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In this study, a common-path electronic speckle pattern interferometry system which upholds the natural property of transparency of insect’s wings has been developed to measure the wings’ natural frequencies and mode shapes for the first time. A novel base-exciting method was designed to enable the simultaneous application of sinusoidal and static forces to excite wings and introduce an additional phase. The moiré effect induced by the amplitude modulation was employed to accurately recognize the resonance state. Subsequently, the mode shapes were visualized by phase-shifting and real-time frame subtraction. Eight pairs of forewings from cicadas were investigated. The first three order natural frequencies of the wings are approximately 145 Hz, 272 Hz and 394 Hz, respectively, which are dispersed to prevent modal coupling. The cambered mode shapes exhibit a strongly spanwise-chordwise anisotropy flexural stiffness distribution, generally dominated by bending and twisting deformation. The details of the high-order mode shapes show that the tip exhibits distinct deformation, indicating more flexibility to cope with external impact load, and the nodal lines usually comply with the direction of the wing veins in higher modes, substantiating the fact that the veins play an important role as stiffeners of the membrane. The results are in excellent agreement with the dynamic performance of previous studies, which will potentially affect a broader community of optical measurement specialists and entomologists to enhance our understanding of time-averaged interferograms and insect flights.

This paper proposes a method to merge stereo-digital image correlation (DIC) and electronic speckle pattern interferometry (ESPI) data by camera calibration. The proposed method is employed to verify the accuracy of full-field out-of-plate displacements measured by stereo-DIC in a cantilever beam test. The mean absolute error and the root mean square error (RMSE) of the full-field displacement measured by four-megapixel cameras are 0.849 µm and 1.08 µm at 60 mm field of view, respectively, and the RMSE of the central area is 0.615 µm. The errors are not uniformly distributed because of the imperfect calibration. When the lenses are changed and the field of view reaches 120 mm, the RMSE is 1.48 µm with uniform distribution. These accuracies could be traced back to the laser wavelength to confirm the stereo-DIC data. The proposed method can be used not only to verify the full-field measurement accuracy of DIC but also to determine the rigid-body displacement for ESPI with a high-precision stereo-DIC. Thus, the displacement vector can be obtained. Furthermore, it can unify the coordinate of multiple ESPI systems to achieve a large range of high-precision three-dimensional deformation measurements.

Double speckle pattern interferometry is presented for the measurement of in-plane rotation angle, sign, and center of rotation. The technique employs two conventional in-plane sensitive electronic speckle pattern interferometry systems combined with two-wavelength laser illumination and a phase-shifting method. Angular displacement of micro-rotation including the sign is determined from the wrapped phase difference, and the center of rotation is located by using wrapped phase difference maps related to two-directional displacement. The test setup is described and experimental results indicate that the system can provide angular displacement measurement with accuracy of 1.8 arcsec.