A plasmon surface wave is excited in a thin metallic layer on a dielectric, if the layer is illuminated at an incident angle larger than the critical angle of total reflection. At certain resonance angles, the major part of the incident energy is coupled into the surface wave and the total reflection is attenuated. We probed the resonance peak with a spectrum of incident waves and detected the reflected energy at two incident angles near the resonance peak simultaneously. The ratio of the detected energies is a function of the incident angle, thus facilitating angular measurements. First experimental results indicate a resolution better than 0.001 degrees in a measuring range of 1 degrees.