Vibration measurement by temporal Fourier analyses of a digital hologram sequence

Abstract

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.