based on numerically retrieving the phase from interference patterns are often relying on an a-priori assumption of the wavefront shape. In Coherent X-ray Diffraction Imaging (CXDI) a planar incoming wave field is often assumed for the inversion of the measured diffraction pattern, which allows retrieving the real space image via simple Fourier transformation. It is therefore important to know how reliable the plane wave approximation is to describe the real wavefront. Here, we demonstrate that the quantitative wavefront shape and flux distribution of an X-ray beam used for CXDI can be measured by using a micrometer size metal-coated polymer sphere serving in a similar way as the hole array in a Hartmann wavefront sensor. The method relies on monitoring the shape and center of the scattered intensity distribution in the far field using a 2D area detector while raster-scanning the microsphere with respect to the incoming beam. The reconstructed X-ray wavefront was found to have a well-defined central region of approximately 16 µm diameter and a weaker, asymmetric, intensity distribution extending 30 µm from the beam center. The phase front distortion was primarily spherical with an effective radius of 0.55 m which matches the distance to the last upstream beam-defining slit, and could be accurately represented by Zernike polynomials.