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We present the numerical study of scattering of scalar waves from impenetra­ble two-dimensional periodic surfaces of arbitrary shape. Nearly all numerical simulations of scattering of waves from rough surfaces in the past have been limited to one-dimensional surfaces and moderate angles of incidence. By making the surface infinite and bi-periodic, it becomes possible to simulate numerically scattering from two-dimensional surfaces, even down to grazing angle. Only impenetrable surfaces are considered. Some calculations are presented, and are used to compare with the small perturbation, or Rayleigh–Rice theory. It is found that for near grazing incidence, Neumann boundary condition, the small perturbation theory gives inaccurate values, especially near the backscatter direction.

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An urban scene has very complex variety of length scales ranging from much larger to much smaller than the wavelength of the radiation emitted by a Synthetic Aperture Radar (SAR). The exact solution to this scattering problem requires the solution of Maxwell's equations for the combination of source and scattering objects present in the scene, which for any reasonable size target area is computationally too intensive to be realistic. Hence while a 'numerically exact' solution at present is not possible, some form of approprite modeffing scheme is used as is usual in electromagnetic problems.The geometrical theory of diffraction (GTD) gives an accurate result with a practical amount of computation. This theory is based on the fact that the most important contributions towards the scattered field come from an area in the neighbourhood of some critical points on the scattering surface. For a planar surface, three critical points may be regarded: specular, edge-diffraction and corner-diffraction points. A physical optics version of GTD was taken with the approximate diffraction coefficients derived using physical optics approximations to canonical problems.In this paper, the new model is described in addition to an overview of a ray-tracing procedure adopted and its resultant images.

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