Measurements of the deflection induced by the thermal noise have been performed on a rectangular atomic force microscope cantilever in air. The detection method, based on polarization interferometry, can achieve a resolution of 1E-14 m/rtHz in the frequency range 1 kHz - 800 kHz. The focused beam from the interferometer probes the cantilever at different position along its length and the spatial modes shapes are determined up to the 4th resonance, without external excitation. Results are in good agreement with theoretically expected behavior. From the thermal noise spectrum accurate determination of the elastic constant of the cantilever is also achieved.