In fringe projection profilometry (FPP), non-sinusoidal fringes due to the gamma effect of a projector will cause measurement errors. To solve this problem, a binary defocusing technique has been introduced in recent years, yet the appropriate defocusing is hard to evaluate quantitatively. An innovative approach to quantify binary defocusing in real-time is proposed. No matter how the projector and camera are arranged in FPP system, the fringe period in a captured defocusing fringe image is strictly varying; therefore, unlike previous methods, the proposed method uses a limited window for defocusing evaluation. This not only improves the accuracy of defocusing evaluation, but also greatly improves the evaluation speed, thus in turn enabling real-time evaluation. In addition, numerical differentiation is introduced on the window using a modified five-interval-point algorithm to effectively improve the sensitivity to improper (inadequate or excessive) defocusing. The difference between the numerical differentiation and its fundamental harmonic extracted by Levenberg–Marquardt iterative is taken as an evaluation value of binary defocusing. The smaller the difference, the more appropriate is the defocusing. By minimizing this difference, the most appropriate defocusing can be obtained quantitatively. Both numerical simulations and experiments validate the high sensitivity and high speed of the proposed method.
Multiple digital image correlation (DIC) systems can enlarge the measurement field without losing effective resolution in the area of interest (AOI). However, the results calculated in substereo DIC systems are located in its local coordinate system in most cases. To stitch the data obtained by each individual system, a data merging algorithm is presented in this paper for global measurement of multiple stereo DIC systems. A set of encoded targets is employed to assist the extrinsic calibration, of which the three-dimensional (3-D) coordinates are reconstructed via digital close range photogrammetry. Combining the 3-D targets with precalibrated intrinsic parameters of all cameras, the extrinsic calibration is significantly simplified. After calculating in substereo DIC systems, all data can be merged into a universal coordinate system based on the extrinsic calibration. Four stereo DIC systems are applied to a four point bending experiment of a steel reinforced concrete beam structure. Results demonstrate high accuracy for the displacement data merging in the overlapping field of views (FOVs) and show feasibility for the distributed FOVs measurement.
This study presents the electromechanical response of a piezoelectric laminated micro plate under the excitation of an ultrasonic wave. The laminated plate consists of a piezoelectric layer (AlN), an elastic layer (SiO2) and two electrode layers (Au and Pt). Since the whole thickness of the plate is in micro scale, the size dependence of the dynamic behavior of the laminated plate is evaluated using the couple stress theory. The results show that the bending rigidity of the micro plate increases when the size effect is considered and the amplitudes of output of electric charge and voltage are reduced accordingly when the plate is excited by ultrasonic wave. Also the resonant frequency of the laminated plate increase because of the enhancement of the bending rigidity of the plate. The analysis results can provide a reference for the design of micromachined piezoelectric sensors.
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