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

Braham, Karim Aït; Dusséaux, Richard; Granet, G.

doi:10.1080/17455030701749328

Cited by 12 publications

(27 citation statements)

References 32 publications

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“…The method was investigated in near and far field zones by means of convergence tests on the scattering amplitudes and the power balance criterion. The theory was verified by comparisons with published numerical and experimental data [5][6][7]. We showed that the MonteCarlo simulations based on the C-method have been successful in predicting backscattering enhancement and in analyzing very rough surfaces.…”

Section: Introductionmentioning

confidence: 49%

“…The surface separates the vacuum from a material with a complex relative permittivity. The incident wave vector k 0 is defined from the zenith angle θ 0 and the azimuth angle ϕ 0 [6,7]. In horizontal polarization (a = h), the electric field vector is parallel to the Oxy plane.…”

Section: Formulation Of Problemmentioning

confidence: 99%

“…The scattered field can be obtained by using the C-method [1][2][3][4][5][6][7] and the translation coordinate system defined by:…”

Section: Coordinate System -Covariant Components Of Fieldmentioning

confidence: 99%

“…The boundary value problem allows the scattering amplitudes to be determined. The C-method is an efficient theoretical tool for analyzing grating diffraction [1][2][3] and rough surfaces [4][5][6][7]. The method was investigated in near and far field zones by means of convergence tests on the scattering amplitudes and the power balance criterion.…”

Section: Introductionmentioning

confidence: 99%

“…The backscattering coefficient is estimated by averaging the scattering amplitudes over several realizations. For each realization, the scattering amplitudes are obtained by the curvilinear coordinate method, commonly called the Cmethod [1][2][3][4][5][6][7]. This method is based on Maxwell's equations under their tensorial form written in a nonorthogonal coordinate system where the boundary surfaces coincide with coordinate surfaces.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Dusséaux¹,

Vannier²,

Taconet³

et al. 2012

PIER

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Abstract-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 50 cm by 50 cm 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 differences, we find from Monte-Carlo simulations the bias and variance of estimator for each roughness parameters. We study the roughness and moisture combined influences upon the direct backscattering coefficients by means of an exact method based on Maxwell's 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 different states of seedbed surfaces is clearly linked to its precision.

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Section: Introductionmentioning

confidence: 49%

Section: Formulation Of Problemmentioning

confidence: 99%

“…The scattered field can be obtained by using the C-method [1][2][3][4][5][6][7] and the translation coordinate system defined by:…”

Section: Coordinate System -Covariant Components Of Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Dusséaux¹,

Vannier²,

Taconet³

et al. 2012

PIER

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Semi‐analytical computation of a quasi‐static field induced by a 3D eddy current probe scanning a 2D layered conductor with parallel rough interfaces

Caire

Prémel

Granet

2014

Int J Numerical Modelling

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This paper deals with the fast computation of the quasi‐static fields induced in a conductor with a locally perturbed shape along the longitudinal axis and extruded along the transversal one. Besides, the material is composed of several homogeneous layers with parallel faces. The method used here is based on writing Maxwell's equations in a curvilinear system, which leads to a more simple expression of boundary conditions. The validity of this method for the computation of quasi‐static fields induced by an eddy current probe in a conductive half‐space with a rough surface has been proved recently, and we propose here to complete this innovative formalism in order to solve an eddy current non‐destructive testing (ECNDT) configuration with a rough surface conductive medium composed of several homogeneous layers with parallel faces. This extension allows to tackle new ECNDT configurations such as homogeneous media constituted by rough interfaces. Moreover, it provides sufficient solutions for non‐homogeneous conductive parts presenting a depth‐varying (i.e., along the direction of the normal local vector with respect to the surface) material property, which can be approximated by a piecewise constant function by introducing multiple thin homogeneous layers. Copyright © 2014 John Wiley & Sons, Ltd.

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Development of the curvilinear coordinate method for the computation of quasi‐static fields induced by an eddy current probe scanning a 3D conductor of complex shape characterized by an arbitrary 2D surface

Prémel

Granet

2017

Int J Numerical Modelling

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This paper deals with the development of a semi-analytical model for the fast computation of the quasi-static field induced by any eddy current probe in a 3D conductor of complex shape. The workpiece is considered as a planar half-space mock-up with an interface air conductor characterized by an arbitrary 2D surface a(x, y). The curvilinear coordinate method consists in introducing a change of coordinates to be able to write analytically and easily the boundary conditions at the interface air-metal. Due to the novel generalized metric space, the covariant form of Maxwell equations must be considered. The curvilinear coordinate method is widely used in the optical community for the analysis the diffraction phenomenon on gratings. The method has been applied recently for eddy current calculations in the planar case for 2.5D configurations characterized by a 3D eddy current probe and a 2D layered stratified conducting media. By an extension to 3D problems, this work constitutes the preliminary task for the development of a complete numerical model, which has the capability to address very complex eddy current nondestructive testing configurations such as a stratified layered media constituted by a set rough interfaces. For that purpose, the modal formalism is described for the first time in the 3D case, and several numerical experiments show the validity and the efficiency of the fast numerical model in comparison to the finite element method. KEYWORDS computational electromagnetics, covariant form of Maxwell equations, eddy current nondestructive testing, rough surfaces 1 Int J Numer Model. 2018;31:e2219.wileyonlinelibrary.com/journal/jnm

show abstract

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

Cited by 12 publications

References 32 publications

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

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

Semi‐analytical computation of a quasi‐static field induced by a 3D eddy current probe scanning a 2D layered conductor with parallel rough interfaces

Development of the curvilinear coordinate method for the computation of quasi‐static fields induced by an eddy current probe scanning a 3D conductor of complex shape characterized by an arbitrary 2D surface

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