We have experimentally demonstrated that planar neutron waveguides can be used as resonant beam couplers to efficiently produce a coherent neutron line source with cross sections in the submicrometer range. The Fraunhofer far-field diffraction pattern of the first three resonance modes was measured and found to be in excellent agreement with the theoretical model. Our measurements confirm that an excited exiting mode is fully coherent in the direction perpendicular to the surface of the thin-film coupler and may therefore be used for applications of interest to a broad user community in biochemical and semiconductor nanosciences such as static and time-resolved coherent speckle experiments or phase-contrast imaging