Frequency analysis is a standard method using which, demanding applications can be studied and the frequency dependent mechanical motion of machine parts and work pieces measured.
Vibrations with amplitudes in the range of only few picometers are very challenging to measure and such measurements are beyond the scope of other commercially available measurement techniques. To show that attocube’s fiber-based Industrial Displacement Sensor (IDS) not only has a very low noise floor and high resolution, the resonant vibrations of micro-sized cantilevers which were excited only by their thermal energy at ambient conditions were made.
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.
Experimental and Results
Figure 1 shows the experimental setup, where the cantilevers were fixed to a stack of attocube positioners to allow alignment movements in x-, y-, and z-directions. Using a sensor head with a fixed focal length of 2.8 mm (D12/F2.8), light was focused to a spot size of below 2 µm diameter on the cantilevers.
A Fast Fourier Transform (FFT) analysis up to 2.5 MHz is allowed owing to the bandwidth of the digital signal output of 5 MHz (AquadB). Two different cantilevers of the same length (225 µm), but having different thicknesses and widths were studied: 3x28 µm (thin cantilever A) and 7x38 µm (thick cantilever B).
Clear, high-contrast alignment signals received from the cantilevers were then FFT-analyzed to visualize the mode spectrum. Figure 2(a) presents the FFT result of the two cantilevers in a frequency range of 50-500 kHz. Strong individual resonance peaks are shown by the cantilevers. The resonance peaks at 76.7 kHz and 165.6 kHz, respectively, are only excited by Brownian motion as there was no other excitation present in the setup.
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).
Furthermore, the noise floor is around 2 pm/sqrt(Hz) in the frequency range of 50-500 kHz. The Lorentz fits of the two resonance peaks are represented by the red curves in Figure 2(b) and from this plot, the quality-factors of 161 and 324 for the cantilever A and the cantilever B, respectively, have been calculated.
In this article, the resolution capability of the IDS has been demonstrated by measuring the Brownian motion of micro-sized cantilevers at ambient conditions.
This information has been sourced, reviewed and adapted from materials provided by Attocube Systems AG.
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