Pore filling of SBA-15 silica with nitrogen at 77 K was studied by combining gas adsorption measurements with small-angle neutron scattering. The Bragg peaks resulting from the 2D-hexagonal packing of the cylindrical mesopores exhibit a characteristic dependence of the peak intensity on the amount of adsorbed gas, increasing or decreasing as the thickness of the adsorbed film grows. This modulation of the peak intensities can be reproduced by a structural model in which the cylindrical pores and the adsorbed nitrogen film are taken into account by a form factor F(R,rf) of cylindrical objects, with R the pore radius and rf the radius of the vapor core of the pores. For our SBA-15 sample it is found that the thickness of the adsorbed film t=R-rf is a nearly linear function of the gas pressure, although the adsorption isotherm exhibits a pronounced high-affinity region at low pressures. This behaviour is attributed to adsorption into a microporous corona of the cylindrical mesopores at low pressures. A simple geometrical model is presented which accounts for the observed dependence of the film thickness on the pressure.