Diffraction by a randomly rough knife edge

Summary form only given. Diffraction by a knife edge boundary has long been used as a model to estimate the effect of path-obstructing ridges, mountains, and other natural obstacles in long range communication links. The use of this approximation is now of interest in assessing blockage effects involving much shorter paths, e.g., such as in propagation in an urban environment where buildings and other man-made obstacles cause path blockage. Professor R.E. Collin, in his book Antennas and Radiowave Propagation developed a particularly simple yet very powerful approximate solution to the problem of diffraction by a knife edge boundary. The robustness of his solution is due in part to (a) the careful manner in which he developed the approximation and (b) the general tolerance of the knife edge problem to approximation. Although the knife edge boundary solution has been used extensively to model natural and man-made diffracting objects, there has always been an uncertainty associated with estimating the effects of edge roughness on the diffraction pattern. The purpose of this paper is to present a solution to this edge-roughness problem when the roughness is random in nature. The solution uses Professor Collin's approximate formulation of the problem so that the fundamental physics of the distance-dependent phase interference between the direct and diffracted fields is preserved.