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Diffusion par des surfaces rugueuses: approximations faibles pentes

Diffusion par des surfaces rugueuses: approximations faibles pentes. Marc Saillard LSEET UMR 6133 CNRS-Université du Sud Toulon-Var BP 132, 83957 La Garde cedex, France marc.saillard@lseet.univ-tln.fr. Outline. Boundary integral formalism Approximate scattering theories

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Diffusion par des surfaces rugueuses: approximations faibles pentes

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  1. Diffusion par des surfaces rugueuses: approximations faibles pentes Marc Saillard LSEET UMR 6133 CNRS-Université du Sud Toulon-Var BP 132, 83957 La Garde cedex, France marc.saillard@lseet.univ-tln.fr

  2. Outline • Boundary integral formalism • Approximate scattering theories • Kirchhoff approximation • Small perturbation theory • Two-scale model • Small Slope Approximation • IEM • Small Slope Integral Equation • Conclusion

  3. Integral representation of fields Perfect conductor

  4. Scattering matrix

  5. Approximate scattering theories Kirchhoff approximation

  6. Small height limit of KA Small perturbation theory

  7. Two-scale model (KA + SPM)

  8. Small slope approximation

  9. Numerical examples: Gaussian spectrum Comparison of MoM with Kirchhoff approx. (KA), Small Perturbation Method (SPM) 1st order Small Slope Approx. (SSA) Comparison of MoM (solid line) with 1st order SSA (dashed line) n = 1.6 r.m.s height 0.17 - correlation length

  10. Numerical examples: power-law spectrum Band limited [k/30,4k] power-law spectrum (K-4); h = l/5; s = 0.1; khs = 1/8

  11. IEM

  12. Matrices associated to integral operators are 2D Toeplitz Storage : 2N instead of N2 Product : 2Nlog2N instead of N2 Small slope integral equation (Meecham – Lysanov) distance R Height h = sd Slope s Horizontal distance d Validity : khs<<1. 1st order

  13. Band limited [k/30,4k] power-law spectrum (K-4); khs = 1/8 Gaussian spectrum ; khs = 1/4

  14. Conclusion • Domain of validity that covers both that of SSA1 and of the tangent plane approximation (as SSA2 or OEM) • No assumption on the surface statistics • The accuracy can be estimated • Very low computational cost • It provides an estimation of the cross-polarized component in the plane of incidence • It is an alternative to statistical approximate methods • but requires Monte-Carlo process

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