Phase-based displacement measurement on a straight edge using an optimal complex Gabor filter

In recent years, a number of phase-based motion processing techniques have been developed, and these allow for motion signals to be extracted from the local phase. The phase is generated by applying a pair of even- and odd-symmetric filters, and it is more robust to the intensity change. However, the phase can be unstable in certain areas where it is not linearly correlated with motion. This paper proposes an accurate and robust displacement measurement technique using an optimal complex Gabor filter and phase-based optical flow (POF) to measure the vibration response of a straight edge with the generated linear phase. The causes of nonlinear phase are discussed, and the nonlinearity of phase is used as an indicator of the measurement accuracy. Three types of nonlinear phase caused by noise background and inappropriate filter parameters for a straight edge are presented, along with solutions that optimize the parameters of the complex Gabor filter to obtain the phase with low nonlinearity. A numerical experiment is conducted on artificially created patterns to demonstrate the correlation between the proposed phase nonlinearity and the measurement accuracy. The validation experiments are carried out on a 5-story structure using a Laser Doppler Vibrometer (LDV) and a camera to demonstrate the accuracy and robustness of the proposed technique using the phase with low nonlinearity. The results show that the proposed technique can measure the vibration at 0.01-pixel scale. In addition, the robustness of the proposed technique is validated by performing experiments under different illumination conditions. The vibration responses of the 5-story structure with noisy background are measured using both accelerometers and a camera to perform the output-only modal identification. The results confirm that the proposed method can accurately identify modal frequencies, damping ratios, and high-resolution operational deflection shapes (ODS) requiring no pure background.