Acquisition and Visualization of Micro-Vibration of a Sound Wave in 3D Space

The acquisition of micro-vibrations is important for analyzing machinery. In the present study, we propose a method for measuring and visualizing the three-dimensional (3D) displacements of such microvibrations, especially in the case of sound waves propagating through space. The proposed method uses the speckle patterns of coherent light to measure the minute displacements. Speckle patterns are useful for detecting extremely small displacements owing to their sensitivity to the pose of the object. However, it is impossible to measure the displacement at each position because the pattern changes nonlinearly with respect to large depth changes. Therefore, a method of nonlinear low-dimensional embedding of the speckle pattern is proposed to analyze the displacements and extended to measure micro-displacements in a 3D space. We divided the 3D space into multiple slices and synchronously captured each speckle pattern. The displacements in the entire 3D space were simultaneously recovered by optimizing the embedded vectors, which were consistent in a 3D lattice. The propagation of sound waves in the 3D space was visualized using the volume-rendering technique. The experiments confirmed that the proposed method correctly measured the displacements by comparing them with the ground truth captured by microphones. We also visualized the wavefront of the sound wave propagating through space.