A method for whole-field noncontact measurement of displacement, velocity, and acceleration of a vibrating object based on image-plane digital holography is presented. A series of digital holograms of a vibrating object are captured by use of a high-speed CCD camera. The result of the reconstruction is a three-dimensional complex-valued matrix with noise. We apply Fourier analysis and windowed Fourier analysis in both the spatial and the temporal domains to extract the displacement, the velocity, and the acceleration. The instantaneous displacement is obtained by temporal unwrapping of the filtered phase map, whereas the velocity and acceleration are evaluated by Fourier analysis and by windowed Fourier analysis along the time axis. The combination of digital holography and temporal Fourier analyses allows for evaluation of the vibration, without a phase ambiguity problem, and smooth spatial distribution of instantaneous displacement, velocity, and acceleration of each instant are obtained. The comparison of Fourier analysis and windowed Fourier analysis in velocity and acceleration measurements is also presented.
In recent years, optical interferometry has been applied to the whole-field, noncontact measurement of vibrating or continuously deforming objects. In many cases, a high resolution measurement of kinematic (displacement, velocity, and acceleration, etc.) and deformation parameters (strain, curvature, and twist, etc.) can give useful information on the dynamic response of the objects concerned. Different signal processing algorithms are applied to two types of interferogram sequences, which were captured by a high-speed camera using different interferometric setups: (1) a speckle or fringe pattern sequence with a temporal carrier and (2) a wrapped phase map sequence. These algorithms include Fourier transform, windowed Fourier transform, wavelet transform, and even a combination of two of these techniques. We will compare these algorithms using the example of a 1D temporal evaluation of interferogram sequences and extend these algorithms to 2D and 3D processing, so that accurate kinematic and deformation parameters of moving objects can be evaluated with different types of optical interferometry.
A 20-point laser Doppler vibrometer with single photodetector is presented for noncontact dynamic measurement. A 5×4 beam array with various frequency shifts is generated by a 1.55 μm distributed feedback laser and four acousto-optic devices, and illuminating different points on vibrating objects. The reflected beams are coupled into a single-mode fiber by a pigtailed collimator and interfere with a reference beam. The signal output from a high-speed photodetector is amplified and then digitized by a high-speed analog-to-digital converter with a sampling rate of 1 gigasample per second (1 GS/s). Several methods are introduced to avoid the cross talk among different frequencies and extract the vibration information of 20 points from a one-dimensional signal. Two signal processing algorithms based on Fourier transform and windowed Fourier transform are illustrated to extract the vibration signals at different points. The experimental results are compared with that from a commercial single-point laser vibrometer. The results show simultaneous vibration measurement can be realized on multiple points using a single laser source and a single photodetector.
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