Diffraction Imaging Experiments Research Articles

Schwartz Symmetry Condition for Coherent Diffraction Imaging Patterns

We demonstrate a symmetry condition for the mixed partial derivatives of measured data when performing a coherent diffraction imaging (CDI) experiment for differentiable samples under scientific investigation. The proposed condition can be used as a physical restriction to improve real data measurements and has been used within the most celebrated phase-retrieval inversion algorithms as an ad hoc constraint without proof. The symmetry relies on John’s ultrahyperbolic equation for the X-ray transform, which is also demonstrated to be valid in the imaging regime for CDI. The obtained conditions are easy to implement and can be used as a constraint by computational imaging methods.

Enhancing electrospray ionization efficiency forparticle transmission through an aerodynamic lens stack.

This work investigates the performance of the electrospray aerosol generator at the European X-ray Free Electron Laser (EuXFEL). This generator is, together with an aerodynamic lens stack that transports the particles into the X-ray interaction vacuum chamber, the method of choice to deliver particles for single-particle coherent diffractive imaging (SPI) experiments at the EuXFEL. For these experiments to be successful, it is necessary to achieve high transmission of particles from solution into the vacuum interaction region. Particle transmission is highly dependent on efficient neutralization of the charged aerosol generated by the electrospray mechanism as well as the geometry in the vicinity of the Taylor cone. We report absolute particle transmission values for different neutralizers and geometries while keeping the conditions suitable for SPI experiments. Our findings reveal that a vacuum ultraviolet ionizer demonstrates a transmission efficiency approximately seven times greater than the soft X-ray ionizer used previously. Combined with an optimized orifice size on the counter electrode, we achieve >40% particle transmission from solution into the X-ray interaction region. These findings offer valuable insights for optimizing electrospray aerosol generator configurations and data rates for SPI experiments.

Flexible and universal autofocus based on amplitude difference of fractional Fourier transform

Autofocus technology is a crucial technique in computational optical imaging. The clarity evaluation function (CEF) serves as the criterion for autofocus, making it the core of the autofocus algorithm. In this paper, we propose a CEF based on amplitude differences of fractional Fourier transform (ADFrFT). ADFrFT extracts information from the fractional domain, which corresponds to the fusion of the spatial and frequency domains. This renders ADFrFT highly accurate and robust to noise, making it suitable for various types of sample images. Additionally, ADFrFT provides an added dimension of flexibility to address different autofocus requirements for distinct sample image types and focusing scenarios. Simulations and experiments confirmed the effectiveness of ADFrFT, and we improved the imaging resolution via distance calibration in the coaxial multi-distance coherent diffraction imaging (MDCDI) experiment.

New aerodynamic lens injector for single particle diffractive imaging

An aerodynamic lens injector was developed specifically for the needs of single-particle diffractive imaging experiments at free-electron lasers. Its design allows for quick changes of injector geometries and focusing properties in order to optimize injection for specific individual samples. Here, we present results of its first use at the FLASH free-electron-laser facility. Recorded diffraction patterns of polystyrene spheres are modeled using Mie scattering, which allowed for the characterization of the particle beam under diffractive-imaging conditions and yielded good agreement with particle-trajectory simulations.The complex refractive index of polystyrene at λ=4.5nm was determined as m=0.976−0.001i.

Coherent diffractive imaging of lipid vesicles and synaptic vesicles by femtosecond x-ray FEL pulses.

The structure of biological vesicles, in particular synaptic vesicles (SVs), as well as synthetic lipid model systems, in particular small unilamellar lipid vesicles (LVs) has been subject of abiding interest. Given the small size of both LVs and SVs (R≈20 nm), high spatial resolution is required to identify the distribution of lipids and protein constituents. Cryogenic electron microscopy studies of synaptic vesicles have revealed the outer and inner layer of proteins around the lipid bilayer. However, the samples have to be cryogenically fixed for this technique and throughput is limited. Another standard technique for structural characterization is solution small angle x-ray scattering (SAXS), which enables the measurement of vesicles in a quasi-physiological environment combined with a high spatial resolution. However, due to the average over an extremely large ensemble, SAXS yields information only about the average structure (size and electron density profile). The distribution function of structural parameters is not accessible, and many structural details are lost or screened by polydispersity, as well as by powder averaging. To overcome these limitations, we now have performed coherent diffractive imaging experiments on single vesicles using single femtosecond x-ray free electron laser (XFEL) pulses. For these measurements, single vesicles surrounded by a thin buffer layer are delivered into a nano-focused XFEL beam by an aerosol injector. By the ‘diffract-before-destroy’ principle, the individual vesicles can be probed without radiation damage. This approach leads to the measurement of thousands of diffraction patterns that can now be analyzed and reconstructed. The (preliminary) results of this analysis will be presented.

Theoretical and experimental study on responsivity of ultra-fast X-ray semiconductor chip based on the rad-optic effect

Semiconductor sensors based on the rad-optic effect enable ultra-fast detection of X-rays and play an important role in fusion diagnostics. Obtaining the responsivity of the semiconductor ultrafast response material is an important part of characterization. In this work, the refractive index change mechanism of the semiconductor under X-ray irradiation was analyzed, and the quantitative relationship between the diffraction efficiency and the X-ray photon energy was established through the LT-AlGaAs diffraction imaging experiments. The impulse responses of LT-AlGaAs under 1 keV–10 keV X-ray radiation were calculated, revealing the variation of responsivity with radiated photon energy. Imaging experiments of LT-AlGaAs were performed by bombarding an Al target to generate 1.5 keV X-rays. The diffraction images were obtained in agreement with the simulations. The responsivity of the semiconductor chip increases with the square of the incident X-ray power density. This study provides meaningful analyses for the development of ultra-fast X-ray imaging systems based on the rad-optic effect.

Simulation of Bragg coherent diffraction imaging

The arrangement of atoms within a crystal and information on deviations from the ideal lattice is encoded in the diffraction pattern obtained from an appropriately conducted Bragg coherent diffraction imaging (BCDI) experiment. A foreknowledge of how specific displacements of atoms within the unit cell alter the BCDI diffraction pattern and the subsequent real-space image is often useful for interpretation and can provide valuable insight for materials design. Here we report on an atomistic approach to efficiently simulate BCDI diffraction patterns by factorising and eliminating certain redundancies in the conventional approach. Our method is able to reduce the computation time by several orders of magnitude without compromising the recovered phase information and therefore enables feasible atomistic simulations on nanoscale crystals with arbitrary lattice distortions.

On Compton scattering as a source of background in coherent diffraction imaging experiments.

Compton scattering is generally neglected in diffraction experiments because the incoherent radiation it generates does not give rise to interference effects and therefore is negligible at Bragg peaks. However, as the scattering volume isreduced, the difference between the Rayleigh (coherent) and Compton (incoherent) contributions at Bragg peaks diminishes and the incoherent part may become substantial. The consequences can be significant for coherent diffraction imaging at high scattering angles: the incoherent radiation produces background that smears out the secondary interference fringes, affecting thus the achievable resolution of the technique. Here, a criterion that relates the object shape and the resolution is introduced. The Compton contribution for several object shapes is quantified, and it is shown that the maximum achievable resolution along different directions has a strong dependence on the crystal shape and size.

Deep neural networks in real-time coherent diffraction imaging.

The potential for convolutional neural networks to provide real-time imaging capabilities for coherent diffraction imaging experiments at XFELs is discussed.

Multi-wavelength phase retrieval for coherent diffractive imaging.

Phase retrieval is a numerical procedure concerned with the recovery of a complex-valued signal from measurements of its amplitude. We describe a generalization of this method for multi-wavelength data acquired in a coherent diffractive imaging experiment. It exploits the wavelength-dependent scaling of the support domain to recover separate reconstructions for each wavelength, providing new possibilities for coherent diffractive imaging experiments. Limitations on the number of wavelengths are discussed through adaptation of the constraint ratio, and the method's performance is investigated as a function of the source spectrum, sample geometry, and degree of complexity through numerical simulations.

Potential of Attosecond Coherent Diffractive Imaging.

Attosecond science has been transforming our understanding of electron dynamics in atoms, molecules, and solids. However, to date almost all of the attoscience experiments have been based on spectroscopic measurements because attosecond pulses have intrinsically very broad spectra due to the uncertainty principle and are incompatible with conventional imaging systems. Here we report an important advance towards achieving attosecond coherent diffractive imaging. Using simulated attosecond pulses, we simultaneously reconstruct the spectrum, 17 probes, and 17 spectral images of extended objects from a set of ptychographic diffraction patterns. We further confirm the principle and feasibility of this method by successfully performing a ptychographic coherent diffractive imaging experiment using a light-emitting diode with a broad spectrum. We believe this work clears the way to an unexplored domain of attosecond imaging science, which could have a far-reaching impact across different disciplines.

Nanoscale Mapping of Heterogeneous Strain and Defects in Individual Magnetic Nanocrystals

We map the three-dimensional strain heterogeneity within a single core-shell Ni nanoparticle using Bragg coherent diffractive imaging. We report the direct observation of both uniform displacements and strain within the crystalline core Ni region. We identify non-uniform displacements and dislocation morphologies across the core–shell interface, and within the outer shell at the nanoscale. By tracking individual dislocation lines in the outer shell region, and comparing the relative orientation between the Burgers vector and dislocation lines, we identify full and partial dislocations. The full dislocations are consistent with elasticity theory in the vicinity of a dislocation while the partial dislocations deviate from this theory. We utilize atomistic computations and Landau–Lifshitz–Gilbert simulation and density functional theory to confirm the equilibrium shape of the particle and the nature of the (111) displacement field obtained from Bragg coherent diffraction imaging (BCDI) experiments. This displacement field distribution within the core-region of the Ni nanoparticle provides a uniform distribution of magnetization in the core region. We observe that the absence of dislocations within the core-regions correlates with a uniform distribution of magnetization projections. Our findings suggest that the imaging of defects using BCDI could be of significant importance for giant magnetoresistance devices, like hard disk-drive read heads, where the presence of dislocations can affect magnetic domain wall pinning and coercivity.

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I

This two-part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real-space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this series provides the experimental BCDI community with the general form of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase-retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X-ray science community with a set of generalized BCDI shear-correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.

A Monte Carlo ray-tracing simulation of coherent X-ray diffractive imaging.

Coherent diffractive imaging (CDI) experiments are adequately simulated assuming the thin sample approximation and using a Fresnel or Fraunhofer wavefront propagator to obtain the diffraction pattern. Although this method is used in wave-based or hybrid X-ray simulators, here the applicability and effectiveness of an alternative approach that is based solely on ray tracing of Huygens wavelets are investigated. It is shown that diffraction fringes of a grating-like source are accurately predicted and that diffraction patterns of a ptychography dataset from an experiment with realistic parameters can be sampled well enough to be retrieved by a standard phase-retrieval algorithm. Potentials and limits of this approach are highlighted. It is suggested that it could be applied to study imperfect or non-standard CDI configurations lacking a satisfactory theoretical formulation. The considerable computational effort required by this method is justified by the great flexibility provided for easy simulation of a large-parameter space.

Domain Texture of the Orthorhombic Phase of La2\u2212xBaxCuO4

Bragg coherent diffraction imaging (BCDI) experiments have been carried out at the Advanced Photon Source using a new cryostat system developed to achieve high mechanical stability and low vibrations. We measured the (012)LTO Bragg peak which is unique to the low-temperature orthorhombic (LTO) phase of micron-sized crystals of the high-temperature superconductor La2−xBaxCuO4 (LBCO) to study the formation of structural domains. Each time the sample was cooled into the orthorhombic phase, the diffraction pattern of domains was different. This confirms the interpretation of pinning of the lower-temperature charge density Wave domains observed in coherent resonant X-ray speckle correlation analysis experiments.

All semiconductor enhanced high-harmonic generation from a single nanostructured cone

The enhancement and control of non-linear phenomena at a nanometer scale has a wide range of applications in science and in industry. Among these phenomena, high-harmonic generation in solids is a recent focus of research to realize next generation petahertz optoelectronic devices or compact all solid state EUV sources. Here, we report on the realization of the first nanoscale high harmonic source. The strong field regime is reached by confining the electric field from a few nanojoules femtosecond laser in a single 3D semiconductor waveguide. We reveal a strong competition between enhancement of coherent harmonics and incoherent fluorescence favored by excitonic processes. However, far from the band edge, clear enhancement of the harmonic emission is reported with a robust sustainability offering a compact nanosource for applications. We illustrate the potential of our harmonic nano-device by performing a coherent diffractive imaging experiment. Ultra-compact UV/X-ray nanoprobes are foreseen to have other applications such as petahertz electronics, nano-tomography or nano-medicine.

Supervised classification methods for flash X-ray single particle diffraction imaging.

Current Flash X-ray single-particle diffraction Imaging (FXI) experiments, which operate on modern X-ray Free Electron Lasers (XFELs), can record millions of interpretable diffraction patterns from individual biomolecules per day. Due to the practical limitations with the FXI technology, those patterns will to a varying degree include scatterings from contaminated samples. Also, the heterogeneity of the sample biomolecules is unavoidable and complicates data processing. Reducing the data volumes and selecting high-quality single-molecule patterns are therefore critical steps in the experimental setup. In this paper, we present two supervised template-based learning methods for classifying FXI patterns. Our Eigen-Image and Log-Likelihood classifier can find the best-matched template for a single-molecule pattern within a few milliseconds. It is also straightforward to parallelize them so as to match the XFEL repetition rate fully, thereby enabling processing at site. The methods perform in a stable way on various kinds of synthetic data. As a practical example we tested our methods on a real mimivirus dataset, obtaining a convincing classification accuracy of 0.9.

5D operando\xa0tomographic diffraction imaging of a catalyst bed

We report the results from the first 5D tomographic diffraction imaging experiment of a complex Ni–Pd/CeO2–ZrO2/Al2O3 catalyst used for methane reforming. This five-dimensional (three spatial, one scattering and one dimension to denote time/imposed state) approach enabled us to track the chemical evolution of many particles across the catalyst bed and relate these changes to the gas environment that the particles experience. Rietveld analysis of some 2 × 106 diffraction patterns allowed us to extract heterogeneities in the catalyst from the Å to the nm and to the μm scale (3D maps corresponding to unit cell lattice parameters, crystallite sizes and phase distribution maps respectively) under different chemical environments. We are able to capture the evolution of the Ni-containing species and gain a more complete insight into the multiple roles of the CeO2-ZrO2 promoters and the reasons behind the partial deactivation of the catalyst during partial oxidation of methane.

Diffraction apparatus and procedure in tomography X-ray diffraction imaging for biological cells at cryogenic temperature using synchrotron X-ray radiation.

X-ray diffraction imaging is a technique for visualizing the structure of biological cells. In X-ray diffraction imaging experiments using synchrotron radiation, cryogenic conditions are necessary in order to reduce radiation damage in the biological cells. Frozen-hydrated biological specimens kept at cryogenic temperatures are also free from drying and bubbling, which occurs in wet specimens under vacuum conditions. In a previous study, the diffraction apparatus KOTOBUKI-1 [Nakasako et al. (2013), Rev. Sci. Instrum. 84, 093705] was constructed for X-ray diffraction imaging at cryogenic temperatures by utilizing a cryogenic pot, which is a cooling device developed in low-temperature physics. In this study a new cryogenic pot, suitable for tomography experiments, has been developed. The pot can rotate a biological cell over an angular range of ±170° against the direction of the incident X-ray beam. Herein, the details and the performance of the pot and miscellaneous devices are reported, along with established experimental procedures including specimen preparation. The apparatus has been used in tomography experiments for visualizing the three-dimensional structure of a Cyanidioschyzon merolae cell with an approximate size of 5 µm at a resolution of 136 nm. Based on the experimental results, the necessary improvements for future experiments and the resolution limit achievable under experimental conditions within a maximum tolerable dose are discussed.

Necessary Experimental Conditions for Single-Shot Diffraction Imaging of DNA-Based Structures with X-ray Free-Electron Lasers.

It has been proposed that the radiation damage to biological particles and soft condensed matter can be overcome by ultrafast and ultraintense X-ray free-electron lasers (FELs) with short pulse durations. The successful demonstration of the "diffraction-before-destruction" concept has made single-shot diffraction imaging a promising tool to achieve high resolutions under the native states of samples. However, the resolution is still limited because of the low signal-to-noise ratio, especially for biological specimens such as cells, viruses, and macromolecular particles. Here, we present a demonstration single-shot diffraction imaging experiment of DNA-based structures at SPring-8 Angstrom Compact Free Electron Laser (SACLA), Japan. Through quantitative analysis of the reconstructed images, the scattering abilities of gold and DNA were demonstrated. Suggestions for extracting valid DNA signals from noisy diffraction patterns were also explained and outlined. To sketch out the necessary experimental conditions for the 3D imaging of DNA origami or DNA macromolecular particles, we carried out numerical simulations with practical detector noise and experimental geometry using the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory, USA. The simulated results demonstrate that it is possible to capture images of DNA-based structures at high resolutions with the technique development of current and next-generation X-ray FEL facilities.