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At least 469 records · Page 26

A Methodology for Investigating Adaptive Postural Control

Our research on postural control and human-environment interactions provides an appropriate scientific foundation for understanding the skill of mass handling by astronauts in weightless conditions (e.g., extravehicular activity or EVA). We conducted an investigation of such skills in NASA's principal mass-handling simulator, the Precision Air-Bearing Floor, at the Johnson Space Center. We have studied skilled movement-body within a multidisciplinary context that draws on concepts and methods from biological and behavioral sciences (e.g., psychology, kinesiology and neurophysiology) as well as bioengineering. Our multidisciplinary research has led to the development of measures, for manual interactions between individuals and the substantial environment, that plausibly are observable by human sensory systems. We consider these methods to be the most important general contribution of our EVA investigation. We describe our perspective as control theoretic because it draws more on fundamental concepts about control systems in engineering than it does on working constructs from the subdisciplines of biomechanics and motor control in the bio-behavioral sciences. At the same time, we have attempted to identify the theoretical underpinnings of control-systems engineering that are most relevant to control by human beings. We believe that these underpinnings are implicit in the assumptions that cut across diverse methods in control-systems engineering, especially the various methods associated with "nonlinear control", "fuzzy control," and "adaptive control" in engineering. Our methods are based on these theoretical foundations rather than on the mathematical formalisms that are associated with particular methods in control-systems engineering. The most important aspects of the human-environment interaction in our investigation of mass handling are the functional consequences that body configuration and stability have for the pick up of information or the achievement of overt goals. It follows that an essential characteristic of postural behavior is the effective maintenance of the orientation and stability of the sensory and motor "platforms" (e.g., head or shoulders) over variations in the human, the environment and the task. This general skill suggests that individuals should be sensitive to the functional consequences of body configuration and stability. In other words, individuals should perceive the relation between configuration, stability, and performance so that they can adaptively control their interaction with the surroundings. Human-environment interactions constitute robust systems in that individuals can maintain the stability of such interactions over uncertainty about and variations in the dynamics of the interaction. Robust interactions allow individuals to adopt orientations and configurations that are not optimal with respect to purely energetic criteria. Individuals can tolerate variation in postural states, and such variation can serve an important function in adaptive systems. Postural variability generates stimulation which is "textured" by the dynamics of the human-environment system. The texture or structure in stimulation provides information about variation in dynamics, and such information can be sufficient to guide adaption in control strategies. Our method were designed to measure informative patterns of movement variability.

McDonald, P. V.↗

Saturn Deep Atmospheric Entry Probes Delivered by INSIDE Jupiter Derivative Spacecraft

In situ probes are the most reliable means for sampling composition and conditions deep in giant planet atmospheres. Deep constituent abundances at the giant planets offer clues to conditions in the solar systems protoplanetary disk and variations with heliocentric distance. Currently in situ atmospheric data are available from only one giant planet, Jupiter, and probes that penetrate deeper than the Galileo probe are needed there to measure the deep abundances of such important species as H2O and H2S. Deep probes at Saturn would extend the sampled heliocentric range to Saturn, providing important constraints on the conditions and variability of the protoplanetary disk, and would provide significant new information about Saturn and its evolutionary processes. Such a probe mission could be implemented using a derivative of the INSIDE Jupiter mission's spacecraft as the Carrier/Relay Spacecraft (CRSC), with probes per JPL/Team X and other design studies. Additional information is contained in the original extended abstract.

Spilker, T. R.↗

Temperature Dependence and Recoil-free Fraction Effects in Olivines Across the Mg-Fe Solid Solution

Olivine and pyroxene are the major ferromagnesian minerals in most meteorite types and in mafic igneous rocks that are dominant at the surface of the Earth. It is probable that they are the major mineralogical components at the surface of any planetary body that has undergone differentiation processes. In situ mineralogical studies of the rocks and soils on Mars suggest that olivine is a widespread mineral on that planet s surface (particularly at the Gusev site) and that it has been relatively unaffected by alteration. Thus an understanding of the characteristics of Mossbauer spectra of olivine is of great importance in interpreting MER results. However, variable temperature Mossbauer spectra of olivine, which are needed to quantify recoil-free fraction effects and to understand the temperature dependence of olivine spectra, are lacking in the literature. Thus, we present here a study of the temperature dependence and recoil-free fraction of a series of synthetic olivines.

Sklute, E. C.↗

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

Shaykhian, Gholam Ali↗

Aqua-planet simulations of the formation of the South Atlantic convergence zone

The impact of Amazon Basin convection and cold fronts on the formation and maintenance of the South Atlantic convergence zone (SACZ) is studied using aqua-planet simulations with a general circulation model. In the model, a circular patch of warm sea-surface temperature (SST) is used to mimic the effect of the Amazon Basin on South American monsoon convection. The aqua-planet simulations were designed to study the effect of the strength and latitude of Amazon Basin convection on the formation of the SACZ. The simulations indicate that the strength of the SACZ increases as the Amazon convection intensifies and is moved away from the equator. Of the two controls studied here, the latitude of the Amazon convection exerts the strongest effect on the strength of the SACZ. An analysis of the synoptic-scale variability in the simulations shows the importance of frontal systems in the formation of the aqua-planet SACZ. Composite time series of frontal systems that occurred in the simulations show that a robust SACZ occurs when fronts penetrate into the subtropics and become stationary there as they cross eastward of the longitude of the Amazon Basin. Moisture convergence associated with these frontal systems produces rainfall not along the model SACZ region and along a large portion of the northern model Amazon Basin. Simulations in which the warm SST patch was too weak or too close to the equator did not produce frontal systems that extended into the tropics and became stationary, and did not form a SACZ. In the model, the SACZ forms as Amazon Basin convection strengthens and migrates far enough southward to allow frontal systems to penetrate into the tropics and stall over South America. This result is in agreement with observations that the SACZ tends to form after the onset of the monsoon season in the Amazon Basin.

South American Monsoon↗

Optimization of KINETICS Chemical Computation Code

NASA JPL has been creating a code in FORTRAN called KINETICS to model the chemistry of planetary atmospheres. Recently there has been an effort to introduce Message Passing Interface (MPI) into the code so as to cut down the run time of the program. There has been some implementation of MPI into KINETICS; however, the code could still be more efficient than it currently is. One way to increase efficiency is to send only certain variables to all the processes when an MPI subroutine is called and to gather only certain variables when the subroutine is finished. Therefore, all the variables that are used in three of the main subroutines needed to be investigated. Because of the sheer amount of code that there is to comb through this task was given as a ten-week project. I have been able to create flowcharts outlining the subroutines, common blocks, and functions used within the three main subroutines. From these flowcharts I created tables outlining the variables used in each block and important information about each. All this information will be used to determine how to run MPI in KINETICS in the most efficient way possible.

planetary atmospheres↗

Future Changes in Major Stratospheric Warmings in CCMI Models

Major stratospheric warmings (MSWs) are one of the most important phenomena of wintertime Arctic stratospheric variability. They consist of a warming of the Arctic stratosphere and a deceleration of the polar night jet, triggered by an anomalously high injection of tropospheric wave activity into the stratosphere. Due to the relevance and the impact of MSWs on the tropospheric circulation, several model studies have investigated their potential responses to climate change. However, a wide range of results has been obtained, extending from a future increase in the frequency of MSWs to a decrease. These discrepancies might be explained by different factors such as a competition of radiative and dynamical contributors with opposite effects on the Arctic polar vortex, biases of models to reproduce the related processes, or the metric chosen for the identification of MSWs. In this study, future changes in wintertime Arctic stratospheric variability are examined in order to obtaina more precise picture of future changes in the occurrence of MSWs. In particular, transient REFC2 simulations of different CCMs involved in the Chemistry Climate Model Initiative (CCMI) are used. These simulations extend from 1960 to 2100 and include forcings by halogens and greenhouse gases following the specifications of the CCMI-REF-C2 scenario. Sea surface temperatures (SSTs) and sea-ice distributions are either prescribed from coupled climate model integrations or calculated internally in the case of fully coupled atmosphere-ocean CCMs. Potential changes in the frequency and main characteristics of MSWs in the future are investigated with special focus on the dependence of the results on the criterion for the identification of MSWs and the tropospheric forcing of these phenomena.

Chemistry-Climate Modeling↗

Interpreting Space-Based Trends in Carbon Monoxide with Multiple Models

We use a series of chemical transport model and chemistry climate model simulations to investigate the observed negative trends in MOPITT CO over several regions of the world, and to examine the consistency of timedependent emission inventories with observations. We find that simulations driven by the MACCity inventory, used for the Chemistry Climate Modeling Initiative (CCMI), reproduce the negative trends in the CO column observed by MOPITT for 2000-2010 over the eastern United States and Europe. However, the simulations have positive trends over eastern China, in contrast to the negative trends observed by MOPITT. The model bias in CO, after applying MOPITT averaging kernels, contributes to the model-observation discrepancy in the trend over eastern China. This demonstrates that biases in a model's average concentrations can influence the interpretation of the temporal trend compared to satellite observations. The total ozone column plays a role in determining the simulated tropospheric CO trends. A large positive anomaly in the simulated total ozone column in 2010 leads to a negative anomaly in OH and hence a positive anomaly in CO, contributing to the positive trend in simulated CO. These results demonstrate that accurately simulating variability in the ozone column is important for simulating and interpreting trends in CO.

carbon monoxide↗

Probabilistic Risk Assessment of Aging Layered Pressure Vessels

The National Aeronautics and Space Administration (NASA) operates approximately 300 aging layered pressure vessels that were designed and manufactured prior to ASME Boiler and Pressure Vessel (B&PV) code requirements. In order to make decisions regarding the continued fitness-for-service of these non-code carbon steel vessels, it is necessary to perform a relative risk of failure assessment for each vessel. However, risk assessment of these vessels is confounded by uncertainties and variabilities related to the use of proprietary materials in fabrication, missing construction records, geometric discontinuities, weld residual stresses, and complex service stress gradients in and around the welds. Therefore, a probabilistic framework that can capture these uncertainties and variabilities has been developed to assess the fracture risk of flaws in regions of interest, such as longitudinal and circumferential welds, using the NESSUS® probabilistic modeling software and NASGRO® fracture mechanics software. In this study, the probabilistic framework was used to predict variability in the stress intensity factor associated with different reference flaws located in the head-to-shell circumferential welds of a 4-layer and 14-layer pressure vessel. The probabilistic studies predict variability in flaw behavior and the important uncertain parameters for each reference flaw location.

Riha, D. S.↗

TPSAS-NF1676L-20398-DND

Arctic sea ice is melting at an alarming rate. Many factors influence the acceleration of Arctic sea ice loss e.g., atmospheric and ocean heat transport, circulation patterns, and atmospheric thermodynamic state. Arctic low clouds, however, have been shown to play an especially important role in sea ice extent variability. Due to the nature of clouds, changes in Arctic sea ice cover can profoundly influence cloud characteristics as well. How does the interaction with clouds influence sea ice extent? This question is studied using state-of-the-art NASA satellite observations from CALIPSO, CloudSAT, and CERES. The results indicate that the response of clouds to changing sea ice act to inhibit summer time melting and accelerate winter time growth buffering sea ice loss. Thus, clouds serve as a protector of sea ice.

Patrick C Taylor↗

Cloud Detection over Sunglint Regions with Observations from the Earth Polychromatic Imaging Camera (EPIC)

With the ability to observe the entire sunlit side of the Earth, EPIC data have become an important resource for studying cloud daily variability. Inaccurate cloud masking is a great source of uncertainty. One main region that is prone to error in cloud masking is the sunglint area over ocean surfaces. Cloud detection over these regions is challenging for the EPIC instrument because of its limited spectral channels. Clear sky ocean surface reflectance from visible channels over sunglint is much larger than that over the non-glint areas and can exceed reflectance from thin clouds. This paper presents an improved EPIC ocean cloud masking algorithm (Version 3). Over sunglint regions (glint angle ≤ 25°), the algorithm utilizes EPIC’s oxygen (O2) A-band ratio (764nm to 780 nm) in addition to the 780 nm reflectance observations in masking tests. Outside the sunglint regions, a dynamic reflectance threshold for the Rayleigh corrected 780 nm reflectance is applied. The thresholds are derived as a function of glint angle. When compared with co-located data from the geosynchronous Earth orbit (GEO) and the low Earth orbit (LEO) observations, the consistency of the new ocean cloud mask algorithm has increased by 4~10% and 4~6% in the glint center and granule edges respectively. The false positive rate is reduced by 10~17%. Overall global ocean cloud detection consistency increases by 2%. This algorithm, along with other improvements to the EPIC cloud masks, has been implemented in the EPIC cloud products Version 3. This algorithm will improve the cloud daily variability analysis by removing the artificial peak at local noon time in the glint center latitudes and reducing biases in the early morning and late afternoon cloud fraction over ocean surfaces.

EPIC↗

IN11B-1621: Quantifying How Climate Affects Vegetation in the Amazon Rainforest

Amazon droughts in 2005 and 2010 have raised serious concern about the future of the rainforest. Amazon forests are crucial because of their role as the largest carbon sink in the world which would effect the global warming phenomena with decreased photosynthesis activity. Especially, after a decline in plant growth in 1.68 million km2 forest area during the once-in-a-century severe drought in 2010, it is of primary importance to understand the relationship between different climatic variables and vegetation. In an earlier study, we have shown that non-linear models are better at capturing the relation dynamics of vegetation and climate variables such as temperature and precipitation, compared to linear models. In this research, we learn precise models between vegetation and climatic variables (temperature, precipitation) for normal conditions in the Amazon region using genetic programming based symbolic regression. This is done by removing high elevation and drought affected areas and also considering the slope of the region as one of the important factors while building the model. The model learned reveals new and interesting ways historical and current climate variables affect the vegetation at any location. MAIAC data has been used as a vegetation surrogate in our study. For temperature and precipitation, we have used TRMM and MODIS Land Surface Temperature data sets while learning the non-linear regression model. However, to generalize the model to make it independent of the data source, we perform transfer learning where we regress a regularized least squares to learn the parameters of the non-linear model using other data sources such as the precipitation and temperature from the Climatic Research Center (CRU). This new model is very similar in structure and performance compared to the original learned model and verifies the same claims about the nature of dependency between these climate variables and the vegetation in the Amazon region. As a result of this study, we are able to learn, for the very first time how exactly different climate factors influence vegetation at any location in the Amazon rainforests, independent of the specific sources from which the data has been obtained.

global warming↗

Variability in surface ECG morphology: signal or noise?

Using data collected from canine models of acute myocardial ischemia, we investigated two issues of major relevance to electrocardiographic signal averaging: ECG epoch alignment, and the spectral characteristics of the beat-to-beat variability in ECG morphology. With initial digitization rates of 1 kHz, an iterative a posteriori matched filtering alignment scheme, and linear interpolation, we demonstrated that there is sufficient information in the body surface ECG to merit alignment to a precision of 0.1 msecs. Applying this technique to align QRS complexes and atrial pacing artifacts independently, we demonstrated that the conduction delay from atrial stimulus to ventricular activation may be so variable as to preclude using atrial pacing as an alignment mechanism, and that this variability in conduction time be modulated at the frequency of respiration and at a much lower frequency (0.02-0.03Hz). Using a multidimensional spectral technique, we investigated the beat-to-beat variability in ECG morphology, demonstrating that the frequency spectrum of ECG morphological variation reveals a readily discernable modulation at the frequency of respiration. In addition, this technique detects a subtle beat-to-beat alternation in surface ECG morphology which accompanies transient coronary artery occlusion. We conclude that physiologically important information may be stored in the variability in the surface electrocardiogram, and that this information is lost by conventional averaging techniques.

NASA Discipline Cardiopulmonary↗

Space Transportation System Availability Requirement and Its Influencing Attributes Relationships

It is important that engineering and management accept the need for an availability requirement that is derived with its influencing attributes. It is the intent of this paper to provide the visibility of relationships of these major attribute drivers (variables) to each other and the resultant system inherent availability. Also important to provide bounds of the variables providing engineering the insight required to control the system's engineering solution, e.g., these influencing attributes become design requirements also. These variables will drive the need to provide integration of similar discipline functions or technology selection to allow control of the total parts count. The relationship of selecting a reliability requirement will place a constraint on parts count to achieve a given availability requirement or if allowed to increase the parts count will drive the system reliability requirement higher. They also provide the understanding for the relationship of mean repair time (or mean down time) to maintainability, e.g., accessibility for repair, and both the mean time between failure, e.g., reliability of hardware and availability. The concerns and importance of achieving a strong availability requirement is driven by the need for affordability, the choice of using the two launch solution for the single space application, or the need to control the spare parts count needed to support the long stay in either orbit or on the surface of the moon. Understanding the requirements before starting the architectural design concept will avoid considerable time and money required to iterate the design to meet the redesign and assessment process required to achieve the results required of the customer's space transportation system. In fact the impact to the schedule to being able to deliver the system that meets the customer's needs, goals, and objectives may cause the customer to compromise his desired operational goal and objectives resulting in considerable increased life cycle cost of the fielded space transportation system.

Rhodes, Russell E.↗

Space Transportation System Availability Requirements and Its Influencing Attributes Relationships

It is important that engineering and management accept the need for an availability requirement that is derived with its influencing attributes. It is the intent of this paper to provide the visibility of relationships of these major attribute drivers (variables) to each other and the resultant system inherent availability. Also important to provide bounds of the variables providing engineering the insight required to control the system's engineering solution, e.g., these influencing attributes become design requirements also. These variables will drive the need to provide integration of similar discipline functions or technology selection to allow control of the total parts count. The relationship of selecting a reliability requirement will place a constraint on parts count to achieve a given availability requirement or if allowed to increase the parts count will drive the system reliability requirement higher. They also provide the understanding for the relationship of mean repair time (or mean down time) to maintainability, e.g., accessibility for repair, and both the mean time between failure, e.g., reliability of hardware and availability. The concerns and importance of achieving a strong availability requirement is driven by the need for affordability, the choice of using the two launch solution for the single space application, or the need to control the spare parts count needed to support the long stay in either orbit or on the surface of the moon. Understanding the requirements before starting the architectural design concept will avoid considerable time and money required to iterate the design to meet the redesign and assessment process required to achieve the results required of the customer's space transportation system. In fact the impact to the schedule to being able to deliver the system that meets the customer's needs, goals, and objectives may cause the customer to compromise his desired operational goal and objectives resulting in considerable increased life cycle cost of the fielded space transportation system.

Rhodes, Russell E.↗

Space Transportation System Availability Requirement and Its Influencing Attributes Relationships

It is important that engineering and management accept the need for an availability requirement that is derived with its influencing attributes. It is the intent of this paper to provide the visibility of relationships of these major attribute drivers (variables) to each other and the resultant system inherent availability. Also important to provide bounds of the variables providing engineering the insight required to control the system's engineering solution, e.g., these influencing attributes become design requirements also. These variables will drive the need to provide integration of similar discipline functions or technology selection to allow control of the total parts count. The relationship of selecting a reliability requirement will place a constraint on parts count to achieve a given availability requirement or if allowed to increase the parts count will drive the system reliability requirement higher. They also provide the understanding for the relationship of mean repair time (or mean down time) to maintainability, e.g., accessibility for repair, and both the mean time between failure, e.g., reliability of hardware and availability. The concerns and importance of achieving a strong availability requirement is driven by the need for affordability, the choice of using the two launch solution for the single space application, or the need to control the spare parts count needed to support the long stay in either orbit or on the surface of the moon. Understanding the requirements before starting the architectural design concept will avoid considerable time and money required to iterate the design to meet the redesign and assessment process required to achieve the results required of the customer's space transportation system. In fact the impact to the schedule to being able to deliver the system that meets the customer's needs, goals, and objectives may cause the customer to compromise his desired operational goal and objectives resulting in considerable increased life cycle cost of the fielded space transportation system.

reliability↗

Assessing within-Field Corn and Soybean Yield Variability from WorldView-3, Planet, Sentinel-2, and Landsat 8 Satellite Imagery

Crop yield monitoring is an important component in agricultural assessment. Multispectral remote sensing instruments onboard space-borne platforms such as Advanced Very High Resolution Radiometer (AVHRR), Moderate Resolution Imaging Spectroradiometer (MODIS), and Visible Infrared Imaging Radiometer Suite (VIIRS) have shown to be useful for efficiently generating timely and synoptic information on the yield status of crops across regional levels. However, the coarse spatial resolution data inherent to these sensors provides little utility at the management level. Recent satellite imagery collection advances toward finer spatial resolution (down to 1 m) alongside increased observational cadence (near daily) implies information on crops obtainable at field and within-field scales to support farming needs is now possible. To test this premise, we focus on assessing the efficiency of multiple satellite sensors, namely WorldView-3, Planet/Dove-Classic, Sentinel-2, and Landsat 8 (through Harmonized Landsat Sentinel-2 (HLS)), and investigate their spatial, spectral (surface reflectance (SR) and vegetation indices (VIs)), and temporal characteristics to estimate corn and soybean yields at sub-field scales within study sites in the US state of Iowa. Precision yield data as referenced to combine harvesters’ GPS systems were used for validation. We show that imagery spatial resolution of 3 m is critical to explaining 100% of the within-field yield variability for corn and soybean. Our simulation results show that moving to coarser resolution data of 10 m, 20 m, and 30 m reduced the explained variability to 86%, 72%, and 59%, respectively. We show that the most important spectral bands explaining yield variability were green (0.560 µm), red-edge (0.726 µm), and near-infrared (NIR - 0.865 µm). Furthermore, the high temporal frequency of Planet and a combination of Sentinel-2/Landsat 8 (HLS) data allowed for optimal date selection for yield map generation. Overall, we observed mixed performance of satellite-derived models with the coefficient of determination (R^2) varying from 0.21 to 0.88 (averaging 0.56) for the 30 m HLS and from 0.09 to 0.77 (averaging 0.30) for 3 m Planet. R^2 was lower for fields with higher yields, suggesting saturation of the satellite-collected reflectance features in those cases. Therefore, other biophysical variables, such as soil moisture and evapotranspiration, at similar fine spatial resolutions are likely needed alongside the optical imagery to fully explain the yields.

agriculture; yield; within-field; corn; soybean; r↗

Toroidal Variable-Line-Space Gratings: The Good, the Bad and The Ugly

Toroidal variable-line-space (VLS) gratings are an important factor in the design of an efficient VUV solar telescope that will measure the CIV (155nm) and MgII (280nm) emissions lines in the Sun's transition region. In 1983 Kita and Harada described spherical VLS gratings but the technology to commercially fabricate these devices is a recent development, especially for toroidal surfaces. This paper will describe why this technology is important in the development of the Solar Ultraviolet Magnetograph Investigation (SUMI) sounding rocket program (the good), the delays due to the conversion between the TVLS grating design and the optical fabrication (the bad), and finally the optical testing, alignment and tolerancing of the gratings (the ugly). The Solar Ultraviolet Magnetograph Investigation, SUMI, has been reported in several papers since this program began in 2000. The emphasis of this paper is to describe SUMI's Toroidal Variable-Line-Space (TVLS) gratings. These gratings help SUMI meet its scientific goals which require both high spectral resolution and high optical efficiency for magnetic field measurements in the vacuum ultraviolet wavelength band of the solar spectrum (the good). Unfortunately, the technology readiness level of these gratings has made their implementation difficult, especially for a sounding rocket payload (the bad). Therefore, this paper emphasizes the problems and solutions that were developed to use these gratings in SUMI (the ugly). Section 2 contains a short review of the scientific goals of SUMI and why this mission is important in the understanding of the 3D structure of the magnetic field on the Sun. The flight hardware that makes up the SUMI payload is described in Section 3 with emphasis on those components that affect the TVLS gratings. Section 4 emphasizes the alignment, testing and optical modeling that were developed to optimize the performance of these gratings.

West, Edward A.↗