Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory

Holliday, Dennis

doi:10.1109/tap.1987.1143978

Cited by 76 publications

(23 citation statements)

References 4 publications

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“…However, as currently formulated [Holliday et al, 1986;Holliday, 1987;Thompson, 1988], the method can be used for a perfect conductor model of seawater only, i.e., in an approximation that considers a relative dielectric constant of water ew = •. Since the actual dielectric constant of water is large (lwl = 65, for 10-GHz frequency), this approximation may appear as reasonable and attractive.…”

Section: Introductionmentioning

confidence: 99%

The integral equation method for electromagnetic scattering from the ocean: Beyond a perfect conductor model

Nedlin¹,

Chubb²,

Cooper³

1999

Radio Science

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Abstract. A version of the integral equation method is developed, which applies to scattering from a surface of a substance with a large dielectric constant e. An "impedance" boundary condition for the tangential components of electric and magnetic fields on the scattering surface is used, and the integral equation for the tangential components of the total magnetic field on a surface is formulated. This equation is applied to the problem of electromagnetic scattering from a slightly rough surface. It is demonstrated that the commonly used perfect conductor approximation (PCA) (e = •) can adequately describe scattering in the case of extremely large e only. The greatest sensitivity in scattering occurs when the incident and/or scattered waves are vertically polarized. For such cases the PCA does not work until e > 10 4. In the particular case of scattering from the ocean (ll 65), the PCA fails to provide an adequate description of the phenomena for either horizontally or vertically polarized waves, for practically all incidence and scattering angles. IntroductionDuring the last three decades, significant effort has been made and progress achieved in the theory of electromagnetic scattering from the ocean, using the integral equation The second reason, which applies to vertically polarized waves only, is of a physical nature. As one can observe from Fresnel's formulae (see also our equation (21)), the perfect conductor approximation fails drastically in properly describing even the reflection phenomenon from a plane boundary for neargrazing incidence angles 0in , when cos 0in --< Iwl-1/2, This deficiency is apparent in scattering as well. When combined with the numerical reason described above, a perfect conductor approximation actually fails not just for near-grazing angles, but over a very broad range of incidence/scattering angles except in cases of extremely large e (e > 10 4 for vertical polarization and e > 10 3 for horizontal). In the case of ocean scattering the effect of finite e is very large for all incidence/scattering angles and polarizations, being in particular most dramatic for vertically polarized waves.The theory presented in this paper extends the integral equation method to cases of finite but large dielectric constant e. The corrections to the results obtained by this method are of the order of e -1, which are really small (several percent, for seawater).The structure of this paper is as follows. Section 2 begins with a review of electromagnetic field representation in terms of electric (Je) and magnetic (Jm)

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Section: Introductionmentioning

confidence: 99%

The integral equation method for electromagnetic scattering from the ocean: Beyond a perfect conductor model

Nedlin¹,

Chubb²,

Cooper³

1999

Radio Science

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“…The latter equality in (12) assumes that the initial data is differentiable. Equation (9) was used in [26] and [35] and solved numerically, although its derivation was not shown there.…”

Section: A Volterra Integral Equation Of the Second Kindmentioning

confidence: 99%

“…By rough surface we mean either a deterministic surface as in the case of an irregular terrain or a statistical one as in the case of a sea surface. Various methods such as physical optics (also known as the Kirchhoff's approximation) [10], small perturbation [9], integral equation [11], [12], [13], [14], [15], modal series [16], [17], partial differential equation [18], [19], [20], etc. are used to study scattering and propagation of waves over rough surfaces, with each offering its own niche advantage under certain situations.…”

Section: Introductionmentioning

confidence: 99%

Direct Solution of Current Density Induced on a Rough Surface by Forward Propagating Waves

Janaswamy

2013

IEEE Trans. Antennas Propagat.

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Abstract-A new Volterra integral equation of the second kind with square integrable kernel is derived for paraxial propagation of radiowaves over a gently varying, perfectly conducting rough surface. The integral equation is solved exactly in terms of a infinite series and the necessary and sufficient conditions for the solution to exist and converge are established. Super exponential convergence of the Neumann series for arbitrary surface slope is established through asymptotic analysis. Expressions are derived for the determination of the number of terms needed to achieve a given accuracy, the latter depending on the parameters of the rough surface, the frequency of operation and the maximum range. Numerical results with truncated series are compared with that obtained by solving the integral equation numerically for a sinusoidal surface, Gaussian hill, and a random rough surface with Pierson-Moskowitz spectrum.

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“…For perfect conductors, this set is decoupled. A fullwave technique following the KA has been developed in [26][27][28] and examined for the magnetic induction. A similar approach for the electric field has been used in [29].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Model of Electromagnetic Wave Scattering FROM Sea Surface with and without Oil Slicks

Timchenko¹,

Serebryannikov²,

Schuenemann³

2002

PIER

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Abstract-The problem of scattering from sea surface covered by oil films is investigated by using a composite random rough surface model. A model is developed which extends the range of validity beyond the small perturbation theory. A general expression for the scattering cross section is obtained taking into account a modulation of the rough surface by long surface waves. A numerical study for the radar scattering cross section is provided in order to investigate the influence of the different ranges of the rough surface spectrum on the backscattering depression. For the case of backscattering, the contrast of radar signals scattered from a slick-free and a slick-covered surface is evaluated. The study is also carried through for two-frequency probing. A possibility to explain the mechanism of the depression of backscattering is discussed. The results of this study demonstrate the importance of the improved model which takes into account the entire spectrum of the sea surface roughness for the description of scattering from an ocean surface with and without oil slicks.

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Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory

Cited by 76 publications

References 4 publications

The integral equation method for electromagnetic scattering from the ocean: Beyond a perfect conductor model

The integral equation method for electromagnetic scattering from the ocean: Beyond a perfect conductor model

Direct Solution of Current Density Induced on a Rough Surface by Forward Propagating Waves

Model of Electromagnetic Wave Scattering FROM Sea Surface with and without Oil Slicks

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