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Water Across Synthetic Aperture Radar Data (WASARD): SAR Water Body Classification for the Open Data Cube

The detection of inland water bodies from Synthetic Aperture Radar (SAR) data provides a great advantage over water detection with optical data, since SAR imaging is not impeded by cloud cover. Traditional methods of detecting water from SAR data involves using thresholding methods that can be labor intensive and imprecise. This paper describes Water Across Synthetic Aperture Radar Data (WASARD): a method of water detection from SAR data which automates and simplifies the thresholding process using machine learning on training data created from Geoscience Australia’s WOFS algorithm. Of the machine learning models tested, the Linear Support Vector Machine was determined to be optimal, with the option of training using solely the VH polarization or a combination of the VH and VV polarizations. WASARD was able to identify water in the target area with a correlation of 97% with WOFS. Sentinel-1, Open Data Cube, Earth Observations, Machine Learning, Water Detection 1. INTRODUCTION Water classification is an important function of Earth imaging satellites, as accurate remote classification of land and water can assist in land use analysis, flood prediction, climate change research, as well as a variety of agricultural applications [2]. The ability to identify bodies of water remotely via satellite is immensely cheaper than contracting surveys of the areas in question, meaning that an application that can accurately use satellite data towards this function can make valuable information available to nations which would not be able to afford it otherwise. Highly reliable applications for the remote detection of water currently exist for use with optical satellite data such as that provided by LANDSAT. One such application, Geoscience Australia’s Water Observations from Space (WOFS) has already been ported for use with the Open Data Cube [6]. However, water detection using optical data from Landsat is constrained by its relatively long revisit cycle of 16 days [5], and water detection using any optical data is constrained in that it lacks the ability to make accurate classifications through cloud cover [2]. The alternative solution which solves these problems is water detection using SAR data, which images the Earth using cloud-penetrating microwaves. Because of its advantages over optical data, much research has been done into water detection using SAR data. Traditionally, this has been done using the thresholding method, which involves picking a polarization band and labeling all pixels for which this band’s value is below a certain threshold as containing water. The thresholding method works since water tends to return a much lower backscatter value to the satellite than land [1]. However, this method can be flawed since estimating the proper threshold is often imprecise, complicated, and labor intensive for the end user. Thresholding also tends to use data from only one SAR polarization, when a combination of polarizations can provide insight into whether water is present. [2] In order to alleviate these problems, this paper presents an application for the Open Data Cube to detect water from SAR data using support vector machine (SVM) classification. 2. PLATFORM WASARD is an application for the Open Data Cube, a mechanism which provides a simple yet efficient means of ingesting, storing, and retrieving remote sensing data. Data can be ingested and made analysis ready according to whatever specifications the researcher chooses, and easily resampled to artificially alter a scene’s resolution. Currently WASARD supports water detection on scenes from ESA’s Sentinel-1 and JAXA’s ALOS. When testing WASARD, Sentinel-1 was most commonly used due to its relatively high spatial resolution and its rapid 6 day revisit cycle [5]. With minor alterations to the application's code, however, it could support data from other satellites. 3. METHODOLOGY Using supervised classification, WASARD compares SAR data to a dataset pre-classified by WOFS in order to train an SVM classifier. This classifier is then used to detect water in other SAR scenes outside the training set. Accuracy was measured according to the following metrics:  Precision: a measure of what percentage of the points WASARD labels as water are truly water  Recall: a measure of what percentage of the total water cover WASARD was able to identify.  F1 Score: a harmonic average of the precision and recall scores Both precision and recall are calculated at the end of the training phase, when the trained classifier is compared to a testing dataset. Because the WOFS algorithm’s classifications are used as the truth values when training a WASARD classifier, when precision and recall are mentioned in this paper, they are always with respect to the values produced by WOFS on a similar scene of Landsat data, which themselves have a classification accuracy of 97% [6]. Visual representations of water identified by WASARD in this paper were produced using the function wasard_plot(), which is included in WASARD. 3.1 Algorithm Selection The machine learning model used by WASARD is the Linear Support Vector Machine (SVM). This model uses a supervised learning algorithm to develop a classifier, meaning it creates a vector which can be multiplied by the vector formed by the relevant data bands to determine whether a pixel in a SAR scene contains water. This classifier is trained by comparing data points from selected bands in a SAR scene to their respective labels, which in this case are “water” or “not water” as given by the WOFS algorithm. The SVM was selected over the Random Forest model, which outperformed the SVM in training speed, but had a greater classification time and lower accuracy, and the Multilayer Perceptron Artificial Neural Network, which had a slightly higher average accuracy than the SVM, but much greater training and classification times. Figure 1: Visual representation of the SVM Classifier. Each white point represents a pixel in a SAR scene. In Figure 1, the diagonal line separating pixels determined to be water from those determined not to be water represents the actual classification vector produced by the SVM. It is worth noting that once the model has been trained, classification of pixels is done in a similar manner as in the thresholding method. This is especially true if only one band was used to train the model. 3.1 Feature Selection Sentinel-1 collects data from two bands: the Vertical/Vertical polarization (VV) and the Vertical/Horizontal polarization (VH). When 100 SVM classifiers were created for each polarization individually, and for the combination of the two, the following results were achieved: Figure 2: Accuracy of classifiers trained using different polarization bands. Precision and Recall were measured with respect to the values produced by WOFS. Figure 2 demonstrates that using both the VV and VH bands trades slightly lower recall for significantly greater precision when compared with the VH band alone, and that using the VV band alone is inferior in both metrics. WASARD therefore defaults to using both the VV and VH bands, and includes the option to use solely the VH band. The VV polarization’s lower precision compared to the VH polarization is in contrast to results from previous research and may merit further analysis [4]. 3.2 Training a Classifier The steps in training a classifier with WASARD are 1. Selecting two scenes (one SAR, one optical) with the same spatial extents, and acquired close to each other in time, with a preference that the scenes are taken on the same day. 2. Using the WOFS algorithm to produce an array of the detected water in the scene of optical data, to be used as the labels during supervised learning 3. Data points from the selected bands from the SAR acquisition are bundled together into an array with the corresponding labels gathered from WOFS. A random sample with an equal number of points labeled “Water” and “Not Water” is selected to be partitioned into a training and a testing dataset 4. Using Scikit-Learn’s LinearSVC object, the training dataset is used to produce a classifier, which is then tested against the testing dataset to determine its precision and recall The result is a wasard_classifier object, which has the following attributes: 1. f1, recall, and precision: 3 metrics used to determine the classifier’s accuracy 2. Coefficient: Vector which the SVM uses to make its predictions. The classifier detects water when the dot product of the coefficient and the vector formed by the SAR bands is positive 3. Save(): allows a user to save a classifier to the disk in order to use it without retraining 4. wasard_classify(): Classifies an entire xarray of SAR data using the SVM classifier All of the above steps are performed automatically when the user creates a wasard_classifier object. 3.3 Classifying a Dataset Once the classifier has been created, it can be used to detect water in an xarray of SAR data using wasard_classify(). By taking the dot product of the classifier’s coefficients and the vector formed by the selected bands of SAR data, an array of predictions is constructed. A classifier can effectively be used on the same spatial extents as the ones where it was trained, or on any area with a similar landscape. While

Kreiser, Zachary↗

Asteroid rotation. I - Tabulation and analysis of rates, pole positions and shapes. II - A theory for the collisional evolution of rotation rates

Rotation properties and shape data for 182 asteroids are compiled and analyzed, and a collisional model for the evolution of the mean rotation rate of asteroids is proposed. Tabulations of asteroid rotation rates, taxonomic types, pole positions, sizes and shapes and plots of rotation frequency and light curve amplitude against size indicate that asteroid rotational frequency increases with decreasing size for all asteroids except those of the C or S classes. Light curve data also indicate that small asteroids are more irregular in shape than large asteroids. The dispersion in rotation rates observed is well represented by a three dimensional Maxwellian distribution, suggestive of collisional encounters between asteroids. In the proposed model, the rotation rate is found to tend toward an equilibrium value, at which spin-up due to infrequent, large collisions is balanced by a drag due to the larger number of small collisions. The lower mean rotation rate of C-type asteroids is attributed to a lower means density of that class, and the increase in rotation rate with decreasing size is interpreted as indicative of a substantial population of strong asteroids.

Harris, A. W.↗

RadLab: A Comprehensive Database and Graphical and Programming Interfaces for Biologically Relevant Space Radiation Data

RadLab, a new component of the NASA Open Science Data Repository (OSDR), is a platform built upon a database of radiation data relevant to space biology. RadLab provides visual and programmatic interfaces for interrogation of its database, as well as a submission process for inclusion of data from investigators. The RadLab application programming interface (API) implements a request syntax enabling users to retrieve data filtered by various combinations of parameters (detector type, location, direction, timespan, etc), which are delivered in machine-readable text formats, ready to be ingested by downstream analysis pipelines; while the graphical user interface (GUI) provides easy means to iteratively modify query parameters and incorporates a number of standard analyses and visualizations (time series plots, geospatial visualizations, detector comparison). Investigators from many countries, including US, Russia, Japan, Canada, the Czech Republic, Germany, Hungary, and Italy, have committed to provide data from their instruments located on the ISS; RadLab will also include data from other spacecraft in LEO (e.g., the Space Shuttle, the Mir space station), BLEO (e. g. BioSentinel, Mars Orbiter, among others), and on other celestial bodies (e. g. Chang’e 4, Curiosity). The first release of RadLab has been made available to the public. Once fully operational, RadLab will provide a comprehensive and ever-growing compendium of space radiation data, facilitating straightforward access to multiple types of readings and enabling space biology researchers to perform intercomparisons of detectors and to determine the radiation environment of research missions, both via programmatic retrieval of these data and via the graphical analysis toolkit; as well as a user-friendly submission portal for ingesting data from space agencies and research institutions. Radiation scientists will be able to use RadLab to gain a deeper understanding of the space radiation environment for future human space exploration. The RadLab Working Group has been formed to foster close collaborations among data contributors and users, to identify data sources, to put in place standards for data normalization, to guide the development of features of the analysis toolkit, to establish the use of RadLab in space radiation biology research, and eventually to provide a forum for discussing relevant research issues that can take advantage of RadLab's capabilities.

radiation↗

D-region differential-phase measurements and ionization variability studies

Measurements of electron densities in the D region are made by the partial-reflection differential-absorption and differential-phase techniques. The differential-phase data are obtained by a hard-wired phase-measuring system. Electron-sensity profiles obtained by the two techniques on six occasions are plotted and compared. Electron-density profiles obtained at the same time on 30 occasions during the years 1975 through 1977 are averaged to form a single profile for each technique. The effect of varying the assumed collision-frequency profile on these averaged profiles is studied. Time series of D-region electron-sensity data obtained by 3.4 minute intervals on six days during the summer of 1977 are examined for wave-like disturbances and tidal oscillations.

Weiland, R. M.↗

A general algorithm for the construction of contour plots

An algorithm is described that performs the task of drawing equal level contours on a plane, which requires interpolation in two dimensions based on data prescribed at points distributed irregularly over the plane. The approach is described in detail. The computer program that implements the algorithm is documented and listed.

Johnson, W.↗

Rotary balance data for a typical single-engine general aviation design for an angle of attack range of 8 deg to 90 deg. 1: Low wing model C

Aerodynamic characteristics obtained in a helical flow environment utilizing a rotary balance located in the Langley spin tunnel are presented in plotted form for a 1/6 scale, single engine, low wing, general aviation model (model C). The configurations tested included the basic airplane and control deflections, wing leading edge and fuselage modification devices, tail designs and airplane components. Data are presented without analysis for an angle of attack range of 8 deg to 90 deg and clockwise and counter clockwise rotations covering an omega b/2v range from 0 to .9.

Mulcay, W. J.↗

Preliminary analysis of STS-1 entry flight data

A preliminary analysis of data acquired during the first shuttle orbiter reentry is presented. Heating levels were higher than predicted. Variations in measured versus predicted lift to drag ratio and trim are discussed, as are plots showing time histories of control surface and jet activity. The confidence felt in the stability and control derivatives is only fair. Confidence in the derivatives extracted for Mach numbers below 3.5 is especially weak, because these derivatives were affected by sideslip data contaminated by wind and turbulence, nonindependent rudder motions, and buffet. The sources of the data used are described. Recommendations are presented for changes to the Aerodynamic Data Book, and for planning future flights.

Source record↗

ESCA study of the effect of hydrocarbon contamination on poly(tetrafluoroethylene) exposed to atomic oxygen plasma

The ESCA spectra and data obtained by Morra et al. (1989) on poly(tetrafluoroethylene) (PTFE) exposed to atomic oxygen plasma are closely reexamined. It is shown that the spikes observed in Morra et al. plots of O/C or F/C versus time of the exposure of PTFE to atomic oxygen plasma were not characteristic of PTFE per se but were instead a result of a contamination by hydrocarbon present in their PTFE samples. This was demonstrated experimentally by comparing data derived for a very clean PTFE sample exposed for 10, 20, and 30 min to oxygen plasma with data obtained on PTFE samples with very small amounts of hydrocarbon contamination.

Golub, Morton A.↗

Research on Spectroscopy, Opacity, and Atmospheres

I propose to continue providing observers with basic data for interpreting spectra from stars, novas, supernovas, clusters, and galaxies. These data will include allowed forbidden line lists both laboratory and computed, for the first five to ten ions of all atoms and for all relevant diatomic molecules. I will eventually expend to all ions of the first thirty elements to treat far UV end X-ray spectra, and for envelope opacities. I also include triatomic molecules providing by other researchers. I have made CDs with Partridge and Schwanke's water data for work on M stars.The luna data also serve as input to my model atmosphere and synthesis programs that generated energy distributions, photometry, limb darkening, and spectra that can be used for planning observations and for fitting observed spectra. The spectrum synthesis programs produce detailed plots with the line identified. Grids of stellar spectra can be used for radial velocity-, rotation-, or abundance templates and for population synthesis. I am fitting spectra of bright stars to test the data and to produce atlases to guide observer. For each star the whole spectrum is computed from the UV to the far IR. The line data, opacities, models, spectra, and programs are freely distributed on CDs and on my web site and represent a unique resource for many NASA programs.

Oliversen, Ronald↗

Research on Spectroscopy, Opacity, and Atmospheres

I propose to continue providing observers with basic data for interpreting spectra from stars, novas, supernovas, clusters, and galaxies. These data will include allowed and forbidden line lists, both laboratory and computed, for the first five to ten ions of all atoms and for all relevant diatomic molecules. I will eventually expand to all ions of the first thirty elements to treat far UV and X-ray spectra, and for envelope opacities. I also include triatomic molecules provided by other researchers. I have also made CDs with Partridge and Schwenke's water data for work on UV stars. The line data also serve as input to my model atmosphere and synthesis programs that generate energy distributions, photometry, limb darkening, and spectra that can be used for planning observations and for fitting observed spectra. The spectrum synthesis programs produce detailed plots with the lines identified. Grids of stellar spectra can be used for radial velocity-, rotation-, or abundance templates and for population synthesis. I am fitting spectra of bright stars to test the data and to produce atlases to guide observers. For each star the whole spectrum is computed from the UV to the far IR. The line data, opacities, models, spectra, and programs are freely distributed on CDs and on my Web site and represent a unique resource for many NASA programs. I am now in full production of new line lists for atoms. I am computing all ions of all elements from H to Zn and the first 5 ions of all the heavier elements, about 800 ions. For each ion I treat as many as 61 even and 61 odd configurations, computing all energy levels and eigenvectors. The Hamiltonian is determined from a scaled-Hartree-Fock starting guess by least squares fitting the observed energy levels. The average energy of each configuration is used in computing scaled-Thomas-Fermi-Dirac wavefunctions for each configuration which in turn are used to compute allowed and forbidden transition integrals. These are multiplied into the LS allowed and forbidden transition arrays. The transition arrays are transformed to the observed coupling to yield the allowed and forbidden line lists. Results are put on the web as they are finished. Provided I get funding,there will be more than 500 million lines. I will then compare ion by ion, to all the laboratory and computed data in the literature and make up a working line list for spectrum synthesis and opacity calculations with the best available data. As the laboratory spectrum analyses are improved, I will redo the calculations with the new energy levels. My original plan when I started the new calculations was to run through all the atoms using my old Cray programs from the 1980's that were limited to 1100 x 1100 arrays in the Hamiltonian for each J. Then I would go back and rerun the more complicated cases with 3000 x 3000 arrays so that I could include many more configurations and more configuration interactions. At present I am limited to 61 even and 61 odd configurations and I try to include everything up through n = 9. The current program runs on Alpha workstations. I decided to test the big program on Fe I and Fe II to see whether there was any great difference in the low configurations compared to those from the Cray program. Besides increasing the number of E1 lines by a factor of 6 to 7.7 million, there was an unexpected result: the electric quadrupole transitions were 10 times stronger than before because the transition integrals are weighted by r(exp 2) ---they become very large for high n, and because there are numerous configuration interactions that mix the low and high configurations. As a check I was able to reproduce Carstang's (1962) lower results by running his three configurations with my program. Since my model atom is still only a subset of a real Fe II ion, the true quadrupole A values are probably larger than mine. The magnetic dipole lines are affected by the mixing but the overall scale does not change. Because of this scovery I decided that there was no point in computing the small array cases. I have been running with as many configurations as I can and with thousands of parameters in the Hamiltonian. The computer runs take much longer to set up and produce than I had expected. I have concentrated on redoing the low iron group spectra, especially to get data for supernova modelers. I have done only Ca I -- Zn I, Ca II -- Zn II, CU I -- Cu XXIX, Zn I - Zn XXX, for practice at high stages of ionization, C I, C II, S I, and CL I and Ag I for people who were working on the laboratory spectra. Check my web site kurucz.harvard.edu for current additions. My latest calculations have been for carbon I and sulphur I, and silicon I is under way using the same elaborate approach as for C I, which took many months to do. These line lists greatly increase the number of lines in the ultraviolet, in the visible, and especially in the infrared. They will increase the opacity in A, F, and G stars. They will account for many unidentified lines in the sun.

Kurucz, Robert L.↗

Combined Use of Airborne Lidar and DBInSAR Data to Estimate LAI in Temperate Mixed Forests

The objective of this study was to determine whether leaf area index (LAI) in temperate mixed forests is best estimated using multiple-return airborne laser scanning (lidar) data or dual-band, single-pass interferometric synthetic aperture radar data (from GeoSAR) alone, or both in combination. In situ measurements of LAI were made using the LiCor LAI-2000 Plant Canopy Analyzer on 61 plots (21 hardwood, 36 pine, 4 mixed pine hardwood; stand age ranging from 12-164 years; mean height ranging from 0.4 to 41.2 m) in the Appomattox-Buckingham State Forest, Virginia, USA. Lidar distributional metrics were calculated for all returns and for ten one meter deep crown density slices (a new metric), five above and five below the mode of the vegetation returns for each plot. GeoSAR metrics were calculated from the X-band backscatter coefficients (four looks) as well as both X- and P-band interferometric heights and magnitudes for each plot. Lidar metrics alone explained 69% of the variability in LAI, while GeoSAR metrics alone explained 52%. However, combining the lidar and GeoSAR metrics increased the R2 to 0.77 with a CV-RMSE of 0.42. This study indicates the clear potential for X-band backscatter and interferometric height (both now available from spaceborne sensors), when combined with small-footprint lidar data, to improve LAI estimation in temperate mixed forests.

leaf area index↗

The effects of vegetation and soil hydraulic properties on passive microwave sensing of soil moisture: Data report for the 1982 fiels experiments

Field experiments to (1) study the biomass and geometrical structure properties of vegetation canopies to determine their impact on microwave emission data, and (2) to verify whether time series microwave data can be related to soil hydrologic properties for use in soil type classification. Truck mounted radiometers at 1.4 GHz and 5 GHz were used to obtain microwave brightness temperatures of bare vegetated test plots under different conditions of soil wetness, plant water content and canopy structure. Observations of soil moisture, soil temperature, vegetation biomass and other soil and canopy parameters were made concurrently with the microwave measurements. The experimental design and data collection procedures for both experiments are documented and the reduced data are presented in tabular form.

Oneill, P.↗

NASA Scout ST-1 Flight-Test Results and Analyses, Launch Operations, and Test Vehicle Description

The first of a series of flight tests for the development of the four-stage, solid-propellant Scout vehicle was conducted at the NASA Wallops Station under the direction of the Langley Research Center. Vehicle designation for the test was NASA Scout ST-1. Performance characteristics of the vehicle and components were recorded during a high-altitude probe mission. Flight-simulation studies are presented and show that the accuracy of the guidance system during the flight was within control-system design specifications. The control system functioned normally during the flight with the exception of an overpowering of the reaction-control roll jets near burnout of the third-stage rocket motor. The resulting roll displacement of the vehicle is shown to have caused the monitor tracking radar which had been erroneously tracking a radar beacon in the vehicle on a side lobe to reorient to the major lobe of the receiving antenna. This tracking switch falsely indicated a violent turning maneuver on the monitor plot board and resulted in a hold-fire decision for the fourth-stage rocket motor. Although data for the final thrusting and coast phase of the flight were not obtained, the majority of the test objectives were achieved. In-flight thrust misalignment angles for the second- and third-stage rocket motors derived from control-system error data and for the first-stage motor determined from flight-simulation studies are presented. All rocket-motor thrust misalignment angles were well within the tolerances used for control-system design. Rocket-motor flight performance is presented, and velocity increments attained from the first three stages substantiated the predicted nominal performance. Operation of the rocket motors was satisfactory with the exception of high-level vibrations which were encountered during third-stage motor burning. Rolling moments which overpowered the reaction-control jets are also attributed to the burning characteristics of the third-stage motor. A discussion of the premature loss of the third-stage heat shield is given and shows that the heat-shield latching mechanism failed from pressure loads as the vehicle entered the transonic speed range. Although venting was provided to relieve the high negative pressures known to exist on the heat shield at these speeds, a field modification of the wiring tunnel had the same effect as opening the inside of the heat shield to ambient pressures. Consequently, the latching mechanism failed from pressure loads which were of about the same magnitude as the latching-mechanism yield loads. Skin temperatures were recorded at several locations on the vehicle and were generally in good agreement with theoretical values. Aerodynamic heating presented no problem during the flight since the maximum temperatures recorded during the flight were only about half the design values because of the high-launch-angle trajectory. Environmental vibrations recorded in the vicinity of the guidance package showed that no significant continuous amplitude levels above the general instrumentation noise level were present during first- and second-stage burning. Large vibration amplitudes were recorded during third-stage burning which coincided with the large roll disturbance experienced by the vehicle near burnout of the third-stage motor.

Scout Launch Vehicle↗

POGO observations of the equatorial electrojet

During intervals in 1967 to 1970, the OGO-4 and 6 spacecraft made over 2000 traversals over the equatorial electrojet in the altitude range 400-800 km when local times were between 9 and 15 hours. These spacecraft carried total field magnetometers making measurements to an accuracy of 2 gamma with a sample rate greater than once a second. Delta F values, the deviations from these observations, were formed from an internal reference model. The results were plotted for a 30 deg band about the equator, and the characteristics of the electrojet effect in the data were investigated. This effect was characterized by a sharp negative V-signature of some 16-19 deg in width and a variable amplitude. The position of this minimum was found to lie within 0.5 deg of the dip equator. A slight northward shift was noted at the longitude of Huancayo. The jet amplitudes were normalized to 400 km amplitudes and observed to be highly variable in time. Amplitudes over the longitude range 50 to 90 deg W averaged 60% higher than elsewhere, as expected, due to the weaker main field. However, though the scatter of amplitudes is high, the expected minima in east Asia was not evident. It was speculated that this could be due to a less conducting upper mantle in this area.

Cain, J. C.↗

Tracking radar techniques for studying migratory birds

The use of NASA tracking radar at Wallops Island and the islands of Bermuda and Antigua to plot the paths of migatory birds in three dimensional space is discussed. Attempts were also made to obtain data on the direction, speed, and density of large numbers of migrating birds. Observational results show that the performance of tracking radars vary considerably with the density of bird migration. At light to moderate levels of migration it is possible to obtain tracks of a variety of types of targets, both large and small. During heavy periods of migration the sky is so filled with targets, that only the largest targets can be tracked for more than a few minutes.

Williams, T. C.↗

Evaluation of circumferential airflow uniformity entering combustors from compressors. Volume 2: Data supplement

A study of the airflow uniformity leaving compressors and entering combustors was made using compressors from two advanced engines, the J58 and F100/F401. The data used in the analysis of each case is presented in tabular form and computer-generated profile plots. A plot of the square root of the dynamic pressure ratio, which is similar to airflow deviation, is also presented.

Shadowen, J. H.↗

Analysis of a dual-reflector antenna system using physical optics and digital computers

The application of physical-optics diffraction theory to a deployable dual-reflector geometry is discussed. The methods employed are not restricted to the Conical-Gregorian antenna, but apply in a general way to dual and even multiple reflector systems. Complex vector wave methods are used in the Fresnel and Fraunhofer regions of the reflectors. Field amplitude, phase, polarization data, and time average Poynting vectors are obtained via an IBM 360/91 digital computer. Focal region characteristics are plotted with the aid of a CalComp plotter. Comparison between the GSFC Huygens wavelet approach, JPL measurements, and JPL computer results based on the near field spherical wave expansion method are made wherever possible.

Schmidt, R. F.↗

Yield and ion distribution for the barium cloud at 31,000 kilometers, September 21, 1971.

The photon flux density associated with the 4554-A resonance radiation for Ba II was measured at Mount Hopkins, Arizona, and Cerro Morado, Chile, and was determined to be 36,000 photon/sq cm sec outside the atmosphere; this measurement was made when the cloud was optically thin at 120 sec after release. Using this and a photon scattering efficiency of 0.66 photon/ion sec we estimate a 1.7-kg yield of barium ions that are formed from the initially released atomic barium and are thus associated with the main core of the cloud. Photographic and photometric data are combined to obtain preliminary values for the brightness throughout the cloud for two photographs, and isobrightness plots are presented. These plots indicate that the cloud is quite narrow, that a considerable portion of the ionized barium is outside the main core after a few minutes, and that the striations contain only a small fraction of the total material.

Manring, E. R.↗