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Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector (q)-dependent surface tension sigma(eff)(q), have encountered difficulties. There is no consensus as to even the shape of sigma(eff)(q). By analyzing a simple density functional model of the liquid-gas interface, we identify different schemes for separating microscopic observables into background and interfacial contributions. In order for the backgrounds of the density-density correlation function and local structure factor to have a consistent and physically meaningful interpretation in terms of weighted bulk gas and liquid contributions, the background of the total structure factor must be characterized by a microscopic q-dependent length zeta(q) not identified previously. The necessity of including the q dependence of zeta(q) is illustrated explicitly in our model and has wider implications; i.e., in typical experimental and simulation studies, an indeterminacy in zeta(q) will always be present, reminiscent of the cutoff used in capillary-wave theory. This leads inevitably to a large uncertainty in the q dependence of sigma(eff)(q).