Iterative approach for the numerical simulation of scattering from one- and two-dimensional rough surfaces

Abstract

We describe the use of iterative techniques for the solution of the integral equation that arises in an exact treatment of scalar wave scattering from randomly rough surfaces. The surfaces vary in either one or two dimensions, and the special case of a Dirichlet boundary condition is treated. It is found that these techniques, particularly when preconditioning is applied, are much more efficient than direct inversion techniques. Moreover, convergence is obtained for rms roughness of the order of 1, so the techniques have applicability over a wide parameter regime. Convergence is always to the exact solution found by direct inversion, exceptly for cases of extremely large-scaled rms surface heights in which the iterative techniques fail. In addition, by monitoring the residuals in the iteration process, it is immediately clear if the iterative techniques are failing, or performing badly in any given case. Finally, numerical results are compared with existing data in the enhanced backscattering regime.

Comparison of various approximation theories for randomly rough surface scattering

“…7 shows different-order Born series approximations to the smallscale topography for the case of ka = 3.14, demonstrating the performance of different-order approximations. A Born-series-based iteration technique for wave scattering at a randomly rough surface has been explored in [28] with the virtue of simplicity of implementation and speed, but as indicated that the rate of convergence decreases as h/a increases. Our studies show that for seismic frequencies the second-order Born approximation might be sufficient to guarantee the accuracy of rough surface scattering for general rough surfaces without infinite gradients and large surface heights.…”

Measurement of defects by measuring of light scattering from surfaces using focused illumination

“…In particular, it have been reported for applications of remote sensing, printed circuit testing and measuring surface patterns for growth of nanometric structures [1][2][3][4][5][6][7] . In the literature, theoretical studies [8][9][10][11][12][13][14][15][16][17][18] and experimental studies [5][6][7][19][20][21][22][23][24][25][26][27][28] have been reported. There are experimental works on measurements of light scattering from one-dimensional rough surfaces, and in reference [29] calculations are performed to study the angular distribution of the scattered light from a one-dimensional rough surface.…”

“…There are very few works on the part of inverse methods (to calculate the surface when the pattern of scattering is give) due to the complex mathematics involved. A lot of methods have been used to calculate the pattern of diffraction, including perturbation methods [12][13][14][15] , Kirchhoff Approximation 16-18, integral methods 11 and modal methods for periodic surface 4,[8][9][10] . It is important to highlight because of the complexity of the problem, in general, the results reported in the literature are the results of the numerical calculations, because it is not possible to resolve the equations involved analytically.…”

Fast Numerical Solution for Scattering From Rough Surfaces With Small Slopes

“…Diagonal matrix elements are computed separately, using the method described in [13], as applied to (1). These terms corresponds to the strong matrix AS of SMFSIA with strong interaction radius r d = 0.…”