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At least 1,693 records · Page 94

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

Work done in the period Jan. - June 1994 is summarized. Two threads of research have been followed. First, the thermodynamics approach was used to model the chemical and mechanical responses of composites exposed to high temperatures. The thermodynamics approach lends itself easily to the usage of variational principles. This thermodynamic-variational approach has been applied to the transpiration cooling problem. The second thread is the development of a better algorithm to solve the governing equations resulting from the modeling. Explicit finite difference method is explored for solving the governing nonlinear, partial differential equations. The method allows detailed material models to be included and solution on massively parallel supercomputers. To demonstrate the feasibility of the explicit scheme in solving nonlinear partial differential equations, a transpiration cooling problem was solved. Some interesting transient behaviors were captured such as stress waves and small spatial oscillations of transient pressure distribution.

Mcmanus, Hugh L.↗

Computer modeling of the sensitivity of a laser water vapor sensor to variations in temperature and air speed

Currently, there is disagreement among existing methods of determining atmospheric water vapor concentration at dew-points below -40 C. A major source of error is wall effects which result from the necessity of bringing samples into the instruments. All of these instruments also have response times on the order of seconds. NASA Langley is developing a water vapor sensor which utilizes the absorption of the infrared radiation produced by a diode laser to estimate water vapor concentration. The laser beam is directed through an aircraft window to a retroreflector located on an engine. The reflected beam is detected by an infrared detector located near the laser. To maximize signal to noise, derivative signals are analyzed. By measuring the 2f/DC signal and correcting for ambient temperature, atmospheric pressure and air speed (which results in a Doppler shifting of the laser beam), the water vapor concentration can be retrieved. Since this is an in situ measurement there are no wall effects and measurements can be made at a rate of more than 20 per second. This allows small spatial variations of water vapor to be studied. In order to study the sensitivity of the instrument to variations in temperature and air speed, a computer program which generated the 2f, 3f, 4f, DC and 2f/DC signals of the instrument as a function of temperature, pressure and air speed was written. This model was used to determine the effect of errors in measurement of the temperature and air speed on the measured water vapor concentration. Future studies will quantify the effect of pressure measurement errors, which are expected to be very small. As a result of these studied, a retrieval algorithm has been formulated, and will be applied to data taken during the PEM-West atmospheric science field mission. Spectroscopic studies of the water vapor line used by the instrument will be used to refine this algorithm. To prepare for these studies, several lasers have been studied to determine their output frequency range and power.

Tucker, George F.↗

TPSAS-NF1676L-10574-DND

The Infrared Atmospheric Sounding Interferometer (IASI) aboard of MetOP-A was successfully launched on 19 October 2006 and has been providing excellent data for more than 3 years. The IASI spectra can be converted into proxy data for the NPOESS Crosstrack Infrared Sounder (CrIS) through a rigorous mathematical transformation by taking into account of instrument characteristics of both the IASI and the CrIS. The 15-channel AMSU temperature sounder, and the 5-channel and Microwave Humidity Sounder (MHS) aboard of MetOP-A can be used to generate proxy data for the NPOESS Advanced Technology Mircrowave Sounder (ATMS). The CrIS and ATMS make up the Cross-track Infrared and Microwave Sounder Suite (CrIMSS). CrIMSS will primarily provide global temperature, moisture, and pressure profiles. We will describe the method used in generating the proxy data and show results of using the proxy data for evaluation of the NPOESS CrIMSS Environmental Data Record (EDR) retrieval algorithm.

Xu Liu↗

TPSAS-NF1676L-10898-DND

The Infrared Atmospheric Sounding Interferometer (IASI) aboard of MetOP-A was successfully launched on 19 October 2006 and has been providing excellent data for more than 3 years. The IASI spectra can be converted into proxy data for the NPOESS Crosstrack Infrared Sounder (CrIS) through a rigorous mathematical transformation by taking into account of instrument characteristics of both the IASI and the CrIS. The 15-channel AMSU temperature sounder, and the 5-channel and Microwave Humidity Sounder (MHS) aboard of MetOP-A can be used to generate proxy data for the NPOESS Advanced Technology Mircrowave Sounder (ATMS). The CrIS and ATMS make up the Cross-track Infrared and Microwave Sounder Suite (CrIMSS). CrIMSS will primarily provide global temperature, moisture, and pressure profiles. We will describe the method used in generating the proxy data and show results of using the proxy data for evaluation of the NPOESS CrIMSS Environmental Data Record (EDR) retrieval algorithm.

Xu Liu↗

Systematic Errors in Simulated L-Band Brightness Temperature in the SMAP Level-4 Soil Moisture Analysis

The NASA Soil Moisture Active Passive (SMAP) mission has been providing L-band (1.4 GHz) brightness temperature (Tb) observations since April 2015. By assimilating the Tb observations into the NASA Catchment land surface model using a spatially distributed ensemble Kalman filter (EnKF), the SMAP Level-4 Soil Moisture (L4_SM) product provides global, 3-hourly, 9-km resolution estimates of surface (0-5 cm) and root-zone (0-100 cm) soil moisture with ~2.5-day latency for use in research and applications. The EnKF-based L4_SM analysis assumes unbiased forecast errors. Consequently, the seasonally varying bias between the model forecast Tb and the observed values is removed prior to the assimilation of the SMAP Tb observations. The L4_SM system is thus designed to only correct errors in synoptic-scale and interannual variations from the long-term mean seasonal cycle while maintaining the model’s (possibly wrong) climatology. In this paper, we examine the Tb observation-minus-forecast (O-F) residuals from the L4_SM Version 7 product (computed after rescaling the Tb observations to the mean seasonal cycle of the simulated Tb). The long-term average of the Tb O-F residuals has a global mean of only 0.13 K and locally small values, ranging from -1 to 3 K. The model forecast Tb, however, still exhibits undesirable systematic errors relative to the (rescaled) Tb observations. At some locations, the time-average Tb O-F values strongly depend on surface soil moisture (SM). At the Yanco SMAP core validation site, for example, the Tb O-F residuals typically range from 5 to 15 K under dry soil moisture conditions (SM < 0.15 m3 m-3) yet are predominantly negative under wet soil moisture conditions (SM > 0.25 m3 m-3), with values ranging from 0 to -40 K. This results in soil moisture analysis increments that persistently make the soil drier under dry SM conditions and persistently make the soil wetter under wet SM conditions, suggesting an error in the dynamic range of the simulated Tb, soil moisture or soil temperature. In this paper, we describe the higher-order systematic Tb forecast errors in more detail, examine their impact on the L4_SM product quality, and explore potential avenues to improve the L4_SM algorithm.

Rolf Reichle↗

Machine Learning-Assisted High-Temperature Reservoir Thermal Energy Storage Optimization: Numerical Modeling and Machine Learning Input and Output Files

This data set includes the numerical modeling input files and output files used to synthesize data, and the reduced-order machine learning models trained from the synthesized data for reservoir thermal energy storage site identification. In this study, a machine-learning-assisted computational framework is presented to identify High-Temperature Reservoir Thermal Energy Storage (HT-RTES) site with optimal performance metrics by combining physics-based simulation with stochastic hydrogeologic formation and thermal energy storage operation parameters, artificial neural network regression of the simulation data, and genetic algorithm-enabled multi-objective optimization. A doublet well configuration with a layered (aquitard-aquifer-aquitard) generic reservoir is simulated for cases of continuous operation and seasonal-cycle operation scenarios. Neural network-based surrogate models are developed for the two scenarios and applied to generate the Pareto fronts of the HT-RTES performance for four potential HT-RTES sites. The developed Pareto optimal solutions indicate the performance of HT-RTES is operation-scenario (i.e., fluid cycle) and reservoir-site dependent, and the performance metrics have competing effects for a given site and a given fluid cycle. The developed neural network models can be applied to identify suitable sites for HT-RTES, and the proposed framework sheds light on the design of resilient HT-RTES systems. All the simulations and the neural network model were done by Idaho National Laboratory. A detailed description of the work was reported in publication linked below.

15 GEOTHERMAL ENERGY↗

Ross Sea Polynyas: Response of Ice Concentration Retrievals to Large Areas of Thin Ice

For a 3-month period between May and July of 2005, we examine the response of the Advanced Microwave Scanning Radiometer (AMSR-E) Enhanced NASA Team 2 (NT2) and AMSR-E Bootstrap (ABA) ice concentration algorithms to large areas of thin ice of the Ross Sea polynyas. Coincident Envisat Synthetic Aperture Radar (SAR) coverage of the region during this period offers a detailed look at the development of the polynyas within several hundred kilometers of the ice front. The high-resolution imagery and derived ice motion fields show bands of polynya ice, covering up to approximately 105 km(sup 2) of the Ross Sea, that are associated with wind-forced advection. In this study, ice thickness from AMSR-E 36 GHz polarization information serves as the basis for examination of the response. The quality of the thickness of newly formed sea ice (<10 cm) from AMSR-E is first assessed with thickness estimates derived from ice surface temperatures from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. The effect of large areas of thin ice in lowering the ice concentration estimates from both NT2/ABA approaches is clearly demonstrated. Results show relatively robust relationships between retrieved ice concentrations and thin ice thickness estimates that differ between the two algorithms. These relationships define the approximate spatial coincidence of ice concentration and thickness isopleths. Using the 83% (ABA) and 91% (NT2) isopleths as polynya boundaries, we show that the computed coverage compares well with that using the estimated 10-cm thickness contour. The thin ice response characterized here suggests that in regions with polynyas, the retrieval results could be used to provide useful geophysical information, namely thickness and coverage.

algorithms↗

Sea Surface Salinity Distribution in the Southern Ocean as Observed from Space

Large-scale spatial and temporal variabilities of sea surface salinity (SSS) in the Southern Ocean from 2011 to 2017 were studied using products derived from microwave sensors on board Aquarius, Soil Moisture and Ocean Salinity (SMOS), and Soil Moisture Active and Passive (SMAP) satellites. Four products, three from Aquarius and one from SMOS, were evaluated and shown to be generally consistent within 0.3 to 0.6 psu and agree favorably with in situ measurements. However, although the Aquarius products show consistent seasonality of SSS with high values of 34.45 psu in October and low values of 33.40 psu in May, theSMOS and SMAP products lack such seasonal variations. This may be caused by larger uncertainties in the SMOS and SMAP data due in part to the lack of concurrent scatterometer measurements that is used to correct for roughness effects. The four products provide similar spatial distributions of SSS with root mean square difference from 0.25 to 0.58 psu. Differences among Aquarius products are mainly due to varying salinity retrieval algorithms, smoothing, and masking of sea ice, while the SMOS product showed the highest SSS deviation that is likely due to the bias adjustment done on the data set. Our analyses show that SSS in the Southern Ocean region has significant meridional variations with the lowest SSS near the ice edge and highest at lower latitudes. The SSS is also lowest in summer indicating the predominant influence of sea ice and glacial melt, but it stays low near ice edges even during the growth season. Salinity together with temperature is the key parameters that control the state and circulation of the World's oceans. The large‐scale distribution of the sea surface salinity of the Southern Ocean is quantified for the first time using Aquarius, Soil Moisture and Ocean Salinity, and Soil Moisture Active and Passive satellite microwave data. Seasonal and interannual changes in the distribution as affected by the sea ice cover, surface temperature, and precipitation are evaluated. Comparative studies were done, using four different products that are publicly available, in conjunction with in situ observations to gain insights into the true nature of the distribution and how consistently the sea surface salinity is depicted by the different products. There are general consistencies in the products, and discrepancies are attributed to different algorithms, smoothing techniques, and sea ice masking. Aquarius data are shown to have higher accuracy than Soil Moisture and Ocean Salinity and Soil Moisture Active and Passive products in part because of having concurrent scatterometer that provides accurate correction to roughness effects.

Garcia-Eidell, Cynthia↗

Errors in Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) Kinetic Temperature Caused by Non-Local Thermodynamic Equilibrium Model Parameters

The vast set of near global and continuous atmospheric measurements made by the SABER instrument since 2002, including daytime and nighttime kinetic temperature (T(sub k)) from 20 to 105 km, is available to the scientific community. The temperature is retrieved from SABER measurements of the atmospheric 15 micron CO2 limb emission. This emission separates from local thermodynamic equilibrium (LTE) conditions in the rarefied mesosphere and thermosphere, making it necessary to consider the CO2 vibrational state non-LTE populations in the retrieval algorithm above 70 km. Those populations depend on kinetic parameters describing the rate at which energy exchange between atmospheric molecules take place, but some of these collisional rates are not well known. We consider current uncertainties in the rates of quenching of CO2 (v2 ) by N2 , O2 and O, and the CO2 (v2 ) vibrational-vibrational exchange to estimate their impact on SABER T(sub k) for different atmospheric conditions. The T(sub k) is more sensitive to the uncertainty in the latter two and their effects depend on altitude. The T(sub k) combined systematic error due to non-LTE kinetic parameters does not exceed +/- 1.5 K below 95 km and +/- 4-5 K at 100 km for most latitudes and seasons (except for polar summer) if the Tk profile does not have pronounced vertical structure. The error is +/- 3 K at 80 km, +/- 6 K at 84 km and +/- 18 K at 100 km under the less favourable polar summer conditions. For strong temperature inversion layers, the errors reach +/- 3 K at 82 km and +/- 8 K at 90 km. This particularly affects tide amplitude estimates, with errors of up to +/- 3 K.

Garcia-Comas, Maya↗

Calibration of the advanced microwave sounding unit-A for NOAA-K

The thermal-vacuum chamber calibration data from the Advanced Microwave Sounding Unit-A (AMSU-A) for NOAA-K, which will be launched in 1996, were analyzed to evaluate the instrument performance, including calibration accuracy, nonlinearity, and temperature sensitivity. The AMSU-A on NOAA-K consists of AMSU-A2 Protoflight Model and AMSU-A1 Flight Model 1. The results show that both models meet the instrument specifications, except the AMSU-A1 antenna beamwidths, which exceed the requirement of 3.3 +/- 10%. We also studied the instrument's radiometric characterizations which will be incorporated into the operational calibration algorithm for processing the in-orbit AMSU-A data from space. Particularly, the nonlinearity parameters which will be used for correcting the nonlinear contributions from an imperfect square-law detector were determined from this data analysis. It was found that the calibration accuracies (differences between the measured scene radiances and those calculated from a linear two-point calibration formula) are polarization-dependent. Channels with vertical polarizations show little cold biases at the lowest scene target temperature 84K, while those with horizontal polarizations all have appreciable cold biases, which can be up to 0.6K. It is unknown where these polarization-dependent cold biases originate, but it is suspected that some chamber contamination of hot radiances leaked into the cold scene target area. Further investigation in this matter is required. The existence and magnitude of nonlinearity in each channel were established and a quadratic formula for modeling these nonlinear contributions was developed. The model was characterized by a single parameter u, values of which were obtained for each channel via least-squares fit to the data. Using the best-fit u values, we performed a series of simulations of the quadratic corrections which would be expected from the space data after the launch of AMSU-A on NOAA-K. In these simulations, the cosmic background radiance corresponding to a cold space temperature 2.73K was adopted as one of the two reference points of calibration. The largest simulated nonlinear correction is about 0.3K, which occurs at channel 15 when the instrument temperature is at 38.09 deg C. Others are less than 0.2K in the remaining channels. Possible improvement for future instrument calibration is also discussed.

Mo, Tsan↗

On Polymorphic Circuits and Their Design Using Evolutionary Algorithms

This paper introduces the concept of polymorphic electronics (polytronics) - referring to electronics with superimposed built-in functionality. A function change does not require switches/reconfiguration as in traditional approaches. Instead the change comes from modifications in the characteristics of devices involved in the circuit, in response to controls such as temperature, power supply voltage (VDD), control signals, light, etc. The paper illustrates polytronic circuits in which the control is done by temperature, morphing signals, and VDD respectively. Polytronic circuits are obtained by evolutionary design/evolvable hardware techniques. These techniques are ideal for the polytronics design, a new area that lacks design guidelines, know-how,- yet the requirements/objectives are easy to specify and test. The circuits are evolved/synthesized in two different modes. The first mode explores an unstructured space, in which transistors can be interconnected freely in any arrangement (in simulations only). The second mode uses a Field Programmable Transistor Array (FPTA) model, and the circuit topology is sought as a mapping onto a programmable architecture (these experiments are performed both in simulations and on FPTA chips). The experiments demonstrated the synthesis. of polytronic circuits by evolution. The capacity of storing/hiding "extra" functions provides for watermark/invisible functionality, thus polytronics may find uses in intelligence/security applications.

Stoica, Adrian↗

Stratospheric Temperature Trends from Small Rockets Between 1969-1995

Between 1958-1995 a significant number of small meteorological rocketsondes were launched by United States (US) agencies from as many as 30 sites to as few as 3-4 sites in 1995. Stratospheric temperature trends were derived for many of the sites for the period 1969-1995. Similar long-term trends also were derived using rocketsondes launched from sites of the Former Soviet Union (FSU). The advantage of these two particular sets of rocket temperature measurements is the internal consistency of the data. All measurements were made with the same instrument, i.e., Datasonde in the case of the US sites and the M100B in the case of the FSU sites. Data from each instrument type were processed using its unique reduction method. Thus, all data were processed in the same manner including the method of applying corrections (necessary because of thermal heating of the thermistor from the high fall velocities experienced and from radiation effects). Straight-line least squares fit to the data made to monthly-mean measurements gave a downward change of 2-3 K per decade. A more complex fitting algorithm would have resulted in finer results but the straight-line fit was adequate for the analysis presented. Trend data are presented for 50 km, 40 km, and 25 km altitude levels. Trends for the US and FSU sites are quite similar. The 25km (50-hPa) level data are compared with radiosonde temperatures. Temperature trends over the 25-year period is different at each of the sites and not always in the same direction.

Schmidlin, F. J.↗

Diesel Engine Waste Heat Driven Absorption Heat Pumps for ECU Applications in Defense Installations

A thermally activated absorption heat pump suitable for use in naval expeditionary Environmental Control Units, as well as residential space-conditioning, is developed. Waste heat characteristic of the exhaust stream from a diesel engine GenSet is used to drive an absorption cycle to provide cooling. The heat source is coupled to the heat pump using an intermediate fluid loop for flexible deployment. With minor modifications, the heat pump could also provide heating at high coefficients of performance, resulting in versatile functionality. This technology capitalizes on heat and mass transfer enhancement possible in microscale passages to provide a compact architecture for the components and the overall system. The working fluid pair with zero Global Warming Potential is contained within this assembly, reducing fluid inventories significantly over conventional systems. Quiet, reliable, long-life operation due to the absence of a compressor and the use of few moving parts are further critical distinguishing advantages. Modularity in cooling capacity has been demonstrated through scaling-up of component geometry and internal features and dimensions. The core technology was initially demonstrated with a proof-of-concept microscale absorption chiller measuring 200 × 200 × 34 mm and weighing 7 kg that delivered 300 W of cooling in laboratory tests. In the previous BEETIT project, the team made significant advances over the proof-of-concept. System and component designs with > 10× scale-up in capacity were developed, in a packaged unit capable of standalone operation with a semi-autonomous control system. A cooling capacity of 3.5 kW with a COP > 0.5 at an ambient temperature of 35°C was demonstrated for this natural gas-fired unit. Significant cost reductions in fabrication were achieved using low-cost brazing instead of diffusion bonding. In companion projects funded by the Southern Company and the Georgia Research Alliance, stamping and fluid forming techniques were investigated to fabricate microscale features instead of photochemical etching, thereby leading to significant cost reductions. In a follow-on effort funded by ARPA-E and NAVFAC, a 2.7 kW cooling unit was developed to provide cooling at a severe ambient condition of 51.7°C. The unit was driven directly by diesel engine exhaust heat. Innovative finned heat and mass exchangers for the ambient-coupled condenser and absorber were developed. In the present effort, a standalone, packaged and controllable 10.5 kW cooling capacity absorption chiller is developed. This demonstrates a 30× scale up from the proof-of-concept, thus validating the scalability of microchannel heat exchangers for absorption heat pumps. Autonomous operation algorithms demonstrated enhanced dynamic performance. The knowledge from previous projects was leveraged to develop novel component designs that further helped in miniaturizing the heat exchangers. All coupling fluids are hydronically coupled to aid flexible field deployment. The prototype unit provides design cooling capacity at high ambient temperature conditions of 44°C at COP > 0.6.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Project Report: High Frequency Axion LDRD - A Multiport Approach to Thermal Noise and Scattering Parameter Simulation of Cryogenic Experiments

In this report, a simple algorithm for detailed system-level thermal noise analysis is developed, demonstrated, and verified. This method uses noise-wave theory and noise covariance matrices to cascade noise and scattering parameters of multiport devices at different temperatures. This method addresses the effects of return loss, multiport isolation/coupling, and static temperature differentials between components, and will work in cases where the noise temperature is at or near the quantum noise limit. An ideal multidevice network will first be demonstrated to show that this method’s results are consistent with the Friis cascade when component parameters such as return loss and isolation are ideal. Following the ideal multidevice example, a cryogenic experiment is conducted to demonstrate that the proposed simulation method is successful when real data are used.

42 ENGINEERING↗

On the Physical Nature of Lyα Transmission Spikes in High-redshift Quasar Spectra

We investigate Lyman-alpha (Lyα) transmission spikes at 5.2 < z < 6.8 using synthetic quasar spectra from the “Cosmic Reionization on Computers” simulations. We focus on understanding the relationship between these spikes and the properties of the intergalactic medium (IGM). Disentangling the complex interplay between IGM physics and the influence of galaxies on the generation of these spikes presents a significant challenge. To address this, we employ Explainable Boosting machines, an interpretable machine learning algorithm, to quantify the relative impact of various IGM properties on the Lyα flux. Our findings reveal that gas density is the primary factor influencing absorption strength, followed by the intensity of background radiation and the temperature of the IGM. Ionizing radiation from local sources (i.e., galaxies) appears to have a minimal effect on Lyα flux. The simulations show that transmission spikes predominantly occur in regions of low gas density. Our results challenge recent observational studies suggesting the origin of these spikes in regions with enhanced radiation. We demonstrate that Lyα transmission spikes are largely a product of the large-scale structure, of which galaxies are biased tracers.

79 ASTRONOMY AND ASTROPHYSICS↗

On the solution of creep induced buckling in general structure

This paper considers the pre and post buckling behavior of general structures exposed to high temperature fields for long durations wherein creep effects become significant. The solution to this problem is made possible through the use of closed upper bounding constraint surfaces which enable the development of a new time stepping algorithm. This permits the stable and efficient solution of structural problems which exhibit indefinite tangent properties. Due to the manner of constraining/bounding successive iterates, the algorithm developed herein is largely self adaptive, inherently stable, sufficiently flexible to handle geometric material and boundary induced nonlinearity, and can be incorporated into either finite element or difference simulations. To illustrate the capability of the procedure, as well as, the physics of creep induced pre and post buckling behavior, the results of several numerical experiments are included.

Padovan, J.↗

Two years of on-orbit gallium arsenide performance from the LIPS solar cell panel experiment

The LIPS on-orbit performance of the gallium arsenide panel experiment was analyzed from flight operation telemetry data. Algorithms were developed to calculate the daily maximum power and associated solar array parameters by two independent methods. The first technique utilizes a least mean square polynomial fit to the power curve obtained with intensity and temperature corrected currents and voltages; whereas, the second incorporates an empirical expression for fill factor based on an open circuit voltage and the calculated series resistance. Maximum power, fill factor, open circuit voltage, short circuit current and series resistance of the solar cell array are examined as a function of flight time. Trends are analyzed with respect to possible mechanisms which may affect successive periods of output power during 2 years of flight operation. Degradation factors responsible for the on-orbit performance characteristics of gallium arsenide are discussed in relation to the calculated solar cell parameters. Performance trends and the potential degradation mechanisms are correlated with existing laboratory and flight data on both gallium arsenide and silicon solar cells for similar environments.

Francis, R. W.↗

Multicolor pyrometer for materials processing in space

The program goals are to design, construct, and program a prototype imaging pyrometer capable of measuring the temperature distribution across the surface of a moving object suspended in space. The approach is to utilize an optical system which operates at short wavelengths compared to the peak of the blackbody spectrum for the temperature range of interest, thus minimizing errors associated with a lack of knowledge about heated sample emissivity. An analysis of the system's temperature measurement capability based on the camera's responsivity was performed and bound to be satisfactory. Details for the evolving optical design and the progress towards construction of a working model are discussed. Details of the algorithm developed for selecting the optimum colors to be used by the pyrometer are reported. Though final selection of the colors will have to await a final design of the optical system, results using a preliminary optical design are presented.

Frish, Michael↗