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Introduction Statistics Statistics, Characteristic Small Dirichlet Neumann Kirchhoff Dirichlet Neumann References of Random Correlation Functions Method for One-Dimensional for One-Dimensional Surface Surface Rough Function Surface and Spectral Density | Scattering of Electromagnetic Waves Theories and Applications Leung Tsang Jin Au Kong Kung-Hau Ding Copyright 2000 John Wiley Sons Inc. ISBNs 0-471-38799-1 Hardback 0-471-22428-6 Electronic Chapter 9 ONE-DIMENSIONAL RANDOM ROUGH SURFACE SCATTERING 1 Introduction 390 2 Statistics of Random Rough Surface 392 2.1 Statistics Correlation Function and Spectral Density 392 2.2 Characteristic Functions 396 3 Small Perturbation Method 397 3.1 Dirichlet Problem for One-Dimensional Surface 397 3.2 Neumann Problem for One-Dimensional Surface 403 4 Kirchhoff Approach 407 4.1 Dirichlet Problem for One-Dimensional Surface 408 4.2 Neumann Problem for One-Dimensional Surface 415 References and Additional Readings 417 - 389 - 390 9 1-D RANDOM ROUGH SURFACE SCATTERING 1 Introduction Consider a plane wave incident on a flat surface Fig. 9.1.1 . We note that the wave is specularly reflected because the specular reflected waves are in phase with each other. The reflected wave only exists in the specular direction. From Fig. 9.1.1 it is clear that the specular reflected waves have the same path lengths accounting for the in-phase condition. Imagine now that the surface is rough. It is clear from Fig. 9.1.2 that the two reflected waves have a path length difference of 2h cos 0Z. This will give a phase difference of 2kh cos 0i 9.1.1 If h is small compared with a wavelength then the phase difference is insignificant. However if the phase difference is significant the specular reflection will be reduced due to interference of the reflected waves that can partially cancel each other. The scattered wave is diffracted into other directions. A Rayleigh condition is defined such that the phase difference is 90 Ishimaru 1978 Ogilvy 1991 . Thus for h cos0i 9.1.2 8 the surface is regarded as smooth and for h cos0i 9.1.3 8 the surface is regarded as rough. For random rough surface h is regarded as the rms height. We will consider rough surface scattering. Both the cases of scalar waves and vector .