Statistical properties of light reflected from a moderately rough surface scanned through a finite size aperture

The probability density function P(I) of the integrated intensity I, reflected from a moderately rough surface, is computed correct to order (2pisigma/lambda)(2), where sigma is the rms of the surface roughness z(x), and lambda is the incident wavelength. By using the assumption that z(x) is a Gaussian random variable, we obtain P(I) as a function of the size of the detector aperture and the correlation length of the surface roughness. Numerical results and a comparison with previous works are given.