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NASA NTRS2018

Impact of Satellite Sea Surface Salinity Observations on ENSO Predictions from the GMAO S2S Forecast System

Sea surface salinity (SSS) observations from space allow us to investigate if improved estimates of near-surface density stratification and associated mixing can positively impact seasonal to interannual variability of tropical Pacific Ocean dynamics as well as dynamical ENSO forecasts. For the first part of the presentation, we utilize our intermediate-complexity coupled model. Baseline experiments assimilate satellite sea level (multi-satellite gridded AVISO, 2013), SST (Reynolds et al., 2004), and in situ subsurface temperature and salinity observations (GTSPP NODC, 2006). These baseline experiments are then compared with experiments that additionally assimilate Aquarius (V5.0 Lilly and Lagerloef, 2008) and SMAP (V4.0 Fore et al., 2016) SSS. Twelve-month forecasts are initialized for each month from September 2011 to September 2017. For initialization of the coupled forecast, the positive impact of SSS assimilation is brought about by surface freshening near the eastern edge of the western Pacific warm pool and density changes that lead to shallower mixed layer between 10S-5N. This pattern enhances air/sea interaction and amplifies the equatorial Kelvin wave signal. We find that including satellite SSS significantly improves NINO3.4 sea surface temperature anomaly validation over most forecast lead times. We next assess how different satellite SSS products impact the validation of ENSO forecasts. SMAP V4 reduces the salty bias in the western Pacific and so is an improvement upon SMAP V2 and SMOS V2 (Boutin et al., 2017) has similar validation characteristics as a combination of Aquarius and SMAP V4. Next we shift to present results from the NASA GMAO Sub-seasonal to seasonal (S2S_v2.1) production coupled model (i.e. the same model that contributes ENSO forecasts to the North American Multi-Model Ensemble Experiment). From March to June 2015, the availability of two overlapping satellite SSS instruments, Aquarius and SMAP, allows a unique opportunity to compare and contrast forecasts initialized with the benefit of these two satellite SSS observation types. We assess the impact of satellite sea surface salinity (SSS) observations on dynamical ENSO forecasts for the big 2015 El Nino event. We will present distinct experiments for the overlap period that include 1) freely evolving SSS (i.e. no satellite SSS as the production system), 2) Aquarius, and 3) SMAP initialization. Our results show that using Aquarius slightly improves validation of the reanalysis (including sea level and temperature statistics). Our production system without SSS assimilation generated too warm forecasts for the 2015 El Nino from March initial conditions. Incorporating Aquarius into initialization of the coupled system leads to a deeper, more realistic MLD that acts to damp the downwelling Kelvin signal and slightly cool NINO3.4 SST. With Aquarius the forecasts better match the observed amplitude of the 2015 event. On the other hand, SMAP V2 relaxation generally degrades validation statistics. At forecast initialization, SMAP is much too salty within 10o of the equator, leading to deeper MLD east of 165W. This deeper MLD leads to over-damping of the downwelling signal (i.e. relative upwelling), in turn leading to relatively too cool ENSO forecasts.

Hackert, E.↗
NASA NTRS2003

Comparison of two weighted integration models for the cueing task: linear and likelihood

In a task in which the observer must detect a signal at two locations, presenting a precue that predicts the location of a signal leads to improved performance with a valid cue (signal location matches the cue), compared to an invalid cue (signal location does not match the cue). The cue validity effect has often been explained with a limited capacity attentional mechanism improving the perceptual quality at the cued location. Alternatively, the cueing effect can also be explained by unlimited capacity models that assume a weighted combination of noisy responses across the two locations. We compare two weighted integration models, a linear model and a sum of weighted likelihoods model based on a Bayesian observer. While qualitatively these models are similar, quantitatively they predict different cue validity effects as the signal-to-noise ratios (SNR) increase. To test these models, 3 observers performed in a cued discrimination task of Gaussian targets with an 80% valid precue across a broad range of SNR's. Analysis of a limited capacity attentional switching model was also included and rejected. The sum of weighted likelihoods model best described the psychophysical results, suggesting that human observers approximate a weighted combination of likelihoods, and not a weighted linear combination.

NASA Program Biomedical Research and Countermeasur↗
NASA NTRS2010

Physics of Life: A Model for Non-Newtonian Properties of Living Systems

This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if the expected scenario is different from the originally planned one. This approach postulates that even a primitive living species possesses additional, non-Newtonian properties that are not included in the laws of Newtonian or statistical mechanics. These properties follow from a privileged ability of living systems to possess a self-image (a concept introduced in psychology) and to interact with it. The proposed mathematical system is based on the coupling of the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. The coupling is implemented by the information-based supervising forces that can be associated with self-awareness. These forces fundamentally change the pattern of the probability evolution, and therefore, lead to a major departure of the behavior of living systems from the patterns of both Newtonian and statistical mechanics. This innovation is meant to capture the signature of life based only on observable behavior, not on any biochemistry. This will not prevent the use of this model for developing artificial living systems, as well as for studying some general properties of behavior of natural, living systems.

Zak, Michail↗
NASA NTRS1991

Regolith-structure modeling

Early lunar missions have provided a basic understanding of the physical and strength properties of lunar regolith, which have been shown to differ from those of dry terrestrial granular soils. Lunar regolith is predominantly a fine sand of which nearly 40 percent can be characterized as silt with a particle size smaller than 100 micrometers. The top 10 to 20 cm of the regolith can be characterized as being in a loose to medium-loose state. The density of the regolith, however, rapidly increases below a depth of 20 cm. The highly irregular and angular shapes of the regolith particles tend to interlock and create relatively strong mechanical bonds that give the particulate mass substantial cohesive properties and smaller amounts of tensile strength properties. In addition, the friction angle of lunar regolith at medium to high densities is quite high and often exceeds 55 degrees. These known properties of lunar regolith have been matched in a terrestrially-manufactured analog known as Minnesota Lunar Simulant. A variety of experiments were conducted using this simulant to both verify existing information and generate new information on the physical and constitutive properties of lunar regolith. These experiments include maximum and minimum density determinations, specific mass of solids, grain-size distribution, conventional triaxial compression and extension, isotropic compression, one-dimensional compression, direct shear, and direct tension. Direct shear experiments were conducted under atmospheric and vacuum conditions. Results of the physical and strength experiments compare closely to results obtained from lunar missions. Results of simulant strength experiments performed in vacuum indicated no observable difference from results obtained in air. A test bed currently under study is one involving a regolith shield covering a first-generation human habitat module. It is understood that regolith in depths ranging from 3 to 5 meters is required for radiation shielding for habitation and workspace. The habitat module is treated as a rigid cylindrical tube with a smooth exterior. By making the cylinder rigid, a complex interaction problem is reduced to a situation where we can consider the support regolith and the shielding regolith as behaving independently of the structural properties of the cylindrical structure. Medium-dense lunar simulant was placed around a scaled model of the habitat module to provide a radiation shield. This embankment-type shield was constructed in relatively thin but fine layers by compacting, by mechanical vibratory means, layer upon layer of simulant placed adjacent to the horizontally-aligned cylinder. The slope angles were constructed at 55 degrees. The model described above was studied in a geotechnical centrifuge, which allows for the scaling of model dimensions to prototype dimensions by increasing the acceleration of gravity on the model. The deformation response can be scaled up to prototype dimensions to provide an assessment of the deformation patterns of the lunar structure. The actual process of local and/or global growth of instabilities or skip planes can also be observed.

Ko, Hon-Yim↗
NASA NTRS2009

Assessment of the Short-Term Radiometric Stability between Terra MODIS and Landsat 7 ETM+ Sensors

The Landsat 7 (L7) Enhanced Thematic Mapper (ETM+) sensor was launched on April 15th, 1999 and has been in operation for over nine years. It has six reflective solar spectral bands located in the visible and shortwave infrared part of the electromagnetic spectrum (0.5 - 2.5 micron) at a spatial resolution of 30 m. The on-board calibrators are used to monitor the on-orbit sensor system changes. The ETM+ performs solar calibrations using on-board Full Aperture Solar Calibrator (FASC) and the Partial Aperture Solar Calibrator (PASC). The Internal Calibrator Lamp (IC) lamps, a blackbody and shutter optics constitute the on-orbit calibration mechanism for ETM+. On 31 May 2003, a malfunction of the scan-line corrector (SLC) mirror assembly resulted in the loss of approximately 22% of the normal scene area. The missing data affects most of the image with scan gaps varying in width from one pixel or less near the centre of the image to 14 pixels along the east and west edges of the image, creating a wedge-shaped pattern. However, the SLC failure has no impacts on the radiometric performance of the valid pixels. On December 18, 1999, the Moderate Resolution Imaging Spectroradiometer (MODIS) Proto-Flight Model (PFM) was launched on-board the NASA's EOS Terra spacecraft. Terra MODIS has 36 spectral bands with wavelengths ranging from 0.41 to 14.5 micron and collects data over a wide field of view angle (+/-55 deg) at three nadir spatial resolutions of 250 m, 500 in 1 km for bands 1 to 2, 3 to 7, and 8 to 36, respectively. It has 20 reflective solar bands (RSB) with spectral wavelengths from 0.41 to 2.1 micron. The RSB radiometric calibration is performed by using on-board solar diffuser (SD), solar diffuser stability monitor (SDSM), space-view (SV), and spectro-radiometric calibration assembly (SRCA). Through the SV port, periodic lunar observations are used to track radiometric response changes at different angles of incidence (AOI) of the scan mirror. As a part of the AM Constellation satellites, Terra MODIS flies approximately 30 minutes behind L7 ETM+ in the same orbit. The orbit of L7 is repetitive, circular, sunsynchronous, and near polar at a nominal altitude of 705 km (438 miles) at the Equator. The spacecraft crosses the Equator from north to south on a descending node between 10:00 AM and 10:15 AM. Circling the Earth at 7.5 km/sec, each orbit takes nearly 99 minutes. The spacecraft completes just over 14 orbits per day, covering the entire Earth between 81 degrees north and south latitude every 16 days. The longest continuous imaging swath that L7 sensor can collect is for a 14-minute subinterval contact period which is equivalent to 35 full WRS-2 scenes. On the other hand, Terra can provide the entire corresponding orbit with wider swath at any given ETM+ collection without contact time limitation. There are six spectral matching band pairs between MODIS (bands 3, 4, 1, 2, 6, 7) and ETM+ (bands 1, 2, 3, 4, 5, 7) sensor. MODIS has narrower spectral responses than ETM+ in all the bands. A short-term radiometric stability was evaluated using continuous ETM+ scenes within the contact period and the corresponding half orbit MODIS scenes. The near simultaneous earth observations (SNO) were limited by the smaller swath size of ETM+ (187 km) as compared to MODIS (2330 km). Two sets of continuous granules for MODIS and ETM+ were selected and mosaiced based on pixel geolocation information for non cloudy pixels over the North American continent. The Top-of- Atmosphere (TOA) reflectances were computed for the spectrally matching bands between ETM+ and MODIS over the regions of interest (ROI). The matching pixel pairs were aggregated from a finer to a coarser pixel resolution and the TOA reflectance values covering a wide dynamic range of the sensors were compared and analyzed. Considering the uncertainties of the absolute calibration of the both sensors, radiometric stability was verified for the band pairs. The Railroad Valley Playa, Nada (RVPN) was included in the path of this continuous orbit, which served as a verification point between the shortterm and the long-term trending results from previous studies. This work focuses on monitoring the short-term on-orbit stability of MODIS and the ETM+ RSB. It also provides an assessment of the absolute calibration differences between the two sensors over their wide dynamic ranges.

Choi, Taeyoung↗
NASA NTRS2012

Potassium Stable Isotopic Compositions Measured by High-Resolution MC-ICP-MS

Potassium isotopic (K-41/K-39) compositions are notoriously difficult to measure. TIMS measurements are hindered by variable fractionation patterns throughout individual runs and too few isotopes to apply an internal spike method for instrumental mass fractionation corrections. Internal fractionation corrections via the K-40/K-39 ratio can provide precise values but assume identical K-40/K-39 ratios (e.g. 0.05% (1sigma) in [1]); this is appropriate in some cases (e.g. identifying excess K-41) but not others (e.g., determining mass fractionation effects and metrologically traceable isotopic abundances). SIMS analyses have yielded measurements with 0.25% precisions (1sigma) [2]. ICP-MS analyses are significantly affected by interferences from molecular species such as Ar-38H(+) and Ar-40H(+) and instrument mass bias. Single collector ICP-MS instruments in "cold plasma" mode have yielded uncertainties as low as 2% (1sigma, e.g. [3]). Although these precisions may be acceptable for some concentration determinations, they do not resolve isotopic variation in terrestrial materials. Here we present data from a series of measurements made on the Thermo Scientific NEPTUNE Plus multi-collector ICP-MS that demonstrate the ability to make K-41/K-39 ratio measurements with 0.07% precisions (1sigma). These data, collected on NIST K standards, indicate the potential for MC-ICP-MS measurements to look for K isotopic variations at the sub-permil level. The NEPTUNE Plus can sufficiently resolve 39K and 41K from the interfering 38ArH+ and 40ArH+ peaks in wet cold plasma and high-resolution mode. Measurements were made on small but flat, interference-free, plateaus (ca. 50 ppm by mass width for K-41). Although ICP-MS does not yield accurate K-41/K-39 values due to significant instrumental mass fractionation (ca. 6%), this bias can be sufficiently stable over the time required for several measurements so that relative K-41/K-39 values can be precisely determined via sample-standard bracketing. As cold plasma conditions can amplify matrix effects, experiments were conducted to test the matrix tolerance of measurements; the use of clean, matrix-matched samples and standards is critical. Limitations of the cold-plasma high-resolution MC-ICP-MS methodology with respect to matrix tolerance are discussed and compared with the limitations of TIMS methodologies.

Morgan, Leah E.↗
NASA NTRS2002

Lipid Biomarkers for Methanogens in Hypersaline Cyanobacterial Mats for Guerrero Negro, Baja California Sur

Analyses of sediments from the vicinity of active methane seeps have uncovered a particular suite of lipid biomarker patterns that characterize methane consuming archaea and their syntrophic, sulfate reducing partners. These isoprenoid biomarkers, largely identified by their anomalously light carbon isotopic signatures, have been a topic of intense research activity and are recorded in numerous methane-rich environments from Holocene to Cenozoic. This phenomenon has implications for depleted kerogens at 2.7 Ga on early Earth (Hinrichs 2002). In contrast, the lipid biosignatures of methane producing archaea are not readily identified through distinct isotopic labels and have received comparably little attention in analyses of archaea in environmental samples. Indeed, environmental analyses generally detect only free archaeal lipids, not the intact, polar molecules found in the membrane of living organisms. As part of the Ames NAI, the 'Early Microbial Ecosystem Research Group' (EMERG) is working to understand microbial processes in the hypersaline cyanobacterial mats growing in the salt evaporation ponds of the Exportadora de Sal at Guerrero Negro, Baja California Sur, Mexico. The aim of this study was to develop methods by which we could identify the organisms responsible for methane generation in this environment. While the ester-bound fatty acids, hopanoids and wax esters provide a means to identify most of the bacterial components of these mats, the archaea which Ere evidently present through genomic assays and the fact of intense methane production (Hoehler et al. 200l), have not been identified through their corresponding lipid signatures. Archaeal core lipids present a number of analytical challenges. The core lipids of methanogens comprise C20, C40 and sometimes C25 isoprenoid chains, linked through ether bonds to glycerol. As well as archaeal (C20), sn-2- and sn-3-hydroxyarchaeol are associated particularly with methylotrophic methanogens. Recently, we have also identified a dihydroxyarchaeol in a hyperthermophilic methanogen (Summons et al. 2002). Additional structural diversity is encoded into the polar head groups that are attached to the glycerol ether cores. The C20 core lipids are readily analyzed by GC-MS as their volatile trimethylsilyl derivatives while compounds with intact polar head groups can only be detected using LC-MS approaches. Our approach was to utilize the alternative of an ether cleavage reagent (BBr3 vs. HI) and a hydride reducing agent to convert all ether lipids to hydrocarbon in order to provide a vertical profile of quantitative information that might be matched to methane fluxes. We have found that while conventional acid hydrolysis and HI treatment will destroy hydroxyarchaeols, molecular information remains intact through use of BBr3 for ether cleavage. This method revealed the presence of traces of biphytane and various ether alkyls associated with some sulfate reducing bacteria within the mat structure. An interesting, and potentially valuable, byproduct of the method utilizing HI was the identification of abundant homohopanoids after superhydride reduction. Evidently present as sulfur-bound diagenetic products these hopanoids are likely cyanobacterial biomarkers in the early stages of diagenetic preservation.

Jahnke, Linda L.↗
NASA NTRS2008

Luciola Hypertelescope Space Observatory

Luciola is a large (one kilometer) "multi-aperture densified-pupil imaging interferometer", or "hypertelescope" employing many small apertures, rather than a few large ones, for obtaining direct snapshot images with a high information content. A diluted collector mirror, deployed in space as a flotilla of small mirrors, focuses a sky image which is exploited by several beam-combiner spaceships. Each contains a pupil densifier micro-lens array to avoid the diffractive spread and image attenuation caused by the small sub-apertures. The elucidation of hypertelescope imaging properties during the last decade has shown that many small apertures tend to be far more efficient, regarding the science yield, than a few large ones providing a comparable collecting area. For similar underlying physical reasons, radio-astronomy has also evolved in the direction of many-antenna systems such as the proposed Low Frequency Array having hundreds of thousands of individual receivers . With its high limiting magnitude, reaching the mv=30 limit of HST when 100 collectors of 25cm will match its collecting area, high-resolution direct imaging in multiple channels, broad spectral coverage from the 1200 Angstrom ultra-violet to the 20 micron infra-red, apodization, coronagraphic and spectroscopic capabilities, the proposed hypertelescope observatory addresses very broad and innovative science covering different areas of ESA s Cosmic Vision program. In the initial phase, a focal spacecraft covering the UV to near IR spectral range of EMCCD photon-counting cameras ( currently 200 to 1000nm), will image details on the surface of many stars, as well as their environment, including multiple stars and clusters. Spectra will be obtained for each resel. It will also image neutron star, black-hole and micro-quasar candidates, as well as active galactic nuclei, quasars, gravitational lenses, and other Cosmic Vision targets observable with the initial modest crowding limit. With subsequent upgrade missions, the spectral coverage can be extended from 120nm to 20 microns, using four detectors carried by two to four focal spacecraft. The number of collector mirrors in the flotilla can also be increased from 12 to 100 and possibly 1,000. The imaging and spectroscopy of habitable exoplanets in the mid infra-red then becomes feasible once the collecting area reaches 6m2 , using a specialized mid infra-red focal spacecraft. Calculations ( Boccaletti et al., 2000) have shown that hypertelescope coronagraphy has unequalled sensitivity for detecting, at mid infra-red wavelengths, faint exoplanets within the exo-zodiacal glare. Later upgrades will enable the more difficult imaging and spectroscopy of these faint objects at visible wavelengths, using refined techniques of adaptive coronagraphy (Labeyrie. & Le Coroller, 2004). Together, the infra-red and visible spectral data carry rich information on the possible presence of life. The close environment of the central black-hole in the Milky Way will be imageable with unprecedented detail in the near infra-red . Cosmological imaging of remote galaxies at the limit of the known universe is also expected, from the ultra-violet to the near infra-red, following the first upgrade, and with greatly increasing sensitivity through successive upgrades. These areas will indeed greatly benefit from the upgrades, in terms of dynamic range, limiting complexity of the objects to be imaged, size of the elementary Direct Imaging Field , and limiting magnitude, approaching that of an 8-meter space telescope when 1000 apertures of 25cm are installed. Similar gains will occur for addressing fundamental problems in physics and cosmology, particularly when observing neutron stars and black holes, single or binary, including the giant black holes, with accretion disks and jets, in active galactic nuclei beyond the Milky Way. Gravitational lensing and micro-lensing patterns, including time-variable patterns and perhaps millisecond lensing flasheshich may be beamed by diffraction from sub-stellar masses at sub-parsec distances (Labeyrie, 1994) , will also be observable initially in the favourable cases, and upgrades will greatly improve the number of observable objects. The observability of gravitational waves emitted by binary lensing masses, in the form of modulated lensing patterns, is a debated issue ( Ragazzoni et al., 2003) but will also become addressable observationally. The technology readiness of Luciola approaches levels where low-orbit testing and stepwise implementation will become feasible in the 2015-2025 time frame. For the following decades beyond 2020, once accurate formation flying techniques will be mastered, much larger hypertelescopes such as the proposed 100km Exo-Earth Imager and the 100,000 km Neutron Star Imager should also become feasible. Luciola is therefore also seen as a precursor toward such very powerful instruments.

Labeyrie, Antoine↗
NASA NTRS2012

Theory of a Traveling Wave Feed for a Planar Slot Array Antenna

Planar arrays of waveguide-fed slots have been employed in many radar and remote sensing applications. Such arrays are designed in the standing wave configuration because of high efficiency. Traveling wave arrays can produce greater bandwidth at the expense of efficiency due to power loss in the load or loads. Traveling wave planar slot arrays may be designed with a long feed waveguide consisting of centered-inclined coupling slots. The feed waveguide is terminated in a matched load, and the element spacing in the feed waveguide is chosen to produce a beam squinted from the broadside. The traveling wave planar slot array consists of a long feed waveguide containing resonant-centered inclined coupling slots in the broad wall, coupling power into an array of stacked radiating waveguides orthogonal to it. The radiating waveguides consist of longitudinal offset radiating slots in a standing wave configuration. For the traveling wave feed of a planar slot array, one has to design the tilt angle and length of each coupling slot such that the amplitude and phase of excitation of each radiating waveguide are close to the desired values. The coupling slot spacing is chosen for an appropriate beam squint. Scattering matrix parameters of resonant coupling slots are used in the design process to produce appropriate excitations of radiating waveguides with constraints placed only on amplitudes. Since the radiating slots in each radiating waveguide are designed to produce a certain total admittance, the scattering (S) matrix of each coupling slot is reduced to a 2x2 matrix. Elements of each 2x2 S-matrix and the amount of coupling into the corresponding radiating waveguide are expressed in terms of the element S11. S matrices are converted into transmission (T) matrices, and the T matrices are multiplied to cascade the coupling slots and waveguide sections, starting from the load end and proceeding towards the source. While the use of non-resonant coupling slots may provide an additional degree of freedom in the design, resonant coupling slots simplify the design process. The amplitude of the wave going to the load is set at unity. The S11 parameter, r of the coupling slot closest to the load, is assigned an arbitrary value. A larger value of r will reduce the power dissipated in the load while increasing the reflection coefficient at the input port. It is now possible to obtain the excitation of the radiating waveguide closest to the load and the coefficients of the wave incident and reflected at the input port of this coupling slot. The next coupling slot parameter, r , is chosen to realize the excitation of that radiating waveguide. One continues this process moving towards the source, until all the coupling slot parameters r and hence the S11 parameter of the 4-port coupler, r, are known for each coupling slot. The goal is to produce the desired array aperture distribution in the feed direction. From an interpolation of the computed moment method data for the slot parameters, all the coupling slot tilt angles and lengths are obtained. From the excitations of the radiating waveguides computed from the coupling values, radiating slot parameters may be obtained so as to attain the desired total normalized slot admittances. This process yields the radiating slot parameters, offsets, and lengths. The design is repeated by choosing different values of r for the last coupling slot until the percentage of power dissipated in the load and the input reflection coefficient values are satisfactory. Numerical results computed for the radiation pattern, the tilt angles and lengths of coupling slots, and excitation phases of the radiating waveguides, are presented for an array with uniform amplitude excitation. The design process has been validated using computer simulations. This design procedure is valid for non-uniform amplitude excitations as well.

Rengarajan, Sembiam↗