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At least 55 records · Page 3

Bidirectional MeV/n ion intervals - Observations from the Goddard Space Flight Center instruments on the ISEE 3/ICE, IMP 8, Helios 1 and Helios 2 spacecraft

A search is made for intervals of bidirectional energetic ion streaming in approximately 1 MeV data from the instruments on ISEE 3/ICE, IMP 8 and Helios 1 and 2 during 1973 to 1989. The longest duration intervals are found around solar maximum, consistent with the expected association with coronal mass ejections. The ISEE 3/ICE intervals are associated with previously identified bidirectional 35-1000 keV ions and solar-wind electron heat fluxes, though additional bidirectional intervals are found.

Richardson, I. G.↗

A simple analytical function for bidirectional reflectance

A simple bidirectional reflectance model based on physical scattering laws is developed to calculate the bidirectional reflectance of a wide variety of surfaces. Chandrasekhar's radiative transfer solution, obtained for the anisotropically scattering semi-infinite medium, is used to compute the multiple-scattered radiances. However, since the radiative transfer solution does not take architectural effects into consideration, we adopt Hapke's (1986) approach and add an empirical term to explain the hot-spot phenomenon and use Cox and Munk's (1954) formulation to take into account the specular reflection. The physical parameters of the model are retrieved from bidirectional reflectance measurements. For each surface, only one set of model parameters is needed for application to all illumination and viewing geometries. The validity of the model is established by comparing the computed and measured reflectances for sets of viewing and illumination angles that were not included in the inversion algorithm. Good agreement is shown between the model-computed and the observed reflectances for dense prairie vegetation canopies, a sparse desert scrub community, a plowed agricultural field, and an alkali flat.

Ahmad, Suraiya P.↗

Automated measurement of polarized bidirectional reflectance

An Automated Bidirectional Reflection Acquisition Measurement System (ABRAMS) has been constructed to facilitate measurement of bidirectional reflectance from soil and vegetative samples in the laboratory. The system illuminates a sample with linearly-polarized laser light, lambda = 632.8 nm, and measures the like- and cross-polarized scattered intensities over half a hemisphere. System design and polarized bidirectional reflectance measurements from a soil sample and SiO2 spherical particles are discussed in this work. It is shown that polarization information in the plane of incidence is useful for identifying certain scattering mechanisms associated with soil reflectance. This is because the like-polarized intensity, Ivv, is influenced by single-scattered light and the cross-polarized intensity, IHv, is strongly influenced by multiple-scattered light. For example, comparable levels of Ivv and IHv indicated that the reflectance of soils, is dominated by significant multiple scattering because single scattering causes minimal depolarization in the plane of incidence.

Gibbs, Daniel P.↗

Spectral bidirectional and hemispherical reflectance characteristics of selected sites in the Streletskaya steppe

Measurements of plant canopy bidirectional reflectance made by the PARABOLA (portable apparatus for rapid acquisition of bidirectional observations of the land and atmosphere) instrument in three spectral bands are analyzed for steppe grassland sites of differing productivity levels. The variation of spectral reflectance and the normalized difference vegetation index in the solar principal plane is presented. Comparisons are made with PARABOLA measurements from selected first ISLSCP field experiment (FIFE) grassland sites in the Konza prairie, Kansas. The Streletskaya steppe sites showed no strong hot spot reflectance, while this effect was present in some FIFE sites but absent in others. The hot spot effect seems to be dependent on canopy geometry and background reflectance characteristics of these sites. Spectral hemispherical reflectance was computed from the angular integration of the bidirectional measurements for the steppe sites. Total shortwave albedo was estimated from these hemispherical reflectance measurements and compared to albedo measured by pyranometers. The albedo estimates from PARABOLA were found to be approximately 12-17 percent higher than the pyranometer measurements.

Eck, Thomas F.↗

Bidirectional Reflectance of Flat, Optically Thick Particulate Layers: An Efficient Radiative Transfer Solution and Applications to Snow and Soil Surfaces

We describe a simple and highly efficient and accurate radiative transfer technique for computing bidirectional reflectance of a macroscopically flat scattering layer composed of nonabsorbing or weakly absorbing, arbitrarily shaped, randomly oriented and randomly distributed particles. The layer is assumed to be homogeneous and optically semi-infinite, and the bidirectional reflection function (BRF) is found by a simple iterative solution of the Ambartsumian's nonlinear integral equation. As an exact Solution of the radiative transfer equation, the reflection function thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. Since this technique bypasses the computation of the internal radiation field, it is by far the fastest numerical approach available and can be used as an ideal input for Monte Carlo procedures calculating BRFs of scattering layers with macroscopically rough surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web at http://ww,,v.giss.nasa.gov/-crmim/brf.html and can be applied to a wide range of remote sensing, engineering, and biophysical problems. We also examine the potential effect of ice crystal shape on the bidirectional reflectance of flat snow surfaces and the applicability of the Henyey-Greenstein phase function and the 6-Eddington approximation in calculations for soil surfaces.

Mishchenko, Michael I.↗

Sensitivity of Cirrus Bidirectional Reflectance at MODIS Bands to Vertical Inhomogeneity of Ice Crystal Habits and Size Distribution

A common assumption in satellite imager-based cirrus retrieval algorithms is that the radiative properties of a cirrus cloud may be represented by those associated with a specific ice crystal shape (or habit) and a single particle size distribution. However, observations of cirrus clouds have shown that the shapes and sizes of ice crystals may vary substantially with height within the clouds. In this study we investigate the sensitivity of the top-of-atmosphere bidirectional reflectances at two MODIS bands centered at 0.65 micron and 2.11 micron to the cirrus models assumed to be either a single homogeneous layer or three distinct but contiguous, layers. First, we define the single- and three-layer cirrus cloud models with respect to ice crystal habit and size distribution on the basis of in situ replicator data acquired during the First ISCCP Regional Experiment (FIRE-II), held in Kansas during the fall of 1991. Subsequently, fundamental light scattering and radiative transfer theory is employed to determine the single scattering and the bulk radiative properties of the cirrus cloud. Regarding the radiative transfer computations, we present a discrete form of the adding/doubling principle by introducing a direct transmission function, which is computationally straightforward and efficient an improvement over previous methods. For the 0.65 micron band, at which absorption by ice is negligible, there is little difference between the bidirectional reflectances calculated for the one- and three-layer cirrus models, suggesting that the vertical inhomogeneity effect is relatively unimportant. At the 2.11 micron band, the bidirectional reflectances computed for both optically thin (tau = 1) and thick (tau = 10) cirrus clouds show significant differences between the results for the one- and three-layer models. The reflectances computed for the three-layer cirrus model are substantially larger than those computed for the single-layer cirrus. Finally, we find that cloud reflectance is very sensitive to the optical properties of the small crystals that predominate in the top layer of the three-layer cirrus model. It is critical to define the most realistic geometric shape for the small "quasi-spherical" ice crystals in the top layer for obtaining reliable single-scattering parameters and bulk radiative properties of cirrus.

Yang, P.↗

Firewall Traversal for CORBA Applications Using an Implementation of Bidirectional IIOP in MICO

The Object Management Group (OMG) has added specifications to the General Inter-ORB Protocol (GIOP 1.2), specifically the Internet Inter-ORB Protocol (IIOP 1.2), that allow servers and clients on opposing sides of a firewall to reverse roles and still communicate freely. This addition to the GIOP specifications is referred to as Bidirectional GIOP. The implementation of these specifications as applied to communication over TCP/IP connections is referred to as 'Bidirectional Internet Inter-ORB Protocol' or BiDirIIOP. This paper details the implementation and testing of the BiDirIIOP Specification in an open source ORB, MICO, that did not previously support Bidirectional GIOP. It also provides simple contextual information and a description of the OMG GIOP/IIOP messaging protocols.

Griffin, Robert I.↗

Analysis of Snow Bidirectional Reflectance from ARCTAS Spring-2008 Campaign

The spring 2008 Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) experiment was one of major intensive field campaigns of the International Polar Year aimed at detailed characterization of atmospheric physical and chemical processes in the Arctic region. A part of this campaign was a unique snow bidirectional reflectance experiment on the NASA P-3B aircraft conducted on 7 and 15 April by the Cloud Absorption Radiometer (CAR) jointly with airborne Ames Airborne Tracking Sunphotometer (AATS) and ground-based Aerosol Robotic Network (AERONET) sunphotometers. The CAR data were atmospherically corrected to derive snow bidirectional reflectance at high 1 degree angular resolution in view zenith and azimuthal angles along with surface albedo. The derived albedo was generally in good agreement with ground albedo measurements collected on 15 April. The CAR snow bidirectional reflectance factor (BRF) was used to study the accuracy of analytical Ross-Thick Li-Sparse (RTLS), Modified Rahman-Pinty-Verstraete (MRPV) and Asymptotic Analytical Radiative Transfer (AART) BRF models. Except for the glint region (azimuthal angles phi less than 40 degrees), the best fit MRPV and RTLS models fit snow BRF to within 0.05. The plane-parallel radiative transfer (PPRT) solution was also analyzed with the models of spheres, spheroids, randomly oriented fractal crystals, and with a synthetic phase function. The latter merged the model of spheroids for the forward scattering angles with the fractal model in the backscattering direction. The PPRT solution with synthetic phase function provided the best fit to measured BRF in the full range of angles. Regardless of the snow grain shape, the PPRT model significantly over-/underestimated snow BRF in the glint/backscattering regions, respectively, which agrees with other studies. To improve agreement with experiment, we introduced a model of macroscopic snow surface roughness by averaging the PPRT solution over the slope distribution function and by adding a simple model of shadows. With macroscopic roughness described by two parameters, the AART model achieved an accuracy of about plus or minus 0.05 with a possible bias of plus or minus 0.03 in the spectral range 0.4-2.2 micrometers. This high accuracy holds at view zenith angles below 55-60 degrees covering the practically important range for remote sensing applications, and includes both glint and backscattering directions.

Lyapustin, A.↗

Laser Pulse Bidirectional Reflectance from CALIPSO Mission

In this Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) study, we present a simple way of determining laser pulse bidirectional reflectance over snow/ice surface using the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) 532 nanometer polarization channels' measurements. The saturated laser pulse returns from snow and ice surfaces are recovered based on surface tail information. The method overview and initial assessment of the method performance will be presented. The retrieved snow surface bidirectional reflectance is compared with reflectance from both CALIOP cloud cover regions and Moderate Resolution Imaging Spectroradiometer (Earth Observing System (EOS)) (MODIS) Bi-directional Reflectance Distribution Function (BRDF) / Albedo model parameters. The comparisons show that the snow surface bidirectional reflectance over Antarctica for saturation region are generally reliable with a mean value of about 0.90 plus or minus 0.10, while the mean surface reflectance from cloud cover region is about 0.84 plus or minus 0.13 and the calculated MODIS reflectance at 555 nanometers from the BRDF / Albedo model with near nadir illumination and viewing angles is about 0.96 plus or minus 0.04. The comparisons here demonstrate that the snow surface reflectance underneath the cloud with cloud optical depth of about 1 is significantly lower than that for a clear sky condition.

Lu, Xiaomei↗

Optimized AC/DC Dual Active Bridge Converter using Monolithic SiC Bidirectional FET (BiDFET) for Solar PV Applications

Grid interface power conversion systems for commercial, industrial and residential solar power generation are becoming ubiquitous due to the competitive cost of solar energy. The AC/DC dual active bridge (DAB) converter is an upcoming topology in industrial PV energy and energy storage applications, providing bidirectional power transfer and galvanic isolation. In this paper, the properties of a DAB-type converter are leveraged to propose a design optimization process. It can optimize the high-frequency RMS current, size of magnetic elements and zero-voltage-switching (ZVS) region of the converter. The resulting design is compared against that derived from a conventional approach. In addition, an algorithm to compute the harmonic currents at the DC and line frequency AC ports of the system is proposed, and the respective filter designs are presented. The optimized design of the AC/DC DAB converter is implemented using the newly developed, 1200 V, 46 mΩ, four quadrant, SiC-based monolithic bidirectional FETs (BiDFET). Experimental results from the 2.3 kW, 400V/277VRMS hardware prototype are finally presented to verify the design process.

Bidirectional isolated AC-DC conversion, solar ene↗

Bidirectional LCC-LCC -Compensated 20 kW Wireless Power Transfer System for Medium-Duty Vehicle Charging

This paper presents the design and demonstration of a bidirectional 20 kW wireless charging system (WCS) with a significantly large airgap (11 inches) and asymmetrical input-output voltage levels. Analytical and experimental sensitivity analyses of the WCS resonant tank were conducted to verify the optimal operating region under the load and frequency variation. The inverter and rectifier were designed with switching components, the charging pads were designed with double-D (DD) coils, and the tuning networks were designed with an LCC-LCC tuning circuit. The grid and vehicle side tuning circuits were designed separately to achieve a ~1:2 gain for the asymmetrical input (800 V dc ) and output (350 V dc ) voltage. The proposed WCS was designed, simulated, and tested to verify the efficiency, power transfer capacity, and sensitivity under load variation. The experimental results show that, at 20-kW output power, the achieved grid to vehicle dc-dc efficiency was 96.1%, and vehicle to grid dc-dc efficiency was 96.2%. The proposed system is the largest-airgap bidirectional WCS with the highest efficiency and power density.

33 ADVANCED PROPULSION SYSTEMS↗

Technology Strategy Assessment: Findings from Storage Innovations 2030 Bidirectional Hydrogen Storage

Hydrogen is the most common element in the universe, comprising nearly 75% of all normal matter, and it has been used by scientists for centuries, but it was not fully recognized as an element until 1766, when it was isolated by Henry Cavendish. Early work focused on the generation of hydrogen through the oxidation of metals in water, which released hydrogen gas. Hydrogen’s lighter-than-air and flammable properties were immediately used in engines, zeppelins, and as feedstock for a wide variety of chemical reactions. Several approaches were developed for the production of hydrogen with the most common being associated with the production and conversion of hydrocarbon-based fuels. Coal gasification, steam methane reforming, and other reformation processes provide the majority of current hydrogen production due to the relatively low cost of hydrogen produced through these processes. More than 95% of hydrogen production is used for industrial processes rather than energy storage. To facilitate affordable decarbonization of these industrial processes and to advance the use of hydrogen as a fuel in transportation, DOE launched the Hydrogen Shot as part of the Energy Earthshots Initiative. The goal of the Hydrogen Shot is to reduce the cost of clean hydrogen by 80% to $1/kg of clean hydrogen production within one decade (known as the “1 1 1” goal). This is distinct from the Long-Duration Storage Shot, which is the primary focus of this report; however, it is intrinsically linked to bidirectional hydrogen storage. Several important chemical synthesis processes are dependent upon hydrogen, and the production and use of hydrogen is generally driven by its connection to one of these markets. For example, ammonia is one of the most highly produced chemicals in the world and it depends chiefly on hydrogen. Ammonia is primarily used for agricultural fertilizer and is considered to be largely responsible for a doubling of agricultural production per unit of land over the last century. Another one of hydrogen’s primary uses is as a catalyst in petroleum refining during the desulfurization process. Beyond chemical production, hydrogen is used as a reductant in the production of steel and has been demonstrated as a substitute for metallurgical coal in the production of raw iron. It is even used in the hydrogenation reaction for food products to create more shelf-stable semi-solid fats. However, while hydrogen is produced on the order of 100 million metric tons/year globally to feed these industries, more than 95% of hydrogen is produced from hydrocarbons that emit CO2 during the process. Conversely, electrolysis is a process by which electricity is used to separate hydrogen and oxygen in water molecules, usually across a membrane. Hydrogen production via electrolysis lowers the carbon intensity of produced hydrogen when coupled with low-carbon electricity. Currently, global electrolysis capacity is on the order of 1 GW, which equates to about 500 metric tons/day of hydrogen production. To support large-scale industrial decarbonization, capacity will likely need to increase by two to three orders of magnitude. Electrolysis technology is broadly separated into groups that are defined by the electrolyte used, with further subdivision based on the operating characteristics. The majority of commercial electrolyzer systems are based around three main technology groups: liquid alkaline, proton exchange membrane, and solid oxide. Liquid Alkaline (LA) electrolysis is the oldest, most mature, least expensive, and most common commercial technology, with 400 plants in operation by 1902. Its hydrogen output is low relative to the size of the system due to a low current density. LA electrolysis utilizes a liquid potassium hydroxide solution as the electrolyte. Proton exchange membrane (PEM) electrolysis (also known as polymer electrolyte membrane electrolysis), described in 1960, relies on an acid-impregnated polymer membrane as the electrolyte and typically offers three to six times higher hydrogen production per unit cell area than LA electrolysis. Solid oxide electrolysis, or high-temperature electrolysis, utilizes a ceramic cell as the electrolyte and operates on steam rather than liquid water, enabling electrical efficiencies of more than 90%, which is up from 60% with PEM. Two pre-commercial electrolyzer technologies to note are alkaline exchange membrane (AEM) and proton-conducting solid oxide electrolysis cell (SOEC). AEM potentially has the advantages of both LA and PEM technologies in that it is able to use low-cost materials like LA but with the ability to operate at higher output pressures with a smaller footprint like PEM. Proton-conducting SOEC is similar to commercial SOEC, which uses an oxide-conducting ceramic; however, it uses a proton-conducting ceramic that has the potential to operate at lower temperatures and has lower capital costs. Each of these technologies is experiencing a rapid improvement in performance and a reduction in installed cost, and each appears to be well suited to specific applications. Besides differences in the type of electrolyzer used, the main difference in the architecture of bidirectional hydrogen systems is how the hydrogen is stored. Currently, the most cost-effective way to store large amounts of hydrogen gas is underground, such as in large salt caverns that have been hollowed out. These salt caverns are geographically concentrated in small portions of the United States and are not generally near large metropolitan areas; however, other subsurface architectures are being investigated to expand this reach. A more widely deployable option is aboveground pressurized tanks. These systems are about 10 times as expensive because of the materials and safety margins required to hold hydrogen at high pressures. A third option is using materials-based storage, such as liquid organic hydrogen carriers. By reversibly attaching the produced hydrogen to other molecules, it can be stored at near atmospheric pressure and room temperature. This has the potential to reduce the material cost of storage but may result in a reduction in the efficiency of the process because there are both hydrogen uptake and release processes. While materials-based storage has not been used extensively for large-scale hydrogen storage in the past, there is currently significant activity regarding developing materials and processes for use in large-scale hydrogen storage applications. Electrolysis-produced hydrogen offers an unusual opportunity for energy storage applications. Unlike more conventional energy storage approaches, such as batteries, which operate entirely within electrical markets, hydrogen is a valuable product beyond the electric market and can be directed to the most lucrative use. Hydrogen also can be directly converted back to electricity using either a fuel cell or turbine, or it can be sold to other markets, such as chemical synthesis, steel production, or even export. In this way, excess electricity can be upgraded to the most valuable product. Finally, its use can be actively managed between multiple off-takers; for example, local hydrogen storage can provide a specific amount of stored electricity and any excess can be exported to ammonia production. This flexibility is amplified by the fact that hydrogen storage has fully decoupled power and energy components, which allows for affordable scaling options. Together, this allows a substantial amount of creativity to enable the economic utilization of variable power resources while supporting decarbonization of the industry.

08 HYDROGEN↗

Measuring the thermal conductivity of hydrogels with a bidirectional 3w method

Hydrogels are soft, water-absorbing polymer materials with diverse applications in biomedicine and agriculture. Recently, hydrogels have been proposed to encapsulate water-soluble phase change materials which store energy in their latent heat of solidification. In these applications, the thermal conductivity of these materials affects their performance. Few methods exist for measuring the thermal conductivity of small quantities of hydrogels. Here, we describe an implementation of the bidirectional 3w technique to measure the thermal conductivity of hydrogels with particular attention to their moisture content. Our implementation of the technique can probe sample volumes as little as ~20 mL and yields the thermal conductivity without requiring fitting of additional thermal parameters. We numerically simulate 3w sensor designs with frequency-domain 3-D models to quantify and reduce errors introduced by the choice of substrate and insulation layer thickness. Frequencies in the ~1−20 Hz range yield less error for the materials considered here. We verify our setup with measurements on water and report values for polyacrylamide and poly(2-acrylamido-2-methylpropane sulfonic acid) (PAMPS) hydrogels. Our swollen hydrogels exhibited thermal conductivities nearly equivalent to water, 0.6 W m-1 K-1, and we estimate thermal conductivities of 0.43 and 0.42 W m-1 K-1 for neat polyacrylamide and PAMPS, respectively. Finally, we estimate an error of ±7%, consistent with other 3ω methods, with the largest error coming from the sensor calibration. We find our implementation of the bidirectional 3w method gives reasonable results and can be employed for prototyping soft materials relevant for thermal storage.

3-omega, thermal conductivity, hydrogel, moisture ↗

Bidirectional titration of yeast gene expression using a pooled CRISPR guide RNA approach

Most classic genetic approaches utilize binary modifications that preclude the identification of key knockdowns for essential genes or other targets that only require moderate modulation. As a complementary approach to these classic genetic methods, we describe a plasmid-based library methodology that affords bidirectional, graded modulation of gene expression enabled by tiling the promoter regions of all 969 genes that comprise the ito977 model of Saccharomyces cerevisiae’s metabolic network. When coupled with a CRISPR-dCas9–based modulation and next-generation sequencing, this method affords a library-based, bidirection titration of gene expression across all major metabolic genes. We utilized this approach in two case studies: growth enrichment on alternative sugars, glycerol and galactose, and chemical overproduction of betaxanthins, leading to the identification of unique gene targets. In particular, we identify essential genes and other targets that were missed by classic genetic approaches.

59 BASIC BIOLOGICAL SCIENCES↗

Bidirectional Multiphoton Communication between Remote Superconducting Nodes

Quantum communication test beds provide a useful resource for experimentally investigating a variety of communication protocols. Here we demonstrate a superconducting circuit test bed with bidirectional multiphoton state transfer capability using time -domain shaped wave packets. Further, the system we use to achieve this comprises two remote nodes, each including a tunable superconducting transmon qubit and a tunable microwave -frequency resonator, linked by a 2 m-long superconducting coplanar waveguide, which serves as a transmission line. We transfer both individual and superposition Fock states between the two remote nodes, and additionally show that this bidirectional state transfer can be done simultaneously, as well as being used to entangle elements in the two nodes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A New Design Consideration for Bidirectional Resonant Converters

This paper introduces innovative design considerations for a bidirectional resonant converter, optimized for Electric Vehicle (EV) charging and vehicle-togrid (V2G) applications. By eliminating the need for complex voltage or current gain functions, the proposed design greatly simplifies the development process, making it more accessible for manufacturers and system integrators. This approach not only reduces engineering time and resource investment but also accelerates time-to-market, giving stakeholders a competitive edge in rapidly expanding EV infrastructure markets. In addition, the streamlined design ensures soft switching at maximum output power, leading to higher efficiency and improved durability, which translates to lower operating costs and a longer service life for EV charging equipment. These benefits provide a clear pathway to more cost-effective, scalable, and sustainable EV charging and V2G solutions, enhancing value for stakeholders by facilitating smoother integration into the grid and supporting energy resilience. To validate the benefits, a 60 kW bidirectional charger with a flexible input range of 700−900VDC and an output range of 400−1250VDC was developed, underscoring the design's adaptability and potential for large-scale implementation.

Asa, Erdem [ORNL] (ORCID:0000000190884812)↗

Fail-safe bidirectional valve driver

Cross-coupled diodes are added to commonly used bidirectional valve driver circuit to protect circuit and power supply. Circuit may be used in systems requiring fail-safe bidirectional valve operation, particularly in chemical- and petroleum-processing control systems and computer-controlled hydraulic or pneumatic systems.

Fujimoto, H.↗

Surface roughness effects on bidirectional reflectance.

An experimental study of surface roughness effects on bidirectional reflectance of metallic surfaces is presented. Samples consisting of glass, aluminum alloy, and stainless steel materials were roughened using standard grinding techniques and coated with a radiatively opaque layer of pure aluminum. Surface roughness parameters, rms height and rms slope, were evaluated from digitized surface profile measurements and are less than 1.0 micron, and 0.28, respectively. Rough-surface specular, bidirectional, and directional reflectance measurements for selected values of polar angle and wavelength of incident energy within the range from 10 to 80 deg and from 1 to 14 microns, respectively, are reported. The influence of surface roughness is discussed in terms of rms height and rms slope.

Smith, T. F.↗