Measurement of Brownian Motion of Commercial Micro-Cantilevers

Frequency analysis is a standard method used for studying challenging applications and measuring the frequency dependent mechanical motion of machine components and workpieces.

It is a very challenging task to measure vibrations with amplitudes of only few picometers, which is not within the capabilities of other commercially available measurement methods. In this article, the resonant vibrations of micro-sized cantilevers excited only by their thermal energy at ambient conditions were measured to demonstrate the high resolution and very low noise floor capabilities of attocube’s fiber-based Industrial Displacement Sensor (IDS).

Experiment and Results

Figure 1 shows the experimental setup. The cantilevers were attached to a stack of attocube positioners to facilitate alignment movements in x-, y-, and z-directions. The light was focused to a spot size of below 2 µm in diameter on the cantilevers using a sensor head with a fixed focal length of 2.8 mm (D12/F2.8).

The bandwidth of the digital signal output of 5 MHz (AquadB) enables a Fast Fourier Transform (FFT) analysis up to 2.5 MHz. Here, two different cantilevers of the same length (225 µm), but with different thicknesses and widths were studied: 3x28 µm (thin cantilever A) and 7x38 µm (thick cantilever B).

Experiment and Results

Figure 1. A stack of three attocube x-, y-, and z-positioners was used to align the D12/F2.8 sensor head onto the micro-cantilever. The distance between the objective and the cantilever was about 2.8 mm.

Clear, high-contrast alignment signals were obtained from the cantilevers. The resulting signals were then subsequently FFT-analyzed to visualize the mode spectrum. The FFT result of the two cantilevers within a frequency range of 50-500 kHz is shown in Figure 2(a). The cantilevers exhibit strong individual resonance peaks at 76.7 kHz and 165.6 kHz, respectively. These resonance peaks are excited only by Brownian motion as there was no other excitation present in the setup.

Furthermore, for the frequency range of 50-500 kHz, the noise floor is around 2 pm/sqrt(Hz). The Lorentz fits of the two resonance peaks are represented by the red curves in Figure 2(b). From this plot, the quality factors for cantilever A and cantilever B have been calculated to be 161 and 324, respectively.

FFT analysis

Figure 2. The figures (a) and (b) show the FFT analysis of the two different cantilevers under investigation. The resonant frequencies of the cantilevers can be seen at 76.7 kHz (thin cantilever A) and 165.6 kHz (thick cantilever B).


In summary, the Brownian motion measurement of micro-sized cantilevers at ambient conditions has demonstrated the resolution capability of the IDS.

Attocube Systems AG.

This information has been sourced, reviewed and adapted from materials provided by Attocube Systems AG.

For more information on this source, please visit Attocube Systems AG.


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