<title>Quantitative three-dimensional measurements of vibration amplitudes and phases as a function of frequency by digital speckle pattern interferometry</title>

Abstract

Vibration measurements by interferometry can be realized with continuous or pulsed lasers. A convenient and less expensive way to measure displacements relative to vibrating objects is to use an acousto-optic modulator in the object beam of an interferometer using a continuous laser. Stroboscopic illumination of vibrating objects can freeze moving speckle patterns when the stroboscopic and vibration frequencies are synchronous. This supposes a monofrequency excitation. We have developed a method for measuring the complex displacement response of vibrating objects at any frequency. The use of spatial phase-shifting and temporal phase-shifting allows consistent measurements of vibration amplitudes and phases without changing the phase of the excitation force. We call 'spatial phase-shifting' a method using the phase-shift of the reference beam in an interferometer and 'time phase-shifting' an original technique based on the relative change of phase between the stroboscopic illumination and the excitation force. Three spatial phase-shift steps and the impact of the choice of the phase-shift amounts in the developed algorithm is discussed. Recording of vibration amplitudes and phases at successive frequencies enabled us to measure the frequency response of objects and to analyze how eigenmodes appear.