Stochastic Theory of Edge 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. The edge roughness is described by a stationary zero-mean Gaussian stochastic process with standard deviation sigma and correlation length L. The Physical Optics (PO) approximation is used to evaluate surface currents; mean and variance of the diffracted field are evaluated by means of asymptotic techniques under the hypotheses lambda/r → 0, where lambda is the wavelength and r is the distance from the edge, sigma not large with respect to lambda, and sigma/r << 1. The main advantages of the proposed method are its simplicity and the fact that, differently from other approaches, the obtained total field is explicitly written as the sum of incident, reflected and diffracted fields. 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). The proposed theoretical results are amenable of interesting practical applications: for instance, the obtained diffracted field statistics can be used to predict the maximum accuracy that can be expected for ray-tracing algorithms that are based on the straight edge assumption.