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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Silicon bulk micromachined, symmetric, degenerate vibratorygyroscope, accelerometer and sensor and method for using the same

When embodied in a microgyroscope, the invention is comprised of a silicon, four-leaf clover structure with a post attached to the center. The whole structure is suspended by four silicon cantilevers or springs. The device is electrostatically actuated and capacitively detects Coriolis induced motions of the leaves of the leaf clover structure. In the case where the post is not symmetric with the plane of the clover leaves, the device can is usable as an accelerometer. If the post is provided in the shape of a dumb bell or an asymmetric post, the center of gravity is moved out of the plane of clover leaf structure and a hybrid device is provided. When the clover leaf structure is used without a center mass, it performs as a high Q resonator usable as a sensor of any physical phenomena which can be coupled to the resonant performance.

Tang, Tony K.↗
NASA NTRS1985

Urban, Forest, and Agricultural AIS Data: Fine Spectral Structure

Spectra acquired by the Airborne Imaging Spectrometer (AIS) near Lafayette, IN, Ely, MN, and over the Stanford University campus, CA were analyzed for fine spectral structure using two techniques: the ratio of radiance of a ground target to the radiance of a standard and also the correlation coefficient of radiances at adjacent wavelengths. The results show ramp like features in the ratios. These features are due to the biochemical composition of the leaf and to the optical scattering properties of its cuticle. The size and shape of the ramps vary with ground cover.

Vanderbilt, V. C.↗
NASA NTRS2012

Media Effects on Lettuce Growth in "Pillows" Designed for the VEGGIE Spaceflight Growth Chamber

VEGGIE is a prototype vegetable production unit for space designed by Orbital Technologies Corporation that is being developed to fly on the International Space Station. A modular plant rooting system "pillow" is being designed to support plant growth in VEGGIE under microgravity conditions. VEGGIE pillows are small self-contained packets of media with time-release fertilizer that can wick water passively from a root mat reservoir. Seeds are planted in pillows and the entire root system of a plant is contained as the crop develops, preventing loss into the spacecraft cabin. This study compared five media types and three lettuce cultivars in pillows growing in a VEGGIE analog environment.. Media consisted of a peat-based potting mix (Fafard #2,Conrad Fafard Inc., Agawam, MA), and a calcined clay, (arcillite, 1-2 mm sifted, Turface Proleague, Profile LLC, Buffalo Grove IL) as well as three different blends of the two, 70:30, 50:50, and 30:70. Lettuce cultivars tested were 'Sierra', a bi-colored French crisp Batavia lettuce, 'Outredgeous', a red romaine lettuce and 'Flandria', a green butter head variety. Plants were grown for 28 days, harvested, biometric data was obtained, and tissue mineral analysis was performed. For all cultivars, lettuce plants grown in the media blends were more productive than those in the individual media types. All cultivars showed bell-shaped curves in response to increases in arcillite / decreases in Fafard #2 for leaf area, fresh, and dry mass. Plants in 100% Fafard #2 and in 100% arcillite were stunted, but only those in higher levels of Fafard #2 (70% and 100%) had reduced shoot percent moisture, possibly indicating that mechanisms causing stunting differed. Variation in tissue nutrient content are consistent with this, with Mg and Mn highest in plants grown in 100% Fafard and decreasing as the concentration of arcillite increased. Color also varied with media, especially in the 'Sierra' lettuce, with plants grown in increasing levels of Fafard #2 being much more red and those in 100% arcillite almost completely green. The red-leaf cultivar 'Outredgeous' showed increasing chlorophyll (SPAD values) with increasing percentage of arcillite. In all cultivars tested it appears that a mixture of media types, usually 50:50 or 30:70 Fafard #2: arcillite, sustained healthier, more productive plants. Smaller, less productive plants in either of the individual media may indicate stress issues, however more work is needed to understand the reasons for this sub-optimal growth. This work was supported by NASA

Massa, Gioia↗
DOE OSTI2022

Leaf habit affects the distribution of drought sensitivity but not water transport efficiency in the tropics

Abstract Considering the global intensification of aridity in tropical biomes due to climate change, we need to understand what shapes the distribution of drought sensitivity in tropical plants. We conducted a pantropical data synthesis representing 1117 species to test whether xylem‐specific hydraulic conductivity (K S ), water potential at leaf turgor loss (Ψ TLP ) and water potential at 50% loss of K S (Ψ P50 ) varied along climate gradients. The Ψ TLP and Ψ P50 increased with climatic moisture only for evergreen species, but K S did not. Species with high Ψ TLP and Ψ P50 values were associated with both dry and wet environments. However, drought‐deciduous species showed high Ψ TLP and Ψ P50 values regardless of water availability, whereas evergreen species only in wet environments. All three traits showed a weak phylogenetic signal and a short half‐life. These results suggest strong environmental controls on trait variance, which in turn is modulated by leaf habit along climatic moisture gradients in the tropics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Modeling Profiles of Micrometeorological Variables in a Tropical Premontane Rainforest Using Multi-Layered CLM (CLM-ML)

This study updates the multi-layered Community Land Model (CLM-ml) for hillslopes and compares predictions from against observations collected in tropical montane rainforest, Costa Rica. Modifications are made in order to capture a wider array of vertical leaf area distributions, predict CO 2 profiles, account for soil respiration, and adjust wind forcings for difficult topographic settings. Test results indicate that the modified multi-layer CLM model can successfully replicate the shape of various micrometeorological profiles (humidity, CO 2 , temperature, and wind speed) under the canopy. In the single-layer models (CLM4.5 and CLM5), excessive day-to-night differences in leaf temperature and leaf wetness were originally noted, but CLM-ml significantly improved these issues, decreasing the amplitudes of diurnal cycles by 67% and 47%. Sub-canopy considerations, such as canopy shapes and turbulent transfer parameters, also played a significant role in model performance. More importantly, unlike single layer models, the results that CLM-ml produces can be compared to variables measured within the canopy to provide far more detailed diagnostic information. Further observations and model developments, aimed at reflecting surface heterogeneity, will be necessary to adequately capture the complexity and the features of the tropical montane rainforest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Genetic variation at transcription factor binding sites largely explains phenotypic heritability in maize

Abstract Comprehensive maps of functional variation at transcription factor (TF) binding sites (cis-elements) are crucial for elucidating how genotype shapes phenotype. Here, we report the construction of a pan-cistrome of the maize leaf under well-watered and drought conditions. We quantified haplotype-specific TF footprints across a pan-genome of 25 maize hybrids and mapped over 200,000 variants, genetic, epigenetic, or both (termed binding quantitative trait loci (bQTL)), linked tocis-element occupancy. Three lines of evidence support the functional significance of bQTL: (1) coincidence with causative loci that regulate traits, includingvgt1,ZmTRE1and the MITE transposon nearZmNAC111under drought; (2) bQTL allelic bias is shared between inbred parents and matches chromatin immunoprecipitation sequencing results; and (3) partitioning genetic variation across genomic regions demonstrates that bQTL capture the majority of heritable trait variation across ~72% of 143 phenotypes. Our study provides an auspicious approach to make functionalcis-variation accessible at scale for genetic studies and targeted engineering of complex traits.

Genetics & Heredity↗
NASA NTRS1985

Discrete Random Media Techniques for Microwave Modeling of Vegetated Terrain

Microwave remote sensing of vegetated terrain has been studied. Vegetation is modeled so that backscattered radar signals can be used to infer parameters which characterize the vegetation and underlying ground. The vegetation is modeled by discrete lossy dielectric scatterers with prescribed characteristics. The goal of the modeling effort is to remotely sense vegetation type (classification), growth stage, and plant/ground moisture. This information can then be used as input into agricultural, forestry and global circulation models. The microwave frequency spectrum, particularly L and C bands, are especially appropriate for this purpose since the wavelength is comparable to plant leaf and stem size. The resulting resonant interaction leads to backscattered data highly depend on plant shape and orientation. In addition, the transparent nature of the atmosphere in this frequency regime allows for algorithm development which requires no atmospheric correction.

Lang, R. H.↗
NASA NTRS1992

A linear spectral matching technique for retrieving equivalent water thickness and biochemical constituents of green vegetation

Over the last decade, technological advances in airborne imaging spectrometers, having spectral resolution comparable with laboratory spectrometers, have made it possible to estimate biochemical constituents of vegetation canopies. Wessman estimated lignin concentration from data acquired with NASA's Airborne Imaging Spectrometer (AIS) over Blackhawk Island in Wisconsin. A stepwise linear regression technique was used to determine the single spectral channel or channels in the AIS data that best correlated with measured lignin contents using chemical methods. The regression technique does not take advantage of the spectral shape of the lignin reflectance feature as a diagnostic tool nor the increased discrimination among other leaf components with overlapping spectral features. A nonlinear least squares spectral matching technique was recently reported for deriving both the equivalent water thicknesses of surface vegetation and the amounts of water vapor in the atmosphere from contiguous spectra measured with the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). The same technique was applied to a laboratory reflectance spectrum of fresh, green leaves. The result demonstrates that the fresh leaf spectrum in the 1.0-2.5 microns region consists of spectral components of dry leaves and the spectral component of liquid water. A linear least squares spectral matching technique for retrieving equivalent water thickness and biochemical components of green vegetation is described.

Gao, Bo-Cai↗
NASA NTRS2010

Understanding the Scalability of Bayesian Network Inference Using Clique Tree Growth Curves

One of the main approaches to performing computation in Bayesian networks (BNs) is clique tree clustering and propagation. The clique tree approach consists of propagation in a clique tree compiled from a Bayesian network, and while it was introduced in the 1980s, there is still a lack of understanding of how clique tree computation time depends on variations in BN size and structure. In this article, we improve this understanding by developing an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN s non-root nodes to the number of root nodes, and (ii) the expected number of moral edges in their moral graphs. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for the total size of each set. For the special case of bipartite BNs, there are two sets and two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, where random bipartite BNs generated using the BPART algorithm are studied, we systematically increase the out-degree of the root nodes in bipartite Bayesian networks, by increasing the number of leaf nodes. Surprisingly, root clique growth is well-approximated by Gompertz growth curves, an S-shaped family of curves that has previously been used to describe growth processes in biology, medicine, and neuroscience. We believe that this research improves the understanding of the scaling behavior of clique tree clustering for a certain class of Bayesian networks; presents an aid for trade-off studies of clique tree clustering using growth curves; and ultimately provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms.

Mengshoel, Ole J.↗
DOE OSTI2023

Investigating the Diurnal Radiative, Turbulent, and Biophysical Processes in the Amazonian Canopy‐Atmosphere Interface by Combining LES Simulations and Observations

Abstract We investigate the atmospheric diurnal variability inside and above the Amazonian rainforest for a representative day during the dry season. To this end, we combine high‐resolution large‐eddy simulations that are constrained and evaluated against a comprehensive observation set, including CO 2 concentrations, gathered during GoAmazon2014/15. We design systematic numerical experiments to quantify whether a multilayer approach in solving the explicit canopy improves our canopy‐atmosphere representation. We particularly focus on the relationship between photosynthesis and plant transpiration, and their distribution at leaf and canopy scales. We found the variability of photosynthesis drivers like vapor pressure deficit and leaf temperature to be about 3 times larger for sunlit leaves compared to shaded leaves. This leads to a large spread on leaf stomatal conductance values with minimum and maximum values varying more than 100%. Regarding the turbulent structure, we find wind‐driven stripe‐like shapes at the canopy top and structures resembling convective cells at the canopy. Wind‐related variables provide the best spatiotemporal agreement between model and observations. The potential temperature and heat flux profiles agree with an observed decoupling near the canopy top interface, although with less variability and cold biases of up to 3 K. The increasing complexity on the biophysical processes leads to the largest disagreements for evaporation, CO 2 plant assimilation and soil efflux. The model is able to capture the correct dependences and trends with the magnitudes still differing. We finally discuss the need to revise leaf and soil models and to complete the observations at leaf and canopy levels.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Tracking seasonal variability in plant traits from spaceborne PRISMA and NEON AOP across forest types and ecoregions

Plant traits serve as critical indicators of how plants adapt to environmental changes and influence ecosystem functions. While airborne hyperspectral remote sensing effectively maps plant traits through detailed reflectance properties, it is limited by cost and scale, making large-scale and temporal studies challenging. The recently launched spaceborne hyperspectral imager, PRecursore IperSpettrale della Missione Applicativa (PRISMA), offers frequent, large scale and high-fidelity observations on a spatial resolution of 30 m and a revisit time of around 29 days, making it suitable for large-scale seasonal trait mapping. However, their potential remains largely unexplored. This study developed a multi-stage framework by leveraging the PRISMA spaceborne hyperspectral data and National Ecological Observatory Network (NEON) Airborne Observation Platform (AOP) hyperspectral data to investigate the seasonal dynamics of four key plant traits — chlorophyll content, carotenoid content, equivalent water thickness, and nitrogen content — across eleven NEON sites representing diverse forest types and ecoregions in the contiguous U.S. Our results demonstrated that PRISMA hyperspectral data can reliably track seasonal variability in plant traits, achieving overall R 2 values ranging from 0.78 to 0.88 and normalized root mean square error (NRMSE) values ranging from 5.4% to 8.4% for the four traits. Seasonal patterns revealed bell-shaped trajectories for chlorophyll and carotenoids, while equivalent water thickness decreased steadily across most sites, driven by structural changes during leaf maturation and senescence. Nitrogen content exhibited less pronounced seasonal variation but followed expected nutrient resorption patterns. Analysis of environmental drivers showed that seasonal variability is primarily controlled by solar radiation and day length in northern sites, vapor pressure in semi-arid regions, and temperature in mid-southeastern sites. Spatial variability, meanwhile, was primarily driven by soil properties, particularly during the peak growing season. However, the influence of soil variables slightly declines toward the end of the season at several sites, as climatic factors become more prominent. This study highlights the capability of PRISMA, and potentially other similar spaceborne hyperspectral data for large-scale, time-series plant trait mapping and provides valuable insights into the interactions between plant traits and environmental factors. In conclusion, these findings contribute to advancing our understanding of plant functional ecology and improving predictions of ecosystem responses to environmental changes.

Environmental drivers↗
NASA NTRSDate not supplied

Simultaneous Convective and Radiative Heating of Materials with the 200 kW Laser Enhanced Arc Jet Facility (LEAF)

Recent installation of the 200-kW Laser Enhanced Arc Jet Facility (LEAF) at the Interaction Heating Facility (IHF) arc jet at NASA Ames Research Center has enabled combined heating of material samples. The LEAF system is permanently located adjacent to IHF. During LEAF operation, IHF can convectively heat material samples with heat fluxes up to 0.16 kW/cm 2 using the 22.86-cm nozzle or up to 0.07 kW/cm 2 using the truncated semi-elliptic nozzle. LEAF can deliver radiant heating with various profiles and sizes to a material sample. In flat-top square configuration, irradiance levels of nearly 0.1 kW/cm 2 have been demonstrated over a 43.2 x 43.2 cm area, and irradiance levels up to 0.39 kW/cm 2 have been demonstrated over a 15.2 x 15.2 cm area. LEAF can also be configured to deliver a super-Gaussian profile over a variety of beam diameters (1.8 to 5.6 cm). This configuration has been demonstrated up to peak irradiance levels of 25.7 kW/cm 2 per laser at the smallest, 1.8 cm, diameter setting. The LEAF system is composed of four 50-kW lasers, so it can also be configured to simultaneously deliver two different beam shapes (e.g., one square beam and one super-Gaussian beam).

Megan MacDonald↗
DOE OSTI2024

Hysteresis area at the canopy level during and after a drought event in the Central Amazon

Understanding forest water limitation during droughts within a warming climate is essential for accurate predictions of forest-climate interactions. In hyperdiverse ecosystems like the Amazon forest, the mechanisms shaping hysteresis patterns in transpiration relative to environmental factors are not well understood. From this perspective, we investigated these dynamics by conducting in situ leaf-level measurements throughout and after the 2015 El Niño-Southern Oscillation (ENSO) drought. Our findings indicate a substantial increase in the hysteresis area (H area ) among transpiration (E), vapor pressure deficit (VPD), and stomatal conductance (g s ) at canopy level during the ENSO peak, attributed to both temporal lag and differences in magnitude between g s and VPD peaks. Specifically, the canopy species Pouteria anomala exhibited an increased H area , due to earlier maximum g s rates leading to a greater temporal lag with VPD compared to the post-drought period. Additionally, leaf water potential (ψ L ) and canopy temperature (T canopy ) showed larger H area during the ENSO peak compared to post-drought conditions across all studied species, suggesting that stomatal closure, particularly during the afternoon, acts to minimize water loss and may explain the counterclockwise hysteresis observed between ψ L and T canopy . Here, the pronounced H area during the drought points to a potential imbalance between water supply and demand, underlining the role of stomatal behavior of isohydric species in response to drought.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

The three major axes of terrestrial ecosystem function

The leaf economics spectrum and the global spectrum of plant forms and functions revealed fundamental axes of variation in plant traits, which represent different ecological strategies that are shaped by the evolutionary development of plant species. Ecosystem functions depend on environmental conditions and the traits of species that comprise the ecological communities. However, the axes of variation of ecosystem functions are largely unknown, which limits our understanding of how ecosystems respond as a whole to anthropogenic drivers, climate and environmental variability. Here we derive a set of ecosystem functions from a dataset of surface gas exchange measurements across major terrestrial biomes. We find that most of the variability within ecosystem functions (71.8%) is captured by three key axes. The first axis reflects maximum ecosystem productivity and is mostly explained by vegetation structure. The second axis reflects ecosystem water-use strategies and is jointly explained by variation in vegetation height and climate. The third axis, which represents ecosystem carbon-use efficiency, features a gradient related to aridity, and is explained primarily by variation in vegetation structure. We show that two state-of-the-art land surface models reproduce the first and most important axis of ecosystem functions. However, the models tend to simulate more strongly correlated functions than those observed, which limits their ability to accurately predict the full range of responses to environmental changes in carbon, water and energy cycling in terrestrial ecosystems.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1990

A landscape view of biomass, LAI, and photosynthetic capacity for FIFE

Canopy properties in the tallgrass prairie are examined in terms of spatial and temporal variability to determine how the variability constrains the ecosystem-atmosphere exchange of H2O, CO2, and momentum. Canopy structure and photosynthetic capacity are examined by measuring soil properties, canopy biomass, and canopy nitrogen along continuous strips. Special attention is given to sites of maximum and minimum biomass where parameters such as leaf-area index (LAI), photosynthetic rate, chemistry, and structures for both burned and unburned areas. The LAI/biomass data and the canopy attributes show that soil properties are shaped by soil-forming and geomorphic processes. The variables that cause the greatest variation in LAI, canopy stratification, and photosynthetic capacity are found to be management (burning and/or grazing) and landscape position.

Kittel, T. G. F.↗
NASA NTRS2021

Moisture and Temperature Influences on Nonlinear Vegetation Trends in Serengeti National Park

While long-term vegetation greening trends have appeared across large land areas over the late 20th century, uncertainty remains in identifying and attributing finer-scale vegetation changes and trends, particularly across protected areas. Serengeti National Park (SNP) is a critical East African protected area, where seasonal vegetation cycles support vast populations of grazing herbivores and a host of ecosystem dynamics. Previous work has shown how non-climate drivers (e.g. land use) shape the SNP ecosystem, but it is still unclear to what extent changing climate conditions influence SNP vegetation, particularly at finer spatial and temporal scales. We fill this research gap by evaluating long-term (1982–2016) changes in SNP leaf area index (LAI) in relation to both temperature and moisture availability using Ensemble Empirical Mode Decomposition and Principal Component Analysis with regression techniques. We find that SNP LAI trends are nonlinear, display high sub-seasonal variation, and are influenced by lagged changes in both moisture and temperature variables and their interactions. LAI during the long rains (e.g. March) exhibits a greening-to-browning trend reversal starting in the early 2000s, partly due to antecedent precipitation declines. In contrast, LAI during the short rains (e.g. November, December) displays browning-to-greening alongside increasing moisture availability. Rising temperature trends also have important, secondary interactions with moisture variables to shape these SNP vegetation trends. Our findings show complex vegetation-climate interactions occurring at important temporal and spatial scales of the SNP, and our rigorous statistical approaches detect these complex climate-vegetation trends and interactions, while guarding against spurious vegetation signals.

Moisture↗
DOE OSTI2022

Bayesian optimization to design a novel x-ray shaping device

In radiation therapy, x-ray dose must be precisely sculpted to the tumor, while simultaneously avoiding surrounding organs at risk. This requires modulation of x-ray intensity in space and/or time. Typically, this is achieved using a multi leaf collimator (MLC) - a complex mechatronic device comprising over one hundred individually powered tungsten ‘leaves’ that move in or out of the radiation field as required. Here, an all-electronic x-ray collimation concept with no moving parts is presented, termed “SPHINX”: Scanning Pencil-beam High-speed Intensity-modulated X-ray source. SPHINX utilizes a spatially distributed bremsstrahlung target and collimator array in conjunction with magnetic scanning of a high energy electron beam to generate a plurality of small x-ray “beamlets.” A simulation framework was developed in Topas Monte Carlo incorporating a phase space electron source, transport through user defined magnetic fields, bremsstrahlung x-ray production, transport through a SPHINX collimator, and dose in water. This framework was completely parametric, meaning a simulation could be built and run for any supplied geometric parameters. This functionality was coupled with Bayesian optimization to find the best parameter set based on an objective function which included terms to maximize dose rate for a user defined beamlet width while constraining inter-channel cross talk and electron contamination. Designs for beamlet widths of 5, 7, and 10 mm 2 were generated. Each optimization was run for 300 iterations and took approximately 40 h on a 24-core computer. For the optimized 7-mm model, a simulation of all beamlets in water was carried out including a linear scanning magnet calibration simulation. Finally, a back-of-envelope dose rate formalism was developed and used to estimate dose rate under various conditions. The optimized 5–, 7–, and 10-mm models had beamlet widths of 5.1 , 7.2 , and 10.1 mm 2 and dose rates of 3574, 6351, and 10 015 Gy/C, respectively. The reduction in dose rate for smaller beamlet widths is a result of both increased collimation and source occlusion. For the simulation of all beamlets in water, the scanning magnet calibration reduced the offset between the collimator channels and beam centroids from 2.9 ±1.9 mm to 0.01 ±0.03 mm. A slight reduction in dose rate of approximately 2% per degree of scanning angle was observed. Based on a back-of-envelope dose rate formalism, SPHINX in conjunction with next-generation linear accelerators has the potential to achieve substantially higher dose rates than conventional MLC-based delivery, with delivery of an intensity modulated 100 x 100 mm 2 field achievable in 0.9 to 10.6 s depending on the beamlet widths used. Bayesian optimization was coupled with Monte Carlo modeling to generate SPHINX geometries for various beamlet widths. A complete Monte Carlo simulation for one of these designs was developed, including electron beam transport of all beamlets through scanning magnets, x-ray production and collimation, and dose in water. These results demonstrate that SPHINX is a promising candidate for sculpting radiation dose with no moving parts, and has the potential to vastly improve both the speed and robustness of radiotherapy delivery. A multi-beam SPHINX system may be a candidate for delivering magavoltage FLASH RT in humans.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1987

Fresnel field interaction applied to scattering from a vegetation layer

Models for scattering from a vegetation layer treated as a collection of discrete scatterers usually assume far field interaction among scatterers. In a real vegetation medium such as a deciduous forest or a soybean field it is not always true that each leaf is in the far field of other leaves. This paper examines the additional effect when scatterers are permitted to be in the Fresnel zone of one another. Both disc-shaped and needle-shaped leaves are considered. It is found that in general this causes the backscattering coefficient to be lower for the disk-shaped leaves and may be higher or lower for the needle-shaped leaves depending upon polarization, incidence angle, and frequency than those computed under the assumption of conventional far field interaction.

Fung, A. K.↗