Allocation of spatial single-mode from multimode oscillation using temporal phase unwrapping in digital holographic...

In this paper, we propose a method based on the temporal phase unwrapping algorithm in digital holographic interferometry enabling reconstruction and the analysis of multimode resonant oscillations. The model metal plate is excited simultaneously at four resonant frequencies. Since the dynamical process had to be evaluated, the conditions of hologram detections and mutual synchronization of setup facilities were considered. The temporal phase unwrapping method requires a time-dependent phase with a small phase difference which is reconstructed from the nearest holograms. In order to meet a condition of temporal unwrapping applicability, the scanning of vibrations with significant discretization has to be applied. In our work, we implemented a standard CCD camera with 15 f/s. Since the camera frame rate was much less than the studied oscillations (160 Hz-720 Hz), the scanning procedure skips over vibration periods at regular intervals of one second with a fixed time delay for each hologram acquisition. This approach samples an oscillation with a sufficient resolution for an application of temporal phase unwrapping. Based on this scanning procedure, thousands of image holograms were acquired and time-dependent phases for each point of the image were reconstructed. The implementation of the temporal phase unwrapping algorithm for the phase sequence reconstructs a displacement of each object's point in time. In order to allocate a single-mode oscillation, Fourier transform for time-dependent displacement is used. The filtering of each frequency in Fourier-domain and utilizing inverse Fourier-transform results in the allocation of spatial single-mode distribution from the multimode oscillation. Finally, the results of the examination of multimode vibration on a metal plate were represented. The spatial allocation of each single-mode oscillation in time is obtained. Nevertheless, limitations of the proposed method are considered and its applicability discussed.