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DOE OSTI2020

Recovery of a high-pressure phase formed under laser-driven compression

The recovery of metastable structures formed at high pressure has been a long-standing goal in the field of condensed matter physics. While laser-driven compression has been used as a method to generate novel structures at high pressure, to date no high-pressure phases have been quenched to ambient conditions. Here we demonstrate, using in situ x-ray diffraction and recovery methods, the successful quench of a high-pressure phase which was formed under laser-driven shock compression. We show that tailoring the pressure release path from a shock-compressed state to eliminate sample spall, and therefore excess heating, increases the recovery yield of the high-pressure ω phase of zirconium from 0% to 48%. Our results have important implications for the quenchability of novel phases of matter demonstrated to occur at extreme pressures using nanosecond laser-driven compression.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Temperature Mapping of Stacked Silicon Dies from X-Ray-Diffraction Intensities

Increasing power densities in integrated circuits have led to an increased prevalence of thermal hotspots in integrated circuits. Tracking these thermal hotspots is imperative to prevent circuit failures. In three- dimensional (3D) integrated circuits, conventional surface techniques like infrared thermometry are unable to measure the 3D temperature distribution, and optical and magnetic resonance techniques are difficult to apply due to the presence of metals and large current densities. X-rays offer a high penetration depth and can be used to probe 3D structures. We report a method utilizing the temperature dependence of x-ray-diffraction intensity via the Debye-Waller factor to simultaneously map the temperature of individual silicon dies in a stack. Here, utilizing beamline 1-ID-E at the Advanced Photon Source (Argonne), we demonstrate, for each individual silicon die, a temperature resolution of 3 K, a spatial resolution of 100 × 400 μm 2 , and a temporal resolution of 20 s. Utilizing a sufficiently high-intensity laboratory source, e.g., from a liquid-anode source, this method can be scaled down to laboratories for noninvasive temperature mapping of 3D integrated circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2020

Validation of Diffraction Models With Experimental Results From the Princeton Starshade Testbed

Starshades are a leading technology to detect and characterize Earth-like exoplanets. In this paper we report on optical experiments of sub-scale starshades that advance critical starlight suppression technologies in preparation for the next generation of space telescopes. These experiments were conducted at the Princeton starshade testbed, an 80 m long enclosure testing 1/1000th scale starshades at a ight-like Fresnel number. In this paper we summarize recent updates made to the starshade testbed and optical model. We present results from recent experiments testing two starshade masks with intentional perturbations built into their shape. One of the perturbed masks has three petals that are shifted radially outward by 7-11 microns and the other mask has two petals shifted radially outward plus two petal edge segments displaced from their nominal position. We show the model agrees with experiment to better than 25% accuracy. These results are placed into context with previous experiments on perturbed shapes and progress made towards satisfying a critical milestone in advancing starshade technology to TRL 5.

Galvin, Michael↗

NASA NTRS2000

Optical Performance Modeling of FUSE Telescope Mirror

We describe the Metrology Data Processor (METDAT), the Optical Surface Analysis Code (OSAC), and their application to the image evaluation of the Far Ultraviolet Spectroscopic Explorer (FUSE) mirrors. The FUSE instrument - designed and developed by the Johns Hopkins University and launched in June 1999 is an astrophysics satellite which provides high resolution spectra (lambda/Delta(lambda) = 20,000 - 25,000) in the wavelength region from 90.5 to 118.7 nm The FUSE instrument is comprised of four co-aligned, normal incidence, off-axis parabolic mirrors, four Rowland circle spectrograph channels with holographic gratings, and delay line microchannel plate detectors. The OSAC code provides a comprehensive analysis of optical system performance, including the effects of optical surface misalignments, low spatial frequency deformations described by discrete polynomial terms, mid- and high-spatial frequency deformations (surface roughness), and diffraction due to the finite size of the aperture. Both normal incidence (traditionally infrared, visible, and near ultraviolet mirror systems) and grazing incidence (x-ray mirror systems) systems can be analyzed. The code also properly accounts for reflectance losses on the mirror surfaces. Low frequency surface errors are described in OSAC by using Zernike polynomials for normal incidence mirrors and Legendre-Fourier polynomials for grazing incidence mirrors. The scatter analysis of the mirror is based on scalar scatter theory. The program accepts simple autocovariance (ACV) function models or power spectral density (PSD) models derived from mirror surface metrology data as input to the scatter calculation. The end product of the program is a user-defined pixel array containing the system Point Spread Function (PSF). The METDAT routine is used in conjunction with the OSAC program. This code reads in laboratory metrology data in a normalized format. The code then fits the data using Zernike polynomials for normal incidence systems or Legendre-Fourier polynomials for grazing incidence systems. It removes low order terms from the metrology data, calculates statistical ACV or PSD functions, and fits these data to OSAC models for the scatter analysis. In this paper we briefly describe the laboratory image testing of FUSE spare mirror performed in the near and vacuum ultraviolet at John Hopkins University and OSAC modeling of the test setup performed at NASA/GSFC. The test setup is a double-pass configuration consisting of a Hg discharge source, the FUSE off-axis parabolic mirror under test, an autocollimating flat mirror, and a tomographic imaging detector. Two additional, small fold flats are used in the optical train to accommodate the light source and the detector. The modeling is based on Zernike fitting and PSD analysis of surface metrology data measured by both the mirror vendor (Tinsley) and JHU. The results of our models agree well with the laboratory imaging data, thus validating our theoretical model. Finally, we predict the imaging performance of FUSE mirrors in their flight configuration at far-ultraviolet wavelengths.

Saha, Timo T.↗

DOE OSTI2025

Tunable Semiconducting Behavior and Linear-Nonlinear Optical Properties of Ag–Sn Dual-Doped Nanocrystalline CdO Thin Films for Optoelectronics

Semiconductor-based thin films have a great impact on determining the anticipated optoelectronic device construction and the advancement of cutting-edge applications. Herein, Ag and Sn dual-doped nanocrystalline transparent conducting CdO thin films were prepared on glass substrates using a cost-effective spray coating method, and their structural, morphological, optical, and semiconducting behaviors were investigated. The successful incorporation of Ag and Sn resulted in the polycrystalline nature of the deposited films without the additional peaks, as verified by X-ray diffraction (XRD) analysis. The XRD report also revealed the enhanced crystallinity (65%) at the higher doping level (3 wt % Ag and Sn-doped CdO film). All the deposited CdO films exhibited homogeneous, spherical, or round-shaped grains, with agglomeration revealed by scanning electron microscopy analysis. UV–visible spectroscopy was utilized to determine the linear and nonlinear optical properties of the deposited CdO thin films, and a reduction in the band gap from 3.891 to 3.772 eV was observed. A significant enhancement in the first- and third-order nonlinear susceptibility and nonlinear refractive index of the doped CdO films was also observed with increasing doping concentration. Hall effect data were collected at room temperature to investigate the electrical properties of all of the CdO films. The charge carrier concentration of CdO thin films was increased from 142.08 × 10 18 to 169.10 × 10 18 cm –3 , and the highest conductivity was found to be 192 s/cm on doping 3 wt % Ag–Sn. All the CdO thin films exhibited n-type conductivity, while an incredible n-type to p-type charge carrier transition was noticed at a higher doping level (3 wt % Ag–Sn). The findings of the current work are expected to advance the synthesis of semiconductor thin films through cost-effective spray coating methods for optoelectronic device applications.

deposition↗

NASA NTRS2017

Habitable Exoplanet Imager Optical Telescope Concept Design

The Habitable Exoplanet Imaging Mission (HabEx) is one of four missions under study for the 2020 Astrophysics Decadal Survey. Its goal is to directly image and spectroscopically characterize planetary systems in the habitable zone of Sun-like stars. Additionally, HabEx will perform a broad range of general astrophysics science enabled by 100 to 2500 nm spectral range and 3 x 3 arc-minute FOV. Critical to achieving the HabEx science goals is a large, ultra-stable UV/Optical/Near-IR (UVOIR) telescope. The baseline HabEx telescope is a 4-meter off-axis unobscured three-mirror-anastigmatic, diffraction limited at 400 nm with wavefront stability on the order of a few 10s of picometers. This paper summarizes the opto-mechanical design of the HabEx baseline optical telescope assembly, including a discussion of how science requirements drive the telescope's specifications, and presents analysis that the baseline telescope structure meets its specified tolerances.

mirror↗

DOE OSTI2026

New perspectives on materials and device dynamics using time-resolved full-field diffraction X-ray imaging

Understanding how materials evolve during synthesis, processing, or device operation requires experimental access to structural dynamics across wide ranges of length and time scales, often in bulk samples or even within packaged devices. Time-resolved full-field diffraction X-ray microscopy has recently emerged as a powerful way to meet this need by combining the penetration and structural sensitivity of X-ray diffraction with objective-lens-based magnification, sensitive high-resolution X-ray imaging detectors, and pump-probe and real-time imaging strategies. Advances in full-field X-ray diffraction microscopy, often termed dark-field X-ray microscopy (DFXM), enable simultaneous imaging of extended fields of view while retaining crystallographic selectivity. Time-resolved DFXM promises to enable advances in materials processing and dynamics, electrochemical and photochemical processes, and the design of electronic devices. This Perspective summarizes the key instrumental concepts that define the performance of these methods, including the choice of imaging optics, detector considerations, and the impact of source time structure at synchrotron light sources and X-ray free-electron lasers (XFELs). We discuss the simultaneous use of complementary imaging modes that are increasingly used in practice. The early demonstrations of the potential of time-resolved DFXM include real-time defect and grain-boundary dynamics during metal annealing, stroboscopic imaging of functional devices with high strain sensitivity, and ultrafast pump-probe implementations at XFELs that directly visualize acoustic-wave propagation and energy dissipation in bulk crystals.

Dark-field X-ray microscopy↗

DOE OSTI2022

Design and construction of a quantum matter synthesizer

The quantum matter synthesizer (QMS) is a new quantum simulation platform in which individual particles in a lattice can be resolved and re-arranged into arbitrary patterns. The ability to spatially manipulate ultracold atoms and control their tunneling and interactions at the single-particle level allows full control of a many-body quantum system. We present the design and characterization of the QMS, which integrates into a single ultra-stable apparatus a two-dimensional optical lattice, a moving optical tweezer array formed by a digital micromirror device, and site-resolved atomic imaging. We demonstrate excellent mechanical stability between the lattice and tweezer array with relative fluctuations below 10 nm, diffraction-limited imaging at a resolution of 655 nm, and high-speed real-time control of the tweezer array at a 2.52 kHz refresh rate, which will be adopted to realize fast rearrangement of atoms. The QMS also features new technologies and schemes, such as nanotextured anti-reflective windows and all-optical long-distance transport of atoms.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Intrinsic Elastic Anisotropy of Westerly Granite Observed by Ultrasound Measurements, Microstructural Investigations, and Neutron Diffraction

Westerly granite (WG) has been generally accepted as an isotropic homogeneous rock. Here, we return to WG and observe significant elastic anisotropy using multidirectional ultrasonic sounding on spherical samples at pressures up to 400 MPa. Thermal treatment of WG leads to formation of microcracks that reduce elastic wave velocities and increase its elastic anisotropy. The 3D distribution of P-wave velocities at low pressure is close to orthorhombic symmetry. Application of hydrostatic pressure closes most of thermally induced microcracks and decreases elastic anisotropy of WG, but at high pressure the anisotropy is practically reversed compared to low pressure: maximum P-wave velocity direction at low pressures is near minimum velocity direction at high pressure and vice versa. To understand this effect, microstructures of the rock were investigated by optical and scanning electron microscopy. Preferred orientations of four major rock-forming minerals—quartz, orthoclase, plagioclase, and biotite—were measured by time-of-flight neutron diffraction, which confirms significant crystal alignment. All these data were used to numerically model anisotropic elastic properties of WG. It is shown that WG possesses weak intrinsic elastic anisotropy related mainly to the preferred orientation of feldspars formed during igneous crystallization. Observed microcracks are mostly related to the cleavage planes of feldspars and biotite, and thus also demonstrate preferred orientation. Higher preheating temperatures produce larger quantity of longer microcracks. A numerical model shows that these microcracks act against the weak intrinsic elastic anisotropy of WG, and define the elastic anisotropy at low pressures.

58 GEOSCIENCES↗

NASA NTRS2019

WFIRST Grism Characterization

We had presented the optical design and early test result of WFIRST grism spectrometer in previous SPIE conferences. This paper reports the follow-on activity of the spectral and radiometric calibrations, including the calibration methods, experiment designs, and test equipment calibration, such as the light source and detectors used in the test. The real grism calibration includes the throughput versus wavelength, which is largely determined by the diffraction efficiency of the two diffractive surfaces. It also includes spectral resolution, point spread function, and encircle energy measurements. The measured data are presented. The comparisons between the test data and the simulation from theory or optical model are also presented.

Optics↗

DOE OSTI2020

Local atomic structure and Ni nanophase segregation in Zn 1-x Ni x S thin films

Here, the local atomic structure of Zn 1-x Ni x S thin films was investigated using X-ray absorption spectroscopy. The films were grown using RF-sputtering at atomic concentrations x = 0.00, x = 0.04, x = 0.08 and x = 0.14. X-ray diffraction shows that the lattice parameter contracts with increasing Ni concentration, consistent with the smaller atomic radii of Ni compared to that one of Zn. Optical absorption reveals a reduction of the bandgap as Ni concentration increases, except for sample x = 0.14 where a complex behavior is observed. Results from X-ray absorption near edge structure (XANES) spectroscopy indicate a shift in the valence state of Ni for the x = 0.14 sample. The analysis of the extended X-ray absorption fine structure (EXAFS) spectra indicate a contraction of ~0.7 Å in the Ni–S bond distance when compared to the Zn–S bond length, which generates local lattice distortions and an increment of the static disorder as the Ni concentration increases. The EXAFS results for sample x = 0.14 show the presence of a Zn 1-x Ni x S phase and a nanoscopic metallic Ni phase with domain sizes below the diffraction limit. These results reveal that the local atomic structure differs in a significant manner from the average crystalline structure, implying its importance for the determination of the electronic properties of this material.

36 MATERIALS SCIENCE↗

NASA NTRS2014

Upgrade of the NASA 4STAR (Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research) to its Full Science Capability of Sun-Sky-Cloud-Trace Gas Spectrometry in Airborne Science Deployments

The objectives of this task in the AITT (Airborne Instrument Technology Transition) Program are to (1) upgrade the NASA 4STAR (Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research) instrument to its full science capability of measuring (a) direct-beam sun transmission to derive aerosol optical depth spectra, (b) sky radiance vs scattering angle to retrieve aerosol absorption and type (via complex refractive index spectra, shape, and mode-resolved size distribution), (c) zenith radiance for cloud properties, and (d) hyperspectral signals for trace gas retrievals, and (2) demonstrate its suitability for deployment in challenging NASA airborne multiinstrument campaigns. 4STAR combines airborne sun tracking, sky scanning, and zenith pointing with diffraction spectroscopy to improve knowledge of atmospheric constituents and their links to air pollution, radiant energy budgets (hence climate), and remote measurements of Earth's surfaces. Direct beam hyperspectral measurement of optical depth improves retrievals of gas constituents and determination of aerosol properties. Sky scanning enhances retrievals of aerosol type and size distribution. 4STAR measurements are intended to tighten the closure between satellite and ground-based measurements. 4STAR incorporates a modular sun-tracking/sky-scanning optical head with fiber optic signal transmission to rack mounted spectrometers, permitting miniaturization of the external optical head, and future detector evolution. 4STAR test flights, as well as science flights in the 2012-13 TCAP (Two-Column Aerosol Project) and 2013 SEAC4RS (Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys) have demonstrated that the following are essential for 4STAR to achieve its full science potential: (1) Calibration stability for both direct-beam irradiance and sky radiance, (2) Improved light collection and usage, and (3) Improved flight operability and reliability. A particular challenge for the AITT-4STAR project has been conducting it simultaneously with preparations for, and execution of, ARISE (Arctic Radiation - IceBridge Sea&Ice Experiment), a NASA airborne science deployment (unplanned when AITT-4STAR was selected for funding) in which 4STAR will deploy to Thule, Greenland, and Fairbanks, Alaska, on the NASA C- 130. This presentation describes progress to date in accomplishing AITT-4STAR goals, and plans for project completion.

Sun-Sky-Cloud-Trace↗

DOE OSTI2024

Performance and properties evolution of near-term accident tolerant fuel: Cr-doped UO 2

Chromium-doped UO 2 fuel has received significant interest due to the ability for chromium to produce pellets with large average grain size (>30 μm), which has shown to increase fission gas retention during operation. Sintering of chromium-doped UO 2 pellets was pursued with oxygen potential and sintering atmosphere controlled to tailor the final microstructure of the material. Chromium additions in this study ranged from 750 to 7800 ppm. Cr concentrations were studied pre and post sintering using Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES). Effects of chromium content on lattice parameter and microstructure were examined with X-ray diffraction (XRD) and scanning electron microscopy (SEM). Contraction of the UO 2 lattice parameter was observed, as well as enlargement of grain size with increasing chromium content up to 4900 ppm Cr 2 O 3 . In addition, SEM indicated Cr incorporation within the matrix and the formation of chromium oxide precipitates throughout the microstructure at high Cr concentrations. Evaluation of thermophysical properties of Cr-doped UO 2 pellets were conducted up to 1200 °C to illustrate their evolution with increased dopant concentration and microstructural changes. The results show that grain size is maximized at 52 μm with Cr 2 O 3 concentration equal to 4900 ppm; however, grain size decreases at higher Cr 2 O 3 concentrations. No significant changes were observed in specific heat capacity, linear thermal expansion, and coefficient of thermal expansion compared to undoped UO 2 . The thermal conductivity also decreased through the incorporation of Cr 2 O 3 dopants above 750 ppm and is shown to be ~15 % lower than reported UO 2 values.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Synthesis of a series of rare-earth-based multi-anion chalcogenide iodides RE 3 Si 2 Se x S 8− x I (RE = La, Ce, Pr, and Nd) using the flux-assisted boron–chalcogen mixture method

Single crystals and polycrystalline powders of rare earth mixed chalcogenide iodides La 3 Si 2 Se 1.21 S 6.79 I, Ce 3 Si 2 Se 1.39 S 6.61 I, Pr 3 Si 2 Se 1.22 S 6.78 I, and Nd 3 Si 2 Se 1.18 S 6.82 I were prepared using the reactive flux-assisted boron–chalcogen mixture (BCM) method at 850 °C. All compounds crystallized in the monoclinic crystal system, space group C2/c (space group number 15). The series adopts the La 3 Si 2 O 8 Cl structure type, containing isolated SiQ 4 tetrahedra connected by REQ 8 (RE = La, Ce, Pr and Nd) polyhedra; this arrangement creates tunnels that are filled by I atoms. The partial substitution of S by Se was carried out to modulate the optical properties. Phase pure samples and uniform solid solutions were obtained for all compositions as determined using powder X-ray diffraction patterns. Polycrystalline powders were used for physical property measurements, including magnetic susceptibility and UV-Vis diffuse reflectance. The solid-state UV-Vis data for the polycrystalline La 3 Si 2 Se 1.21 S 6.79 I, Ce 3 Si 2 Se 1.39 S 6.61 I, and Pr 3 Si 2 Se 1.22 S 6.78 I samples revealed band gaps of E g = 2.5(1), 2.2(1), and 2.3(1) eV, typical of semiconductors. Magnetic measurements indicated that Ce 3 Si 2 Se 1.39 S 6.61 I and Nd 3 Si 2 Se 1.18 S 6.82 I exhibit paramagnetic behavior with slightly negative Weiss constants θ = −25 and −38. The photoluminescence spectrum of Ce 3 Si 2 Se 1.39 S 6.61 I exhibits a broad emission band around ∼493 nm.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

KS4A-Omics1.0_FspDS682

Soil fungi facilitate the translocation of inorganic nutrients from soil minerals to other microorganisms and plants. This ability is particularly advantageous in impoverished soils, because fungal mycelial networks can bridge otherwise spatially disconnected and inaccessible nutrient hotspots. However, the molecular mechanisms underlying fungal mineral weathering and transport through soil remains poorly understood. Here, we addressed this knowledge gap by directly visualizing nutrient acquisition and transport through fungal hyphae in a mineral doped soil micromodel using a multimodal imaging approach. Here, we observed how a representative of common saprotrophic soil fungi, Fusarium sp. DS 682, exhibited a mechanosensory response (thigmotropism) around obstacles and through pore spaces (~12 μm) in the presence of minerals.This study establishes the significance of fungal biology and nutrient translocation mechanisms in maintaining fungal growth under water and nutrient limitations in a soil-like microenvironment, using a high-throughput multi-omic analysis approach. Data package KS4A-Omics.1.0_FspDS682 (Publication: Fungal Mineral Weathering Mechanisms Revealed Through Direct Molecular Visualization) contents reported here are the first version (1.0) and contain pre- and post-processed data using high throughput data capture technologies for multi-omic analysis and integration, this data package contains raw and post-processed experimental data for X-Ray Absorption Near Edge Structure Spectroscopy (XANES/XRF), Optical Microscopy, Proteomics, Scanning Electron Microscope (SEM), Time-of-Flight Secondary Ion Mass Spectroscopy (ToF-SIMS), X-Ray Diffraction Spectroscopy (XRD) files, and X- Ray Photoelectron Spectroscopy (XPS) using EMSL capabilities. This data package DOI contains a comprehensive collection of high-throughput multi-omics data and process metadata catalog. Support files include additional data download contents “Read Me” with dataset descriptor information and data source method application ontologies (see data dictionary section). Reported data download content is structured for compliance with reported guidelines provided by community standard initiatives and publisher stakeholder policies supporting FAIR data principles.

47 OTHER INSTRUMENTATION↗

NASA NTRS1979

Radar cross section fundamentals for the aircraft designer

Various aspects of radar cross-section (RCS) techniques are summarized, with emphasis placed on fundamental electromagnetic phenomena, such as plane and spherical wave formulations, and the definition of RCS is given in the far-field sense. The basic relationship between electronic countermeasures and a signature level is discussed in terms of the detectability range of a target vehicle. Fundamental radar-signature analysis techniques, such as the physical-optics and geometrical-optics approximations, are presented along with examples in terms of aircraft components. Methods of analysis based on the geometrical theory of diffraction are considered and various wave-propagation phenomena are related to local vehicle geometry. Typical vehicle components are also discussed, together with their contribution to total vehicle RCS and their individual signature sensitivities.

Stadmore, H. A.↗

NASA NTRS1982

Tunable diode laser heterodyne spectrometer for remote observations near 8 microns

Infrared heterodyne spectroscopy is a passive technique employing coherent optical detection for the study of spectral features in remote sources. It employs optical components such as mirrors and lenses normally associated with incoherent optics, but because of it's coherent nature, it offers the advantages of ultrahigh spectral resolving power, high frequency precision, and diffraction limited field-of-view. Attention is given to the development of an ultrahigh resolution diode laser heterodyne spectrometer for observational and laboratory use. The instrument is designed for operation in the spectral range from 7.5 to 8.5 microns. A PbSe tuneable diode laser (TDL) is employed as local oscillator. A closed-cycle cooler is employed to keep the oscillator at operating temperatures in the range from 12 to 60 K. Attention is given to factors determining the TDL heterodyne sensitivity, the spectrometer design, and a survey of 8 micron observations, SiO could be detected in the sunspot spectrum.

Glenar, D. A.↗

NASA NTRS1987

Stellar occultation probes of the Uranian rings at 0.1 and 2.2 microns - A comparison of Voyager UVS and earth-based results

A comparison between Voyager 2 UV spectrometer data for stellar occultations of the Uranian ring system obtained at 0.11 microns and 2.2-micron earth-based occultation data reveals the anticipated factor-of-two reduction in observed optical depths relative to those observed from earth. This is due to Voyager's proximity to the rings, which allows light diffracted out of the direct beam by ring particles to be replaced by light diffracted into the direct beam light from other particles, and further permits the placing of firm lower limits on typical particle sizes of 0.3 and 1 cm for the epsilon and delta rings, respectively. As a function of true anomaly, the epsilon ring profile is noted to remain very similar in shape and essentially constant in equivalent depth, even very near periapse.

Holberg, J. B.↗