Measuring amplitude and phase of vibration with double-exposure stroboscopic TV holography

Abstract

We present a technique for the measurement of both amplitude and phase of sinusoidal vibrations that uses double-exposure stroboscopic TV holography (TVH) with optical and mechanical phase-stepping. This method results of the assembling of two techniques previously contrived by the authors. The first one allows to shift the phase of the fringes generated by sequential subtraction in double-exposure stroboscopic TVH and thus to obtain phase maps representing the local difference of displacement experienced by the object between two instants within its vibration period. The second one yields the amplitude and the phase of vibration from two of such phase maps obtained with a relative mechanical-phase-shift of pi/2 between them and conveniently unwrapped. In this communication we describe how both techniques are combined and demonstrate the use of pulse separation to control the overall sensitivity. The implementation of the resulting technique in a fibre-optic electronic speckle-pattern interferometer (ESPI) and examples of its application to simple and more complex vibrating objects is also presented. The measurement of the amplitude and the phase of vibration allows the total determination of the dynamic displacement of sinusoidally vibrating objects. With double-exposure stroboscopic TVH, measurements can be made "in flight'' (i.e., there is no need of recording a reference state with the object at rest) with less sensitivity to environmental noise and more efficient use of the available laser power than with single-exposure techniques. These features make of this technique a promising tool for the industrial measurement of vibrations.