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

X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation ( i.e. the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Finally, two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.

36 MATERIALS SCIENCE↗

Defect identification in simulated Bragg coherent diffraction imaging by automated AI

X-ray Bragg coherent diffraction imaging is a powerful technique for operando and in situ materials characterization and provides a unique means of quantifying the influence of one-dimensional (1D) and two-dimensional (2D) material defects on material response. However, obtaining full images from raw x-ray diffraction data is nontrivial and computationally intensive, precluding real-time experimental feedback. Here, we present a machine learning approach to identify the presence of crystalline line defects (edge and screw) in samples from the raw, 2D, coherent diffraction data without the need for image reconstruction through iterative phase retrieval. Further, we compare different approaches to designing neural networks for this application and demonstrate the potential of automated ML (autoML) approaches.

36 MATERIALS SCIENCE↗

Coherent diffraction imaging in the undergraduate laboratory

We present an undergraduate optics instructional laboratory designed to teach skills relevant to a broad range of modern scientific and technical careers. In this laboratory project, students image a custom aperture using coherent diffraction imaging, while learning principles and skills related to digital image processing and computational imaging, including multidimensional Fourier analysis, iterative phase retrieval, noise reduction, finite dynamic range, and sampling considerations. After briefly reviewing these imaging principles, we describe the required experimental materials and setup for this project. Our experimental apparatus is both inexpensive and portable, and a software application we developed for interactive data analysis is freely available.

Porter, J. Nicholas↗

Removal of spurious data in Bragg coherent diffraction imaging: an algorithm for automated data preprocessing

Bragg coherent diffraction imaging (BCDI) provides a powerful tool for obtaining high-resolution structural information from nanocrystalline materials. Here a BCDI sample consisting of a large number of randomly oriented nanoscale crystals is considered. Ideally, only one crystal is oriented to produce a Bragg peak on the detector. However, diffraction from other crystals often produces additional signals on the detector. Before the measured diffraction patterns can be processed into structural images, scientists routinely need to manually identify and remove the `alien' intensities from sources other than the intended crystal. With the development of modern high-coherence storage rings, such as the upgraded Advanced Photon Source (APS), the already slow process of manual preprocessing will be untenable for the large volumes of data that will be produced. An automated method of identifying and deleting alien intensities is proposed. This method exploits the fact that BCDI of a perfect crystal produces diffraction data with inversion symmetry around the Bragg peak. This approach uses the machine learning clustering method DBSCAN to distinguish between diffraction from multiple sources, and then calculates cluster size and inversion symmetry to assess whether clusters of intensity belong to desired data or alien signals. This approach can dramatically reduce the amount of time spent manually processing data, allowing BCDI data processing capabilities to keep pace with the technological advances of fourth-generation synchrotron light sources.

36 MATERIALS SCIENCE↗

Multi-beam X-ray ptychography for high-throughput coherent diffraction imaging

X-ray ptychography is a rapidly developing coherent diffraction imaging technique that provides nanoscale resolution on extended field-of-view. However, the requirement of coherence and the scanning mechanism limit the throughput of ptychographic imaging. Herein, we propose X-ray ptychography using multiple illuminations instead of single illumination in conventional ptychography. Multiple locations of the sample are simultaneously imaged by spatially separated X-ray beams, therefore, the obtained field-of-view in one scan can be enlarged by a factor equal to the number of illuminations. We have demonstrated this technique experimentally using two X-ray beams focused by a house-made Fresnel zone plate array. Two areas of the object and corresponding double illuminations were successfully reconstructed from diffraction patterns acquired in one scan, with image quality similar with those obtained by conventional single-beam ptychography in sequence. Multi-beam ptychography approach increases the imaging speed, providing an efficient way for high-resolution imaging of large extended specimens.

47 OTHER INSTRUMENTATION↗

Enabling dynamic 3D coherent diffraction imaging via adaptive latent space tuning of generative autoencoders

Abstract 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.

97 MATHEMATICS AND COMPUTING↗

Detector Tilt Considerations in Bragg Coherent Diffraction Imaging: A Simulation Study

This paper addresses the three-dimensional signal distortion and image reconstruction issues in X-ray Bragg coherent diffraction imaging (BCDI) in the event of a general non-orthogonal orientation of the area detector with respect to the diffracted beam. Growing interest in novel BCDI adaptations at fourth-generation synchrotron light sources has necessitated improvisations in the experimental configuration and the subsequent data analysis. One such possibly unavoidable improvisation that is envisioned in this paper is a photon-counting area detector whose face is tilted away from the perpendicular to the Bragg-diffracted beam during the acquisition of the coherent diffraction signal. We describe a likely circumstance in which one would require such a detector configuration, along with the experimental precedent at third-generation synchrotrons. Using physically accurate diffraction simulations from synthetic scatterers in the presence of such tilted detectors, we analyze the general nature of the observed signal distortion qualitatively and quantitatively and provide a prescription to correct for it during image reconstruction. Our simulations and reconstructions are based on an adaptation of the known theory of BCDI sampling geometry, as well as the recently developed projection-based methods of wavefield propagation. Such configurational modifications and their numerical remedies are potentially valuable in realizing unconventional coherent diffraction measurement geometries, eventually paving the way for the integration of BCDI into new material characterization experiments at next-generation light sources.

36 MATERIALS SCIENCE↗

Combining Laue diffraction with Bragg coherent diffraction imaging at 34-ID-C

Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding a signal from a single nanoscale crystal object which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with ( hkl ) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus localizing in reciprocal space other Bragg reflections becomes time-consuming or requires good knowledge of the orientation of the crystal. Here, the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C endstation of the Advanced Photon Source is reported, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables, through rapid switching from monochromatic to broadband (pink) beam, the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction patterns near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. The design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

X‑ray Coherent Diffractive Imaging of Large Helium Nanodroplets Doped with Small Molecules

We report the first X-ray coherent diffractive imaging experiment on molecule-doped helium nanodroplets. It complements previous work, where we reported single-shot X-ray coherent diffractive imaging studies of Xe dopant clusters formed in 4He and 3He droplets. These noble gas clusters were used to visualize the impact of rotational excitation of the droplets on the spatial distribution of atomic dopants within the droplets, and to study the differences and connections between quantum and classical droplet rotational motion. Here, we expand our studies to the molecular dopants CF4, CHF3, CH3CN, and SF6, imaged with 1.5 keV photons. We find multiple Bragg spots in the diffraction patterns of molecule-doped droplets with radii of approximately 600 nm, which provide evidence that molecules form elongated clusters with preferential alignment along the angular momentum axis of the 4He droplets, in agreement with our previous results on the aggregation of Xe clusters on quantum vortices. Real-space reconstructions of molecular dopant cluster density profiles are obtained for droplets with smaller radii of approximately 300 nm. The diffuse images suggest the formation of low-density, potentially porous, molecular clusters upon aggregation at T = 0.4 K in 4He droplets. In the normal fluid 3He droplets, molecules aggregate into loose clusters on the droplets' equator, similar to previous observations for Xe atoms. Time-of-flight mass spectra reveal that the doped helium nanodroplet moieties fragment extensively into constituent atomic ions, producing only a small fraction of molecular fragment ions. The findings are discussed in the context of previously proposed schemes to use He droplets as potential tamper materials for ultrafast X-ray imaging experiments.

Feinberg, AlexandraJ↗

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. In this paper 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.

36 MATERIALS SCIENCE↗

Three-dimensional coherent Bragg imaging of spontaneously rotating nanoparticles

Series of coherent diffraction patterns were collected from crystalline gold nanoparticles as these rotated under the influence of a focused X-ray beam. The resulting movies show the (111) Bragg peaks crossing the Ewald sphere, and the frames can be assembled into three-dimensional diffraction volumes and phased.

60 nm truncated-octrahedral gold nanoparticles↗

3D Optical Coherence Tomography image processing in BISCAP: characterization of biofilm structure and properties

Abstract Motivation BISCAP is a state-of-the-art tool for automatically characterizing biofilm images obtained from Optical Coherence Tomography. Limited availability of other software tools is reported in the field. BISCAP’s first version processes 2D images only. Processing 3D images is a problem of greater scientific relevance since it deals with the entire structure of biofilms instead of their 2D slices. Results Building on the image-processing principles and algorithms proposed earlier for 2D images, these were adapted to the 3D case, and a more general implementation of BISCAP was developed. The primary goal concerns the extension of the initial methodology to incorporate the depth axis in 3D images; multiple improvements were also made to boost computational performance. The calculation of structural properties and visual outputs was extended to offer new insights into the 3D structure of biofilms. BISCAP was tested using 3D images of biofilms with different morphologies, consistently delivering accurate characterizations of 3D structures in a few minutes using standard laptop machines. Low user dependency is required for image analysis. Availability and implementation BISCAP is available from https://github.com/diogonarciso/BISCAP. All images used in the tutorials and the validation examples are available from https://web.fe.up.pt/∼fgm/biscap3d.

Narciso, Diogo A. C. (ORCID:0000000227767477)↗

A lightweight, user-configurable detector ASIC digital architecture with on-chip data compression for MHz X-ray coherent diffraction imaging

Today, most X-ray pixel detectors used at light sources transmit raw pixel data off the detector ASIC. With the availability of more advanced ASIC technology nodes for scientific application, more digital functionalities from the computing domains (e.g., compression) can be integrated directly into a detector ASIC to increase data velocity. In this paper, we describe a lightweight, user-configurable detector ASIC digital architecture with on-chip compression which can be implemented in 130 nm technologies in a reasonable area on the ASIC periphery. In addition, we present a design to efficiently handle the variable data from the stream of parallel compressors. The architecture includes user-selectable lossy and lossless compression blocks. The impact of lossy compression algorithms is evaluated on simulated and experimental X-ray ptychography datasets. This architecture is a practical approach to increase pixel detector frame rates towards the continuous 1 MHz regime for not only coherent imaging techniques such as ptychography, but also for other diffraction techniques at X-ray light sources.

47 OTHER INSTRUMENTATION↗

Adaptive 3D convolutional neural network-based reconstruction method for 3D coherent diffraction imaging

We present a novel adaptive machine-learning based approach for reconstructing three-dimensional (3D) crystals from coherent diffraction imaging. We represent the crystals using spherical harmonics (SH) and generate the corresponding synthetic diffraction patterns. We utilize 3D convolutional neural networks (CNNs) to learn a mapping between 3D diffraction volumes and the SH, which describe the boundary of the physical volumes from which they were generated. We use the 3D CNN-predicted SH coefficients as the initial guesses, which are then fine-tuned using adaptive model-independent feedback for improved accuracy. We also adaptively tune the locations, intensities, and decay rates of collections of radial basis functions in order to reproduce the non-uniform internal structure of 3D objects and demonstrate the method for a synthetic volume that has an internal void and a density ramp.

36 MATERIALS SCIENCE↗

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.

36 MATERIALS SCIENCE↗

NEURAL NETWORK FOR COHERENT DIFFRACTION IMAGE INVERSION

A deep neural network model plus automatic differentiation is developed for retrieving phase information from 3D coherent diffraction images. The model is implemented using Tensorflow and the training dataset is generated using physics-based atomistic simulations. Custom codes are written to handle the resampling of diffraction images to oversampling ratios appropriate for the neural network model.

CHAN, HENRY↗

Co-notch and independent windowing to mitigate interference in SAR-based imagery

Various technologies for mitigating distortion in coherent image products generated from SAR data are described herein. Synthetic aperture radar (SAR) datasets generated based upon SAR returns from first and second passes of a SAR platform over a scene are received. The SAR datasets can be co-notched at matching sample indices to improve coherence of SAR images generated from the datasets. Windowed SAR data is generated by applying independent windows to subsets of each of the datasets to reduce sidelobe levels of their image impulse responses. Coherent image products are generated based upon the windowed SAR data, wherein an image quality of the coherent image products is improved as compared to coherent image products generated based upon the SAR datasets.

47 OTHER INSTRUMENTATION↗