Demonstration of single-frame coherent X-ray diffraction imaging using triangular aperture: Towards dynamic nanoimaging of extended objects.

Platinum nanoparticles are among the most widely used catalysts due to their high chemical stability, surface reactivity and electron transfer rate. They find applications in chemical and bio-sensing, fuel cells, photocatalysis and methanol formation. Elucidating the catalytic mechanism under in-situ conditions is vital to the structural and chemical design of more efficient catalysts that are urgently needed to meet the energy needs of today. Coherent X-ray diffraction imaging (CDI) is a powerful technique for operando characterization with the ability to provide evolving snapshots of defect structure, lattice dynamics and structural evolution at ~10 nm resolution, while reactive molecular dynamics (MD) simulations provide atomistic details of lattice dynamics, bond breakage and formation as well as reaction kinetics at experimentally inaccessible length and time scales. We present results from combined CDI experiments and reactive MD simulations on the atomistic processes underlying methanol formation from methane on Pt nanoparticles. We observe the preferential oxidation of edge and corner sites on the Pt nanoparticle in an O2 rich atmosphere, which when followed by the introduction of methane, leads to the binding of CH4 to disassociated O atoms. Fig. 1 a) shows the partially oxidized Pt particle in a methane atmosphere. O2 on surface sites is not seen to disassociate while oxygen at corner and edge sites disassociates due to the higher site reactivity at edges and corners. Fig 1. b)-c) shows a close-up of the surface during the binding of CH4 to the disassociated oxygen. Finally, the mechanism predicted by the reactive MD simulations is validated through CDI experiments, with the observation of local lattice strains at edge and corner sites, which arise due to the binding of O2 and CH4 molecules. Figure 1

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.

In this work, a transmission-type, low-kilovolt coherent electron diffractive imaging instrument was constructed. It comprised a single-atom field emitter, a triple-element electrostatic lens, a sample holder, and a retractable delay line detector to record the diffraction patterns at different positions behind the sample. It was designed to image materials thinner than 3 nm. The authors analyzed the asymmetric triple-element electrostatic lens for focusing the electron beams and achieved a focused beam spot of 87 nm on the sample plane at the electron energy of 2 kV. High-angle coherent diffraction patterns of a suspended graphene sample corresponding to (0.62 Å)−1 were recorded. This work demonstrated the potential of coherent diffractive imaging of thin two-dimensional materials, biological molecules, and nano-objects at a voltage between 1 and 10 kV. The ultimate goal of this instrument is to achieve atomic resolution of these materials with high contrast and little radiation damage.

Microscopic imaging techniques have been developed to visualize events occurring in biological cells. Coherent X-ray diffraction imaging is one of the techniques applicable to structural analyses of cells and organelles, which have never been crystallized. In the experiment, a single noncrystalline particle is illuminated by an X-ray beam with almost complete spatial coherence. The structure of the particle projected along the direction of the beam is, in principle, retrieved from a finely recorded diffraction pattern alone by using iterative phase-retrieval algorithms. Here, we describe fundamental theory and experimental methods of coherent X-ray diffraction imaging and the recent application in structural studies of noncrystalline specimens by using X-rays available at Super Photon Ring of 8-Gev and SPring-8 Angstrom Compact Free Electron Laser in Japan.

For centuries, lens-based microscopy, such as optical, phase-contrast, fluorescence, confocal, and electron microscopy, has played an important role in the evolution of modern science and technology. In 1999, a novel form of microscopy, i.e., coherent diffraction imaging (also termed coherent diffraction microscopy or lensless imaging), was developed and transformed our conventional view of microscopy, in which the diffraction pattern of a noncrystalline specimen or a nanocrystal was first measured and then directly phased to obtain a high-resolution image. The well-known phase problem was solved by combining the oversampling method with iterative algorithms. In this paper, we will briefly discuss the principle of coherent diffraction imaging, present various implementation schemes of this imaging modality, and illustrate its broad applications in materials science, nanoscience, and biology. As coherent X-ray sources such as high harmonic generation and X-ray free-electron lasers are presently under rapid development worldwide, coherent diffraction imaging can potentially be applied to perform high-resolution imaging of materials/nanoscience and biological specimens at the femtosecond time scale.

Coherent diffraction imaging (CDI) is a high-resolution technique that does not require x-ray lenses. With advances in scientific technology, such as synchrotron radiation, x-ray free-electron lasers, and coherent electron sources, CDI has been applied to diverse fields, such as biology, medicine, and semiconductors, as a high-resolution, nondestructive measure. With the rapid increase in demand for these applications, enhancing the efficiency of processing high-volume data has become a significant challenge for promotion. In this study, we proposed an algorithm that combines Kramers–Kronig (KK) relations with oversampling smoothness (OSS). The results were evaluated by introducing an error coefficient. We found that the error of the KK-OSS algorithm is always reduced by approximately 50% compared with the error reduction (ER) algorithm, hybrid input–output (HIO) algorithm, and OSS in real space. In the diffraction space, the error in the KK-OSS can be decreased to 0.11. With 100 iterations, KK-OSS spent 218.3 s on reconstructing most of the sample information, while ER was 258.1 s, HIO algorithm took 296.7 s and the reconstruction was still a random value. In Fraunhofer diffraction, it cost KK-OSS 58.8 s to reconstruct, while OSS took 61.9 s. Therefore, this method can reduce the reconstruction error, shorten the reconstruction time, and improve the efficiency compared with the ER, HIO, and OSS algorithms using a random phase as the initial value.

The rapid growth of nanotechnology has increased the need for fast nanoscale imaging. X-ray free electron laser (XFEL) facilities currently provide such coherent sources of directional and high-brilliance X-ray radiation. These facilities require large financial investments for development, maintenance, and manpower, and thus, only a few exist worldwide. In this article, we present an automated table-top system for XUV coherent diffraction imaging supporting the capabilities for multispectral microscopy at high repetition rates, based on laser high harmonic generation from gases. This prototype system aims towards the development of an industrial table-top system of ultrafast soft X-ray multi-spectral microscopy imaging for nanostructured materials with enormous potential and a broad range of applications in current nanotechnologies. The coherent XUV radiation is generated in a semi-infinite gas cell via the high harmonic generation of the near-infrared femtosecond laser pulses. The XUV spectral selection is performed by specially designed multilayer XUV mirrors that do not affect the XUV phase front and pulse duration.

EUV lithography is promising for addressing upcoming, <10nm nodes for the semiconductor industry, but with this promise comes the need for reliable metrology techniques. In particular, there is a need for actinic mask inspection in which the imaging wavelength matches that of the intended lithography process, so that the most relevant defects are detected. Here, we demonstrate tabletop, ptychographic, coherent diffraction imaging (CDI) in reflection- and transmission-modes of extended samples, using a 13 nm high harmonic generation (HHG) source. We achieve the first sub-wavelength resolution EUV image (0.9λ) in transmission, the highest spatial resolution using any 13.5 nm source to date. We also present the first reflection-mode image obtained on a tabletop using 12.7 nm light. This work represents the first 12.7 nm reflection-mode image using any source of a general sample.

Coherent diffractive imaging (CDI) using EUV/X-rays has proven to be a powerful microscopy method for imaging nanoscale objects. In traditional CDI, the oversampling condition limits its applicability to small, isolated objects. A new technique called keyhole CDI was demonstrated on a synchrotron X-ray source to circumvent this limitation. Here we demonstrate the first keyhole CDI result with a tabletop extreme ultraviolet (EUV) source. The EUV source is based on high harmonic generation (HHG), and our modified form of keyhole CDI uses a highly reflective curved EUV mirror instead of a lossy Fresnel zone plate, offering a ~10x increase in photon throughput of the imaging system, and a more uniform illumination on the sample. In addition, we have demonstrated a record 22 nm resolution using our tabletop CDI setup, and also the successful extension to reflection mode for a periodic sample. Combining these results with keyhole CDI will open the path to the realization of a compact EUV microscope for imaging general non-isolated and non-periodic samples, in both transmission and reflection mode.

The quest for understanding the structural mechanisms of material properties and biological cell functions has led to the active development of coherent diffraction imaging (CDI) and its variants in the hard X-ray regime. Herein, we propose multiple-shot CDI, a full-field CDI technique dedicated to the visualisation of local nanostructural dynamics in extended objects at a spatio-temporal resolution beyond that of current instrumentation limitations. Multiple-shot CDI reconstructs a “movie” of local dynamics from time-evolving diffraction patterns, which is compatible with a robust scanning variant, ptychography. We developed projection illumination optics to produce a probe with a well-defined illumination area and a phase retrieval algorithm, establishing a spatio-temporal smoothness constraint for the reliable reconstruction of dynamic images. The numerical simulations and proof-of-concept experiment using synchrotron hard X-rays demonstrated the capability of visualising a dynamic nanostructured object at a frame rate of 10 Hz or higher.

Coherent diffraction imaging (CDI) is an advanced non-destructive 3D X-ray imaging technique for measuring a sample’s electron density. The main challenge of CDI is loss of phase information in diffraction intensity measurements, resulting in lengthy iterative reconstruction processes that can return non-unique solutions, which pose challenges for experiments attempting to track dynamic sample evolution through multiple states. As the increased brightness of fourth-generation light sources enables faster sample measurements and drives operando experiments with Bragg CDI, there is a growing need for faster reconstruction techniques that can keep pace. We have developed an adaptive generative autoencoder approach for uniquely tracking a sample’s electron density as it dynamically evolves. Our approach adaptively tunes the low-dimensional latent embedding of a generative autoencoder, enabling a computationally efficient manner to account for time-varying shifting distributions in real-time. Analytic proof of convergence is provided as well as numerical demonstration of sample tracking with noisy measurements.

Coherent diffraction imaging (CDI) and its scanning version, ptychography, are lensless imaging approaches used to iteratively retrieve a sample’s complex scattering amplitude from its measured diffraction patterns. These imaging methods are most useful in extreme ultraviolet (EUV) and X-ray regions of the electromagnetic spectrum, where efficient imaging optics are difficult to manufacture. CDI relies on high signal-to-noise ratio diffraction data to recover the phase, but increasing the flux can cause saturation effects on the detector. A conventional solution to this problem is to place a beam stop in front of the detector. The pixel masking method is a common solution to the problem of missing frequencies due to a beam stop. This paper describes the information redundancy in the recorded data set and expands on how the reconstruction algorithm can exploit this redundancy to estimate the missing frequencies. Thereafter, we modify the size of the beam stop in experimental and simulation data to assess the impact of the missing frequencies, investigate the extent to which the lost portion of the diffraction spectrum can be recovered, and quantify the effect of the beam stop on the image quality. The experimental findings and simulations conducted for EUV imaging demonstrate that when using a beam stop, the numerical aperture of the condenser is a crucial factor in the recovery of lost frequencies. Our thorough investigation of the reconstructed images provides information on the overall quality of reconstruction and highlights the vulnerable frequencies if the beam stop size is larger than the extent of the illumination NA. The outcome of this study can be applied to other sources of frequency loss, and it will contribute to the improvement of experiments and reconstruction algorithms in CDI.

The challenge of nanometric imaging drives intense efforts in applied sciences and fundamental research. Following the physical law of diffraction, the utilization of extreme ultraviolet (EUV) or X-ray radiation for imaging extends the ultimate resolution limit given by the illumination wavelength down to nanoscale dimensions. However, despite the great potential, the resolution is governed by imperfections inherent to optical elements employed. In this cumulative thesis, a table-top source of EUV radiation based on high harmonic generation (HHG), is developed and applied for lensless coherent diffractive imaging (CDI). Real-space images of microscopic objects are obtained solely on the basis of their far-field diffraction patterns, eliminating the need of any optical element and therefore any aberrations they may have. Benefiting from the exceptional coherence of the source developed, a diffraction-limited imaging is demonstrated with a spatial resolution of illuminating wavelength down to 30 nm. The microscopic images obtained via CDI allow for a detailed study of electric field distributions on the exit surface of the investigated structures. The experiments reveal that electric fields emerging from metallic structures are strongly affected by the polarization of the illuminating probe as well as propagation effects within the sample, indicating the limitations of the projection approximation. The above observations are attributed to waveguiding phenomena, thus, demonstrating extreme ultraviolet waveguiding in nanoscale slab structures. By direct imaging of the spatial distribution of the underlying electromagnetic modes exiting the sample, a strong polarization contrast of metallic waveguides with high aspect-ratio is experimentally identified. The guiding and polarization-sensitiveness are explored through an analytical approach based on the expansion in eigenmodes as well as numerical simulations to corroborate the experimental findings. Additionally, a novel approach to analyze and control the polarization state of EUV radiation by means of single image acquisition is developed. Such an analyzer, employing a set of nanoscale slab waveguides provides for an advanced characterization scheme for the polarization state of high harmonics. These results on CDI beyond the projection approximation using high harmonics demonstrate the potential of such a source for imaging, and pave the way towards applications in material science, for example, the spatial investigation of chiral phenomena, such as magnetism, enabling nanoscale magnetic imaging with a compact tabletop setup. Furthermore, HHG enables to date shortest possible pulse durations offering the opportunity to study ultrafast phenomena with unprecedented temporal resolution.

We have implemented a coherent x-ray diffraction imaging technique that scans a phase plate to modulate wave-fronts of the x-ray beam transmitted by samples. The method was applied to measure a decorative alkyd paint containing iron oxide red pigment particles. By employing an iterative algorithm for wave-front modulation phase retrieval, we obtained an image of the paint sample that shows the distribution of the pigment particles and is consistent with the result obtained from a transmission x-ray microscope. The technique has been experimentally proven to be a feasible coherent x-ray imaging method with about 120 nm spatial resolution and was shown to work well with industrially relevant specimens.

Coherent diffractive imaging using a coherent X-ray source promises to be a useful microscopic method for imaging noncrystalline objects at high spatial resolution. In this article a simple method to estimate the coherently scattered signal as a function of resolution is presented, and it is shown that the required X-ray flux or dose scales as the inverse third power of resolution for a specimen of constant volume and density. A simulated case study using the proposed energy-recovery linac source is also presented, which confirms the estimated flux requirement.