The extended capillary wave theory (ECW) proposed by Robledo et al. and formulated in terms of the unknown direct correlation function C of the two-phase system with a planar interface between liquid and its vapor, is applied to our simulation data on the full inhomogeneous two-point correlation function H from which C is also obtained. The required projection, (C) over bar(q), is shown and discussed. The coefficient of q(4), the apparent bending coefficient, was inequivocally negative, in agreement with the view that the true bending coefficient may be absent in one-component interfaces. The ellipsometric coefficient diverged and its calculation still required an ultraviolet cutoff. It is thus demonstrated that ECW is but the first step and further terms, some discovered earlier, as well as mode-mode coupling, are required. These are discussed.