A uniform double diffraction coefficient for a pair of wedges in arbitrary configuration

Abstract

An analytic closed-form solution is presented for the double diffraction at a pair of arbitrarily placed wedges that is suitable to be used in a uniform theory of diffraction (UTD) ray description framework. Here, the particular assumption, present in all the past literature, that the two diffracting edges are coplanar is removed. The doubly diffracted (DD) field at a pair of wedges is constructed via spectral synthesis. Such a procedure provides a double spectral integral representation of the DD field that is asymptotically evaluated by resorting to transition functions, typical in double diffraction problems, that can be expressed in terms of generalized Fresnel integrals. The final expression is arranged in the typical UTD fashion and contains a uniform double diffraction dyadic coefficient. The DD field behavior is analyzed in its transition regions to show how the DD field smoothly compensates for the total field discontinuities occurring at shadow boundaries where a singly diffracted field from a wedge is shadowed by the other wedge. Numerical examples are provided to verify such analysis and to test the accuracy of our UTD ray description against method of moments full wave results.