Eckart’s formulation of acoustic wave scattering from a randomly rough surface expresses the average pressure as the Fourier transform of the probability density function [C. Eckart, J. Acoust. Soc. Am. 25, 566–570 (1953)]. This implies a complete independence from the correlation function of the surface, a rather surprising result which does not follow from Eckart’s only assumption of statistical homogeneity. A more detailed derivation which takes into account surface correlation is given here.