Higher-order moments for profiles of statistically rough, real surfaces

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Abstract
Although for many applications it suffices to have knowledge of only the first two moments of the probability distribution function for profiles of statistically rough surfaces, it is sometimes necessary to specify higher-order moments as well (in particular, to obtain the dispersion relation for surface polaritons on a randomly rough surface). No reports of work related to real surfaces are available in the literature. In this paper we compute higher-order moments for profiles of various statistically rough, real surfaces (metallic and dielectric deposits, and optical polished surfaces). We show that the third moment is approximately zero and that the fourth moment roughly satisfies the standard relation involving the sum of the products of second-order moments taken two-by-two, different in all possible ways.