Diffraction by a rough knife edge: a first step toward a stochastic theory of diffraction

In this paper we introduce an original formulation for the electromagnetic field diffraction by a knife edge with random roughness: the formulation, based on the asymptotic physical optics (APO) approach, leads to closed form evaluations of the statistics of the diffracted field. A very interesting conclusion is that, for moderate edge roughness, the diffracted field propagation can be described in terms of the same ray congruence as in the straight (smooth) edge case, with the only difference that the field associated to each ray is a random variable whose statistics are, in this paper, computed in closed form. The presented approach can be then considered as a first step toward a general stochastic theory of edge diffraction (STED).