Theoretical characteristics of radiation reflected obliquely from a rough conducting surface

A theoretical estimate is made of the amplitude, phase, angular distribution and polarization of the radiation reflected from a rough surface when it is illuminated by an obliquely incident, plane electromagnetic wave. The surface is assumed to be made of perfectly conducting material and to be rough in one direction only (i.e. corrugated). In part of the paper a simple model rough surface is used together with the methods of geometrical optics to predict the time variation of the amplitude and phase of the signal received at a large distance from the surface when the surface profile is changing with time. The model consists of a series of strips whose heights are independent and randomly distributed. The rest of the paper is devoted to the application of diffraction theory to reflection from a rough surface of the 2-dimensional Gaussian type. By expressing the reflected radiation as an angular spectrum of plane waves and relating it to the incident radiation by means of the boundary conditions at the surface, it is shown that a rough surface may be represented approximately by a phase-changing diffracting screen. Using this approximation, the angular power spectra for the radiation reflected from rough surfaces, of different sizes compared with the average width of the irregularities, are deduced for both horizontally and vertically polarized incident radiation.