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-shiftin g speckle pattern interferometer, the deformation can be tracked with an er ror that depends on the amplitude and frequency of the vibration. We use a numerical simulation based on a detailed mathematical model of the system t o predict the expected frequency response of the root mean square (rms) mea surement error in the time-varying phase difference maps. The performance o f four phase-shifting algorithms (three-frame, four-frame, Carre, and Schwi der-Hariharan five-frame) and a temporal phase unwrapping method is studied over a range of vibrational amplitudes and frequencies. The numerical resu lts indicate that the Carre algorithm is the preferred phase-shifting metho d to measure vibrations with a dynamic electronic speckle pattern interfero metry (ESPI) system. Vibration frequencies up to 30% of the carrier frequen cy can be measured with an rms phase change error less than 10% of the vibr ation amplitude. The numerical results are finally compared with experiment al data, acquired using a 1000 frame/s phase-shifting speckle interferomete r together with a laser vibrometer, which provides a reference phase measur e. (C) 2001 Society of Photo-Optical Instrumentation Engineers.