A stochastic extension of the Uniform Theory of Diffraction accounting for geometrical uncertainty or surface and edge roughness

We present a stochastic extension of the Uniform Theory of Diffraction (UTD) which is capable to account for some uncertainty in the objects position or geometry, including roughness of surfaces or edges. Namely, we derive a solution for the electromagnetic field scattered by a perfectly conducting wedge whose faces are described as a statistical perturbation of a standard flat wedge. We give a uniform closed form expressions for the evaluation of the main statistical moments of the total electric field. The proposed statistical UTD formulation is suitable for engineering applications which involve UTD ray based codes. Some numerical examples highlight the accuracy and the effectiveness of the proposed ray description.