Coherent Diffraction Imaging Research Articles

An adaptive noise-blind-separation algorithm for ptychography

Noise, one of the severe challenges in phase retrieval, may bring the algorithms to fall into local minima or even disrupt the convergence, thereby adversely affecting the imaging quality and convergence efficiency in the ptychography. Here, we propose an adaptive noise-blind-separation (aNBS) algorithm to deal with mixed noises of different types without sensitivity discrepancy in ptychography. In the aNBS algorithm, apart from the coherent probe of the illumination wavelength, virtual probes of different wavelengths are introduced to capture the noise energies, and the coupling mixed noises are adaptively blind-separated into the virtual noise probes in ptychography. The proposed algorithm can blindly separate coherent diffraction signals and noises without requiring additional regularization constraints, noise prior assumptions or dynamic iteration parameters. Simulations and experiments are comparatively conducted with the momentum-accelerated ptychographical iterative engine algorithm without dealing with noises and the least-square maximum-likelihood ptychographical iterative engine algorithm using a mixed Poisson-Gaussian likelihood model. Results indicate that the aNBS-based ptychography significantly enhances the convergence robustness when the noise intensity increases by more than two orders of magnitude. Compared with existing methods, the proposed aNBS algorithm demonstrates superior robustness and generality for the phase retrieval in coherent diffraction imaging and can be widely applied to various fields, such as ptychography, holography, and tomography.

Broadband coherent modulation imaging with no knowledge of the illumination spectrum distribution.

Coherent diffraction imaging (CDI) is an alternative way to achieve high-performance imaging without high-quality imaging lenses. Coherent modulation imaging (CMI) improves CDI's algorithmic convergence and applicability to general samples. A high degree of coherence of the source is essential for CDI, which limits its application to ultrafast pulsed sources with an intrinsically broad spectrum. Here, we propose an algorithm to increase the tolerance of CMI to low temporal coherence that tandemly employs the Wiener and Lucy deconvolution approaches. Simulations and visible light experiments demonstrate the effectiveness of our method. This work could pave the way for implementing CMI with attosecond pulsed lasers, laboratory x-ray sources, or electron microscopes.

Three-dimensional imaging using coherent x rays at grazing incidence geometry.

We have developed a three-dimensional coherent diffraction imaging algorithm to retrieve phases of diffraction patterns of samples in grazing incidence small angle x-ray scattering experiments. The algorithm interprets the diffraction patterns using the distorted-wave Born approximation instead of the Born approximation, as in this case, the existence of a reflected beam from the substrate causes the diffraction pattern to deviate significantly from the simple Fourier transform of the object. Detailed computer simulations show that the algorithm works. Verification with real experiments is planned.

Adaptive constraints by morphological operations for single-shot digital holography

Digital holography provides access to quantitative measurement of the entire complex field, which is indispensable for the investigation of wave-matter interactions. The emerging iterative phase retrieval approach enables to solve the inverse imaging problem only from the given intensity measurements and physical constraints. However, enforcing imprecise constraints limits the reconstruction accuracy and convergence speed. Here, we propose an advanced iterative phase retrieval framework for single-shot in-line digital holography that incorporates adaptive constraints, which achieves optimized convergence behavior, high-fidelity and twin-image-free reconstruction. In conjunction with morphological operations which can extract the object structure while eliminating the irrelevant part such as artifacts and noise, adaptive constraints allow the support region to be accurately estimated and automatically updated at each iteration. Numerical reconstruction of complex-valued objects and the capability of noise immunity are investigated. The improved reconstruction performance of this approach is experimentally validated. Such flexible and versatile framework has promising applications in biomedicine, X-ray coherent diffractive imaging and wavefront sensing.

Strain and crystallographic identification of the helically concaved gap surfaces of chiral nanoparticles

Identifying the three-dimensional (3D) crystal plane and strain-field distributions of nanocrystals is essential for optical, catalytic, and electronic applications. However, it remains a challenge to image concave surfaces of nanoparticles. Here, we develop a methodology for visualizing the 3D information of chiral gold nanoparticles ≈ 200 nm in size with concave gap structures by Bragg coherent X-ray diffraction imaging. The distribution of the high-Miller-index planes constituting the concave chiral gap is precisely determined. The highly strained region adjacent to the chiral gaps is resolved, which was correlated to the 432-symmetric morphology of the nanoparticles and its corresponding plasmonic properties are numerically predicted from the atomically defined structures. This approach can serve as a comprehensive characterization platform for visualizing the 3D crystallographic and strain distributions of nanoparticles with a few hundred nanometers, especially for applications where structural complexity and local heterogeneity are major determinants, as exemplified in plasmonics.

Taking Bragg Coherent Diffraction Imaging to Higher Energies at Fourth Generation Synchrotrons: Nanoscale Characterization

High-energy Bragg coherent diffraction imaging (BCDI) can enable three-dimensional imaging of atomic structure within individual crystallites in complex environments. Here, we show that sufficient coherent photon flux is available to extend the BCDI technique to higher energies to (1) obtain improved strain information and sensitivity at the nanoscale with higher order Bragg reflections, (2) exploit BCDI in embedded materials or complex operando environments, (3) reduce X-ray induced sample modification, and (4) minimize dynamical scattering effects. We demonstrate the nanoscale imaging technique on the same sub-micrometer sized crystal at 8.5, 19.9, and 33.4 keV by taking advantage of the brilliance and coherence of the fourth generation Extremely Brilliant Source of the ID01 beamline at ESRF - The European Synchrotron (Grenoble, France). The photon flux, data quality, resolution and strain information are compared. We also show the first coherent diffraction measurements performed at the ID31-EBS beamline at an energy of 41 keV.

Phase microscopy using band-limited image and its Fourier transform constraints.

In this Letter, we present a new, to the best of our knowledge, form of single-exposure quantitative phase microscopy based on the phase retrieval method by recording the band-limited image and its Fourier image simultaneously. Applying the intrinsic physical constraints of microscopy systems in the phase retrieval algorithm, we remove the inherent ambiguities of the reconstruction and achieve a rapid iterative convergence. In particular, this system does not require tight support of the object and the oversampling needed in coherent diffraction imaging. We have demonstrated that, in both simulations and experiments, the phase can be rapidly retrieved from a single-exposure measurement using our algorithm. The presented phase microscopy provides a promising technique for real-time quantitative biological imaging.

Bragg coherent diffraction imaging with the CITIUS charge-integrating detector.

The CITIUS detector is a next-generation high-speed X-ray imaging detector. It has integrating-type pixels and is designed to show a consistent linear response at a frame rate of 17.4 kHz, which results in a saturation count rate of over 30 Mcps pixel-1 when operating at an acquisition duty cycle close to 100%, and up to 20 times higher with special extended acquisition modes. Here, its application for Bragg coherent diffraction imaging is demonstrated by taking advantage of the fourth-generation Extremely Brilliant Source of the European Synchrotron (ESRF-EBS, Grenoble, France). The CITIUS detector outperformed a photon-counting detector, similar spatial resolution being achieved (20 ± 6 nm versus 22 ± 9 nm) with greatly reduced acquisition times (23 s versus 200 s). It is also shown how the CITIUS detector can be expected to perform during dynamic Bragg coherent diffraction imaging measurements. Finally, the current limitations of the CITIUS detector and further optimizations for coherent imaging techniques are discussed.

Mapping nanocrystal orientations via scanning Laue diffraction microscopy for multi-peak Bragg coherent diffraction imaging.

The recent commissioning of a movable monochromator at the 34-ID-C endstation of the Advanced Photon Source has vastly simplified the collection of Bragg coherent diffraction imaging (BCDI) data from multiple Bragg peaks of sub-micrometre scale samples. Laue patterns arising from the scattering of a polychromatic beam by arbitrarily oriented nanocrystals permit their crystal orientations to be computed, which are then used for locating and collecting several non-co-linear Bragg reflections. The volumetric six-component strain tensor is then constructed by combining the projected displacement fields that are imaged using each of the measured reflections via iterative phase retrieval algorithms. Complications arise when the sample is heterogeneous in composition and/or when multiple grains of a given lattice structure are simultaneously illuminated by the polychromatic beam. Here, a workflow is established for orienting and mapping nanocrystals on a substrate of a different material using scanning Laue diffraction microscopy. The capabilities of the developed algorithms and procedures with both synthetic and experimental data are demonstrated. The robustness is verified by comparing experimental texture maps obtained with Laue diffraction microscopy at the beamline with maps obtained from electron back-scattering diffraction measurements on the same patch of gold nanocrystals. Such tools provide reliable indexing for both isolated and densely distributed nanocrystals, which are challenging to image in three dimensions with other techniques.

Concurrent multi-peak Bragg coherent x-ray diffraction imaging of 3D nanocrystal lattice displacement via global optimization

In this paper we demonstrated a method to reconstruct vector-valued lattice distortion fields within nanoscale crystals by optimization of a forward model of multi-reflection Bragg coherent diffraction imaging (MR-BCDI) data. The method flexibly accounts for geometric factors that arise when making BCDI measurements, is amenable to efficient inversion with modern optimization toolkits, and allows for globally constraining a single image reconstruction to multiple Bragg peak measurements. This is enabled by a forward model that emulates the multiple Bragg peaks of a MR-BCDI experiment from a single estimate of the 3D crystal sample. We present this forward model, we implement it within the stochastic gradient descent optimization framework, and we demonstrate it with simulated and experimental data of nanocrystals with inhomogeneous internal lattice displacement. We find that utilizing a global optimization approach to MR-BCDI affords a reliable path to convergence of data which is otherwise challenging to reconstruct.

High-precision phase retrieval method for speckle suppression based on optimized modulation masks.

Traditional methods of coherent diffraction imaging using random masks result in an insufficient difference between the diffraction patterns, making it challenging to form a strong amplitude constraint, causing significant speckle noise in the measurement results. Hence, this study proposes an optimized mask design method combining random and Fresnel masks. Increasing the difference between diffraction intensity patterns enhances the amplitude constraint, suppresses the speckle noise effectively, and improves the phase recovery accuracy. The numerical distribution of the modulation masks is optimized by adjusting the combination ratio of the two mask modes. The simulation and physical experiments show that the reconstruction results of PSNR and SSIM using the proposed method are higher than those using random masks, and the speckle noises are effectively reduced.

Present status of micro-spectroscopy at BL37XU

X-ray micro-spectroscopy is a combination of X-ray absorption fine structure (XAFS) and various X-ray microscopy methods. This method is used in many scientific fields because it provides more sophisticated information, including valence information and local structure information obtained from XAFS, in addition to two-dimensional electron density or elemental distribution. This paper introduces the current status and recent developments of BL37XU, which provides micro-spectroscopy used as an analytical technique in a wide range of fields. Currently, scanning micro-spectroscopy using X-ray focusing optics and full-field micro-spectroscopy using a two-dimensional detector are the two main methods used. Here, we present recent developments of these two methods and the development of a micro-spectroscopy method using coherent diffraction imaging (CDI), which is seen to offer a higher resolution micro-spectroscopy in the next-generation synchrotron radiation.

Periodic Artifacts Generation and Suppression in X-ray Ptychography

As a unique coherent diffraction imaging method, X-ray ptychography has an ultrahigh resolution of several nanometers for extended samples. However, ptychography is often degraded by various noises that are mixed with diffracted signals on the detector. Some of the noises can transform into periodic artifacts (PAs) in reconstructed images, which is a basic problem in raster-scan ptychography. Herein, we propose a novel periodic-artifact suppressing algorithm (PASA) and present a new understanding of PAs or raster-grid pathology generation mechanisms, which include static intensity (SI) as an important cause of PAs. The PASA employs a gradient descent scheme to iteratively separate the SI pattern from original datasets and a probe support constraint applied in the object update. Both simulative and experimental data reconstructions demonstrated the effectiveness of the new algorithm in suppressing PAs and improving ptychography resolution and indicated a better performance of the PASA method in PA removal compared to other mainstream algorithms. In the meantime, we provided a complete description of SI conception and its key role in PA generation. The present work enhances the feasibility of raster-scan ptychography and could inspire new thoughts for dealing with various noises in ptychography.

Initial probe function construction in ptychography based on zone-plate optics.

X-ray ptychography is a popular variant of coherent diffraction imaging that offers ultrahigh resolution for extended samples. In x-ray ptychography instruments, the Fresnel zone-plate (FZP) is the most commonly used optical probe system for both soft x-ray and hard x-ray. In FZP-based ptychography with a highly curved defocus probe wavefront, the reconstructed image quality can be significantly impacted by the initial probe function form, necessitating the construction of a suitable initial probe for successful reconstruction. To investigate the effects of initial probe forms on FZP-based ptychography reconstruction, we constructed four single-mode initial probe models (IPMs) and three multi-mode IPMs in this study, and systematically compared their corresponding simulated and experimental reconstructions. The results show that the Fresnel IPM, spherical IPM, and Fresnel-based multi-mode IPMs can result in successful reconstructions for both near-focus and defocus cases, while random IPMs and constant IPMs work only for near-focus cases. Consequently, for FZP-based ptychography, the elaborately constructed IPMs that closely resemble real probes in wavefront phase form are more advantageous than natural IPMs such as the random or constant model. Furthermore, these IPMs with high phase similarity to the high-curvature large-sized probe adopted in experiments can help greatly improve ptychography experiment efficiency and decrease radiation damage to samples.

Near-field multi-slice ptychography: quantitative phase imaging of optically thick samples with visible light and X-rays.

Ptychography is a form of lens-free coherent diffractive imaging now used extensively in electron and synchrotron-based X-ray microscopy. In its near-field implementation, it offers a route to quantitative phase imaging at an accuracy and resolution competitive with holography, with the added advantages of extended field of view and blind deconvolution of the illumination beam profile from the sample image. In this paper we show how near-field ptychography can be combined with a multi-slice model, adding to this list of advantages the unique ability to recover high-resolution phase images of larger samples, whose thickness places them beyond the depth of field of alternative methods.

Operando Interaction and Transformation of Metastable Defects in Layered Oxides for Na‐Ion Batteries

AbstractNon‐equilibrium defects often dictate the macroscopic properties of materials. They largely define the reversibility and kinetics of processes in intercalation hosts in rechargeable batteries. Recently, imaging methods have demonstrated that transient dislocations briefly appear in intercalation hosts during ion diffusion. Despite new discoveries, the understanding of impact, formation and self‐healing mechanisms of transient defects, including and beyond dislocations, is lacking. Here, operando X‐ray Bragg Coherent Diffractive Imaging (BCDI) and diffraction peak analysis capture the stages of formation of a unique metastable domain boundary, defect self‐healing, and resolve the local impact of defects on ionic diffusion in NaxNi1−yMnyO2 intercalation hosts in a charging sodium‐ion battery. Results, applicable to a wide range of layered intercalation materials due to the shared nature of framework layers, elucidate new dynamics of transient defects and their connection to macroscopic properties, and suggest how to control the nanostructure dynamics.

Coherent diffractive imaging of proteins and viral capsids: simulating MS SPIDOC

MS SPIDOC is a novel sample delivery system designed for single (isolated) particle imaging at X-ray Free-Electron Lasers that is adaptable towards most large-scale facility beamlines. Biological samples can range from small proteins to MDa particles. Following nano-electrospray ionization, ionic samples can be m/z-filtered and structurally separated before being oriented at the interaction zone. Here, we present the simulation package developed alongside this prototype. The first part describes how the front-to-end ion trajectory simulations have been conducted. Highlighted is a quadrant lens; a simple but efficient device that steers the ion beam within the vicinity of the strong DC orientation field in the interaction zone to ensure spatial overlap with the X-rays. The second part focuses on protein orientation and discusses its potential with respect to diffractive imaging methods. Last, coherent diffractive imaging of prototypical T = 1 and T = 3 norovirus capsids is shown. We use realistic experimental parameters from the SPB/SFX instrument at the European XFEL to demonstrate that low-resolution diffractive imaging data (q < 0.3 nm−1) can be collected with only a few X-ray pulses. Such low-resolution data are sufficient to distinguish between both symmetries of the capsids, allowing to probe low abundant species in a beam if MS SPIDOC is used as sample delivery.

Phase retrieval via nonlocal complex-domain sparsity.

Phase retrieval is indispensable for a number of coherent imaging systems. Owing to limited exposure, it is a challenge for traditional phase retrieval algorithms to reconstruct fine details in the presence of noise. In this Letter, we report an iterative framework for noise-robust phase retrieval with high fidelity. In the framework, we investigate nonlocal structural sparsity in the complex domain by low-rank regularization, which effectively suppresses artifacts caused by measurement noise. The joint optimization of sparsity regularization and data fidelity with forward models enables satisfying detail recovery. To further improve computational efficiency, we develop an adaptive iteration strategy that automatically adjusts matching frequency. The effectiveness of the reported technique has been validated for coherent diffraction imaging and Fourier ptychography, with ≈7 dB higher peak SNR (PSNR) on average, compared with conventional alternating projection reconstruction.

Single-pulse characterization of the focal spot size of X-ray free-electron lasers using coherent diffraction imaging.

The characterization of X-ray focal spots is of great significance for the diagnosis and performance optimization of focusing systems. X-ray free-electron lasers (XFELs) are the latest generation of X-ray sources with ultrahigh brilliance, ultrashort pulse duration and nearly full transverse coherence. Because each XFEL pulse is unique and has an ultrahigh peak intensity, it is difficult to characterize its focal spot size individually with full power. Herein, a method for characterizing the spot size at the focus position is proposed based on coherent diffraction imaging. A numerical simulation was conducted to verify the feasibility of the proposed method. The focal spot size of the Coherent Scattering and Imaging endstation at the Shanghai Soft X-ray Free Electron Laser Facility was characterized using the method. The full width at half-maxima of the focal spot intensity and spot size in the horizontal and vertical directions were calculated to be 2.10 ± 0.24 µm and 2.00 ± 0.20 µm, respectively. An ablation imprint on the silicon frame was used to validate the results of the proposed method.

Multislice forward modeling of coherent surface scattering imaging on surface and interfacial structures.

To study nanostructures on substrates, surface-sensitive reflection-geometry scattering techniques such as grazing incident small angle X-ray scattering are commonly used to yield an averaged statistical structural information of the surface sample. Grazing incidence geometry can probe the absolute three-dimensional structural morphology of the sample if a highly coherent beam is used. Coherent surface scattering imaging (CSSI) is a powerful yet non-invasive technique similar to coherent X-ray diffractive imaging (CDI) but performed at small angles and grazing-incidence reflection geometry. A challenge with CSSI is that conventional CDI reconstruction techniques cannot be directly applied to CSSI because the Fourier-transform-based forward models cannot reproduce the dynamical scattering phenomenon near the critical angle of total external reflection of the substrate-supported samples. To overcome this challenge, we have developed a multislice forward model which can successfully simulate the dynamical or multi-beam scattering generated from surface structures and the underlying substrate. The forward model is also demonstrated to be able to reconstruct an elongated 3D pattern from a single shot scattering image in the CSSI geometry through fast-performing CUDA-assisted PyTorch optimization with automatic differentiation.