Millimetre-wave scattering from one-dimensional surfaces of different surface correlation functions

This paper presents radar-altimeter scattering models for each of the diagenetic zones of the Greenland ice sheet. AAFE radar-altimeter waveforms obtained during the 1991 and 1993 NASA multi-sensor airborne altimetry experiments over Greenland reveal that the Ku-band return pulse changes significantly with the different diagenetic zones. These changes are due to varying amounts of surface and volume scattering in the return waveform.In the ablation and soaked zones, where surface scattering dominates the AAFE return, geophysical parameters such as rms surface height and rms surface slope are obtained by fitting the waveforms to a surface-scattering model. Waveforms from the percolation zone show that sub-sruface ice features have a much more significant effect on the return pulse than the surrounding snowpack. Model percolation waveforms, created using a combined surface- and volume-scattering model and an ice-feature distribution obtained during the 1993 field season, agree well with actual AAFE waveforms taken in the same time period. Using a combined surface- and volume-scattering model for the dry-snow-zone return waveforms, the rms surface height and slope and the attenuation coefficient of the snowpack are obtained. These scattering models not only allow geophysical parameters of the ice sheet to he measured but also help in the understanding of satellite radar-altimeter data.

Scattering of a TE incident wave from a perfectly conducting one-dimensional composite random rough surface is studied. A composite random surface contains roughness of more than one scale. With the recently developed efficient numerical technique known as the banded-matrix iterative approach, we are able to study large-scale composite roughness with two correlation lengths that are many times different from each other. It is shown that small-scale roughness, with its large rms slope, rather than large-scale roughness, with its small rms slope, can dominate bistatic scattering. It is also shown that backscattering enhancement can also exist in a composite rough surface.

We present experimental results on the scattering of electromagnetic waves at millimeter‐wave frequencies from one‐dimensional very rough conducting surfaces with controlled surface roughness statistics. Very rough surfaces are defined as surfaces with rms height and correlation length of the order of a wavelength such that the rms slope is at least unity. It is expected that scattering experiments using these surfaces can provide useful insights since their statistics lie outside the range of validity of the present theories, namely, the Kirchhoff and perturbation theories. Strong backscattering enhancement at different incident angles, both in the transverse electric and transverse magnetic polarizations, are observed experimentally. Numerical calculations based on the exact integral equation method for cylindrical beam wave illumination compare favorably with the experimental results. The agreement between measurements and numerical calculations is good over a wide range of incident angles and for all scattering angles. The close agreement between the experimental results and numerical simulations indicates that this controlled experimental setup can be used to study scattering phenomena from one‐dimensional very rough surfaces with different roughness statistics as well as from two‐dimensional rough surfaces.

In this paper we study the depolarized backscatter enhancement phenomenon for electromagnetic wave scattering from rough surfaces. Some new experimental data on light scattering from rough metallic surfaces shows a phenomenon of backscattering enhancement existing in the antispecular direction under some conditions, such as the surface parameters, wave polarization and operating frequency. From a roughly random surface the backscattering enhancement is predicted due to the constructive interference of multiple surfaces scattering. The study is based upon the integral equation method modified to be able to predict the phenomenon of multiple scattering and backscattering enhancement. From the study we found the backscattering enhancement takes place on the specialized surface parameters large compared with the incident wavelength. Further we also conclude that the depolarized multiple scattering makes much contribution along the plane of incidence from random rough surfaces, but depolarized single scattering makes little contributions as our expectation. In comparison of model prediction of total multiple scattering strength with measured data along the specular plane, excellent agreement is obtained.

This article describes a simple ray theoretic model of scattering in the Arctic which couples ray theory to the scattering strength formalism of scattering from a rough surface. This model has one free parameter in it, the root-mean-square (rms) slope of the rough surface. A comparison between model predictions and experimental data is made, where the rms slope is adjusted to fit the data. At short ranges, agreement between theory and experiment is of the order 3 dB. At longer ranges, agreement between theory and experiment deteriorates to 6 dB. This deterioration is thought to be due to the effects of shadowing due to large scale ice features, which are neglected in the present model.

A new iterative solution to the problem of sea surface scattering is obtained which has the Kirchhoff approximation as its leading term. This solution is obtained by transforming an integral equation of the first kind for the surface potential to one of the second kind, and applying the method of successive approximations. The advantages of this method are that the conditions under which this solution converges may be readily established and the solution may be iterated to sufficiently high order in the interaction to examine the rate at which it converges. A numerical example of scattering from an echelette grating is considered, and the regime of convergence established. It is found that the new iterative solution converges only for such surfaces on which kσσ′<π><π where k is the wave number of the scattered radiation and σ and σ′ are, respectively, the rms surface height and slope. This finding raises doubts concerning the regime in which the Kirchhoff approximation is traditionally deemed applicable. Finally, numerical studies are presented to illustrate the convergence of the iterative solution.

Roughness of surfaces and interfaces

Wide-band electromagnetic scattering from multiple objects shallowly buried beneath rough earth soil surfaces has been an important research topic in recent years because of its extensive applications in detecting the buried objects such as mines, pipes, and tunnels. Due to the advantages of finite-difference time-domain (FDTD) method in simulating wide-band electromagnetic scattering from rough surface in the presence of multiple objects, the FDTD method under Gaussian differential pulse wave incidence is utilized in the present study to analyze the frequency response of rough soil surfaces with shallowly buried objects, which serves as a basis for the detection and discrimination of objects buried below rough soil surfaces. The Topp equation model that can predict the dielectric constant of soil-water mixture is adopted in the present study to properly describe the dielectric property of earth soil with water. The actual rough land surface is modeled as the realization of a Gaussian random process with exponential spectrum by using Monte Carlo method. Simulation results show that the variation of composite scattering coefficient with frequency is oscillatory. It is also shown that the composite scattering coefficient versus frequency increases with the increase of root-mean-square of soil surface, water ratio of soil, the target section height, and the separation distance of target. However, simulation results indicate that the composite scattering coefficient versus frequency decreases with the increase of target section width. In summary, the variation of wide-band scattering coefficient is very complicated and is very sensitive to the incidence angle of electromagnetic wave. However, the wide-band scattering coefficient under Gaussian differential pulse wave incidence is less sensitive to the correlation length of rough soil surface, the depth of buried objects, and the dielectric constant of target. These qualitative results relating to the frequency response of rough soil surfaces in the presence of multiple objects are potentially valuable for detecting and discriminating the objects buried below rough soil surfaces by utilizing a wide-band ground penetrating radar system, although the present study is limited to one-dimensional rough soil surface due to the severe computational burden encountered in the large-scale Monte Carlo simulations. In addition, compared with frequency-domain numerical methods, the FDTD method has significant advantages in calculating wide-band composite scattering from rough surfaces in the presence of multiple objects, and thus has extensive applications in radar imaging simulation of multiple objects below or above rough surfaces, which goes beyond the scope of this paper.

Bistatic Electromagnetic Scattering from Randomly Rough Surfaces

In bistatic radar observations, reflected echoes from the surface of a target planet can be analyzed to infer its surface statistics and near-surface constituents. In this work, a preliminary inspection of two X-band bistatic radar observations gathered by the Cassini spacecraft about Titan’s polar regions is presented. Profiles of relative dielectric constant and root-mean-square (rms) surface slope are provided as outputs of the analysis, discussed, and compared with the present knowledge of Titan geomorphology. For the assessment of the rms slope, proportional to the spectral broadening of reflected echoes, a basic fitting procedure was applied to the received spectra using a Gaussian template, to later evaluate the full-width half-maximum of the fitting curve. The dielectric constant was computed from the power ratio between orthogonally circularly polarized components of signal reflections from Titan. Dielectric constant estimates are, on average, consistent with the expected materials covering the dry surfaces of the planet, while slightly low values were found over the seas. The rms slopes are generally low compared to past bistatic observations of other targets. Titan’s north polar seas are revealed to feature an unprecedented smoothness, with 0.01^circ of slope as an upper bound. Similar values were inferred for isolated spots in the southern pole, hinting at the possible presence of basins filled with liquid hydrocarbons. The main issues with the analysis are emphasized throughout the document, and some ideas for future work are presented in the conclusions.

This paper discusses the measurement of the finish of diamond-turned surfaces by differential light scattering. Experimental scattering data are analyzed by electromagnetic theory to give the two-dimensional power spectral density of the surface roughness. These spectral densities are direct functional measures of the surface quality, and may be characterized in terms of topographic finish parameters. These parameters can then be used to specify surface finish, to predict scattering under a variety of conditions, and to aid in studies of other functional properties of these surfaces. Scattering spectra are separated in-to three groups corresponding to three classes of surface roughness: periodic tool marks and one- and two-dimensional random roughness. Periodic tool marks give rise to discrete diffraction lines in the scattering spectrum and are characterized by their surface periods and their Fourier amplitudes. Random one- and two-dimensional roughness give rise to one- and two-dimensional continua underlying the diffraction lines and are characterized by band-limited values of the rms surface heights and slopes, and transverse length parameters. Using HeNe light, vertical roughnesses are measured from a fraction of an Angstrom to several hundred Angstroms, for transverse spatial wavelengths from a fraction of a micron to several hundred microns. We re-view experimental techniques for making these measurements with emphasis on the scatterometer developed in our laboratory, which uses a fixed source-detector geometry and a rotating sam-ple. Results are illustrated by a number of scattering spectra taken with this instrument.

Temporal evolution characteristics and prediction methods of spatial correlation function shape of rough soil surfaces

For perfect surface roughness description is not enough to know characteristics of surface profile. It is necessary to use topography methods, so called microtopography. Thereby, surface roughness in microtopographycal understanding must be described with three coordinates, whose in Cartesian coordinates system compose point under consideration height h, abscissa and ordinate, determines point position in the plane. Most efficient methods in irregular surface roughness research are random function theory methods. Therefore, microtopography, analogically to profile, may consider as random function, but two dimensional function, i.e. two variable x and y random field h(x,y). From analogy with random process, random field can be normal – ordinates are distributed by normal (Gaussian) distribution. Moreover, random field can be homogeneous and heterogeneous. Random field is deemed homogeneous if its mean value is discretionary and correlation function depends only from distance between surface points. Important characteristic of random field is correlation function, whose depends of two variables t1 and t2 – orthogonal Cartesian coordinates of vector t. Random field is homogeneous and isotropic when its characteristics are equivalent in any direction. There are three types of surface anisotropy: • General event of surface anisotropy. Characteristics of this event roughness parameters are depend of surface split direction. • Surface roughness with direct anisotropy. Those surfaces are with typical traces of tool and they proper two mutually perpendicular surface roughness directions. • Extended anisotropy area – special event of anisotropy roughness. Of analytical opinion, gainfully anisotropy roughness see as extended occasional isotropy area. This let easy cross from anisotropy surface to isotropy and contrariwise, thereby embrace amount class of surface roughness. Let’s formulate microtopography model of rough surface [1]. Surface roughness is described with homogeneous normal random field h(x,y) that has uninterrupted correlation function and uninterrupted deriviates. We may consider that E{h(x,y)}=0. The mean random field value is plane called mean plane. For describing random field we must know mathematical expectation and field correlation function, what in fact reduces on determining dispersion and rationed correlation function r(t1, t2). Homogeneous random field dispersion D{h} doesn’t depends of direction and can be founded in any surface split. Given model of rough surface let inspect surfaces produced by abrasive instruments and friction surfaces after wear-in period.

The global distribution of the reflectivity of the surface of Venus as determined by the Pioneer Venus orbital radar instrument has been analyzed in a geological context and statistically correlated with elevation. In addition, a comparison between the reflectivity and rms slope (roughness) correlations with elevation permits radar‐geologic topographic zones to be identified. The radar reflectivity ρ at normal incidence and at a wavelength of 17 cm (1.76 GHz) is a model‐dependent measure of the bulk dielectric constant κ of surfaces dominated by dry rocks and soils and depends on surface material properties such as porosity and conductivity. Only the quasi‐specular component of the radar echo was used in determining the reflectivity values analyzed in this study, and for very rough surfaces the absolute magnitude of ρ may be underestimated by 10–15%. Empirically derived relationships between ρ, κ, and bulk density γ are used to interpret geologically the ρ distribution. The global mean ρ of 0.13 is significantly greater than the average lunar and typical martian values of ∼0.07, suggesting the absence of a continuous soil mantle on Venus. The ρ distribution is well described by a two‐stage Gaussian distribution with modes at 0.11 and 0.14. The close proximity of these modes suggests that there is no fundamental dichotomy of surfaces on Venus insofar as their ρ properties, in contrast with roughness. Less than 15% of Venus has ρ values low enough to indicate a major soil component on the surface. Approximately 27% of the surface is dominated by low‐porosity materials such as bedrock, and less than 15% is enriched in high dielectrics. The rest of the surface (43%) is most simply envisioned as partially mantled bedrock, perhaps an extension of the types of terrain viewed by the Venera 10 and 13 landers. The most plausible model for the highest ρ (and thus highest κ) materials requires enrichment in Ti and Fe (e.g., minerals such as rutile, ilmenite, and magnetite). High‐titanium basalts such as those found on the moon would produce the required enrichment, as would pyrites. Since surface geochemical measurements demonstrate that there are basalts in the Venusian plains, a model in which high‐titanium basalts are exposed at the highest elevations (Maxwell, Theia, Atla, Ovda) is favored. Possible weathering of ilmenite in such basalts to produce rutile could explain the high‐κ materials in less elevated regions. When correlated with elevation, κ exhibits a complex nonmonotonic trend in which both decreases and increases are observed. A major decrease in ρ of ∼0.02 km−1 in the upper plains contrasts with the almost 1° rms km−1 increase in surface roughness over the same interval and may be an expression of increased soil production, perhaps due to enhanced breakdown of silicates into carbonates in the lower highlands. Alternately, the decrease could be due to increased centimeter scale roughening, perhaps caused by the increase in regional slope in the highlands. A major increase in ρ (0.05 km−1) in the middle highlands correlates with a rapid rise in rms slope. Unlike rms slope, however, there is no overall correlation of ρ with either elevation or regional slope, suggesting that it may be a more locally controlled parameter. Hierarchical clustering analysis of the ρ, roughness, and regional slope properties of Venus demonstrates that distinct subregions are best defined on the basis of topographic zones in which the radar parameters follow well‐defined trends. The lowland plains are extremely smooth at scales from centimeters to 100 km. In general, no single radar parameter (e.g., ρ) serves to subdivide the surface into distinct geologic regions, but taken together, the radar parameters can be statistically correlated to define meaningful radar geologic units. Such units appear to correlate with the kinds of surfaces that can be seen on Venus at kilometer resolution.

One goal of radar remote sensing is the extraction of terrain statistics and surface dielectric properties from backscatter data for some range of wavelengths, incidence angles, and polarizations. This paper addresses empirical approaches used to estimate terrain properties from radar data over a wider range of roughness than permitted by analytical models. Many empirical models assume, at least implicitly, that roughness parameters like rms height or correlation length are independent of the horizontal length scale over which they are measured, in contrast to recent surveys of natural terrain, which show that self-affine, or power-law scaling, between horizontal scale and roughness statistics is very common. The rms slope at the horizontal scale of the illuminating wavelength s(lambda) is directly related to the variogram or structure function of a self-affine surface, can be readily obtained from field-measured topography, and, when used in an empirical model, avoids the need for arbitrary wavelength-dependent terms. To facilitate comparison with earlier approaches, an expression that links the rms height at some profile length with the rms (Allan) deviation at an equivalent horizontal sampling interval is obtained from numerical simulations. An empirical model for polarimetric scattering as a function of s(lambda) at 35deg-60deg incidence from smooth to rugged lava surfaces is derived and compared with earlier models for backscatter from modestly rough soil surfaces. The asymptotic behavior of polarization ratios for the lava flows suggests that the depolarization of linear-polarized illuminating signals occurs as a first-order process, likely through single scattering by rock edges or other discontinuities, rather than as the solely multiple-scattering effect predicted by some analytical models. Efforts to fully understand radar scattering from geological surfaces need to incorporate wavelength-scale roughness, perhaps through computational simulations.