Richard Dusséaux

On the Co-Polarized Phase Difference of Rough Layered Surfaces: Formulae Derived From the Small Perturbation Method

We determine the statistical distribution of the co-polarized phase difference of fields scattered from a stack of two two-dimensional rough interfaces in the incidence plane. The electromagnetic fields are represented by Rayleigh expansions and a perturbation method is used to solve the boundary value problem and to determine the first-order scattering amplitudes. For slightly rough interfaces with infinite length and Gaussian height distributions, we show that the probability density function is only a function of two parameters. For a sand layer on a granite surface in backscattering configurations, we study the influence of the incidence angle, the layer thickness, the cross-spectral density and the wave frequency upon both parameters of the probability law.

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces – study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwells equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.

Scattering by Anisotropic Rough Layered 2D Interfaces

We propose a statistical study of the scattering of an incident plane wave by a stack of two two-dimensional rough interfaces. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. The electromagnetic fields are represented by Rayleigh expansions, and a perturbation method is used for solving the boundary value problem and determining the first-order scattering amplitudes. For slightly rough interfaces with a finite extension, we show that the modulus of the co- and cross-polarized scattering amplitudes follows a Hoyt law and that the phase is not uniformly distributed. For interfaces with an infinite extension, the modulus follows a Rayleigh law and the phase is uniformly distributed. We show that these results are true for correlated or uncorrelated interfaces and for isotropic or anisotropic interfaces.

Electromagnetic Scattering From 3D Layered Structures With Randomly Rough Interfaces: Analysis With the Small Perturbation Method and the Small Slope Approximation

We propose a theoretical study on the electromagnetic wave scattering from three-dimensional layered structures with an arbitrary number of rough interfaces by using the small perturbation method and the small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not, isotropic or not. The electromagnetic field in each medium is represented by a continuum of plane waves and a perturbation theory is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitudes under the first-order small slope approximation are deduced from results derived from the first-order small perturbation method. We analyze with the small slope approximation model the combined influence of the anisotropy and cross-correlation upon the electromagnetic signature of a natural stratified structure.

Electromagnetic Wave Scattering from Rough Layered Interfaces: Analysis with the Small Perturbation Method and the Small Slope Approximation

We propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using the small perturbation method and the small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not. The electromagnetic fleld in each medium is represented by a Rayleigh expansion and a perturbation method is used for solving the boundary value problem and determining the flrst-order scattering amplitudes by recurrence relations. The scattering amplitude under the flrst-order small slope approximation are deduced from results derived from the flrst-order small perturbation method. Comparison between these two analytical models and a numerical method based on the combination of scattering matrices is presented. The study of electromagnetic wave scattering from rough layered interfaces has many applications in remote sensing, communication techniques, civil engineering, geophysics and optics. Several models give the average scattered fleld and the average intensity. Analytical methods are based on physical approximations and give closed-form formulae for the flrst- and second-order moments of the scattered fleld. Exact methods estimate the average scattered fleld and the average intensity from the results over many realizations of rough layered interfaces. In this paper, we propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using two analytical models: the flrst-order small perturbation method (SPM) and the flrst-order small slope approximation (SSA). Elson was one of the flrst authors to develop a vector theory of scattering from a stratifled medium. This vector theory allows the angular distribution of scattered light to be determined and can be used with correlated or uncorrelated surface roughness (1,2). The SPM has been used for the study of light scattering from multilayer optical coatings (1{5) and many authors have also implemented a perturbative theory for analyzing remote sensing problems (6{12). The small slope approximation (SSA1) has an extended domain of applicability (13{15) which includes the domain of the small-perturbation method that is only valid for surfaces with small roughness (16) and the domain of the Kirchhofi approximation that is applicable to surfaces with long correlation length (17,18). In the present paper, the structure under consideration is a stack of several rough one-dimensional interfaces. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. The electromagnetic fleld in each region is represented by a continuous spectrum of plane waves, the amplitudes of which are found by matching the boundary conditions

New perturbation theory of diffraction gratings and its application to the study of ghosts

A new perturbation method for the diffraction of a plane wave by a grating with periodic imperfections is presented. The originality of the method lies in the fact that the perturbation occurs on a reference profile that is not a plane but a grating. First, the diffraction by a reference grating is treated. At this stage Maxwell’s equations are used in covariant form written in a nonorthogonal coordinate system fitted to the surface geometry. Second, the periodic errors are taken into account. The tensorial formalism permits the elaboration of this two-roughness-level model. The grating profile appears only through two fundamental functions. The variations of these functions under the effect of variation in the profile are expanded in power series of the perturbation parameter v1. v1 represents the maximum of the derivative of the function describing the perturbation. By using this formalism, we determine the efficiencies.

Study of Backscatter Signature for Seedbed Surface Evolution Under Rainfall - Influence of Radar Precision

We propose a 3D-approach of the soil surface height variations, either for the roughness characterization by the mean of the bidimensional correlation function, or as input of a backscattering model. We consider plots of 50cm by 50cm and two states of roughness of seedbed surfaces: an initial state just after tillage and a second state corresponding to the soil roughness evolution under a rainfall event. We show from stereovision data that the studied surfaces can be modelled as isotropic Gaussian processes. We study the change of roughness parameters between the two states. To discuss the relevance of their difierences, we flnd from Monte-Carlo simulations the bias and variance of estimator for each roughness parameters. We study the roughness and moisture combined in∞uences upon the direct backscattering coe-cients by means of an exact method based on Maxwells equations written in a nonorthogonal coordinate system and by averaging the scattering amplitudes over several realizations. We discuss results taking into account the numerical errors and the precision of radar. We show that the ability of the radar to discriminate the difierent states of seedbed surfaces is clearly linked to its precision.

On the Co-Polarized Scattered Intensity Ratio of Rough Layered Surfaces: The Probability Law Derived From the Small Perturbation Method

We determine the probability law of the ratio between the co-polarized intensities scattered from a stack of two two-dimensional rough interfaces in the incidence plane. Calculations are carried out within the framework of the first-order small perturbation method. For slightly rough interfaces with infinite length and Gaussian height distributions, we show that the probability density function is only a function of two parameters and has an infinite average and an infinite variance. For a sand layer on a granite surface in backscattering configurations, we study the influence of the incidence angle and the cross-spectral density upon this probability law.

Statistical distribution of the field scattered by rough layered interfaces: formulae derived from the small perturbation method

We present a statistical study of electromagnetic wave scattering by a stack of two random rough interfaces that are characterised by Gaussian distributed heights and by exponential correlation functions. These interfaces can be correlated or not. The coherent and incoherent intensities and the statistical distribution of the scattered field in modulus and phase are obtained using the Rayleigh expansion and the small perturbation method. For a structure of finite extension, we show that the modulus follows a Hoyt law and the phase is not uniform. For a structure of infinite extension, whether the interfaces are correlated or not, the modulus of the field follows a Rayleigh law while the phase is uniform.

Statistical study of radiation loss from planar optical waveguides: the curvilinear coordinate method and the small perturbation method.

This article presents an original method for the theoretical analysis of the intensity radiated by a dielectric waveguide with rough walls. The method is based on Maxwells equations under their covariant form written in nonorthogonal coordinate systems adapted to the geometry of the waveguide. The solutions are found by using a perturbation method starting from a guide with smooth walls. The statistical characteristics of the radiant intensity, the mean value, and the probability density function are analytically determined.