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At least 559 records · Page 31

Reflecting Solutions of High Order Elliptic Differential Equations in Two Independent Variables Across Analytic Arcs

Consideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.

Carleton, O.↗

Asteroid spectral reflectivities.

We measured spectral reflectivities (0.3-1.1 micron) for 32 asteroids. There are at least 14 different curve types. Common types are: (a) reddish curves with 10% absorptions near 0.95 micron or beyond 1.0 micron, due to Fe(2+) in minerals such as pyroxenes; (b) flat curves in the visible and near-IR with sharp decreases in the UV and (c) flat curves even into the UV. Several asteroids show probable color variations with rotation, especially 6 Hebe. A sample of 102 asteroids with reliably known colors is derived from the reflectivities and from earlier colorimetry. Several correlations of colors and spectral curve types with orbital and physical parameters are examined: (1) asteroids with large aphelia have flat reflectivities while those with small perihelia are mostly reddish, (2) curve types show evidence for clustering on an a vs e plot, with 0.95 micron bands occuring mainly for Mars-approaching asteroids, (3) no strong correlation exists between color and either proper eccentricity or proper inclination.

Chapman, C. R.↗

Path-length distributions of photons diffusely reflected from a semi-infinite atmosphere.

Knowledge of the probability distribution of photon path lengths for diffuse reflection in the continuum from a planetary atmosphere greatly simplifies computation of the shape and strength of absorption lines formed under conditions of multiple scattering. Graphs of this probability distribution are presented for diffuse reflection from a semiinfinite conservative atmosphere for both isotropic and forward-directed scattering, and for several angles of incidence and reflection. Graphs showing distributions for the case of absorption in the continuum are also discussed. The distributions are obtained from an analytic expression for the path-length distribution for nth-order scattering and a tabulation of nth-order intensities. It is found that te shape of the probability distribution depends markedly on the degree of forward scattering due to the phase function. The results are compared with those obtained by a Monte Carlo computation of the sort which might be used if tabulated nth-order intensities were not available.

Appleby, J. F.↗

Comparison of the Beckmann model with bidirectional reflectance measurements.

The Beckmann model is compared with recently reported bidirectional reflectance measurements. Comparisons revealed that monochromatic specular and bidirectional reflectance measurements are not adequately described by corresponding results evaluated from the model using mechanically acquired surface roughness parameters (rms height and rms slope). Significant improvement between measurements and predictions of the model is observed when optically acquired surface roughness parameters are used. Specular reflectance measurements for normal to intermediate polar angles of incidence are adequately represented by the model provided values of optical roughness multiplied by cosine of polar angle of incidence are less than 27 times average optical rms slope.

Smith, T. F.↗

Partial-reflection studies of D-region winter variability

D-region electron densities were measured from December, 1972, to July, 1973, at Urbana, Illinois (latitude 40.2N) using the partial-reflection technique. During the winter, electron densities at altitudes of 72, 76.5, and 81 km show cyclical changes with a period of about 5 days that are highly correlated between these altitudes, suggesting that the mechanism responsible for the winter anomaly in D-region ionization applies throughout this height region. From January 13 to February 3, a pronounced wave-like variation occurred in the partial-reflection measurements, apparently associated with a major stratospheric warming that developed in that period. During the same time period, a traveling periodic variation is observed in the 10-mb height; it is highly correlated with the partial-reflection measurements. Electron density enhancements occur approximately at the same time as increases in the 10-mb height. Comparison of AL and A3 absorption measurements with electron density measurements below 82 km indicates that the winter anomaly in D-region ionization is divided into two types. Type 1, above about 82 km, extends horizontally for about 200 km while type 2, below about 82 km, extends for a horizontal scale of at least 1000 km.

Denny, B. W.↗

Experimental test of plant canopy reflectance models on cotton

Spectroradiometric data on the bidirectional reflectance function was collected for a cotton canopy as a function of observer zenith angle, observer angle, and solar zenith angle. The area under study was about 40 miles from the Gulf of Mexico and the prevailing winds blew inland such that cloud formation increased during the day. The standard reflectance panel was constructed of plywood that had been spray painted with a flat white latex paint. Physical and optical plant parameters were measured. A time lapse mechanism was constructed to operate a 16 mm movie camera such that single frames could be exposed at intervals of one per second up to one per hour. Data were digitized from a strip chart recorder and reflectance panel measurements.

Lemaster, E. W.↗

The surface brightness of reflection nebulae

Hubble's equation relating the maximum apparent angular extent of a reflection nebula to the apparent magnitude of the illuminating star has been reconsidered under a set of less restrictive assumptions. A computational technique is developed which permits the use of fits to observed m, log a values to determine the albedo of the particles composing reflection nebulae, providing only that one assumes a particular phase function. Despite the fact that all orders of scattering, anisotropic phase functions, and illumination by the general stellar field are considered, the albedo which is determined for reflection nebulae by this method appears larger than that for interstellar particles in general. The possibility that the higher surface brightness might be due to a continuous fluorescence mechanism is considered both theoretically and observationally.

Rush, W. F.↗

The albedo of particles in reflection nebulae

The relation between the apparent angular extent of a reflection nebula and the apparent magnitude of its illuminating star was reconsidered under a less restrictive set of assumptions. A computational technique was developed which permits the use of fits to the observed m-log a values to determine the albedo of particles composing reflection nebulae, providing only that a phase function and average optical thickness are assumed. Multiple scattering, anisotropic phase functions, and illumination by the general star field are considered, and the albedo of reflection nebular particles appears to be the same as that for interstellar particles in general. The possibility of continuous fluorescence contributions to the surface brightness is also considered.

Rush, W. F.↗

Reflectance of vegetation, soil, and water

The author has identified the following significant results. The Kubelka-Munk model, a regression model, and a combination of these models were used to extract plant, soil, and shadow reflectance components of vegetated surfaces. The combination model was superior to the others; it explained 86% of the variation in band 5 reflectance of corn and sorghum, and 90% of the variation in band 6 reflectance of cotton. A fractional shadow term substantially increased the proportion of the digital count sum of squares explained when plant parameters alone explained 85% or less of the variation. Overall recognition of 94 agricultural fields using simultaneously acquired aircraft and spacecraft MSS data was 61.8 and 62.8%, respectively; recognition of vegetable fields larger than 10 acres and taller than 25 cm, rose to 88.9 and 100% for aircraft and spacecraft, respectively. Agriculture and rangeland, were well discriminated for the entire county but level 2 categories of vegetables, citrus, and idle cropland, except for citrus, were not.

Wiegand, C. L.↗

Reflectance and unsteady temperature distribution of diffuse reflectors

The applicability of a previously derived solution of the Kubelka-Munk differential equations for the reflectance of an absorbing and scattering material for the case of a zero absorption coefficient to the description of the reflectance of a weakly absorbing, highly scattering material is examined. A solution for the transient heating of a one-dimensional volume reflector is obtained, and the error incurred in the use of the zero absorption coefficient solution is assessed for early times appropriate to the entry heat protection system application. It is found that the small difference in reflectance causes a significant difference in internal temperature.

Weston, K. C.↗

Reflectance and optical constants for Cer-Vit from 250 to 1050 A

The reflectance for a bowl-feed polished Cer-Vit sample was measured at nine wavelengths and five angles of incidence from 15 to 85 deg. Optical constants were derived by the reflectance-vs-angle-of-incidence method and compared to previously reported values for ultralow-expansion fused silica and several other glasses. Surface-roughness corrections of the reflectance data and optical constants are discussed.

Osantowski, J. F.↗

Effects of leaf age within growth stages of pepper and sorghum plants on leaf thickness, water, chlorophyll, and light reflectance

Pepper and sorghum plants (characterized by porous and compact leaf mesophylls, respectively) were used to study the influence of leaf age on light reflectance. Measurements were limited to the upper five nodal positions within each growth stage, since upper leaves make up most of the reflectance surfaces remotely sensed. The increase in leaf thickness and water content with increasing leaf age was taken into consideration, since each of these factors affects the reflectance as well as the selection of spectral wavelength intervals for optimum discrimination of vegetation.

Gausman, H. W.↗

Spectral reflectance properties of electroplated and converted zinc for use as a solar selective coating

The spectral reflectance properties of electroplated and chemically converted zinc were measured for both chromate and chloride conversion coatings. The reflectance properties were measured for various times of conversion and for conversion at various chromate concentrations. The values of absorptance, integrated over the solar spectrum, and of infrared emittance, integrated over black body radiation at 250 F were then calculated from the measured reflectance values. The interdependent variations of absorptance and infrared emittance were plotted. The results indicate that the optimum combination of the highest absorptance in the solar spectrum and the lowest emittance in the infrared of the converted electroplated zinc is produced by chromate conversion at 1/2 concentration of the standard NEOSTAR chromate black solution for 0.50 minute or by chloride conversion for 0.50 minute.

Mcdonald, G. E.↗

Multilayered models for electromagnetic reflection amplitudes

The remote sensing of snowpack characteristics with surface installations or with an airborne system could have important applications in water resource management and flood prediction. To derive some insight into such applications, the electromagnetic response of multilayer snow models is analyzed. Normally incident plane waves are assumed at frequencies ranging from 10 to the 6th power to 10 to the 10th power Hz, and amplitude reflection coefficients are calculated for models having various snow-layer combinations, including ice sheets. Layers are defined by a thickness, permittivity, and conductivity; the electrical parameters are constant or prescribed functions of frequency. To illustrate the effect of various layering combinations, results are given in the form of curves of amplitude reflection coefficients, versus frequency for a variety of models. Under simplifying assumptions, the snow thickness and effective dielectric constant can be estimated from the reflection coefficient variations as a function of frequency.

Linlor, W. I.↗

Interactions of satellite-speed helium atoms with satellite surfaces. 2: Energy distributions of reflected helium atoms

Energy transfer in collisions of satellite-speed (7,000 m/sec) helium atoms with a cleaned 6061-T6 satellite-type aluminum surface was investigated using the molecular-beam technique. The amount of energy transferred was determined from the measured energy of the molecular-beam and the measured spatial and energy distributions of the reflected atoms. Spatial distributions of helium atoms scattered from a 6061-T6 aluminum surface were measured. The scattering pattern exhibits a prominent backscattering, probably due to the gross surface roughness and/or the relative lattice softness of the aluminum surface. Energy distributions of reflected helium atoms from the same surface were measured for six different incidence angles. For each incidence angle, distributions were measured at approximately sixty scattering positions. At a given scattering position, the energy spectra of the reflected helium atoms and the background gas were obtained using the retarding-field energy analyzer.

Liu, S. M.↗

Further laboratory study of the diffuse reflectance spectra of frosts occurring on astronomical objects

Oligoclase and bloedite, two mined samples, have been investigated, and the diffuse reflectance spectra are presented. These data are for powdered material, 50 microns to 5 microns size mixture, cooled to 160 K. The reflectivity of the oligoclase sample was also measured at room temperature, about 290 K, and the results at these two temperatures do indicate some tentative differences. A frost of ordinary water was prepared and its spectral reflectance is presented. This result compares reasonably well with measurements made by other investigators.

Glaser, F. M.↗

Variability of wetland reflectance and its effect on automatic catergorization of satellite imagery

The author has identified the following significant results. A technique for training automated analysis of satellite multispectral data based on in situ measurements of target reflectance was tested and applied in delineating cover communities in Delaware's tidal wetlands. Land cover categorization of data from the same overpass in four test wetland areas was carried out using a four category classification system. The tests indicate that training data based on in situ reflectance measurements and atmospheric correction of LANDSAT data can produce comparable accuracy of categorization to that achieved using more conventional relative radiance training. Analysis of the four wetlands cover categories (salt marsh cordgrass, salt hay, water, and unvegetated tidal flat) produced average categorization accuracies of 82.1% by conventional relative radiance training and 81.4% by use of in situ reflectance measurements.

Klemas, V.↗

Spectral reflectance properties of electroplated and converted zinc for use as a solar selective coating

The spectral reflectance properties of electroplated and chemically converted zinc were measured for both chromate and chloride conversion coatings. The reflectance properties were measured for various times of conversion and for conversion at various chromate concentrations. The values of absorptance, alpha, integrated over the solar spectrum, and of infrared emittance, epsilon, integrated over black body radiation at 250 F were then calculated from the measured reflectance values. The interdependent variations of alpha and epsilon were plotted. The results indicate that the optimum combination of the highest absorptance in the solar spectrum and the lowest emittance in the infrared of the converted electroplated zinc is produced by chromate conversion at 1/2 concentration of the standard NEOSTAR chromate black solution for 0.50 minute or by chloride conversion for 0.50 minute.

Mcdonald, G. E.↗