Coherent 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.

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.

The Scatman: an approximate method for fast wide-angle scattering simulations.

Single-shot coherent diffraction imaging (CDI) is a powerful approach to characterize the structure and dynamics of isolated nanoscale objects such as single viruses, aerosols, nanocrystals and droplets. Using X-ray wavelengths, the diffraction images in CDI experiments usually cover only small scattering angles of a few degrees. These small-angle patterns represent the magnitude of the Fourier transform of the 2D projection of the sample's electron density, which can be reconstructed efficiently but lacks any depth information. In cases where the diffracted signal can be measured up to scattering angles exceeding ∼10°, i.e. in the wide-angle regime, some 3D morphological information of the target is contained in a single-shot diffraction pattern. However, the extraction of the 3D structural information is no longer straightforward and defines the key challenge in wide-angle CDI. So far, the most convenient approach relies on iterative forward fitting of the scattering pattern using scattering simulations. Here the Scatman is presented, an approximate and fast numerical tool for the simulation and iterative fitting of wide-angle scattering images of isolated samples. Furthermore, the open-source software implementation of the Scatman algorithm, PyScatman, is published and described in detail. The Scatman approach, which has already been applied in previous work for forward-fitting-based shape retrieval, adopts the multi-slice Fourier transform method. The effects of optical properties are partially included, yielding quantitative results for small, isolated and weakly interacting samples. PyScatman is capable of computing wide-angle scattering patterns in a few milliseconds even on consumer-level computing hardware, potentially enabling new data analysis schemes for wide-angle coherent diffraction experiments.

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.

Quantitative analysis of the effect of radiation on mitochondria structure using coherent diffraction imaging with a clustering algorithm.

Radiation damage and a low signal-to-noise ratio are the primary factors that limit spatial resolution in coherent diffraction imaging (CDI) of biomaterials using X-ray sources. Introduced here is a clustering algorithm named ConvRe based on deep learning, and it is applied to obtain accurate and consistent image reconstruction from noisy diffraction patterns of weakly scattering biomaterials. To investigate the impact of X-ray radiation on soft biomaterials, CDI experiments were performed on mitochondria from human embryonic kidney cells using synchrotron radiation. Benefiting from the new algorithm, structural changes in the mitochondria induced by X-ray radiation damage were quantitatively characterized and analysed at the nanoscale with different radiation doses. This work also provides a promising approach for improving the imaging quality of biomaterials with XFEL-based plane-wave CDI.

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.

A wave optics model for the effect of partial coherence on coherent diffractive imaging

With the development of fourth-generation synchrotron sources, coherent diffractive imaging (CDI) will be a mainstream method for 3D structure determination at nanometre resolution. The partial coherence of incident X-rays plays a critical role in the reconstructed image quality. Here a wave optics model is proposed to analyze the effect of partial coherence on CDI for an actual beamline layout, based on the finite size of the source and the influence of the optics on the wavefront. Based on this model, the light field distribution at any plane, the coherence between any two points on this plane and CDI experiments can be simulated. The plane-wave CDI simulation result also shows that in order to reconstruct good image quality of complex samples the visibility of the interference fringes of any two points in the horizontal and vertical directions of the incident light field at the sample needs to be higher than 0.95.

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.

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

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

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.

Quantum coherent diffractive imaging

Coherent diffractive imaging (CDI) has enabled the structural analysis of individual free nanoparticles in a single shot and offers the tracking of their light induced dynamics with unprecedented spatial and temporal resolution. The retrieval of structural information from scattering images in CDI experiments is so far mostly based on the assumption of classical scattering in linear response. For strong laser fields and in particular for resonant excitations, both the linear and the classical description may no longer be valid as population depletion and stimulated emission become important. Here we develop a density matrix-based scattering model in order to include such quantum effects in the local medium response and explore the transition from linear to non-linear CDI for the resonant scattering from Helium nanodroplets. We find substantial departures from the linear response case already for experimentally reachable pulse parameters and show that non-linear spatio-temporal excitation dynamics results in rich features in the scattering, leading to the proposal of quantum coherent diffractive imaging as a promising novel branch in strong-field XUV and x-ray physics.

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.

Iterative phase retrieval in coherent diffractive imaging: practical issues.

In this work, issues in phase retrieval in the coherent diffractive imaging (CDI) technique, from discussion on parameters for setting up a CDI experiment to evaluation of the goodness of the final reconstruction, are discussed. The distribution of objects under study by CDI often cannot be cross-validated by another imaging technique. It is therefore important to make sure that the developed CDI procedure delivers an artifact-free object reconstruction. Critical issues that can lead to artifacts are presented and recipes on how to avoid them are provided.