Coherent X-ray Diffraction Imaging Research Articles

Signal enhancement and Patterson-search phasing for high-spatial-resolution coherent X-ray diffraction imaging of biological objects.

In this decade coherent X-ray diffraction imaging has been demonstrated to reveal internal structures of whole biological cells and organelles. However, the spatial resolution is limited to several tens of nanometers due to the poor scattering power of biological samples. The challenge is to recover correct phase information from experimental diffraction patterns that have a low signal-to-noise ratio and unmeasurable lowest-resolution data. Here, we propose a method to extend spatial resolution by enhancing diffraction signals and by robust phasing. The weak diffraction signals from biological objects are enhanced by interference with strong waves from dispersed colloidal gold particles. The positions of the gold particles determined by Patterson analysis serve as the initial phase, and this dramatically improves reliability and convergence of image reconstruction by iterative phase retrieval. A set of calculations based on current experiments demonstrates that resolution is improved by a factor of two or more.

Visualizing and Improving the Robustness of Phase Retrieval Algorithms

Coherent x-ray diffractive imaging is a novel imaging technique that utilizes phase retrieval and nonlinear optimization methods to image matter at nanometer scales. We explore how the convergence properties of a popular phase retrieval algorithm, Fienup's HIO, behave by introducing a reduced dimensionality problem allowing us to visualize and quantify convergence to local minima and the globally optimal solution. We then introduce generalizations of HIO that improve upon the original algorithm's ability to converge to the globally optimal solution.

Cellular Diffraction: Scanning X-Ray Nanodiffraction from Living Cells

Cellular diffraction, or scanning x-ray nanodiffraction applied to cells, is a new technique that promises insight into cellular organization at length scales of 1–200 nm, covering the features of molecules and organelles. Filling a niche between the length scales probed by optical and electron microscopy, cellular diffraction rasters a nanofocused x-ray beam across living cells in an aqueous medium and records a two-dimensional image of, for instance, the small-angle scattering signal at each position. This results in a real-space image of the cell where the contrast is based on the average intensity of the small-angle x-ray scattering (SAXS) signal (dark-field image), or phase contrast, or other modalities such as the x-ray fluorescence intensity, with spatial resolution determined by the step-size of the raster scan ranging from submicron to a few microns. But the individual diffraction patterns can also be analyzed, providing higher-resolution limited by the signal/noise of the scattering pattern, currently ∼6 nm. With the cells bound to a solid support, the SAXS patterns do not result from isotropic averaging of the scatterers, and no staining or labeling is required for the technique. The development of cellular diffraction is spearheaded by two groups from the Institute for X-Ray Physics at the University of Gottingen, led by Sarah Koster and Tim Salditt, who exploit recent advances in x-ray detectors, x-ray optics, and microfluidics in order to apply scanning SAXS imaging (1) to hydrated, living cells and address subcellular dimensions. In a collaborative first effort at beamline ID13 of the European Synchrotron Radiation Facility, they imaged freeze-dried epithelial cells and saw distinctive scattering from the network of keratin fibers in the cell (2). More recent work using a specially developed instrument and beamline P10 of PETRA III imaged both fixed and live cells. The Koster team, together with collaborators from the European Synchrotron Radiation Facility, HASYLAB, and Ghent University, observed that the azimuthally averaged SAXS signal from the cells follows a power-law decay, with different exponents for living and fixed cells (3). Moreover, the scattering decays more rapidly after repeated exposure, so the value of the exponent serves as a diagnostic for beam damage in the sample. This issue of the Biophysical Journal contains a report from the Salditt team and collaborators from the Max Planck Institute for Dynamics and Self-Organization about their studies on living and fixed amoeboid cells (4), one which provides the best realization yet of the full potential of this exciting new technique. Chemotaxis in amoeboids is accomplished by extending pseudopods with controlled polymerization of actin fibers and the retraction of receding edges by depolymerization of actin and contraction of myosin motor proteins, but the details of the actin networks remain unknown. The molecular signature of this mechanism is revealed by cellular diffraction, which shows highly anisotropic scattering streaks resulting from oriented fiber bundles in the periphery of the cell. Using an automated algorithm to convert this anisotropy to a contrast neatly outlines the advancing edges of the cell. Further modeling of the scattering streaks is necessary to characterize quantitatively the nature of the fiber bundles that give rise to the SAXS signal, but the richness of the data should allow the extraction of meaningful parameters such as the number of fibers in the bundle, their spacing, and the density of cross-links. The authors note that their data and instrument are both complementary to and compatible with x-ray coherent diffraction imaging, so that with suitable modifications, users could first apply coherent diffraction imaging to image the whole cell and then scanning nanodiffraction to examine particular regions in greater detail. Indeed, the team has already demonstrated this approach by examining freeze-dried bacterial cells with both ptychography and cellular diffraction at the coherent SAXS beamline of the Swiss Light Source (5). With the synchrotron community preparing for fourth-generation facilities that approach the diffraction limit, which will greatly improve the coherence of the x-ray beam and the ability to focus the beam (6), cellular diffraction will surely grow in application and impact.

Resolution enhancement in coherent x-ray diffraction imaging by overcoming instrumental noise.

We report that reference objects, strong scatterers neighboring weak phase objects, enhance the phase retrieval and spatial resolution in coherent x-ray diffraction imaging (CDI). A CDI experiment with Au nano-particles exhibited that the reference objects amplified the signal-to-noise ratio in the diffraction intensity at large diffraction angles, which significantly enhanced the image resolution. The interference between the diffracted x-ray from reference objects and a specimen also improved the retrieval of the phase of the diffraction signal. The enhancement was applied to image NiO nano-particles and a mitochondrion and confirmed in a simulation with a bacteria phantom. We expect that the proposed method will be of great help in imaging weakly scattering soft matters using coherent x-ray sources including x-ray free electron lasers.

Dark-field phase retrieval under the constraint of the Friedel symmetry in coherent X-ray diffraction imaging.

Coherent X-ray diffraction imaging (CXDI) is a lensless imaging technique that is suitable for visualizing the structures of non-crystalline particles with micrometer to sub-micrometer dimensions from material science and biology. One of the difficulties inherent to CXDI structural analyses is the reconstruction of electron density maps of specimen particles from diffraction patterns because saturated detector pixels and a beam stopper result in missing data in small-angle regions. To overcome this difficulty, the dark-field phase-retrieval (DFPR) method has been proposed. The DFPR method reconstructs electron density maps from diffraction data, which are modified by multiplying Gaussian masks with an observed diffraction pattern in the high-angle regions. In this paper, we incorporated Friedel centrosymmetry for diffraction patterns into the DFPR method to provide a constraint for the phase-retrieval calculation. A set of model simulations demonstrated that this constraint dramatically improved the probability of reconstructing correct electron density maps from diffraction patterns that were missing data in the small-angle region. In addition, the DFPR method with the constraint was applied successfully to experimentally obtained diffraction patterns with significant quantities of missing data. We also discuss this method's limitations with respect to the level of Poisson noise in X-ray detection.

Curvature-induced and thermal strain in polyhedral gold nanocrystals

We use coherent x-ray diffractive imaging to map the local distribution of strain in gold (Au) polyhedral nanocrystals grown on a silicon (Si) substrate by a single-step thermal chemical vapor deposition process. The lattice strain at the surface of the octahedral nanocrystal agrees well with the predictions of the Young-Laplace equation quantitatively, but exhibits a discrepancy near the nanocrystal-substrate interface. We attribute this discrepancy to the dissimilar interfacial energies between Au/Air and Au/Si and to the difference in thermal expansion between the nanocrystal and the substrate during the cooling process.

Atomic diffusion within individual gold nanocrystal.

Due to their excess surface free energy and structural instabilities, nanoparticles exhibit interesting physical and chemical properties. There has been an ever-growing interest in investigating these properties, driven by the desire to further miniaturize electronic devices, develop new functional materials and catalysts. Here, the intriguing question of how diffusion evolves in a single nanoparticle is investigated by measuring the spatial and temporal variations of the diffracted coherent X-ray intensity during copper diffusion into a gold nanocrystal. Dislocation loops formed from the insertion of single layer of extra atoms between neighbouring gold host lattice planes are detected. Au-Cu alloy channels are found to penetrate the nanocrystal due to the differential diffusion rate along different directions. With the advent of higher brilliance sources and free-electron-lasers, Bragg Coherent X-ray Diffraction Imaging can play an important role in unveiling atomic behaviours in three dimensions for nanomaterials during various fundamental processes.

IDATEN and G-SITENNO: GUI-assisted software for coherent X-ray diffraction imaging experiments and data analyses at SACLA.

Using our custom-made diffraction apparatus KOTOBUKI-1 and two multiport CCD detectors, cryogenic coherent X-ray diffraction imaging experiments have been undertaken at the SPring-8 Angstrom Compact free electron LAser (SACLA) facility. To efficiently perform experiments and data processing, two software suites with user-friendly graphical user interfaces have been developed. The first is a program suite named IDATEN, which was developed to easily conduct four procedures during experiments: aligning KOTOBUKI-1, loading a flash-cooled sample into the cryogenic goniometer stage inside the vacuum chamber of KOTOBUKI-1, adjusting the sample position with respect to the X-ray beam using a pair of telescopes, and collecting diffraction data by raster scanning the sample with X-ray pulses. Named G-SITENNO, the other suite is an automated version of the original SITENNO suite, which was designed for processing diffraction data. These user-friendly software suites are now indispensable for collecting a large number of diffraction patterns and for processing the diffraction patterns immediately after collecting data within a limited beam time.

Intensity of Diffracted X-rays from Biomolecules with Radiation Damage Caused by Strong X-ray Pulses

In order to realize the coherent X-ray diffractive imaging of single biomolecules, the diffraction intensities, per effective pixel of a single biomolecule with radiation damage, caused by irradiation using a strong coherent X-ray pulse, were examined. A parameter survey was carried out for various experimental conditions, using a developed simulation program that considers the effect of electric field ionization, which was slightly reported on in previous studies. The two simple relationships among the parameters were identified as follows: (i) the diffraction intensity of a biomolecule slightly increases with the incident X-ray energy; and that (ii) the diffraction intensity is approximately proportional to the target radius, when the radius is longer than 400 A, since the upper limit of the incident intensity for damage to the biomolecules marginally changes with respect to the target radius.

Time-resolved coherent X-ray diffraction imaging of surface acoustic waves.

Time-resolved coherent X-ray diffraction experiments of standing surface acoustic waves, illuminated under grazing incidence by a nanofocused synchrotron beam, are reported. The data have been recorded in stroboscopic mode at controlled and varied phase between the acoustic frequency generator and the synchrotron bunch train. At each time delay (phase angle), the coherent far-field diffraction pattern in the small-angle regime is inverted by an iterative algorithm to yield the local instantaneous surface height profile along the optical axis. The results show that periodic nanoscale dynamics can be imaged at high temporal resolution in the range of 50 ps (pulse length).

Single particle nanomechanics in operando batteries via lensless strain mapping.

We reveal three-dimensional strain evolution in situ of a single LiNi0.5Mn1.5O4 nanoparticle in a coin cell battery under operando conditions during charge/discharge cycles with coherent X-ray diffractive imaging. We report direct observation of both stripe morphologies and coherency strain at the nanoscale. Our results suggest the critical size for stripe formation is 50 nm. Surprisingly, the single nanoparticle elastic energy landscape, which we map with femtojoule precision, depends on charge versus discharge, indicating hysteresis at the single particle level. This approach opens a powerful new avenue for studying battery nanomechanics, phase transformations, and capacity fade under operando conditions at the single particle level that will enable profound insight into the nanoscale mechanisms that govern electrochemical energy storage systems.

High-dynamic-range coherent diffractive imaging: ptychography using the mixed-mode pixel array detector.

Coherent (X-ray) diffractive imaging (CDI) is an increasingly popular form of X-ray microscopy, mainly due to its potential to produce high-resolution images and the lack of an objective lens between the sample and its corresponding imaging detector. One challenge, however, is that very high dynamic range diffraction data must be collected to produce both quantitative and high-resolution images. In this work, hard X-ray ptychographic coherent diffractive imaging has been performed at the P10 beamline of the PETRA III synchrotron to demonstrate the potential of a very wide dynamic range imaging X-ray detector (the Mixed-Mode Pixel Array Detector, or MM-PAD). The detector is capable of single photon detection, detecting fluxes exceeding 1 × 10(8) 8-keV photons pixel(-1) s(-1), and framing at 1 kHz. A ptychographic reconstruction was performed using a peak focal intensity on the order of 1 × 10(10) photons µm(-2) s(-1) within an area of approximately 325 nm × 603 nm. This was done without need of a beam stop and with a very modest attenuation, while `still' images of the empty beam far-field intensity were recorded without any attenuation. The treatment of the detector frames and CDI methodology for reconstruction of non-sensitive detector regions, partially also extending the active detector area, are described.

Cryogenic coherent X-ray diffraction imaging of biological particles at SACLA

Coherent X-ray diffraction imaging (CXDI) is a promising technique to visualize internal structures of whole biological cells without sectioning. Utilizing X-ray free-electron laser (XFEL) for CXDI has potential to collect huge number of projected electron densities of such samples at higher resolutions than that limited by radiation damage. For biological application of XFEL-CXDI, sample particles must be kept in a hydrated state to maintain their functional structures, but be placed in vacuum to obtain weak diffraction signals. In addition, we need to deliver fresh sample particles one after another for XFEL exposure because every particle explodes just after X-ray irradiation. To handle these problems, we have been developing a system to fulfill cryogenic XFEL-CXDI of frozen-hydrated specimens. For cryogenic XFEL-CXDI, we prepare frozen-hydrated specimens by plunge-freezing sample particles dispersed onto thin film with humidity-controlling [1]. The diffraction experiments are conducted by using the cryogenic X-ray diffractometer KOTOBUKI-1 [2]. In a vacuum chamber of KOTOBUKI-1, a cryogenic pot equipped on a goniometer is filled with liquid nitrogen, which cools the specimen via thermal contact. Thus, KOTOBUKI-1 allows data collection at a specimen temperature of ~66 K with a positional fluctuation of less than 0.4 μm. A small angle-resolution of better than 500 nm is attainable by using a pair of L-shaped Si-slits placed before the specimen, which eliminate almost all parasite scattering from upstream. Diffraction patterns recorded on two MPCCD detectors in tandem arrangement are automatically processed and phase-retrieved by program suite SITENNO [3]. In our recent experiments performed in Japanese XFEL facility SACLA, we were able to collect a large number of diffraction patterns from biological samples at a resolution of 50 - 30 nm at an XFEL hit-rate of 20 - 100%. We report details of the cryogenic XFEL-CXDI and introduce imaging of chloroplasts as an example.

Single-Shot X-Ray Coherent Diffractive Imaging of Superfluid He Nanodroplets

Single-shot coherent diffractive imaging (CDI) experiments were performed on pure and doped helium nanodroplets using femtosecond X-ray pulses from the Linac Coherent Light Source (LCLS). The superfluid nature of helium droplets presents a rare opportunity to study the onset of macroscopic quantum phenomena in finite, sub-micron scale systems. Despite the small X-ray scattering cross sections of atomic helium, high-quality single-shot CDI data were obtained that give direct access to sizes and shapes of individual nanodroplets. The diffraction patterns from helium droplets doped with xenon atoms differ starkly from the patterns from pure droplets. Strong indications for the formation of complex xenon structures inside the superfluid helium environment are observed, giving access to information about the structure and aggregation dynamics of the dopant species. The results are discussed with respect to the hydrodynamic properties of the superfluid droplets and compared to those of classical drops. An outlook on femtosecond time-resolved CDI experiments to study dynamics in pure and Xe-doped He nanodroplets will be given based on a new undulator-based X-ray pump/X-ray probe technique that is currently under development at LCLS.

Partially coherent x-ray diffractive imaging of complex objects

Lack of both spatial and temporal coherence at present x-ray light sources has hindered the application of coherent diffractive imaging techniques, as the computational algorithms which solve the phase problem to invert coherent speckle patterns have traditionally required fully coherent illumination. For this reason, new algorithms which incorporate knowledge of the illumination's coherence properties have been developed and shown to improve the reconstructed image of the scatterer in relatively simple test systems. In this paper we examine the performance of a reconstruction algorithm which incorporates knowledge of the spatial coherence of the illumination in the case of samples with complicated phase structure, and find that even perfect knowledge of the illumination's coherence does not improve the reconstructed image. We speculate that this failure to improve the reconstruction results from an underdetermination of the phase problem in the case of partially coherent illumination.

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.

A multiple-common-lines method to determine the orientation of snapshot diffraction patterns from single particles.

With the development of X-ray free-electron lasers (XFELs), it is possible to determine the three-dimensional structures of noncrystalline objects with coherent X-ray diffraction imaging. In this diffract-and-destroy mode, many snapshot diffraction patterns are obtained from the identical objects which are presented one by one in random orientations to the XFEL beam. Determination of the orientation of an individual object is essential for reconstruction of a three-dimensional structure. Here a new method, called the multiple-common-lines method, has been proposed to determine the orientations of high- and low-signal snapshot diffraction patterns. The mean errors of recovered orientations (α, β, γ) of high- and low-signal patterns are about 0.14, 0.06, 0.12 and 0.77, 0.31, 0.60°, respectively; both sets of errors can meet the requirements of the reconstruction of a three-dimensional structure.

In Operando Nanoscale Imaging for Lithium and Sodium Intercalation Compounds

Coherent x-ray diffractive imaging (CXDI), a lensless form of microscopy capable of discerning electron density and strain with 20 nm resolution, is used to map the strain evolution of a single cathode particle in a functional battery as it is cycled in-situ. The evolution of compressive/tensile strain reveals a number of interesting phenomena. For instance, a strain front nucleates and propagates inward/outward during discharge/charge. Strain can be quantitativley correlated to the Lithium amount in the initial cycles, eventually becoming uncorrelated upon longterm cycling. We demonstrate that CXDI is a powerful diagnostic tool to reveal correlation between strain and electrochemistry at the single particle level and offers valuable information for electrode/battery modeling and future battery design. Scanning electron microsocpy and electron energy loss spectroscopy (STEM/EELS) offers unprecendented spatial resolution, which has enabled nanoscale imaging and chemical anslysis of the interfaces, ground boundaries and phase boundaries. By combinign electron based and X-ray based novel imaging techniques, we showcase the state-of-the-art diagnostic tools developed for probling functional battery materials in operando.

High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions.

The smaller pixel size and high frame rate of next-generation photon counting pixel detectors opens new opportunities for the application of X-ray coherent diffractive imaging (CDI). In this manuscript we demonstrate fast image acquisition for ptychography using an Eiger detector. We achieve above 25,000 resolution elements per second, or an effective dwell time of 40 μs per resolution element, when imaging a 500 μm × 290 μm region of an integrated electronic circuit with 41 nm resolution. We further present the application of a scheme of sharing information between image parts that allows the field of view to exceed the range of the piezoelectric scanning system and requirements on the stability of the illumination to be relaxed.

Macromolecular structures probed by combining single-shot free-electron laser diffraction with synchrotron coherent X-ray imaging.

Nanostructures formed from biological macromolecular complexes utilizing the self-assembly properties of smaller building blocks such as DNA and RNA hold promise for many applications, including sensing and drug delivery. New tools are required for their structural characterization. Intense, femtosecond X-ray pulses from X-ray free-electron lasers enable single-shot imaging allowing for instantaneous views of nanostructures at ambient temperatures. When combined judiciously with synchrotron X-rays of a complimentary nature, suitable for observing steady-state features, it is possible to perform ab initio structural investigation. Here we demonstrate a successful combination of femtosecond X-ray single-shot diffraction with an X-ray free-electron laser and coherent diffraction imaging with synchrotron X-rays to provide an insight into the nanostructure formation of a biological macromolecular complex: RNA interference microsponges. This newly introduced multimodal analysis with coherent X-rays can be applied to unveil nano-scale structural motifs from functional nanomaterials or biological nanocomplexes, without requiring a priori knowledge.