Full-field high-frequency surface vibration amplitude measurement from an out-of-focus and blurred speckle image

In this work, we present a method for obtaining a full-field vibration amplitude distribution of a vibrating surface from only two slightly out-of-focus speckle images. A blurred, slightly out-of-focus speckle image of the vibrating surface is recorded with exposure times far longer than the surface oscillation period. This image is divided into zones of interest, and each one is compared to the corresponding zone of the other slightly out-of-focus speckle image, the one with the surface at rest. The quantity compared is the width of the cross-correlation function, in the same way as detailed in our previous work [Appl. Opt.63, 5706 (2024)10.1364/AO.527541]. From this local variation, the speckle vibration amplitude is obtained, and finally, the surface tilt vibration amplitude of each zone of interest is deduced from the speckle vibration amplitude. In our previous work, only the speckle vibration amplitude at the illuminated spot was obtained because a free propagation configuration was used. Here, the speckle image configuration makes it easy to see the vibration modes and allows one to obtain a quantitative full-field distribution of the vibration amplitudes. The technique was tested up to several tens of kHz; however, we did not see a reason for a limit to the maximum operating frequency. The interferometric validation of the method indicates a precision of 15%.