Direct measurement of spatial modes of a microcantilever from thermal noise

Measurements of the deflection induced by 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 10−14 m/Hz in the frequency range 1–800 kHz. The focused beam from the interferometer probes the cantilever at different positions along its length, and the spatial modes’ shapes are determined up to the fourth resonance, without external excitation. Results are in good agreement with theoretically expected behavior. From this analysis accurate determination of the elastic constant of the cantilever is also achieved.