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 micro-vibrations, 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.

1. [1] J. Goodman, “Some fundamental properties of speckle,” JOSA, Vol.66, No.11, pp. 1145-1150, 1976.
2. [2] C. Dainty (Ed.), “Laser Speckle and Related Phenomena,” 2nd ed., Springer-Verlag, 1984.
3. [3] R. Sagawa, Y. Higuchi, H. Kawasaki, R. Furukawa, and T. Ito, “Dense pixel-wise micro-motion estimation of object surface by using low dimensional embedding of laser speckle pattern,” Proc. of the Asian Conf. on Computer Vision, 2020.
4. [4] G. D’Emilia, L. Razzè, and E. Zappa, “Uncertainty analysis of high frequency image-based vibration measurements,” Measurement, Vol.46, No.8, pp. 2630-2637, 2013.
5. [5] E. Caetano, S. Silva, and J. Bateira, “A vision system for vibration monitoring of civil engineering structures,” Experimental Techniques, pp. 74-82, 2011.
6. [6] H.-Y. Wu, M. Rubinstein, E. Shih, J. Guttag, F. Durand, and W. Freeman, “Eulerian video magnification for revealing subtle changes in the world,” ACM Trans. Graph. (Proc. SIGGRAPH 2012), Vol.31, No.4, 2012.
7. [7] A. Davis, M. Rubinstein, N. Wadhwa, G. Mysore, F. Durand, and W. Freeman, “The visual microphone: Passive recovery of sound from video,” ACM Trans. on Graphics (Proc. SIGGRAPH), Vol.33, No.4, Article No.79, 2014.
8. [8] A. Davis, K. Bouman, J. Chen, M. Rubinstein, F. Durand, and W. Freeman, “Visual vibrometry: Estimating material properties from small motions in video,” IEEE TPAMI, Vol.39, No.4, pp. 732-745, 2017.
9. [9] O. Løkberg and K. Høgmoen, “Vibration phase mapping using electronic speckle pattern interferometry,” Applied Optics, Vol.15, No.11, pp. 2701-2704, 1976.
10. [10] K. Creath, “Phase-shifting speckle interferometry,” Applied Optics, Vol.24, No.18, pp. 3053-3058, 1985.
11. [11] V. Bavigadda, E. Mihaylova, R. Jallapuram, and V. Toal, “Vibration phase mapping using holographic optical element-based electronic speckle pattern interferometry,” Optics and Lasers in Engineering, Vol.50, No.8, pp. 1161-1167, 2012.
12. [12] J. García, Z. Zalevsky, P. García-Martínez, C. Ferreira, M. Teicher, and Y. Beiderman, “Three-dimensional mapping and range measurement by means of projected speckle patterns,” Applied Optics, Vol.47, No.16, pp. 3032-3040, 2008.
13. [13] I. Yamaguchi, “Real-time measurement of in-plane translation and tilt by electronic speckle correlation,” Jpn. J. Appl. Phys., Vol.19, No.3, pp. L133-L136, 1980.
14. [14] H. Fujii, K. Nohira, Y. Yamamoto, H. Ikawa, and T. Ohura, “Evaluation of blood flow by laser speckle image sensing, part 1,” Appl. Opt., Vol.26, No.24, pp. 5321-5325, 1987.
15. [15] J. Zizka, A. Olwal, and R. Raskar, “Specklesense: fast, precise, low-cost and compact motion sensing using laser speckle,” Proc. of the 24th Annual ACM Symposium on User Interface Software and Technology, pp. 489-498, 2011.
16. [16] Y. C. Shih, A. Davis, S. W. Hasinoff, F. Durand, and W. Freeman, “Laser speckle photography for surface tampering detection,” Proc. of IEEE Computer Society Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 33-40, 2012.
17. [17] Z. Zalevsky, Y. Beiderman, I. Margalit, S. Gingold, M. Teicher, V. Mico, and J. Garcia, “Simultaneous remote extraction of multiple speech sources and heart beats from secondary speckles pattern,” Opt. Express, Vol.17, No.24, pp. 21566-21580, 2009.
18. [18] P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” OptEn, Vol.36, pp. 2302-2310, 1997.
19. [19] M. L. Jakobsen, H. Yura, and S. G. Hanson, “Spatial filtering velocimetry of objective speckles for measuring out-of-plane motion,” Applied Optics, Vol.51, No.9, pp. 1396-1406, 2012.
20. [20] P. Jacquot and P. K. Rastogi, “Speckle motions induced by rigid-body movements in free-space geometry: an explicit investigation and extension to new cases,” Applied Optics, Vol.18, No.12, pp. 2022-2032, 1979.
21. [21] K. Jo, M. Gupta, and S. K. Nayar, “Spedo: 6 dof ego-motion sensor using speckle defocus imaging,” Proc. of the IEEE Int. Conf. on Computer Vision, pp. 4319-4327, 2015.
22. [22] B. M. Smith, P. Desai, V. Agarwal, and M. Gupta, “Colux: Multi-object 3d micro-motion analysis using speckle imaging,” ACM Trans. on Graphics (TOG), Vol.36, No.4, pp. 1-12, 2017.
23. [23] B. M. Smith, M. O’Toole, and M. Gupta, “Tracking multiple objects outside the line of sight using speckle imaging,” Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition, pp. 6258-6266, 2018.
24. [24] A. Henderson, “ParaView Guide, A Parallel Visualization Application,” Kitware Inc., 2005.