Direct measurement of spatial modes of a micro-cantilever from thermal noise

TL;DR

This paper presents a method to directly measure the spatial mode shapes of a micro-cantilever using thermal noise detection via polarization interferometry, achieving high resolution and accurate elastic constant estimation.

Contribution

The study introduces a non-invasive technique to map spatial modes of a micro-cantilever from thermal noise without external excitation, aligning well with theoretical models.

Findings

Spatial mode shapes up to the fourth resonance were determined.

The method achieved a resolution of 1E-14 m/rtHz.

Elastic constant of the cantilever was accurately measured.

Abstract

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 1E-14 m/rtHz in the frequency range 1 kHz ? 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.