Gabriel Soriano

Scattering of electromagnetic waves from two-dimensional rough surfaces with an impedance approximation

The sparse-matrix-flat-surface iterative approach has been implemented for perfectly conducting surfaces and modified to enhance convergence stability and speed for very rough surfaces. Monte Carlo simulations of backscattering enhancement using a beam decomposition technique are compared with millimeter-wave laboratory experimental data. Strong but finite conductivity for metals or thin skin depth for dielectrics is simulated by an impedance approximation. This gives rise to a nonhypersingular integral equation derived from the magnetic field integral equation. The effect of finite conductivity for a metal at visible wavelengths is shown.

A Cutoff Invariant Two-Scale Model in Electromagnetic Scattering From Sea Surfaces

The two-scale model (TSM) is one of the most frequently employed approaches in scattering from multiscale surfaces such as ocean surfaces. It consists of combining geometrical optics (GO) with the small-perturbation model (SPM) to be able to cope with both the small- and large-scale components of the surface. However, well-known shortcomings of this method are the arbitrariness of the dividing scale and the sensitivity of the scattering cross section to the choice of this parameter. We propose to replace SPM with the first-order small-slope approximation (SSA1) to treat the small-scale roughness and derive the formulas for the corresponding TSM, referred to as GO-SSA. We show that GO-SSA is robust to the choice of the frequency cutoff and give a numerical illustration for the sea surface.

Doppler Spectra From a Two-Dimensional Ocean Surface at L-Band

An approximate time-harmonic three-dimensional electromagnetic boundary-integral method, the small-slope integral equation, is combined with a series expansion of the Creamer surface representation at second order with respect to the height, denoted by Creamer (2). The resulting model provides at low numerical cost simulations of the nonlinear ocean surface Doppler spectrum at L-band. As a result of approximations, the model is designed for a low-wind speed, typically up to 5 m/s. It is shown that applying directly a second-order model such as Creamer (2) to a semiempirical sea surface spectrum induces an unrealistic magnification of small-scale roughness that is involved in the scattering process at microwave frequencies. This paper thus proposes an undressed version of the Pierson-Moskowitz spectrum that corrects this artifact. Full-polarized Doppler simulations at L-band and 70deg incidence are presented. Effects of the surface nonlinearities are outlined, and the simulated Doppler spectra show correct variations with respect to wind speed and direction

The weighted curvature approximation in scattering from sea surfaces

A family of unified models in scattering from rough surfaces is based on local corrections of the tangent plane approximation through higher-order derivatives of the surface. We revisit these methods in a common framework when the correction is limited to the curvature, that is essentially the second-order derivative. The resulting expression is formally identical to the weighted curvature approximation, with several admissible kernels, however. For sea surfaces under the Gaussian assumption, we show that the weighted curvature approximation reduces to a universal and simple expression for the off-specular normalized radar cross-section (NRCS), regardless of the chosen kernel. The formula involves merely the sum of the NRCS in the classical Kirchhoff approximation and the NRCS in the small perturbation method, except that the Bragg kernel in the latter has to be replaced by the difference of a Bragg and a Kirchhoff kernel. This result is consistently compared with the resonant curvature approximation. Some numerical comparisons with the method of moments and other classical approximate methods are performed at various bands and sea states. For the copolarized components, the weighted curvature approximation is found numerically very close to the cut-off invariant two-scale model, while bringing substantial improvement to both the Kirchhoff and small-slope approximation. However, the model is unable to predict cross-polarization in the plane of incidence. The simplicity of the formulation opens new perspectives in sea state inversion from remote sensing data.

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

Abstract 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.

Weighted curvature approximation: numerical tests for 2D dielectric surfaces

Abstract The weighted curvature approximation (WCA) was recently introduced by Elfouhaily et al [7] as a unifying scattering theory that reproduces formally both the tangent-plane and the small-perturbation model in the appropriate limits, and is structurally identical to the former approximation with some different slope-dependent kernel. Due to the simplicity of its formulation, the WCA is interesting from a numerical point of view and the aim of the present paper is to establish its accuracy on some representative test cases. We derive statistical formulae for the coherent field and the cross-section in the case of stationary Gaussian random surfaces. We then specialize to the case of isotropic Gaussian spectra and perform numerical comparisons against rigorous method of moments (MoM)-based results on 2D dielectric surfaces. We show that the WCA remains extremely accurate in a roughness range where other first-order classical approximations (small-slope and Kirchhoff) clearly fail, at the same computational cost. (Some figures in this article are in colour only in the electronic version)

Scattering of Electromagnetic Waves From Rough Surfaces: A Boundary Integral Method for Low-Grazing Angles

We present a boundary integral method for the numerical solution of the rigorous problem of wave scattering from rough surfaces under grazing illumination. The model of a locally perturbated plane is adopted: a finite patch of rough surface has its roughness flattened at the edges. The boundary formulation unknowns are the tangential components of the scattered field, defined as the contribution from the rough area. This way, the numerical domain of study is correctly bounded, even with a plane wave as incident field, and the sampled area is made independent of the incidence. This rigorous approach, called the grazing method of moments, is implemented on two-dimensional perfectly conducting surfaces and validated by comparison with a reference numerical solution for surfaces with Gaussian correlation functions. Now, the validity of approximate models at low-grazing-angles can be investigated; the small perturbation method and the small slope approximation are addressed in this paper. Scattering diagrams show how the performances of these methods deteriorate drastically at backward scattering angles as the incidence goes to grazing.

Modelization of the Scattering of Electromagnetic Waves from the Ocean Surface

In this paper, two models for the solution of the electromagnetic bistatic scattering from sea surface are suggested. A rigorous formalism leading to weakly singular integral equations is presented, as well as the surface impedance approximation for low penetrable media and the beam simulation method to synthesize incident beams with arbitrary size. This rigorous integral method is used to test first order approximations, and it is shown that the Small Slope Approximation is very accurate in predicting the scattering crosssection from the high spatial frequencies of the sea surface. This result led us to suggest an improvement of the classical two-scale model, consisting in replacing the small perturbation theory by the small slope approximation. This change allows the cut-off spatial frequency to be shifted so that the use of geometrical Optics is restricted to the large scales.

Sea Surface Microwave Scattering at Extreme Grazing Angle: Numerical Investigation of the Doppler Shift

We present a numerical investigation of horizontally polarized microwave scattering from 1-D sea surfaces at extreme grazing angles. Rigorous electromagnetic calculations are performed with a specific integral formalism dedicated to grazing angles. Sample sea surfaces are simulated using a classical Pierson-Moskowitz elevation spectrum together with weakly nonlinear hydrodynamic models, namely, the Creamer solution, the “choppy wave model,” and a recent improved version thereof. For this, the electromagnetic integral formalism is extended to surfaces with irregular sampling. For the different nonlinear surface models and assuming no large-scale current, we evidence a dramatic increase, followed by a saturation of the mean Doppler shift in the last few grazing degrees, with a limiting value depending quasi-linearly on the significant wave height. Our numerical investigations confirm that breaking events are not necessary to produce fast scatterers but tend to show that they are necessary to reproduce the elevated level of backscattered power. The results of this study also support the hypothesis that the blow-up of the mean Doppler shift at grazing angle is associated to an electromagnetic sharp edge effect on the large surface crests rather than geometrical shadowing of the troughs.

Light enpolarization by disordered media under partial polarized illumination: The role of cross-scattering coefficients

We show how disordered media allow to increase the local degree of polarization (DOP) of an arbitrary (partial) polarized incident beam. The role of cross-scattering coefficients is emphasized, together with the probability density functions (PDF) of the scattering DOP. The average DOP of scattering is calculated versus the incident illumination DOP.