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Image segmentation of nanoscale Zernike phase contrast X-ray computed tomography images

Zernike phase contrast is a useful technique for nanoscale X-ray computed tomography (CT) imaging of materials with a low X-ray absorption coefficient. It enhances the image contrast by phase shifting X-ray waves to create changes in amplitude. However, it creates artifacts that hinder the use of traditional image segmentation techniques. We propose an image restoration method that models the X-ray phase contrast optics and the three-dimensional image reconstruction method. We generate artifact-free images through an optimization problem that inverts this model. Though similar approaches have been used for Zernike phase contrast in visible light microscopy, this optimization employs an effective edge detection method tailored to handle Zernike phase contrast artifacts. We characterize this optics-based restoration method by removing the artifacts in and thresholding multiple Zernike phase contrast X-ray CT images to produce segmented results that are consistent with the physical specimens. We quantitatively evaluate and compare our method to other segmentation techniques to demonstrate its high accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

X-ray Nanocomputed Tomography in Zernike Phase Contrast for Studying 3D Morphology of Li–O 2 Battery Electrode

In this work, we investigated the lithium peroxide (Li 2 O 2 ) and pore size distribution in lithium-O 2 battery electrodes at different states of charge using transmission X-ray microscopy coupled with Zernike phase contrast to carry out nano-Computed Tomography. We report that such technique enables, at the nanoscale, to distinguish light elements such as carbon and Li 2 O 2 in Li-O 2 battery cathode electrodes. We verified by wave-propagation simulation that this approach efficiently improves the contrast of images in comparison with the pure absorption. The Li 2 O 2 distribution and thickness, interphases, and pore network are visualized and quantified, which give a valuable insight into our cathode architecture. From this 3D analysis, we highlight modifications of the air-cathode morphology and the Li 2 O 2 spatial organization as well as their potential implication in terms of carbon surface passivation and pore-clogging. After the full recharge process, this technique can also reveal the spatial distribution of the residual Li 2 O 2 and other byproducts.

25 ENERGY STORAGE↗

Morphological and Electrochemical Characterization of Nanostructured Li 4 Ti 5 O 12 Electrodes Using Multiple Imaging Mode Synchrotron X-ray Computed Tomography

In this study, synchrotron X-ray computed tomography has been utilized using two different imaging modes, absorption and Zernike phase contrast, to reconstruct the real three-dimensional (3D) morphology of nanostructured Li 4 Ti 5 O 12 (LTO) electrodes. The morphology of the high atomic number active material has been obtained using the absorption contrast mode, whereas the percolated solid network composed of active material and carbon-doped polymer binder domain (CBD) has been obtained using the Zernike phase contrast mode. The 3D absorption contrast image revealed that some LTO nano-particles tend to agglomerate and form secondary micro-sized particles with varying degrees of sphericity. The tortuosity of electrode’s pore and solid phases were found to have directional dependence, different from Bruggeman’s tortuosity commonly used in macro-homogeneous models. The electrode’s heterogeneous structure was investigated by developing a numerical model to simulate galvanostatic discharge process using the Zernike phase contrast mode. The inclusion of CBD in the Zernike phase contrast results in an integrated percolated network of active material and CBD that is highly suited for continuum modeling. As a result, the simulation results highlight the importance of using the real 3D geometry since the spatial distribution of physical and electrochemical properties have a strong non-uniformity due to microstructural heterogeneities.

25 ENERGY STORAGE↗

A broader view on EUV-masks: adding complementary imaging modes to the SHARP microscope

The authors are expanding the capabilities of the SHARP microscope by implementing complementary imaging modes. SHARP (the SEMATECH High-NA Actinic Reticle review Project) is an actinic, synchrotron-based microscope dedicated to extreme ultraviolet (EUV) photomask research. SHARP’s programmable Fourier Synthesis Illuminator and its use of Fresnel zoneplate lenses as imaging optics provide a versatile framework, facilitating the implementation of diverse modes beyond conventional imaging. In addition to SHARP’s set of standard zoneplates, we have created more than 100 zoneplates for complementary imaging modes, all designed to extract additional information from photomasks, improve navigation and enhance defect detection. More than 50 new zoneplates are installed in the tool; the remaining lenses are currently in production. Here in this paper we discuss the design and fabrication of zoneplates for complementary imaging modes and present image data, obtained using Zernike Phase Contrast and different implementations of Differential Interference Contrast.

36 MATERIALS SCIENCE↗

Laboratory micro- and nanoscale X-ray tomographic investigation of Al–7 at.%Cu solidification structures

X-ray computed tomography across multiple length scales provides an opportunity to non-destructively visualize and quantify the micro- to nano-scale microstructural features of solidification structures in three dimensions. Aluminum–7 at.%copper samples were directionally solidified at three cooling rates (0.44, 0.67, and 1.33 °C/s), resulting in systematic changes in the as-solidified microstructure, which are difficult to quantify using traditional microscopic techniques. The cooling rate of a material affects its ultimate microstructure, and characterizing that microstructure is key to predicting and understanding its bulk properties. Here, two different laboratory X-ray computed tomography instruments were used to characterize as-solidified microstructures, including micro-scale computed tomography with approximately 1 mm field-of-view, ∼ 1.7 μm resolution, and nano-scale X-ray computed tomography ∼ 65 μm FOV, 150 nm resolution. Micro-scale X-ray radiography and computed tomography enabled a quantitative investigation of changes in the primary dendritic solidification structure with increasing cooling rate. Nano-scale absorption contrast X-ray computed tomography resolved the distinct phases of the lamellar eutectic structure and three dimensional measurements of the ∼ 1 μm interlamellar spacing. It is found that the lamella eutectic structure thickness is inversely proportional to the cooling rate. Nano-scale Zernike phase contrast was also used to image voids at eutectic colony boundaries. The application and resolution of these two instruments are discussed with respect to the resolvable features of the solidification structures. - Highlights: • Al–Cu eutectic is a model system for studying solidification microstructure. • X-ray computed tomography provides a 3D picture of these complex structures. • Micro-scale tomography images the primary and secondary dendritic structures. • Nano-scale tomography images the eutectic lamella and measures its thickness. • The ∼ 1 micrometer thickness of the eutectic lamella correlates to the cooling rate.

36 MATERIALS SCIENCE↗

Information transfer as a framework for optimized phase imaging

In order to efficiently image a non-absorbing sample (a phase object), dedicated phase contrast optics are required. Typically, these optics are designed with the assumption that the sample is weakly scattering, implying a linear relation between a sample’s phase and its transmission function. In the strongly scattering, nonlinear case, the standard optics are ineffective, and the transfer functions used to characterize them are uninformative. We use the Fisher information (FI) to assess the efficiency of various phase imaging schemes and to calculate an information transfer function (ITF). We show that a generalized version of Zernike phase contrast is efficient given sufficient prior knowledge of the sample. We show that with no prior knowledge, a random sensing measurement yields a significant fraction of the available information. Finally, we introduce a generalized approach to common path interferometry that can be optimized to prioritize sensitivity to particular sample features. Each of these measurements can be performed using Fourier lenses and phase masks.

Koppell, Stewart↗

Pollen structure visualization using high-resolution laboratory-based hard X-ray tomography

A laboratory-based X-ray microscope is used to investigate the 3D structure of unstained whole pollen grains. For the first time, high-resolution laboratory-based hard X-ray microscopy is applied to study pollen grains. Based on the efficient acquisition of statistically relevant information-rich images using Zernike phase contrast, both surface- and internal structures of pine pollen - including exine, intine and cellular structures - are clearly visualized. The specific volumes of these structures are calculated from the tomographic data. The systematic three-dimensional study of pollen grains provides morphological and structural information about taxonomic characters that are essential in palynology. Such studies have a direct impact on disciplines such as forestry, agriculture, horticulture, plant breeding and biodiversity. - Highlights: • The unstained whole pine pollen was visualized by high-resolution laboratory-based HXRM for the first time. • The comparison study of pollen grains by LM, SEM and high-resolution laboratory-based HXRM. • Phase contrast imaging provides significantly higher contrast of the raw images compared to absorption contrast imaging. • Surface and internal structure of the pine pollen including exine, intine and cellular structures are clearly visualized. • 3D volume data of unstained whole pollen grains are acquired and the specific volumes of the different layer are calculated.

60 APPLIED LIFE SCIENCES↗

Quantitative phase retrieval with arbitrary pupil and illumination

We present a general algorithm for combining measurements taken under various illumination and imaging conditions to quantitatively extract the amplitude and phase of an object wave. The algorithm uses the weak object transfer function, which incorporates arbitrary pupil functions and partially coherent illumination. The approach is extended beyond the weak object regime using an iterative algorithm. Finally, we demonstrate the method on measurements of Extreme Ultraviolet Lithography (EUV) multilayer mask defects taken in an EUV zone plate microscope with both a standard zone plate lens and a zone plate implementing Zernike phase contrast.

97 MATHEMATICS AND COMPUTING↗

The ABCs of phase retrieval: Connecting the acronyms of scanning transmission electron microscopy

High-resolution scanning transmission electron microscopy (S/TEM) is an indispensable tool for characterizing the structure and properties of materials down to the atomic scale. Conventional S/TEM imaging, however, is limited by the phase problem, whereby the phase of the electron exit wave is lost upon detection. Recent advances in diffractive imaging and 4D-STEM have enabled a range of phase-retrieval techniques that computationally reconstruct the missing information encoded in the phase of the transmission function. These approaches offer improved dose efficiency and enhanced sensitivity to weakly scattering signals, extending quantitative imaging to beam-sensitive materials composed of light elements. In this work, we introduce the phase problem in electron microscopy and survey the diverse landscape of phase-retrieval techniques used in the field. Despite their many acronyms and algorithmic variations, these techniques share a common physical and mathematical foundation. We present a unified framework that connects these seemingly distinct methods, from parallax imaging and tilt-corrected bright-field (tcBF-STEM), to aberration-corrected bright-field (acBF-STEM), optimum bright-field (OBF-STEM) and single-sideband (SSB) ptychography, as well as first-moment integrated center of mass techniques (iCOM) and iterative ptychographic algorithms. Based on these insights, we discuss the opportunities and practical limitations of applying these methods across different materials systems, detector designs, and microscope configurations.Graphical abstractRepresentative electron microscopy configurations used for phase retrieval and diffractive imaging in S/TEM: (a) Zernike phase-contrast transmission electron microscopy (TEM), (b) small-convergence-angle four-dimensional scanning transmission electron microscopy (4D-STEM) for nanobeam-based phase reconstruction methods, and (c) large-convergence-angle 4D-STEM for ptychographic and related diffractive imaging techniques reviewed in this work.

36 MATERIALS SCIENCE↗

A method for measuring the nonlinear refractive index from the contrast of an amplitude object image in the optical scheme with phase Zernike filters based on electronic Kerr nonlinearity

We propose a method for determining the nonlinear refractive index from the image contrast of amplitude objects in the phase-contrast scheme with a sample acting as a phase Zernike filter based on the electronic Kerr nonlinearity. This method implies the measurement of the calibration dependence of the contrast of an amplitude object image on the laser pulse energy for a test sample with a known nonlinearity and makes it possible to find the nonlinear refractive index of samples under study using a single laser pulse. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Reflective Phase-Contrast for High-Contrast Imaging of van der Waals Heterostructure

Optical microscopy plays a critical role in the fabrication of two-dimensional (2D) van der Waals heterostructures. An outstanding challenge in conventional microscopy is to visualize transparent 2D layers as well as embedded monolayers in a stacked heterostructure with high optical contrast. Phase-contrast microscopy, first developed by Frits Zernike in the 1930s, leverages the interference effect between specimen scattered light and background light to increase the contrast of transparent specimens. Such phase-contrast microscopy, always in a transmission configuration, revolutionized the study of transparent cellular structures in biology. Here, we develop a versatile reflective phase-contrast microscopy for imaging 2D heterostructures. We employ two spatial light modulators to flexibly control the intensity and phase of the illumination and the reflected light. This reflective phase-contrast microscopy achieves unprecedented high contrast for imaging a transparent 2D monolayer. In conclusion, it also enables direct observation of 2D monolayers embedded inside a thick heterostructure that are "invisible" in conventional microscopy.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Holographic Imaging of Evolving Laser-Plasma Structures

In the 1870s, English photographer Eadweard Muybridge captured motion pictures within one cycle of a horse’s gallop, which settled a hotly debated question of his time by showing that the horse became temporarily airborne. In the 1940s, Manhattan project photographer Berlin Brixner captured a nuclear blast at a million frames per second, and resolved a dispute about the explosion’s shape and speed. In this project, we developed methods to capture detailed motion pictures of evolving, light-velocity objects created by a laser pulse propagating through matter. These objects include electron density waves used to accelerate charged particles, laser-induced refractive index changes used for micromachining, and ionization tracks used for atmospheric chemical analysis, guide star creation and ranging. Our “movies”, like Muybridge’s and Brixner’s, are obtained in one shot, since the laser-created objects of interest are insufficiently repeatable for accurate stroboscopic imaging. Our high-speed photographs have begun to resolve controversies about how laser-created objects form and evolve, questions that previously could be addressed only by intensive computer simulations based on estimated initial conditions. Resolving such questions helps develop better tabletop particle accelerators, atmospheric ranging devices and many other applications of laser-matter interactions. Our photographic methods all begin by splitting one or more “probe” pulses from the laser pulse that creates the light-speed object. A probe illuminates the object and obtains information about its structure without altering it. We developed three single-shot visualization methods that differ in how the probes interact with the object of interest or are recorded. (1) Frequency-Domain Holography (FDH). In FDH, there are 2 probes, like “object” and “reference” beams in conventional holography. Our “object” probe surrounds the light-speed object, like a fleas swarming around a sprinting animal. The object modifies the probe, imprinting information about its structure. Meanwhile, our “reference” probe co-propagates ahead of the object, free of its influence. After the interaction, object and reference combine to record a hologram. For technical reasons, our recording device is a spectrometer (a frequency-measuring device), hence the name “frequency-domain” holography. We read the hologram electronically to obtain a “snapshot” of the object’s average structure as it transits the medium. Our published work shows numerous snapshots of electron density waves (“laser wakes”) in ionized gas (“plasma”), analogous to a water wake behind a boat. Such waves are the basis of tabletop particle accelerators, in which charged particles surf on the light-speed wave, gaining energy. Comparing our snapshots to computer simulations deepens understanding of laser wakes. FDH takes snapshots of objects that are quasi-static --- i.e. like Muybridge’s horse standing still on a treadmill. If the object changes shape, FDH images blur, as when a subject moves while a camera shutter is open. Many laser-generated objects of interest do evolve as they propagate. To overcome this limit of FDH, we developed .... (2) Frequency-Domain Tomography (FDT). In FDT, 5 to 10 probe pulses are fired simultaneously across the object’s path at different angles, like a crossfire of bullets. The object imprints a “streaked” record of its evolution on each probe, which we record as in FDH, then recover a multi-frame “movie” of the object’s evolving structure using algorithms of computerized tomography. When propagation distance exceeds a few millimeters, reconstructed FDT images distort. This is because the lenses that image probes to detector have limited depth of field, like cameras that cannot focus simultaneously on both nearby and distant objects. But some laser-generated objects of interest propagate over meters. For these applications we developed … (3) Multi-Object-Plane Phase-Contrast Imaging (MOP-PCI). In MOP-PCI, we image FDT-like probes to the detector from multiple “object planes” --- like recording an event simultaneously with several cameras, some focused on nearby, others on distant, objects. To increase sensitivity, we exploit a phase-contrast imaging technique developed by Dutch Nobel laureate Fritz Zernike in the 1930s. Using MOP-PCI we recorded single-shot movies of laser pulse tracks through more than 10 cm of air. We plan to record images of meter-long tracks of electron bunches propagating through plasma in an experiment at the Stanford Linear Accelerator Center (SLAC). This will help SLAC scientists understand, optimize and scale small plasma-based particle accelerators that have applications in medicine, industry, materials science and high-energy physics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Speciation and Organic Phase Structure in Nitric Acid Extraction with Trioctylamine

Understanding chemical speciation and intermolecular interactions in multicomponent liquids is essential to understanding their phase and chemical equilibria, which underpin chemical separation processes, including solvent extraction. Here we report on the extraction of nitric acid from its aqueous solutions into organic solutions of trioctylamine (TOA) in toluene, investigated with spectroscopic, X-ray scattering, and computational tools to understand molecular speciation in the organic phase and its relationship with the nanoscale structure of the organic phase. Trends in acid and water extraction clearly show two and three regimes, respectively, indicating different stoichiometric relationships, but speciation of HNO 3 , water, and amine in these regimes is not apparent. 1 H NMR of the organic phase shows that there are at least two distinct acidic protons in the organic phase while ATR-FTIR results show that the organic phase with excess acid extraction is a mixture of trioctylammonium-nitrate ion pairs (TOAHNO 3 ), and undissociated HNO 3 molecules. Comparison with DFT-computed IR spectra show that the chain-like configurations of TOAHNO 3 HNO 3 H 2 O are favored over TOAHNO 3 H 2 OHNO 3 , i.e., direct interaction between the nitrate and HNO 3 molecules is more favored compared to a water-mediated interaction. SAXS of the organic phases were modeled as sums of Ornstein-Zernike (O-Z) scattering and a prepeak feature in the higher Q region that corresponds to extractant packing. The extraction of undissociated HNO 3 by the ion pairs leads to an increased X-ray scattering contrast in the organic phase without any significant change in the correlation length. These results show that the organic phase nanostructure is more sensitive to the concentration of TOAHNO 3 and is relatively unaffected by excess acid extraction. Finally, these findings will enable a molecular understanding of the mechanisms behind metal extraction from acidic media with basic extractants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗