Wavelets in Rough Surface Scattering In this chapter we will study scattering of electromagnetic waves from rough surfaces numerically, using the Coifman wavelets. Owing to the orthogonality, vanishing moments, and multiresolution analysis, a very sparse moment matrix is obtained. In addition the wavelet bases are continuous. Hence the sampling rate for wavelet bases is reduced to one-half the rate of the pulse cases, allowing the same computer resource to deal with quadruple the truncated surface area. More important, the Coiflets allow the development of one-point quadrature formula, which reduces the computational effort in filling matrix entries to O(n). As a result. | Wavelets in Electromagnetics and Device Modeling. George W. Pan Copyright 2003 John Wiley Sons Inc. ISBN 0-471-41901-X CHAPTER EIGHT Wavelets in Rough Surface Scattering In this chapter we will study scattering of electromagnetic waves from rough surfaces numerically using the Coifman wavelets. Owing to the orthogonality vanishing moments and multiresolution analysis a very sparse moment matrix is obtained. In addition the wavelet bases are continuous. Hence the sampling rate for wavelet bases is reduced to one-half the rate of the pulse cases allowing the same computer resource to deal with quadruple the truncated surface area. More important the Coiflets allow the development of one-point quadrature formula which reduces the computational effort in filling matrix entries to O n . As a result the wavelet-Galerkin method with twofold integrals is faster than the traditional pulse-collocation approach with onefold integrals. SCATTERING OF EM WAVES FROM RANDOMLY ROUGH SURFACES Rough surface scattering has potential applications in remote sensing semiconductor processing radar and sonar among others. Figure demonstrates a computer generated random surface which will be discussed in Section . Scattering of electromagnetic waves from rough surfaces has been studied by analytical 1 2 numerical 3-6 and experimental means 7-9 . Analytic methods provide fast solutions and allow users to foresee the effects and trends of the solution due to individual parameters in the formulas. However there are many geometric and physical limitations restricting the utility of analytical models in general applications. For instance the tangential plane approximation known as the Kirchhoff model works only for undulating surfaces without shadowing while the small perturbation method known as the Rice model is valid only for small roughness. Attempts were made to extend these analytical models including the iterated Kirchhoff 10 11 and Wiener-Hermite expansion 12 among others. .
