Ocean-like Surfaces Research Articles

Efficient Calculation of the Kirchhoff Integral for Predicting the Bistatic Normalized Radar Cross Section of Ocean-Like Surfaces

Efficient Calculation of the Kirchhoff Integral for Predicting the Bistatic Normalized Radar Cross Section of Ocean-Like Surfaces

Composite Scattering Analysis of the Ship on a Rough Surface Based on the Forward Parametric Scattering Center Modeling Method

A novel forward method to establish the three-dimensional parametric scattering center models is developed to extract scattering centers from the combined target/rough surface models. Both scattering centers from the ship, including single-order and higher order scattering contributions, and from the multiple interactions between the ship and random rough sea surface would be described concisely with physically relevant parameters by this proposed method. Due to the statistical nature of the random rough surface for the Monte Carlo simulation, we acquire a large number of realizations for estimations of the amplitude and position parameters to overcome the problem that single realization cannot extract scattering centers effectively. This method is validated through parametric models of the ship in free space and on the sea surface, and a good agreement has been demonstrated between the constructed and simulated radar characteristics. Furthermore, we analyze the composite target/surface model's physics and feature stability in a visually spatial range and direct connections between scattering centers and scattering sources, which would be valuable to future target recognitions and classifications. Finally, we quantitatively calculate and analyze the coupling scattering centers from interactions between the ship and the ocean-like surface that provide more abundant contour information of the inverse synthetic aperture radar (ISAR) image to facilitate contour detections.

Time-Varying Ocean-Like Surface Scattering at Grazing Incidence: Numerical Analysis of Doppler Spectrum at HF/VHF/UHF Bands

This paper numerically analyzes the characteristics of the Doppler spectrum at HF/VHF/UHF bands from 1D time-varying ocean-like surfaces at grazing incidence in vertical polarization mode. The rough surface is transformed into a local perturbation plane which has its roughness flattened at the edges. The scattering waves include coherent reflected wave and incoherent scattering waves. The surface currents exciting the incoherent scattering waves are regarded as the unknowns which can be solved from the improved surface integral equation using the method of moments (MoM). The incident plane wave allows the incident angle to reach up to 90° (grazing incidence). Then the backscattering wave in the far field can be calculated, and the Doppler spectrum is obtained by coherent Monte-Carlo simulation. Firstly, the validity of the method is verified by comparing with the mature small perturbation method at the HF band. Then the incident wave frequency is asymptotically increased from HF to UHF, and the application range of the SPM is quantitatively evaluated in the Doppler spectrum domain. Finally, the paper focuses on analyzing the characteristics of Doppler spectrum in different bands and different sea states and comparing the influence of nonlinear ocean waves on the Doppler spectrum at different frequencies.

Rigorous Simulations of Microwave Scattering From Finite Conductivity Two-Dimensional Sea Surfaces at Low Grazing Angles

We present a boundary integral method for the solution of the rigorous problem of microwave scattering from finite conductivity sea surfaces under grazing illumination. Following the locally perturbated plane approach, the roughness is flattened at the edges of a finite patch, allowing us to use a plane wave as incident field. Both theoretical formulation and numerical implementation are addressed. We present simulations of full-polarization radar cross-sectional diagrams for 2-D ocean-like surfaces in both bistatic and monostatic configurations. The conductivity of the sea water is taken into account with a curved surface-impedance approximation, and results are compared with a perfectly conducting surface model. Simulations are finally confronted to approximate theories and empirical sea backscatter models for low grazing angles at L-band, vertical polarization, and a wind speed of 3 m/s.

A Study of Sea Surface Range-Resolved Doppler Spectra Using Numerically Simulated Low-Grazing-Angle Backscatter Data

A numerical study of sea surface range-resolved Doppler spectra using low-grazing-angle backscatter measurements is described. Backscattered fields as a function of frequency are computed using the method of moments (MOM) for a single realization of a 1-D oceanlike surface profile as the realization evolves in time. Transformation into the range-Doppler domain enables examination of properties of the resulting Doppler spectra (for both HH and VV polarizations) and their relationship to properties of the surface profile. In general, a strong correspondence between the “long-wave” orbital velocity of the surface projected along the radar line of sight and the Doppler centroid frequency is observed for visible portions of the surface, as well as some evidence of relationships between the “width” of the Doppler spectrum and variations of the projected velocity in time at a given range point. Evidence of similar relationships even in some shadowed portions of the surface is also provided. Doppler spectra from HH and VV polarizations are qualitatively similar, despite differences in total power levels, although the portion of shadowed surface points from which Doppler information is available is somewhat larger in VV polarization. A further examination is conducted using backscattered fields computed with a single-scattering method, which neglects shadowing and any multiple-scattering effects. The remarkable similarities observed between MOM and single-scattered Doppler spectra even in some shadowed portions of the surface suggest that non-line-of-sight propagation effects do not significantly influence Doppler properties in such regions.

Numerical Simulations and Analysis of Wide-Band Range-Resolved HF Backscatter From Evolving Ocean-Like Surfaces

Low-grazing wide-band HF radar echoes from evolving ocean-like surfaces in 2-D space are simulated employing a first-principles boundary integral equation technique. The synthesized signals achieve range resolution of about 15 m and correspond to observations with a hypothetical narrow-beam system having a 10-MHz effective bandwidth. Range-time plots of backscatter magnitude appear to contain a pattern consistent with the long surface waves. The double Fourier transform of the signal magnitude or power in range and time reveals strong harmonics located along the dispersion curve of the propagating gravity waves. The effect is discernable due to the high range resolution employed and is not predicted by the first-order Small Perturbation Method (SPM) approximation. It is explained by considering the next, second order of the SPM under certain simplifying assumptions such as perfect surface conductivity (with the Norton attenuation factor set to 1). The derived analytical expression is then used to investigate the feasibility of the surface profile retrieval from such time-varying range-resolved HF backscatter (gathered in the course of the “numerical experiment” through the exact scattering simulations). For the case of perfectly conducting sea-like surface developed under 10-m/s wind conditions, the results are very encouraging. The approach is sensitive to the surface harmonics with wavelengths far exceeding the Bragg resonance scales of the HF band. Extending this type of analysis to cases with realistic finite conductivity and/or rougher surface (assuming that the second-order SPM is still valid) will require proper accounting for ground-wave propagation effects in perturbation expressions. The study offers a glimpse into ocean observation possibilities that the wide-band HF systems can provide if and when they become a reality.

Backscattering measurements from double-scale randomly rough surfaces

We present experimental measurements of light backscattered from double-scale randomly rough surfaces (oceanlike surfaces) with different statistical parameters illuminated at small and large angles of incidence. The surfaces are composed of a small-scale roughness superimposed on a slowly (large-scale) varying surface. The large-scale surfaces are diamond-machined periodic surfaces made on aluminum substrates and have either a sinusoidal or a Stokes wave profile. The small-scale roughness is added with lithographic techniques, and the surfaces are then gold coated. For a linearly polarized incident beam, it is found that the backscattered light is strongly depolarized mainly at small angles of incidence and strong shadowing effects are present for large angles of incidence (θ(inc) > 60°).

A Study of Interferometric Phase Statistics and Accuracy for Sea Surface Height Retrievals from Numerically Simulated Low-Grazing-Angle Backscatter Data

A numerical study of the retrieval of sea surface profiles from low-grazing-angle interferometric radar measurements is described. Backscattered fields computed using the method of moments for 1-D ocean-like surface profiles are used to examine statistical properties of the single-look interferometric phase estimator, in order to investigate the applicability of standard expectations for height retrieval accuracy in this problem. The results show that shadowing and multipath propagation effects cause errors in interferometric phase estimation beyond those caused by speckle effects alone. In addition, the decorrelation between the fields received at two antennas is found to be impacted by shadowing and multipath propagation effects, making standard models for this quantity inapplicable as well. These results show that modeling the expected performance of interferometric sea surface height retrieval approaches at low grazing angles is difficult at present, and that further research is required to address this issue.

Analysis of Electromagnetic Scattering from the 3D Conducting Object on the Random Ocean-Like Rough Surfaces

Analysis of Electromagnetic Scattering from the 3D Conducting Object on the Random Ocean-Like Rough Surfaces

Low-Frequency Limit of Unified Models for Backscattering From Oceanlike Surfaces

In the context of electromagnetic-wave backscattering from oceanlike surfaces, by using the first two orders of unified models, like the small slope approximation and the local curvature approximation, we recently proposed an original technique to reduce the number of numerical integrations to two for easier numerical implementation. In this letter, this technique is simplified in the low-frequency limit, allowing us to bring a correction to the first-order small perturbation method.

Numerical implementation of local unified models for backscattering from random rough sea surfaces

In the context of electromagnetic wave backscattering from ocean-like surfaces, by using the lowest order of the SSA (SSA-1) model, Bourlier et al. proposed an original technique to reduce the number of numerical integrations to two for easier numerical implementation. To be consistent with microwave measurements, closed-form expressions of the Fourier coefficients with respect to the wind direction of the backscattering normalized radar cross-section (NRCS) are obtained. For Gaussian statistics, previous work is extended in this paper to kernels of unified models expanded up to second order, like full SSA and full LCA. Thus, with the help of Bessel functions and by analytical integrations over the azimuthal angles, the second-order backscattering (BNRCS) is expressed in terms of two-fold integrations and another independent integration instead of four-fold integrations, if no analytical integration is made. This approach allows us to obtain fast results (less than one second). Numerical results are then presented for different microwave frequencies and wind speeds.

ROBUST SEMI-DETERMINISTIC FACET MODEL FOR FAST ESTIMATION ON EM SCATTERING FROM OCEAN-LIKE SURFACE

A robust semi-deterministic facet model for the computa- tion of the radar scattering cross section from the ocean-like surface is presented. As a facet-based theory, it is a more comprehensive model which can re∞ect the specular and difiuse conflgurations, as well as the mono- and bistatic features. Signiflcant computational e-ciency and good agreement with experimental data are observed, which makes the proposed facet model well suitable for fast estimation on EM scatter- ing and synthetic aperture radar (SAR) imagery simulation of marine scene.

Study on the Doppler shift and the spectrum widening of the scattered echoes from the 2-D rough sea surface

Based on the 2-D ocean-like surface of linear model and the first-order small slope approximation，the characteristic of Doppler shift for different order Doppler spectra of scattered echoes is investigated and the formula of Doppler shift is derived. Comparing with the conventional formula of Doppler shift，the influence of the wind speed and the orbit motion of the sea wave in large scale is considered in our result. By employing the two-scale model of rough surface and physical mechanism of Doppler shift，a formula of the spectrum widening for the scattered field from the oceanic surface is also presented. The numerical results evaluated by the formulae in this study are compared with the simulated and the measured data，the dependence of the Doppler shift and the spectrum widening on the parameters，such as the wind speed，the frequency of the incident wave and the incident angle, etc. are discussed. It is found that the formulae obtained in this research can be used to predict the Doppler shift and the spectrum widening.

Computation of Oceanlike Surface Thermal Emission and Bistatic Scattering With the Reduced Local Curvature Approximation

The reduced local curvature approximation of third order (RLCA3) is a recently proposed model for rough surface scattering that matches the Kirchhoff approximation as well as the first-order and second-order small perturbation methods in appropriate limits. Predictions of bistatic scattering, thermal emission, and reflected atmospheric brightnesses from the RLCA3 model are presented in this paper through a Monte Carlo simulation process. The surfaces considered are realizations of an oceanlike spectrum and contain features ranging from 64 to 0.5 electromagnetic wavelengths. Results are compared with predictions from the commonly applied ldquotwo-scalerdquo theory of sea emission, as well as results from a previous similar study using the small slope approximation (SSA) of Voronovich. Results show a high level of agreement between RLCA3 and SSA predicted bistatic scattering patterns, but appreciable differences in predicted surface brightnesses, particularly in the third Stokes' parameter.

Comparison of asymptotic backscattering models (SSA, WCA, and LCA) from one-dimensional Gaussian ocean-like surfaces

In this paper, recent asymptotic backscattering models are compared for one-dimensional multiscale dielectric sea surfaces with Gaussian statistics and by considering the Elfouhaily et al. height spectrum. We focus on the calculations of the normalized radar cross sections (NRCS) obtained from the weighted and local curvature approximations (WCA and LCA), recently published by Elfouhaily, and of the first- and second-order small slope approximation (SSA(1) plus SSA(2) denoted as SSA), developed by Voronovich. Voronovich et al. (2002 Waves Random Media 11 247-269) presented simulations of the SSA by making an assumption over the SSA(2) contribution (the model is referred to as SSAM). The NRCS computation is then similar to SSA(1), where the sea spectrum is substituted by a modified spectrum defined as the product of the sea spectrum by the second-order polarization term. The second-order statistical moment of WCA is calculated rigorously for any two-dimensional height correlation of the surface with Gaussian statistics. The NRCS of the WCA, WCAQ (obtained from a quadratic approximation of WCA), LCA, SSA, and SSAM backscattering models are compared for moderate wind speeds, for microwave frequencies and for backscattering angles ranging from 0 (nadir) to 70/spl deg/.

A study of ocean-like surface thermal emission and reflection using Voronovich's small slope approximation

Monte Carlo simulations are used to compute average direct surface thermal emission and reflected atmospheric radiation using the active small slope approximation of Voronovich. The surfaces considered are realizations of an ocean-like spectrum and contain features ranging from 64 to 0.5 electromagnetic wavelengths. The parallel computing approach of the study is described, and results are compared with predictions from the commonly applied two-scale theory of sea emission. Results show a reasonable level of agreement in a small height surface case, which degrades as the surface height is increased.

Experimental light-scattering measurements from large-scale composite randomly rough surfaces.

We present experimental measurements of the angular distribution of light scattered from large-scale composite randomly rough surfaces (oceanlike surfaces) with different statistical parameters illuminated at small and large angles of incidence. The surfaces are composed of a small-scale roughness superimposed on a slowly (large-scale) varying surface. The large-scale surfaces are diamond-machined periodic surfaces made on aluminum substrates and have either a sinusoidal or a Stokes wave profile. The small-scale roughness is added with microlithographic techniques, and the surfaces are then gold coated. For a linearly polarized incident beam, it is found that the diffusely scattered light is strongly depolarized and that its pattern is rather different for each large-scale surface profile. Enhanced backscattering is also observed.

Numerical study of the extended Kirchhoff approach and the lowest order small slope approximation for scattering from ocean-like surfaces: Doppler analysis

The validity of the lowest order small slope approximation (SSA(1)) and the extended Kirchhoff approach (EKA) (Elfouhaily et al., 1999) has been studied by comparing the Doppler spectra of the backscattered signals predicted by these models to their counterparts from exact integral equation-based numerical simulations. The study is conducted at L and S bands (electromagnetic wavelengths 23 and 10 cm); the rough ocean-like surfaces correspond to the wind speed of 5 m/s and were generated using both linear and nonlinear (Creamer) models. The incidence angle varies from normal to low grazing. Expressions for the two analytical models possess many similarities but contain different incidence/scattering angle-dependent factors. The analysis of the bistatic scattering cross sections predicted by the two models reveals that SSA(1) follows the exact numerical results more closely than the EKA. Moreover, at horizontal polarization the extended Kirchhoff bistatic cross section displays certain anomalies (unlimited growth at grazing scattering angles) that are indicative of the problems with this model. However, in the backscattering direction, the expressions for the two models are identical. Doppler analysis of the backscattered signals shows that in general, the analytical models provide better agreement with the numerical results for smaller incident angles. In addition, the agreement between the models and the exact numerical simulations is always better in the case of vertical polarization for which the analytical models give a satisfactory prediction of the Doppler spectrum for incident angles as large as 85/spl deg/ from the normal for both linear and nonlinear surfaces. For horizontal polarization, the models give increasingly poor predictions of the shape, magnitude, and location of the Doppler spectrum for incident angles in the range from 60/spl deg/ to low grazing. Doppler analysis proves to be a much more precise and sensitive tool in assessing the scattering model's validity than the usual comparison of cross sections.

Scattering by two-dimensional rough surfaces: comparison between the method of moments, Kirchhoff and small-slope approximations

We use a rigorous numerical code based on the method of moments to test the accuracy and validity domains of two popular first-order approximations, namely the Kirchhoff and the small-slope approximation(SSA), in the case of two-dimensional rough surfaces. The experiment is performed on two representative types of surfaces: surfaces with Gaussian spectrum, which are the paradigm of single-scale surfaces, and ocean-like surfaces, which belong to the family of multi-scale surfaces. The main outcome of these computations in the former case is that the SSA is outperformed by the Kirchhoff approximation(KA) outside the near-perturbative domain and in fact is quite unpredictable in that its accuracy does not depend only on the slope. For ocean-like surfaces, however, SSA behaves surprisingly well and is more accurate than the KA.

Studies on accuracy of numerical simulations of emission from rough ocean-like surfaces

Numerical simulation of passive microwave remote sensing of ocean surfaces has a strict requirement of accuracy. This is because the key output of the simulations is the difference of brightness temperature between a rough surface and a flat surface. Since the difference can be as small as 0.5 K, it is important to simulate the scattering and emission accurately. The authors perform accurate simulations of transverse electric (TE) and transverse magnetic (TM) waves for ocean surfaces with relative permittivity=28.9541/spl plusmn/i36.8430 at 19 GHz. Because ocean permittivity is large, the authors used up to 80 points per free space wavelength. Furthermore, accurate numerical integration is also performed to obtain accurate impedance matrix elements. To ensure accuracy, a matrix equation obtained from the surface integral equation formulation is solved by matrix inversion. Conservation of energy is required to be accurate to a relative error of 0.001, which corresponds to 0.3 K in brightness temperature. Numerical results are illustrated for rough surfaces with Gaussian spectrum and bandlimited ocean spectrum and bandlimited fractal surfaces. The authors show convergence with respect to the density of sampling points and with respect to raising the upper limit of the bandlimited ocean spectrum. Comparisons are also made with results with an impedance boundary condition approximation. Numerical results indicate that fine discretization is required for ocean-like surfaces with fine scale roughness.