New contributions of capillary waves to the density-density correlation function H(z(1),z(2),k(perpendicular to)) are calculated in the Gaussian approximation and compared with those found earlier "experimentally" in a MD simulation. The k(perpendicular to) dependence of the correlation function or of the scattering factor is examined and compared with the dominant 1/k(perpendicular to)(2) form. General equations valid to all orders in the gradients of the density profile are given and the k(perpendicular to) dependence of the structure factor (in the Born approximation) is found. The latter may be different from the 1/k(perpendicular to)(2) form. Regularization of the integrals is examined with two procedures applied.