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Diffuse reflection and transmission coefficients computed for radiative transfer in homogeneous slabs of finite thickness with isotropic scattering
Traditionally microstrip or printed reflectarrays are designed using the transmit mode technique. In this method, the size of each printed element is chosen so as to provide the required value of the reflection phase such that a collimated beam results along a given direction. The reflection phase of each printed element is approximated using an infinite array model. The infinite array model is an excellent engineering approximation for a large microstrip array since the size or orientation of elements exhibits a slow spatial variation. In this model, the reflection phase from a given printed element is approximated by that of an infinite array of elements of the same size and orientation when illuminated by a local plane wave. Thus the reflection phase is a function of the size (or orientation) of the element, the elevation and azimuth angles of incidence of a local plane wave, and polarization. Typically, one computes the reflection phase of the infinite array as a function of several parameters such as size/orientation, elevation and azimuth angles of incidence, and in some cases for vertical and horizontal polarization. The design requires the selection of the size/orientation of the printed element to realize the required phase by interpolating or curve fitting all the computed data. This is a substantially complicated problem, especially in applications requiring a computationally intensive commercial code to determine the reflection phase. In dual polarization applications requiring rectangular patches, one needs to determine the reflection phase as a function of five parameters (dimensions of the rectangular patch, elevation and azimuth angles of incidence, and polarization). This is an extremely complex problem. The new method employs the reciprocity principle and reaction concept, two well-known concepts in electromagnetics to derive the receive mode analysis and design techniques. In the "receive mode design" technique, the reflection phase is computed for a plane wave incident on the reflectarray from the direction of the beam peak. In antenna applications with a single collimated beam, this method is extremely simple since all printed elements see the same angles of incidence. Thus the number of parameters is reduced by two when compared to the transmit mode design. The reflection phase computation as a function of five parameters in the rectangular patch array discussed previously is reduced to a computational problem with three parameters in the receive mode. Furthermore, if the beam peak is in the broadside direction, the receive mode design is polarization independent and the reflection phase computation is a function of two parameters only. For a square patch array, it is a function of the size, one parameter only, thus making it extremely simple.
The potential of short wave infrared (SWIR) measurements in vegetation discrimination is further substantiated through a discussion of field studies and an examination of the physical bases which cause SWIR measurements to vary with the vegetation type observed. The research reported herein supported the AGRISTARS program objective to incorporate TM measurements in the analysis of agricultural activity. Field measurements on corn and soybeans in Iowa were conducted, and the mean and variance of canopy reflectance were computed for each observation date. The Suits canopy reflectance model was used to evaluate possible explanations of the observed corn/soybeans reflectance patterns /39/. The SWIR measurements were shown to effectively discriminate corn and soybeans on the basis of leaf absorption properties.
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The author has identified the following significant results. Significant findings are: (1) one-acre lakes and one-acre islands are detectable; (2)removal of atmospheric parameters derived from RPMI measurements show test lakes to have reflectances of 3.1 to 5.5% in band 4 and 0.3 to 2.3% in band 5; (3) failure to remove reflectance caused by atmosphere results in errors up to 500% in computing lake reflectance from ERTS-1 data; (4) in band 4, up to seven reflectance levels were observed in test lakes; (5) reflectance patterns have been displayed on a color-coded TV monitor and on computer-generated gray scales; (6) deep and shallow water can be separated by a trained photointerpreter and automatic machine processing, with estimates of water depth possible in some cases; (7) RPMI provides direct spectral signature measurements of lakes and lake features such as algal scums and floating plants; (8) a method is reported for obtaining lake color, as estimated by Forel-Ule standards, from ERTS-1 data; (9) a strong correlation between browner water color, diminishing water transparency; and (10) classifying lake eutrophication by observation of surface scums or macrophytes in shallow water seems straightforward.
The validity and limitations of assuming bright surfaces are icy and dark surfaces are stony are investigated, and the limitations of JHK colorimetry for distinguishing icy versus stony objects are studied. The broadband JHK reflectances of a large range of minerals and mineral assemblages were computed, the visual albedo obtained, and the J-H and H-K colors computed. Visual reflectance was found to vary easily from 0.15 to 1.0 when the surface contains 99 percent or more water by weight. The effect of varying particulate weight fraction and grain size are described. Visual albedo is found to give no indication of the purity of an icy surface. The JHK colors of an ice and particulate mixture can fall anywhere in the classical J-H versus H-K diagram, and thus the diagram cannot be used to distinguish a predominantly rock surface from a predominantly ice one in a specific case, except where both J-H and H-K colors are less than about -0.2.
A novel technique for the fabrication of binary-phase computer-generated reflection holograms is described. By use of integrated circuit technology, the holographic pattern is etched into a silicon wafer and then aluminum coated to make a reflection hologram. Because these holograms reflect virtually all the incident radiation, they may find application in machining with high-power lasers. A number of possible modifications of the hologram fabrication procedure are discussed.
Uncertainties in the derivation of the ground reflectance and temperature relative to the uncertainty in the estimation of aerosol loading and water vapor amount are presented. To compute the reflectance for TM 1 (thematic mapper) through TM6, a doubling model is used, and to compute satellite-received radiance for TM7, an emission-transmission model is employed. It is shown that at a water vapor concentration of higher than 50% above normal, the relative sensitivity remains as low as 8% for ground reflectance determinations. The relative sensitivity for determining ground temperature for midlatitude summer climatological profile is less than 5%, but as the ground temperature is approximately 300 K, low sensitivity still means a variation of a few degrees. An increase in water vapor amount causes an uncertainty in ground temperature and reflectance calculations comparable to the uncertainty in aerosol loading and water vapor amount estimations.
The theoretical reflectance of X-rays from various materials and evaporated films is presented. A computer program was written that computes the reflected intensity as a function of the angle of the incident radiation. The quantities necessary to generate the efficiency and their effect on the data are demonstrated. Five materials were chosen for evaluation: (1) fused silica, (2) chromium, (3) beryllium, (4) gold, and (5) a thin layer contaminant. Fused silica is a versatile and common material; chromium has high reflection efficiency at X-ray wavelengths and is in the middle of the atomic number range; beryllium contains a single atomic shell and has a low range atomic number; gold contains multiple atomic shells and has a high atomic number; the contaminant is treated as a thin film in the calculations and results are given as a function of thickness for selected wavelengths. The theoretical results are compared to experimental data at lambda = 8.34 A.
The recent work of Allen, Gayle, and Richardson (1970) and Suits (1972) has been extended to compute directional reflectance from a crop row. A model is constructed which takes into account edge effects and aids in discriminating crops with leaf orientation in preferred directions. This report only contains the development of the mathematical equations. Numerical results will be published in a forthcoming report.
A technique has been developed for simulating the effects of haze, sun angle, and background reflectance in Landsat data and correcting for them. The atmospheric model assumes a two-layer atmosphere: a Rayleigh scattering molecular layer and a Mie scattering haze layer next to the earth's surface. Reflection and transmission matrices describe the reflection and transmission properties of the plane parallel scattering layers. The multispectral scanner response is computed for various values of the parameters under evaluation. This yields expressions for Landsat gray-scale levels used for determining the effect of changes in any parameter. The Atmospheric Correction computer program is used to determine the haze level from the data, to compute the reflectance, and to interpolate in order to find the correction coefficients necessary to make the desired correction.
A theory is described for computing the reflected or scattered field from a smooth body with inflection points. These inflections occur in certain directions at each surface point for which the total (Gaussian) curvature is zero or negative. For surface illumination in one of these critical directions, the usual reflection formulas obtained by the high-frequency approximation are inapplicable, and a shadow zone exists in the reflected field. Scattering into the shadow zone is treated, as well as specular reflection. This theory should have a variety of applications such as for certain optics problems, computer graphics modeling of three-dimensional shapes, and the design and analysis of specialized microwave reflector antennas.
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.
Candidates for reflector panel design concepts, including materials and configurations, were identified. The large list of candidates was screened and reduced to the five most promising ones. Cost and technical factors were used in making the final choices for the panel conceptual design, which was a stiffened steel skin substrate with a bonded, acrylic overcoated, aluminized polyester film reflective surface. Computer simulations were run for the concentrator optics using the selected panel design, and experimentally determined specularity and reflectivity values. Intercept factor curves and energy to the aperture curves were produced. These curves indicate that surface errors of 2 mrad (milliradians) or less would be required to capture the desired energy for a Brayton cycle 816 C case. Two test panels were fabricated to demonstrate manufacturability and optically tested for surface error. Surface errors in the range of 1.75 mrad and 2.2 mrad were measured.
We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu under high-velocity solidification conditions and SCN-0.46wt% camphor under microgravity conditions from National Aeronautics and Space Administration (NASA) DECLIC-DSI-R experiments. Both codes, one employing finite-difference discretization with uniform mesh and GPU-acceleration (GPU-PF) and the other one employing finite-element discretization with adaptive-mesh and CPU-parallelization (PRISMS-PF), solve the same quantitative phase-field formulation that incorporates an anti-trapping current for the solidification of dilute alloys. We evaluate the predictions of each code for dendritic morphology, primary spacing, and tip dynamics in both 2D and 3D, as well as their numerical convergence and computational performance. While existing benchmark problems have primarily focused on simplified or small-scale simulations, they do not reflect the computational and modeling challenges posed by employing experimentally relevant time and length scales. Our results provide a practical framework for assessing phase-field code performance as well as validating and facilitating their application in integrated computational materials engineering (ICME) workflows that require integration with realistic experimental data.
Suitably formulated spatial modulation of a scene imaged by a computed-tomography imaging spectrometer (CTIS) has been found to be useful as a means of improving the imaging performance of the CTIS. As used here, "spatial modulation" signifies the imposition of additional, artificial structure on a scene from within the CTIS optics. The basic principles of a CTIS were described in "Improvements in Computed- Tomography Imaging Spectrometry" (NPO-20561) NASA Tech Briefs, Vol. 24, No. 12 (December 2000), page 38 and "All-Reflective Computed-Tomography Imaging Spectrometers" (NPO-20836), NASA Tech Briefs, Vol. 26, No. 11 (November 2002), page 7a. To recapitulate: A CTIS offers capabilities for imaging a scene with spatial, spectral, and temporal resolution. The spectral disperser in a CTIS is a two-dimensional diffraction grating. It is positioned between two relay lenses (or on one of two relay mirrors) in a video imaging system. If the disperser were removed, the system would produce ordinary images of the scene in its field of view. In the presence of the grating, the image on the focal plane of the system contains both spectral and spatial information because the multiple diffraction orders of the grating give rise to multiple, spectrally dispersed images of the scene. By use of algorithms adapted from computed tomography, the image on the focal plane can be processed into an image cube a three-dimensional collection of data on the image intensity as a function of the two spatial dimensions (x and y) in the scene and of wavelength (lambda). Thus, both spectrally and spatially resolved information on the scene at a given instant of time can be obtained, without scanning, from a single snapshot; this is what makes the CTIS such a potentially powerful tool for spatially, spectrally, and temporally resolved imaging. A CTIS performs poorly in imaging some types of scenes in particular, scenes that contain little spatial or spectral variation. The computed spectra of such scenes tend to approximate correct values to within acceptably small errors near the edges of the field of view but to be poor approximations away from the edges. The additional structure imposed on a scene according to the present method enables the CTIS algorithms to reconstruct acceptable approximations of the spectral data throughout the scene.
This dataset contains scenarios of hourly total electricity demand with and without projected loads from data centers over the period 2022-2040. The root projections without data center demands are identical to those documented in Burleyson et al. 2024. In short, those projections encompass hourly electricity demands for 54 Balancing Authorities (BAs) in the United States across a range of eight of weather and socioeconomic scenarios. Refer to the root dataset and accompanying publication, Burleyson et al. 2025, for information about how those projections were generated. For this derivative dataset we used the base loads from the following scenarios: rcp45hotter_ssp3 rcp45hotter_ssp5 rcp85hotter_ssp3 rcp85hotter_ssp5 The root load projections did not reflect the drastic expansion of data centers that has occurred in the last several years to support artificial intelligence and cloud computing. To reflect growth in data center demand, a second set of load projections were created in which we layered in additional data center load projections based on the data center load growth scenarios described in a 2024 report by the Electric Power Research Institute (EPRI): "Powering Intelligence: Analyzing Artificial Intelligence and Data Center Energy Consumption". The EPRI projections from the report are included in this dataset (EPRI_2024_Projections.xlsx). That report contained annual state-level data center load projections for four year-over-year growth rates for data center demands: Low (3.71% annual growth) Moderate (5% annual growth) High (10% annual growth) Higher (15% annual growth) To homogenize the load projections with and without data centers we had to get them to a common scale. The first step was to take the EPRI annual state-level data center energy consumption values and convert them to 8760-hr loads for each year. We did that by assuming a flat (e.g., not weather- or time-sensitive) load profile and distributing the data center loads in each state evenly across all hours in a year. From there the loads were downscaled from the state-level to the county-level using 2019 county-level populations as weights. Finally, the county-level hourly data center loads were summed to the BA-level using the county-to-BA mapping underpinning the root load projections. The net result is 16 (4 weather and socioeconomic scenarios crossed with 4 data center load growth scenarios) unique load projections for the period 2022-2040. The file format follows that of the root dataset with a single additional column "Scaled_TELL_BA_Load_with_DC_MWh" that contains the hourly loads with the added data center loads for a given BA-year-scenario combination. Please refer to the readme file in the root dataset for more information on the file format.
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.