A Method of a Tangent Cylinder in the Theory of Wave Scattering by Convex Surfaces

The solution to the problem of wave scattering from an object requires the calculation of the total field at the surface of the object. This task generally does not have an exact, explicit solution. In 1952, L. M. Brekhovskikh put forward an approximate solution, so-called the tangent-plane approximation (TPA), which is also referred to as the Kirchhoff approximation. In the TPA at each point of a smooth surface, the latter is approximated by a tangent plane at the point. Since in the case of reflection from a plane, the total field can be readily calculated by Fresnel-type formulas, the scattering problem acquires, in this case, an explicit, approximate solution. A natural generalization of the TPA in 2-D follows when the scattering surface at each point is approximated by a tangent cylinder [a tangent-cylinder approximation (TCA)]. The TCA is considered, in this communication, in the simplest case of convex surfaces, a scalar field, and an impedance boundary condition in 2-D. It is demonstrated that the TCA possesses significantly better accuracy and provides better treatment of the shadowing associated with scattering from rough surfaces being only slightly more demanding than TPA computationally.