Signal analysis is a familiar used method in technical and scientific disciplines to analyze the properties of time signals and waveforms. Here, we present the functionality of the PicoScale to detect and calculate the Fourier spectrum of oscillations and dynamic shifts from objects on different length scales with highest time and spacial resolution. This ability makes the PicoScale a very powerful tool for challenges in the fields of nanotechnology and microsystem engineering, where signal analysis ranging from the millimeter length scale down to the very small picometer length scale are of interest.

The range of application of SmarAct’s PicoScale interferometer concerning signal analysis, ranging from the millimeter down to the picometer scale, is demonstrated by giving three short examples from practice. For each example, the Hanning window function is used for analysis.

### Damped Oscillation

In a first example, the damped oscillation of a simple spring-mass (bumper) system is detected by the interferometer. Correspondingly, an exponential decrease of the oscillation amplitude can be observed in the time domain. The resonance characteristics can be extracted from the Fourier domain by applying a fast Fourier transformation and enables the access to resonance frequency f_{res}= 8 Hz and damping properties Q = 12.5 ( Q -factor) of the system.

### Nanometer-Scale Oscillations

In a next step, the spring-mass system is replaced by piezo actuated target mirror. An electronically excited low-frequency oscillation is depicted in Fig. 3 and exhibits an amplitude on the nanometer scale. The desired frame rate is set to 4.88 kHz and the block-size amounts to 8192 samples. The minimal measurement time to fill the block-size is easily be derived by 8192 /4880 s −1 = 1.68s. In the corresponding Fourier domain, the main oscillation component at 16.6 Hz has an 12 nm (RMS) amplitude, which fits well to the time domain signal. Additionally, signal at the second and third harmonic can be recognized due to small nonlinearities in the piezo dynamics.

### Picometer-Scale Oscillations

In Fig. 4 the same signal with a lower voltage amplitude is applied to the piezo-element. In the averaged Fourier spectrum (frame rate: 2.44 kHz / block-size: 8192) the oscillation at 16.6 Hz and at higher harmonics can be recognized with amplitudes down to single picometers. This example demonstrates the ability of SmarAct’s PicoScale to measure oscillations with highest accuracy down to the picometer scale.

The low noise level in Fig. 4 paves the way towards detections on the picometer scale. The double-log representation reveals a decreasing 1 /f 2 noise floor which ranges from several tens of picometers for low frequencies down to single picometers for higher frequencies. This low noise characteristics makes the PicoScale an ideal scientific instrument for distance measurements on small length-scales.

### Summary

SmarAct’s PicoScale is very powerful and compact scientific instrument for distance measurements and signal analysis on different length scales. Three short examples demonstrate the field of applications ranging from oscillations on the millimeter scale down to very small picometer scale.