## 3 Experimental Verifications  
### Light-Weight Beam Property Analysis  
A laboratory experiment on the saw blade in Figure 1 was carried out to evaluate the effectiveness of the proposed method. The experimental setup is shown in Figure 5. The saw blade in Figure 1 was clamped with a table vice and can be approximately considered as a light-weight cantilever beam. The dimensions of the test beam is 0.29 m \(\times\) 0.0126 m \(\times\) 0.00065 m. The Young's modulus of the material is 2.06 \(\times\) 10\({}^{11}\) N\(\cdot\)m\({}^{-2}\), and the density is 7.85 \(\times\) 10\({}^{3}\) kg\(\cdot\) m\({}^{-3}\). An audio file with frequency band from 10 Hz-500 Hz was played by a loudspeaker from approximately 0.1 m away from the target to excite the beam. The sound volume was set to 80 dB. Air fluctuations can induce subtle vibration on the surface of the cantilever beam. These vibrations were captured with the high-speed camera system (Mode-5 KF10M, Agile Device Inc., Hefei, China) at 500 fps with a resolution of 580 \(\times\) 180 pixels.  
Figure 4: Flowchart of the low-level variation magnification and extraction process.  
An LED light source was used to ensure environmental illumination because the exposure time of the high-speed camera is short and ambient light cannot provide adequate illumination.  
The captured video file was first handled by the phase-based acceleration magnification algorithm. Laplacian kernels in motion magnification were calculated according to the theoretical resonant frequencies that were obtained by using Euler-Bernoulli beam theory. Two subimage areas were then selected within the red (the jagged side) and blue (the smooth side) rectangles to extract deviation signals. The size of the selected two subimages was 300 \(\times\) 30 pixels. The analysis matrix can be generated with deviation variation signals in all frames calculated. The SVD results indicate that the signals corresponding to the first two singular values took over 90% of the energy in the obtained analysis matrix. The rest of the components in the analysis matrix were considered to be noise and ignored in the low-rank approximation matrix. The waveforms and frequency spectrums of the vibration signals from the smooth side and jagged side of the saw blade are shown in Figures 6 and 7.  
Figure 5: Setups of the beam property estimation experiment.  
Figure 6: Vibration signals and their frequency spectrums extracted from the original video (blue line) and the magnified video (red line) along the smooth edge of the saw blade.  
From the following spectra, four obvious peaks for 6.37 Hz, 40.16 Hz, 113.10 Hz, and 221.60 Hz were found using the magnified video file. The edge variations corresponding to these four peaks were not extracted effectively from the original video. The peak for 40.16 Hz was difficult to find in the vibration signal from the original jagged edge. The low-level vibration signals over 40 Hz were successfully magnified in the video processed by acceleration magnification. Table 1 shows the first four resonant frequencies estimated according to the classical Euler-Bernoulli beam theory. These four peaks match well with the theoretical ones. Given that the vibration signal of the first-order resonant frequency is clear, the magnification was not applied to the first-order resonant frequency. The Laplacian kernels and video magnification factors are given in Table 1.  
In practical applications, the experimental modal frequencies can help estimate structural vibration properties, such as elasticity. Although acceleration magnification rarely induces image blurring and artifacts, a large amplification factor may induce image motion-blurred images and affect the extraction result. In this particular case, the amplification factors were controlled to less than 15.