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The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum
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1988
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Numerical AnalysisEngineeringEarth ScienceRough Surface ScatteringIntegral EquationComputational ElectromagneticsApproximation TheoryReflectance ModelingPhysicsInverse Scattering TransformsRough SurfaceInverse ProblemsSurface FinishKirchhoff ApproximationRadarNatural SciencesRadar ScatteringCivil EngineeringWave ScatteringLight ScatteringGeomechanicsHigh-frequency ApproximationSurface ModelingGaussian Roughness SpectrumMultiscale Modeling
The study assumes a pressure release boundary condition. The study examines the validity of the Kirchhoff approximation for rough surface scattering and the accuracy of its shadow‑corrected cross section by comparing with exact integral‑equation solutions. The authors compute the bistatic scattering cross section via a Monte Carlo method for randomly rough surfaces with a Gaussian spectrum, and provide a quantitative accuracy assessment of the shadow‑corrected Kirchhoff approximation for rms slope angles γ ≲ 20° and grazing angles θ ≳ 2γ. They find that the surface correlation length most strongly determines the valid region of the Kirchhoff approximation away from low grazing angles, and illustrate this with examples at grazing angles θ ≲ 2γ.
The validity of the Kirchhoff approximation for rough surface scattering is examined by comparison with exact results obtained by solving an integral equation. The pressure release boundary condition is assumed. The field quantity calculated is the bistatic scattering cross section, which is obtained with a Monte Carlo technique. The accuracy of correcting the Kirchhoff scattering cross section for shadowing is also addressed. The surface realizations used are randomly rough with a Gaussian roughness spectrum and have height variations in only one direction. The surface correlation length is found to be the most important parameter in defining the valid region of the Kirchhoff approximation away from the low grazing angle region. A procedure is given that provides a quantitative measure of the accuracy of the shadow-corrected approximation when the root-mean-square (rms) slope angle of the surface γ is ≲20° and when the incident grazing angle θ is ≳2γ. Examples with θ≲2γ are also discussed.