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

Afifi, Saddek; Dusséaux, Richard; Oliveira, Rodrigo de

doi:10.1080/17455030903329374

Cited by 9 publications

(9 citation statements)

References 45 publications

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“…We find that the scattered field amplitude is given by a Hoyt law [20,22,[28][29] and the phase is not uniformly distributed [28]. Equations (28) and (29) are applicable to the intermediate zone for infinite surfaces.…”

Section: Statistical Distributionsmentioning

confidence: 95%

“…The phase law does not gradually change for a slight variation of the incidence angle around zero degree. The phase law given by relation (29) at 0 ¼ 0 is not uniform. Under oblique incidence, the phase of the scattered field is spatially uniform.…”

Section: Validation Of the Spatial Properties Of The Scattered Fieldmentioning

confidence: 96%

“…The observation point coordinates are x 0 ¼ 0:48 and y 0 ¼ 15. Results are presented in Figure 9 where normalised histograms are superimposed upon the analytical probability laws (28)- (29).…”

Section: Validation Of the Spatial Properties Of The Scattered Fieldmentioning

confidence: 99%

“…We have also shown that when the length is infinite, these probability density functions tend toward the Rayleigh law and the uniform law, respectively. We have pointed out that the parameters of these laws depend on the polarisation, the relative permittivity and the length L of the surface [13][14][15][28][29] and we have shown that the phase probability density function is sensitive to the variation of the deformation length.…”

Section: Introductionmentioning

confidence: 97%

See 3 more Smart Citations

Analytical derivation of the stationarity and the ergodicity of a field scattered by a slightly rough random surface

Oliveira

Dusséaux

Afifi

2010

Waves in Random and Complex Media

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International audienceIn the framework of the small perturbation method, we present a new theoretical derivation of the statistical and spatial properties of a field scattered by a one-dimensional slightly rough random surface. The work concerns the intermediate field zone where the scattered field is reduced to the contribution of the progressive plane waves. The surface is assumed to be stationary, ergodic and Gaussian. First, from a statistical point of view, we demonstrate that under oblique incidence the scattered field is not stationary while it is strictly stationary under normal incidence. For an infinite surface, the scattered field modulus obeys to Hoyt law and the phase is not uniform. Second, from a spatial point of view, for a given altitude and under all incidences, we show that the scattered field is ergodic. Under oblique incidence, the phase is spatially uniform and the modulus is given by a Rayleigh law. Under normal incidence, the phase is not uniform and the modulus is given by a Hoyt law. Third, from a practical point of view, we show that the field measured by a directional antenna is ergodic and stationary if the angular transfer function of the antenna does not contain the specular direction

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Section: Statistical Distributionsmentioning

confidence: 95%

Section: Validation Of the Spatial Properties Of The Scattered Fieldmentioning

confidence: 96%

Section: Validation Of the Spatial Properties Of The Scattered Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Analytical derivation of the stationarity and the ergodicity of a field scattered by a slightly rough random surface

Oliveira

Dusséaux

Afifi

2010

Waves in Random and Complex Media

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“…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][2][3][4][5] and many authors have also implemented a perturbative theory for analyzing remote sensing problems [6][7][8][9][10][11][12]. The small slope approximation (SSA1) has an extended domain of applicability [13][14][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 Kirchhoff approximation that is applicable to surfaces with long correlation length [17,18].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Wave Scattering From Rough Layered Interfaces: Analysis With the Small Perturbation Method and the Small Slope Approximation

Berrouk¹,

Dusséaux²,

Afifi³

2014

PIER B

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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 field in each medium is represented by a Rayleigh expansion and a perturbation method is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitude under the first-order small slope approximation are deduced from results derived from the first-order small perturbation method. Comparison between these two analytical models and a numerical method based on the combination of scattering matrices is presented.

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

Afifi

Dusséaux

2011

IEEE Trans. Antennas Propagat.

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International audienceWe 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

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

Cited by 9 publications

References 45 publications

Analytical derivation of the stationarity and the ergodicity of a field scattered by a slightly rough random surface

Analytical derivation of the stationarity and the ergodicity of a field scattered by a slightly rough random surface

Electromagnetic Wave Scattering From Rough Layered Interfaces: Analysis With the Small Perturbation Method and the Small Slope Approximation

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

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