Diffraction by a randomly rough knife edge

The intent of this paper is to predict the effects of random edge roughness on the knife-edge diffraction of an incident wave. This has been accomplished by approximating the field beyond the diffracting half plane with spectral techniques and the Kirchhoff approximation. By restricting the point of observation of the diffracted field to the side opposite from the incident field and not too far into the shadow zone of the edge, the results for a straight knife edge should be very accurate. By similarly restricting the spatial frequency spectrum of the knife-edge roughness to contain no frequencies comparable to or shorter than the electromagnetic wavenumber, the method used to estimate the effects of the roughness is also accurate. The relationships developed for the mean or average diffracted field and the incoherent diffracted power are studied for a range of electrophysical parameters that are representative of the situation encountered in a point-to-point communications link with blockage by a rough-edged half plane. The interpretation of the results is facilitated by the observation that the total diffracted field is a superposition of the incident field and the edge-diffracted field. Thus, the conventional oscillating behavior of the total field as the point of observation recedes from the edge and is attributed to the phase interference between these two fields. When the roughness on the edge increases, the edge diffracted-field becomes more incoherent and the phase interference diminishes; this leads to an attenuation of the oscillations in the coherent or mean total field. The model also predicts that the incoherent power is strongest near to the rough knife and is not generally appreciable when the point of observation of the diffracted field is far away from the edge. This, of course, is in complete agreement with our understanding that shadows, and hence, the details of the shadow-causing boundary (knife-edge), exists only a finite distance behind the boundary.