Vibration measurement using additive speckle interferometry

A method for obtaining structural vibration amplitudes quantitatively is proposed based on the stroboscopic speckle interferometer. The technique requires five frames of additive speckle patterns: the first one (S0) taken with the laser illumination pulsed at instants when the vibration achieves its two zero amplitude positions within one sinusoidal vibration cycle of the specimen; and the remaining four (S1 through S4) taken with the illumination pulses arranged at times when the vibration is at its maximum and minimum amplitudes. During the acquisition of speckle patterns S1 through S4, the phase of the reference beam is appropriately shifted between the two pulses within each vibration cycle. The last four speckle patterns are then subtracted from the first one to yield four correlation fringe patterns with relative phase shifts of 0, π/2, π and 3π/2 respectively. These fringe patterns are then utilized to derive a phase map using a four-step phase calculation algorithm and finally the vibration amplitude and the sign of the vibrational nodes can be readily obtained from the phase map quantitatively. Results have been obtained using a speckle shearographic setup for the vibration measurement of a flat bottom-holed aluminum specimen vibrating at different frequencies.