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Quasi-specular bistatic radar measurements of oblique scattering properties of lunar surface using telemetry carrier from Explorer 35 as lunar orbiting radar beacon
This paper examines the statistical behavior of the phase difference Delta-phi between the HH-polarized and VV-polarized backscattered signals recorded by an L-band SAR over an agricultural test site in Illinois. Polarization-phase difference distributions were generated for about 200 agricultural fields for which ground information had been acquired in conjunction with the SAR mission. For the overwhelming majority of cases, the Delta-phi distribution is symmetric and has a single major lobe centered at the mean value of the distribution Delta-phi. Whereas the mean Delta-phi was found to be close to zero degrees for bare soil, cut vegetation, alfalfa, soybeans, and clover, a different pattern was observed for the corn fields; the mean Delta-phi increased with increasing incidence angle Theta = 35 deg. The explanation proposed for this variation is that the corn canopy, most of whose mass is contained in its vertical stalks, acts like a uniaxial crystal characterized by different velocities of propagation for waves with horizontal and vertical polarization. Thus, it is hypothesized that the observed backscatter is contributed by a combination of propagation delay, forward scatter by the soil surface, and specular bistatic reflection by the stalks. Model calculations based on this assumption were found to be in general agreement with the phase observations.
Signals of opportunity (SoOp) reflectometry (SoOp-R) is a maturing field for geophysical remote sensing as evidenced by the growing number of airborne and spaceborne experiments. As this approach receives more attention, it is worth analyzing SoOp-R’s capabilities to retrieve subsurface soil moisture (SM) by leveraging communication and navigation satellite transmitters. In this research, the CRLB is used to identify the effects of variable SoOp-R parameters on the best achievable estimation error for root-zone soil moisture (RZSM). This study investigates the use of multiple frequency, polarization, and incidence angle measurement configurations on a two-layered dielectric profile. The results also detail the effects of variable SM conditions on the capability of SoOp-R systems to predict subsurface SM. The most prevalent observation is the importance of using at least two frequencies to limit uncertainties from subsurface SM estimates. If at least two frequencies are used, the CRLB of a profile is retrievable within the root-zone depending on the surface SM content as well as the number of independent measurements of the profile. For a depth of 30 cm, it is observed that a CRLB corresponding to 4% RZSM estimation accuracy is achievable with as few as 2 dual-frequency-based SoOp-R measurements. For this depth, increasing number of measurements provided by polarization and incidence angle allow for sensing of increasingly wet SM profile structures. This study, overall, details a methodology by which SoOp-R receiver system can be designed to achieve a desired CRLB using a trade-off study between the available measurements and SM profile.
Bistatic radar observations of quasi-specular scatter from the lunar surface at 13 and 116 cm wavelengths have been expressed in terms of probability densities of the underlying surface slope distributions. These show best agreement with a Hagfors scattering function, although other forms having predominantly Gaussian or exponential characteristics also occur. Estimates of root mean square (rms) surface slope derived from these function range from 4 deg rms in maria to at least 8 deg rms in highlands. These are values appropriate to 25 m horizontal scales and represent averages over tens of square kilometers of surface area. The effective scattering roughness varies with wavelength, most strongly in maria, where its behavior is consistent with that expected from an immature, i.e., unsaturated cratered surface. There is very little variation in scattering roughness with wavelength in highlands area.
BISTAT is a computer program for use in aiming a spaceborne bistatic-radar transmitting antenna at a remote planet that has an atmosphere, such that after refraction by the atmosphere and reflection from the surface of the planet, the radar signal travels toward a receiver on Earth. BISTAT includes an algorithm that neglects atmospheric refraction and calculates a specular-reflection point for a spacecraft at a given location. The specular-reflection point is then used as an initial guess for a modified limb-track algorithm that takes atmospheric refraction into account. The output of BISTAT for all spacecraft positions of interest constitutes a pointing profile; the output data are in the form of an inertial-vector file and a Doppler-residual file. The inertial-vector file is used to command the attitude of the spacecraft; the Doppler-residual file is used to determine a downlink frequency file for the receiver.
The scattering of a plane wave obliquely incident on a half space of densely distributed spherical dielectric scatterers is studied. The quasi-crystalline approximation is applied to truncate the hierarchy of multiple scattering equations, and the Percus-Yevick and the Verlet-Weis results are used to represent the pair distribution function. The coherent reflected wave is studied with these approximations. The incoherent scattered wave is calculated with the distorted Born approximation. In the low-frequency limit, closed-form expressions are obtained for the effective propagation constants, the coherent reflected wave, and the bistatic scattering coeficients. Results at higher frequencies are calculated numerically. The advantage of the present approach is that, in the low-frequency limit, it reproduces the effects of specular reflection, Fresnel reflection coefficient, Brewster angle, and Clausius-Mosotti relation. In addition to the classical results, the bistatic scattering coefficients are also calculated. The theory is also applied to match backscattering data from dry snow at microwave frequencies.
This paper presents a case study of a simple yet robust target for demonstration of the EM visualization process. A five lambda square plate exhibits many scattering mechanisms depending on excitation angle and polarization: specular scattering, leading and trailing edge diffraction, traveling wave, and edge wave scattering. Bistatic k space radiation images, currents maps, and near scattered / total fields are examined for each of these scattering mechanisms.
In this paper, three approximate physical microwave radiometry models have been used to calculate brightness temperatures from a forest canopy at L-band. These models are (1) tau-omega model (zero order scattering approximation to radiative transfer equations), (2) successive order of scattering model up to first order (first order scattering approximation to the radiative transfer equations), and (3) Peak technique utilizing the active solution obtained from the Distorted Born Approximation (DBA). These models are physically-based and treat vegetation as a layer of discrete scatterers over a rough surface. Vegetation components within the canopy are represented by canonical shapes such as dielectric discs and cylinders. The tau-omega model is based on a zero-order solution to the radiative transfer (RT) equations. The model ignores scattering except for the effect of the scatterers in the attenuation of the emission through the vegetation. Application of the tau-omega model to data acquired during airborne and ground-based campaigns over the years has solidified scientific understanding of microwave interactions with different landscapes. In particular, shrubland, grasslands, agricultural crops, and light to moderate vegetation have been investigated. Its applicability to areas with a significant tree fraction is unknown. The first order scattering model is based on an iterative solution of the RT equation up to the first order. The first order solution is obtained by substituting the zeroth-order solution into the scattering source term and then solving the resulting radiative transfer equations. This formulation adds a new scattering term to the tau-omega model. It represents emission by particles in the layer and emission by the ground that is scattered once by particles in the layer. The resulting model represents an improvement over the standard zero-order solution (the tau-omega model) since it accounts for the scattered vegetation and ground radiation that can have a pronounced effect on the observed brightness temperature. The third model is based on the Peake formulation in conjunction with the DBA. The procedure for calculation of forest emission is accomplished by first calculating the bistatic scattering cross section for each type of scatterer, then by using the DBA to calculate specular albedo of the ground and the diffused albedo of the layer. Once the albedos are determined, Peake s principle relating active and passive problems can be used to determine the effective emissivity of the forest layer.
Bistatic radar experiments carried out during the Apollo 14, 15, and 16 missions provide a very useful data set with which to compare theoretical models and experimental data. Vesecky, et al. report that their model for near grazing angles compares favorably with experimental data. However, for angles of incidence around 80 degrees, all the analytical models considered by Vesecky, et al. predict values for the quasi-specular cross sections that are about half the corresponding values taken from the Apollo 16 data. In this work, questions raised by this discrepancy between the reported analytical and experimental results are addressed. The unified full wave solutions are shown to be in good agreement with the bistatic radar taken during Apollo 14 and 16 missions. Using the full wave approach, the quasi-specular contributions to the scattered field from the large scale surface roughness as well as the diffuse Bragg-like scattering from the small scale surface roughness are accounted for in a unified self-consistent manner. Since the full wave computer codes for the scattering cross sections contain ground truth data only, it is shown how it can be reliably used to predict the rough surface parameters of planets based on the measured data.
The bistatic scattering from a perfectly conducting cone frustum is investigated using the Geometrical Theory of Diffraction (GTD). The first-order GTD edge-diffraction solution has been extended by correcting for its failure in the specular region off the curved surface and in the rim-caustic regions of the endcaps. The corrections are accomplished by the use of transition functions which are developed and introduced into the diffraction coefficients. Theoretical results are verified in the principal plane by comparison with the moment method solution and experimental measurements. The resulting solution for the scattered fields is accurate, easy to apply, and fast to compute.
Electromagnetic-wave scattering by a quasi-periodic surface with random perturbations (as in the remote sensing of plowed fields) is investigated analytically, applying the Kirchhoff approximation and modeling the plowed fields by means of Gaussian random variation, sinusoidal variation, and Gaussian random variation about the spatial frequency. Coherent and incoherent bistatic scattering coefficients are derived in closed form by evaluating the physical-optics integral and shown to be proportional, in the geometric-optics limit, to the occurrence probability of slopes which reflect the incident wave specularly in the direction of the scattered wave. Backscattering cross sections are plotted as functions of incidence angle for a number of cases, demonstrating the strong effect of row direction.
The detection of echoes produced by oblique reflection of the RF (2300 MHz) spacecraft carrier from the Martian surface as Mariner 6 and 7 flew behind Mars in 1969, is described. Changes in echo center frequency and bandwidth are utilized to study the radius and roughness of the surface along a quasi-specular radar track that led from an optically dark and densely cratered region of Meridiani Sinus over into a smoother and brighter looking area of Thymiamata. A 3 to 1 decrease in surface roughness of large size compared to the wavelength (13 cm) was observed as the reflecting zone moved across the boundary between these two regions. The average radius obtained along the track was 3393 plus or minus 3 km. Due to large angles of incidence (86 to 90 deg), and surface shadowing, the data are not suitable for mapping the reflection coefficient of the surface material.
The field of radiometry is surveyed with reference to coherent light, since the surfaces to be considered here are irradiated with coherent, polarized light. Definitions of some concepts are modified. In light of these modifications calibration problems are analyzed and solutions suggested. The most important task was to develop hard targets exhibiting minimal specular reflection (mirror-like and retroreflection) and following closely a Lambertian scattering curve. Bistable reflectometer experiments and integrating sphere measurements are used to physically characterize the targets. Optical and electron microscopy are used to physically characterize the targets. Since the BRDF matrix is not measured, this capability must be developed preferably for both bistatic and monostatic reflectometer measurements. The equipment is expensive and not yet developed. Calibration can be simplified if it can be proved that the BRDF matrix is diagonal for a diffuse scatterer.
W-band measurements of the bistatic scattering function of some common microwave absorbing structures, including periodic wedge-type and pyramid-type iron-epoxy calibration loads and flat carbon-foam 'Echosorb' samples, were made using a network analyzer interface to a focused-lens scattering range. Swept frequency measurements over the 75-100 GHz band revealed specular and Bragg reflection characteristics in the measured data.
Simultaneous 13- and 116-cm wavelength radio transmissions from the Apollo 14 and 15 spacecraft were received on the earth after reflection from the lunar surface. The received data were processed to obtain complete polarization and power spectra of the echo signal; the ellipticity, orientation, and magnitude of the deterministically polarized part were obtained as a function of frequency. The polarized parts of the echo spectra were then reduced according to the theory of quasi-specular scattering from a gently undulating surface. The unpolarized portions of the echo spectra were associated with a diffuse scattering mechanism. Within Mare Serenitatis and Oceanus Procellarum, the 13-cm data follow a classical Fresnel reflection curve corresponding to relative dielectric constant epsilon = 3.1 plus or minus 0.1. Over most of these same areas, the 116-cm data are consistent with this value of relative dielectric constant. In some areas, however, notably between Reiner and Hevelius, there are marked deviations from the reflectivities predicted for epsilon = 3.1. These results cannot be explained on the basis of simple models employing contiguous, semiinfinite, dielectric interfaces.
Strong localized radar echoes have been observed at decimeter wavelengths from the highlands of Venus since the earliest radar maps were obtained over 30 years ago. These echoes are some five to ten times stronger than those from the presumably basaltic rocks seen at lower altitudes elsewhere on Venus. Observations of thermal emission from the visible disk of Venus at wavelengths corresponding to those used in the radar mapping confirm that the regions of high reflectivity also exhibit low emissivity, as expected from considerations of detailed thermodynamic balance. Two possibilities have been put forward to explain this unexpected aspect of the Venus highlands: 1) surface materials of high effective dielectric constant, probably associated with finite electrical conductivity, and 2) volume scattering associated with multiple scattering from a layer of very-low-loss material containing voids and extending down a few hundred wavelengths beneath the surface. Analogs to these two mechanisms are found elsewhere in the solar system, and each is capable of explaining the basic observations. as of the early 1990's. In 1993, however, it became possible to carry out a bistatic observation of the anomalous highland regions using the Magellan spacecraft, then in orbit about Venus. In this experiment the on-board telemetry transmitter was aimed at the planet's surface with its linear S-band polarization vector oriented at 45 deg to the spacecraft-Venus-Earth scattering plane. The pointing of the transmitting antenna was adjusted so that the spacecraft-to-illuminated-surface incidence angle equalled the Earth-to-Venus-surface incidence angle. In this way, the experiment emphasized the specular scattering component. A full Stokes-Vector analysis of the reflected signal as received on Earth was carried out as the illuminated region scanned across the highland regions of Venus. From the observed position angle of the echo, it was possible to calculate the Fresnel reflectivity of a number of regions on Venus, including the high-altitude Maxwell Montes, and to show unequivocally that the complex dielectric constant of that anomalous area was 100 +/- 50i, as compared to 4.0 (real) for the typical lowland area. Thus this experiment was able to rule out definitively an hypothesis of volume scattering as the explanation for the anomalous scattering in the Venus highlands.