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Distorted antenna surfaces forced to produce a uniform wave front. SUBFORMING employs geometric optics in determining subreflector coordinates to match main reflector surface with known distortions. Antenna with distorted paraboloidal reflecting surface forced to produce uniform wave front by using a Cassegrainian geometry with path-length-compensating subreflector. Program written in FORTRAN V for batch execution.
General techniques for producing model lightcurves for a variety of realistic atmospheric irregularities, including turbulence and inertia-gravity waves, are presented and applied. The restrictions of weak scintillation theory are relaxed and model lightcurves are constructed using wave optics for atmospheres with strong, anisotropic turbulence. This is accomplished by numerical simulations which model the propagation of a wave through a phase-changing screen while maintaining complete amplitude and phase information from the wave. The results are compared with available weak scintillation theory and with recent occultation data. The effects of large scale atmospheric waves with realistic horizontal structure are examined, and the reliability of the numerical inversion method in retrieving the true atmospheric vertical structure under conditions of strong ray crossing and horizontal inhomogeneities is assessed. The nature of model lightcurve spikes generated using geometric optics and wave optics are compared.
A generalized solution is found for retrofitting a large dual-shaped reflector antenna for a beamwaveguide. The design is termed as a bypass beamwaveguide. Both highpass design feed imaging and bandpass design feed imaging are considered. Each design was studied using geometrical optics, Gaussian wave analysis, and both low-frequency and high-frequency diffraction analysis. An important extension of the Mizusawa-Kitsuregawa criteria was discovered (Zusama and Kitsuregawa, 1973). The principle revealed shows how a two-reflector cell, although in itself distorting, may be combined with a second cell which compensates for the first and delivers an output beam which is a good image of the input beam.
The dependence of the effects of planetary atmospheric turbulence on radio or optical wavelength in occultation experiments is discussed, and the analysis of Hubbard and Jokipii (1977) is criticized. It is argued that in deriving a necessary condition for the applicability of their method, Hubbard and Jokipii neglect a factor proportional to the square of the ratio of atmospheric or local Fresnel zone radius and the inner scale of turbulence, and fail to establish sufficient conditions, thereby omitting the square of the ratio of atmospheric scale height and the local Fresnel zone radius. The total discrepancy is said to mean that the results correspond to geometrical optics instead of wave optics, as claimed, thus being inapplicable in a dicussion of wavelength dependence. Calculations based on geometrical optics show that the bias in the average bending angle depends on the wavelength in the same way as does the bias in phase path caused by turbulence in a homogeneous atmosphere. Hubbard and Jokipii comment that the criterion of Haugstad and Eshleman is incorrect and show that there is a large wave optical domain where the results are independent of wavelength.
For scattering calculations involving nonspherical particles such as ice crystals, we show that the transverse wave condition is not applicable to the refracted electromagnetic wave in the context of geometric optics when absorption is involved. Either the TM wave condition (i.e., where the magnetic field of the refracted wave is transverse with respect to the wave direction) or the TE wave condition (i.e., where the electric field is transverse with respect to the propagating direction of the wave) may be assumed for the refracted wave in an absorbing medium to locally satisfy the electromagnetic boundary condition in the ray tracing calculation. The wave mode assumed for the refracted wave affects both the reflection and refraction coefficients. As a result, a nonunique solution for these coefficients is derived from the electromagnetic boundary condition. In this study we have identified the appropriate solution for the Fresnel reflection/refraction coefficients in light scattering calculation based on the ray tracing technique. We present the 3 x 2 refraction or transmission matrix that completely accounts for the inhomogeneity of the refracted wave in an absorbing medium. Using the Fresnel coefficients for an absorbing medium, we derive an asymptotic solution in an analytical format for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations. The asymptotic theory can produce reasonable accuracy in the phase function calculations in the infrared window region (wavelengths near 10 micron) if the particle size (in diameter) is on the order of 40 micron or larger. However, since strong absorption is assumed in the computation of the single-scattering albedo in the asymptotic theory, the single scattering albedo does not change with variation of the particle size. As a result, the asymptotic theory can lead to substantial errors in the computation of single-scattering albedo for small and moderate particle sizes. However, from comparison of the asymptotic results with the FDTD solution, it is expected that a convergence between the FDTD results and the asymptotic theory results can be reached when the particle size approaches 200 micron. We show that the phase function at side-scattering and backscattering angles is insensitive to particle shape if the random orientation condition is assumed. However, if preferred orientations are assumed for particles, the phase function has a strong dependence on scattering azimuthal angle. The single-scattering albedo also shows very strong dependence on the inclination angle of incident radiation with respect to the rotating axis for the preferred particle orientations.
The Radio Plasma Imager (RPI) on the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) mission operates like a radar by transmitting and receiving coherent electromagnetic pulses. Long-range echoes of electromagnetic sounder waves are reflected at remote plasma cutoffs. Thus, analyses of RPI observations will yield the plasma parameters and distances to the remote reflection points. These analyses assume that the reflecting plasma surfaces are cold and are sufficiently smooth that they effectively behave as plane mirrors to the incoming sounder waves, i.e., that geometric optics can be used. The RPI will employ pulse compression and spectral integration techniques, perfected in ground-based ionospheric digital sounders, in order to enhance the signal-to-noise ratio in long-range magnetospheric sounding. When plasma irregularities exist in the remote magnetospheric plasmas that are being probed by the sounder waves, echo signatures may become complicated. Ionospheric sounding experience indicates that while topside sounding echo strengths can actually be enhanced by the presence of irregularities, ground-based sounding indicates that coherent detection techniques can still be employed. In this paper we investigate the plasma conditions that will allow coherent signals to be detected by the RPI and the signatures to be expected, such as scattering and plasma resonances, in the presence of multi-scale irregularities, may possibly have on RPI signals. Sounding of irregular plasma structures in the plasmasphere, plasmapause and magnetopause are also discussed.
The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. Explicit matrix formulas for calculating DF are given, and its physical significance is illustrated via examples.
WKB approximation HF gravitational wave solutions to general relativity vacuum Einstein equations with strong gravitational fields, discussing light waves analogy
The transverse wave condition is not applicable to the refracted electromagnetic wave within the context of geometrical optics when absorption is involved. Either the transverse magnetic (TM) or the transverse electric (TE) wave condition can be assumed for the wave to locally satisfy the electromagnetic boundary condition in a ray-tracing calculation. The assumed wave mode affects both the reflection and the refraction coefficients. As a result, nonunique solutions for these coefficients are inevitable. In this study the appropriate solutions for the Fresnel reflection-refraction coefficients are identified in light-scattering calculations based on the ray-tracing technique. In particular, a 3x2 refraction or transmission matrix is derived to account for the inhomogeneity of the refracted wave in an absorbing medium. An asymptotic solution that completely includes the effect of medium absorption on Fresnel coefficients is obtained for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations.
For a well-developed sea at equilibrium with a constant wind, the energy-containing range of the wavenumber spectrum for wind-generated gravity waves is approximated by a generalized power law involving the angular spread function and mu, interpreted as a fractal codimension of a small surface patch. Dependence of mu on the wave age is estimated, and the 'Phillips constant', beta, along with the low-wavenumber boundary, k0, of the inertial subrange are analyzed on the basis of the wave action and energy conservation principles. The resulting expressions are employed to evaluate various non-Gaussian statistics of a weakly nonlinear sea surface, which determine the sea state bias in satellite altimetry. The locally accelerated decay of the spectral density function in a high-wavenumber dissipation subrange is pointed out as an important factor of wave dynamics and the geometrical optics treatment of the sea state bias. The analysis is carried out in the approximation of a unidirectional wave field and confined to the case of a well-developed sea.
Theoretical models developed for simulation of microwave remote sensing of the Earth surface from airborne/spaceborne sensors are described. Theoretical model calculations were performed and the results were compared with data of field measurements. Data studied included polarimetric images at the frequencies of P band, L band, and C band, acquired with airborne polarimeters over a agricultural field test site. Radar polarization signatures from bare soil surfaces and from tree covered fields were obtained from the data. The models developed in this report include: (1) Small perturbation model of wave scatterings from randomly rough surfaces, (2) Physical optics model, (3) Geometrical optics model, and (4) Electromagnetic wave scattering from dielectric cylinders of finite lengths, which replace the trees and branches in the modeling of tree covered field. Additionally, a three-layer emissivity model for passive sensing of a vegetation covered soil surface is also developed. The effects of surface roughness, soil moisture contents, and tree parameters on the polarization signatures were investigated.
The propagation of electromagnetic waves in a nonhomogeneous anisotropic medium is examined from the point of view of geometrical optics. In particular, the propagation of ELF waves in the magnetosphere is described in terms of the electron and ion densities and the intensity and inclination of the earth's magnetic field. The analysis of the variations of wave normal angle along the ray path is extended to include the effects of ions. A comparison of the relative importance of each of the above parameters in controlling the orientation of the wave normals is made in the region of the magnetosphere where most of the ion whistlers have been detected.
The effect of plasma produced by an arc-jet thruster on the performance of on-board reflector antennas was investigated using a configuration in which the arc-jet plume is modeled as an inhomogeneous scatterer with a smoothly varying refractive index. On the basis of laws of geometrical optics, used to calculate the wave propagation, the trajectory, phase, amplitude, and polarization of the high-frequency ray field are computed numerically. The experiments performed to validate the calculated results experimentally are described.
Angular broadening of radiation due to scattering by density irregularities is usually described using geometric optics (GO) or the parabolic wave equation (PWE) with the assumptions that the radiation frequency f greatly exceeds the local plasma frequency f(sub p0) or that f(sub p0)/f is constant along the path. These assumptions are inappropriate for many solar system radio phenomena. Here the PWE and GO formalisms are extended to treat angular broadening in plasmas with nonzero, spatially varying ratios, f(sub p0)(z)/f < 1. The new PWE results show that the correlation function, scattered angular spectrum, and other quantities are modified by inclusion of a denominator factor [1 - f(sup 2, sub p0)(z prime)/f prime] inside the path integral over z prime, while the mean-square scattering angle depends on both f(sub p0)(z)/f at the observer and the foregoing factor inside the path integral. The PWE and GO predictions for are identical and involve equivalent assumptions. Previous GO and PWE results are recovered in the limits that f(sub p0)(z prime)/f is constant or zero. The new PWE and GO results will permit more accurate calculation of angular broadening for solar system and astrophysical sources. Moreover and importantly, due to the PWE and GO results for being identical, previous GO analyses of in solar system contexts are essentially correct, except for the neglect of or minor deficiencies in the treatment of nonzero, spatially varying f(sub p0)/f effects. The identical GO and PWE results for and the form of the PWE equation for the correlation function raise questions as to whether diffraction is unimportant for angular broadening (under the usual PWE conditions). Future direct comparisons of the PWE predictions with angular spectra calculated using existing GO ray-tracing codes should answer these questions. Diffraction effects are probably important when the medium and turbulence are not sufficiently homogeneous transverse to the central ray path. The implications are also discussed for studies of the 2-3.5 kHz radiation observed in the outer heliosphere.
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.
This paper presents a detailed analysis of a space-based telescope requiring an accuracy of 50 pico radians. A relationship between the geometric centroid of a diffraction image and wave aberrations is derived by a combination approach of diffraction optics and geometric optics. Based on sensitivity of the centroid, one-mirror and two-mirror aplanatic telescopes are investigated. The comparison among three telescopes, parabola, Schwartzschild and Ritchey-Chretien are quantitatively carried out in terms of their sensitivities to the systematic errors and random errors. The study shows that the Ritchey-Chretien design is the most preferable.
Laboratory evidence is presented of modulationally unstable electron wave packets which can be described by a nonlinear geometrical optics theory. Growth times for self-contraction are found to be much faster than ion response times and the bursts do not appear to be related to Zakharov Langmuir-wave collapse.
A theory of temporal broadening of pulses propagating in a turbulent medium is developed on the basis of the Markov approximation. The theory may be applied to quite general turbulence spectra and to thin or thick turbulent regions. Since the basis of the theory is the wave equation, no reliance is placed on geometrical optics and no assumptions are made about the scattered angular spectrum. The observed smearing is found to be the combination of three effects: the dispersion effect, the pure refractive effect, and the diffraction effect. The last of these dominates for typical pulsar parameters. Pulse shapes are calculated for both Gaussian and Kolmogorov turbulence spectra and it is shown how these scale with the various turbulence parameters.