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NASA NTRS1978

Icy craters on the Galilean satellites

The high degree of echo depolarization observed for linearly polarized incident waves in the case of radar observations of Europa, Ganymede, and Callisto is consistent with a rough, icy surface. Measurements with circularly polarized waves, however, conducted in 1976 suggest that the types of surface irregularities found on the Galilean satellites must be very different from those on the moon and the inner planets. A description is presented of an investigation in which geometrical optics and the Stokes-vector formalism are employed to examine several possible configurations which could cause the circular polarization transmitted to exceed unity. On the basis of the obtained results it appears that a model which postulates that significant parts of the surfaces of the three satellites are covered with an icy layer at least several kilometers thick and saturated with hemispherical craters can explain nearly all the observed radar behavior.

Ostro, S. J.↗

NASA NTRS1978

Turbulence in planetary occultations. I - A theoretical formulation

The Eikonal equation of geometrical optics and a weak scattering wave-optical formulation are separately used to calculate first- and second-order effects of turbulence on radio propagation through an atmosphere with uniformly varying average refractive index combined with a random component due to turbulence. The extent to which perturbations in bending angle and Doppler frequency affects atmospheric profiles of temperature and pressure derived from Doppler measurements is considered. The determination of the power spectra of turbulence effects, the contribution of different terms, and the use of the spectra for studying planetary atmospheres are discussed.

Haugstad, B. S.↗

NASA NTRS1978

Two-stream theory of spectral reflectance of snow

Spectral reflectance of snow under diffuse illumination is studied using the two-stream approximation of the radiative transfer equation. The scattering and absorption within the snowcover due to the randomly distributed ice grains are characterized by the single scattering albedo and anisotropic phase function. Geometric optics calculations are used to relate the scattering and absorption parameters to grain size and density of snow. Analytical expressions for the intensity within the snowpack and the asymptotic flux extinction coefficient are also obtained. Good agreement is shown between the theory and available experimental data on visible and near-infrared reflectance and asymptotic flux extinction coefficient. The theory also may be used to explain the observed effect of aging on the snow reflectance.

Choudhury, B. J.↗

NASA NTRS1979

The effect of wind on the microwave emission from the ocean's surface at 37 GHz

The microwave brightness temperature measurements from the electrically scanned microwave radiometer (frequency = 37 GHz) are compared with oceanic wind measurements from data buoys. It is shown that the brightness temperature can be manipulated to yield a measure of the surface roughening, which can be very well accounted for by a simple geometric optics model. The data of Hollinger (1971) at 1.4, 8, 36, and 19.34 GHz were similarly manipulated and shown to require a surface with less slope variance than that predicted by the Cox and Munk (1955) optical measurements. It is also shown that the surface may be treated as isotropic to an accuracy equivalent to the roughening produced by a 2-m/s wind speed increment.

Wilheit, T. T.↗

NASA NTRS1980

Image Properties of an X-Ray Telescope of the Wolter-1 Type with Emphasis on Contrast Reduction by Diffuse Reflection

Theoretical and experimental results are presented on the geometrical-optic imaging properties of a Wolter-1 type paraboloid-hyperboloid X-ray telescope. Particular consideration is given to the effect of microroughness of the mirror on the imaging properties. Experiments were conducted in which scattering properties were determined as a function of wavelength, incidence angle, and roughness of the plane mirrors. Results indicate the need for optimization of mirror material and polishing technology as well as the development of improved mirror manufacturing techniques. The use of transmission gratings along with the Wolter-1 type telescope in spectroscopy applications is discussed.

Lenzen, R.↗

NASA NTRS1980

Computer prediction of large reflector antenna radiation properties

A FORTRAN program for calculating reflector antenna radiation patterns was rewritten and extended to include reflectors composed of a number of panels. These individual panels must be analytic surfaces. The theoretical foundation for the program is as follows: Geometrical optics techniques are used to trace rays from a feed antenna to the reflector surface and back to a mathematical plane just in front of the reflector. The resulting tangential electric field distribution, assumed to be the only source of forward radiation, is integrated numerically to calculate the radiation pattern for a desired set of angles. When the reflector is composed of more than one panel, each panel is treated as a separated antenna, the ray-tracing procedure and integration being repeated for each panel. The results of the individual aperture plane integrations are stored and summed to yield the relative electric field strength over the angles of interest. An example and several test cases are included to demonstrate the use of the program and verify the new method of computation.

Botula, A.↗

NASA NTRS1980

On the detection of a stochastic background of gravitational radiation by the Doppler tracking of spacecraft

Consideration is given to the possibility of detection of an isotropic background gravitational radiation of a stochastic nature by the method of Doppler tracking of spacecraft. Attention is given in the geometrical optics limit, to the general formula for the frequency shift of an electromagnetic signal in the gravitational radiation field, and it is shown to be gauge independent. The propagation of a free electromagnetic wave in a gravitational radiation field is examined with the conclusion that no resonance phenomena can be expected. Finally, the 'Doppler noise' due to a stochastic background is evaluated, and it is shown to depend on the total energy density of the background and a parameter that is a characteristic of the radiation spectrum and the detection system used.

Mashhoon, B.↗

NASA NTRS1980

Radio scintillations during occultations by turbulent planetary atmospheres

The radio occultation experiment which uses the radio link between the earth and spacecraft passing behind planets has proven to be an important method for remote sensing turbulence in planetary atmospheres. The effects of defocusing and anisotropic irregularities on the turbulence-induced fluctuations of the radio occultation signal are examined. Rytov's method along with geometrical optics is employed to study the frequency spectra and coherences of the log amplitude and phase fluctuations of spherical waves operating at one as well as two frequencies. Comparison with the Mariner 5 2.3-GHz measurements shows good agreement with the theoretical results.

Woo, R.↗

NASA NTRS1980

Asymptotic behavior of the efficiencies in Mie scattering

Consideration is given to the asymptotic behavior of the Mie scattering and extinction efficiencies for large absorbing spheres as sphere size approaches infinity. It is shown that the method used by Chylek (1975) for evaluating the infinite sums over the Mie partial wave coefficients representing these efficiencies and proving that the extinction efficiency approaches 2 is invalid, despite the correctness of the result, and that the limiting expression for the scattering efficiency obtained by this method is also incorrect. An analytical expression is then derived from geometrical optics considerations for the scattering efficiency limit which is valid when the imaginary component of the refractive index is much less than 1.

Acquista, C.↗

NASA NTRS1980

Energy conservation - A test for scattering approximations

The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.

Acquista, C.↗

NASA NTRS1981

Doppler-cancelled response to VLF gravitational waves

The interaction of long periodic gravitational waves with a three link microwave system known as the Doppler Cancelling System is discussed. This system, which was developed for a gravitational redshift experiment, uses one-way and two-way Doppler informatin to construct the beat signal of two reference oscillators moving with respect to each other. The geometric optics approximation is used to derive the frequency shift produced on a light signal propagating in a gravitational wave space-time. The signature left on the Doppler-cancelled beat by burst and continuous gravitational waves is analyzed. A comparison is made between the response to gravitational waves of the Doppler Cancelling System and that of a Doppler tracking system which employs two-way, round-trip radio waves. A three-fold repetition of the gravitational wave form is found to be a common feature of the response functions of both systems. These two functions otherwise exhibit interesting differences.

Caporali, A.↗

NASA NTRS1981

Determination of specular points on a surface of revolution

For a given source and observation point, specular points on a conducting surface must be found in order to apply the geometrical optics theory to calculate the reflected field. An efficient method is presented for finding all the specular points for the special case in which the conducting surface is a part of a surface of revolution. Our method, which reduces the conventional two-dimensional search to a one-dimensional search also makes it economically feasible to obtain a global solution for certain classes of surface, source, and observation point geometries that do not render solutions in the more conventional two-dimensional searches.

Lee, S. W.↗

NASA NTRS1981

Computer prediction of dual reflector antenna radiation properties

A program for calculating radiation patterns for reflector antennas with either smooth analytic surfaces or with surfaces composed of a number of panels. Techniques based on the geometrical optics (GO) approach were used in tracing rays over the following regions: from a feed antenna to the first reflector surface (subreflector); from this reflector to a larger reflector surface (main reflector); and from the main reflector to a mathematical plane (aperture plane) in front of the main reflector. The equations of GO were also used to calculate the reflected field components for each ray making use of the feed radiation pattern and the parameters defining the surfaces of the two reflectors. These resulting fields form an aperture distribution which is integrated numerically to compute the radiation pattern for a specified set of angles.

Christodoulou, C.↗

NASA NTRS1982

Distorted reflector antenna performance prediction technique

The application of a 3-D curve-fit technique to the electromagnetic analysis of reflector antennas is presented. the reflector antennas are described by the coordinates of an irregular distribution of measured points on the reflector surface. The reflector antenna analysis method used to calculate radiation patterns is geometric-optics with aperture-integration since an efficient and accurate computer code was readily available for modification.

Bailey, M. C.↗

NASA NTRS1982

Synthesis of offset dual reflector antennas transforming a given feed illumination pattern into a specified aperture distribution

The problem of transforming a given primary feed pattern into a desired aperture field distribution through two reflections by an offset dual reflector system is investigated using the concepts of geometrical optics. A numerically rigorous solution for the reflector surfaces is developed which realizes an exact aperture phase distribution and an aperture amplitude distribution that is accurate to within an arbitrarily small numerical tolerance. However, this procedure does not always yield a smooth solution, i.e., the reflector surfaces thus realized may not be continuous or their slopes may vary too rapidly. In the event of nonexistence of a numerically rigorous smooth solution, an approximate solution that enforces the smoothness of the reflector surfaces can be obtained. In the approximate solution, only the requirement for the aperture amplitude distribution is relaxed, and the condition on the aperture phase distribution is continued to be satisfied exactly.

Mittra, R.↗

NASA NTRS1982

Recent advances in electromagnetic synthesis and analysis of dual-shaped reflector antennas

Dual-shaped reflectors have been used for many years. Thus, these reflectors have been used as high gain antennas on Voyagers 1 and 2. The objectives of the geometrical optics (GO) dual shaped synthesis are considered. Concerning the synthesis of dual shaped reflectors, it has been shown for circular symmetric reflectors that an exact GO solution can be found to the problem of transforming, by two reflections, any feed pattern into any aperture distribution. This problem involves solving two simultaneous nonlinear ordinary differential equations. The same approach for offset geometry leads to two simultaneous nonlinear partial differential equations. It is shown that these equations could also be integrated numerically, except that in general these equations are not total and therefore, in general, they do not have a 'smooth' solution. It is further shown that the offset partial differentials often very nearly form a total differential in many cases of practical importance.

Galindo-Israel, V.↗

NASA NTRS1982

Response of a Doppler canceling system to plane gravitational waves

This paper discusses the interaction of long periodic gravitational waves with a three-link microwave system known as the Doppler canceling system. This system, which was developed for a gravitational red-shift experiment, uses one-way and two-way Doppler information to construct the beat signal of two reference oscillators moving with respect to each other. The geometric-optics approximation is used to derive the frequency shift produced on a light signal propagating in a gravitational-wave space-time. The signature left on the Doppler-cancelled beat by bursts and continuous gravitational waves is analyzed. A comparison is made between the response to gravitational waves of the Doppler canceling system and that of a (NASA) Doppler tracking system which employs two-way, round-trip radio waves. A threefold repetition of the gravitational wave form is found to be a common feature of the response functions of both systems. These two functions otherwise exhibit interesting differences.

Caporali, A.↗

NASA NTRS1982

Development of computer models for the prediction of large distorted antenna characteristics

A program for calculating the radiation patterns of analytic reflector antennas, using geometric optics and aperture plane integration techniques, was modified and extended to include nonanalytic surfaces. The original program, while capable of predicting patterns for a variety of reflectors, both smooth and multipanelled, was subject to the restriction that the surface had to be expressed analytically, i.e., described by a set of mathematical equations. This restriction was removed by adapting a technique which allows the reflector configuration to be interpolated from a finite set of points measured on the surface. Criteria for choosing both the number and distribution of these measured surface points were developed by comparing the predicted antenna radiation patterns with measured laboratory results. Test cases involved relatively smooth as well as grossly distorted arbitrary surfaces. Finally, surface point accuracies were established by applying random error analysis to the measurement process.

Moskowitz, S. M.↗