Phase errors in low-frequency vibration measurement with high-speed phase-shifting speckle pattern interferometry

When mechanical vibrations are measured by means of a dynamic phase-shifting speckle pattern interferometer, the deformation can be tracked with an error that depends on the amplitude and frequency of the vibration. We use a numerical simulation based on a detailed mathematical model of the system to predict the expected frequency response of the root mean square (rms) measurement error in the time-varying phase difference maps. The performance of four phase- shifting algorithms (three-frame, four-frame, Carre, and Schwider- Hariharan five-frame) and a temporal phase unwrapping method is studied over a range of vibrational amplitudes and frequencies. The numerical results indicate that the Carre algorithm is the preferred phase-shifting method to measure vibrations with a dynamic electronic speckle pattern interferometry (ESPI) system. Vibration frequencies up to 30% of the carrier frequency can be measured with an rms phase change error less than l0% of the vibration amplitude. The numerical results are finally compared with experimental data, acquired using a 1000 frame/s phase-shifting speckle interferometer together with a laser vibrometer, which provides a reference phase measure.