Gain of antennas with random surface deviations

On-axis gain of antennas with rough reflecting surfaces is computed as a function of rms surface deviation e, correlation distance c, antenna area A and wavelength δ. Gaussian stationary surface deviations, Gaussian correlation functions, and uniform illumination are assumed. Antennas with rectangular and circular apertures are considered. It is shown that a normalized gain can be defined which has the same functional form for both. A principal result of this work is quantitative calculation of the on-axis antenna gain when the normalized variance (4π∊/λ)
²
of the rough surface is larger than 4. The off-axis gain is also considered, and it is shown that in the asymptotic limit (as λ → 0), the gain reduces to that obtained by using geometrical optics.