Double diffraction coefficients for source and observation at finite distance for a pair of wedges

A closed form, high-frequency solution is presented for describing the double diffraction mechanism at a pair of parallel wedges, when they are illuminated by a spherical wave. The solution is obtained by using a spherical waves spectral representation of the first order diffracted field from each wedge. For the sake of simplicity, only the scalar case is considered when either hard or soft boundary conditions may be imposed on the faces of the two wedges. This provides a basic step for constructing the solution in the more general electromagnetic case. Although the procedure is applicable to any couple of parallel wedges, the case of two wedges sharing a common face is explicitly considered in the solution presented. The asymptotic evaluation of the double spectral integral leads to transition functions involving generalized Fresnel integrals. Numerical calculations show that the high frequency formulation fails so gracefully that it gradually blends into the solution of a single wedge when the distance between the two edges vanishes. This is a desirable property for analysing the shadowing effects of a thick screen.