Anti - Vibratory Phase - Shift Interferometry Algorithm And Experimental Study

Phase-shifting interferometry (PSI) has achieved widespread use for reconstructing accurate and reproducible wavefront with high spatial resolution. The great sensitivity of PSI to environmental vibration hinders its application to many cases, such as measurement of large-aperture or long-focal-length mirrors and in-situ measurement for optical manufacturing. To realize wavefront measurement in the presence of vibration, PSI resistant to vibration has been researched in this study.Firstly the error model of PSI under vibration is established. The propagation of vibration during PSI measurement and the mechanism of error generation are analyzed. The numerical simulations of PSI under vibration exhibit that measurement error mainly results from phase-shifting error and fringe contrast fluctuation of collected interferograms, which are caused by vibration ultimately.Two vibration-resistant algorithms, Spectrum Analysis algorithm (SAA) and Three-step Iteration Algorithm (TIA), are proposed for PSI. In SAA the phase shift and contrast are detected from spectra of spatial-carrier interferograms. Then the phase shift and contrast are used as priori information to retrieve wavefront phase from least-square equation. To suppress the detection error of SAA, the parameters related to bandwidth have been optimized and a criterion for spatial carrier frequency has been developed. TIA solves wavefront phase, treated as unknown, from equations of interference intensity with iteration calculation. In TIA, the wavefront phase, x- and y-directional phase shifts are calculated in three individual steps in an iteration cycle. To decouple the nonlinearity of tilt-shifting when determining the tilt factors, orthogonal decomposition and linear regression are utilized. The contrast fluctuation of interferograms could be calculated and compensated as well. And spatial-subsampling method is developed to reduce the computation time. SSA and TIA have relatively reciprocal characteristics. SSA is a deterministic method that indicates higher resistance to vibration, but suffering from retrace error of small amount caused by spatial carrier. Requiring estimations for phase shifts or wavefront phase, TIA shows lower resistance to vibration, but avoiding retrace error.The resistances of SSA and TIA have been verified with experiments. The first experiment, conducted in the presence of a series of harmonic vibration, exhibit that SSA and TIA could retrieve wavefront accurately. Under the vibration of 1μm amplitude and 60Hz frequency, the error of wavefront PV value is less than 0.01λ and 2σ repeatability is less than 0.01λ. The experiment shows that SSA and TIA satisfy the requirement of resistance to vibration in precision and ultra-precision manufacturing. In the second experiment, vibration of a running optical manufacturing machine, magnetorheological finishing (MRF) machine, was reproduced in the measurement. The retrieved wavefronts with SSA and TIA manifest the capability of applying to in-situ surface measurement. For no special hardware is required for the interferometer, the proposed vibration-resistant algorithms, SSA and TIA provide a high-accuracy and low-cost solution for the measurement with PSI in the presence of vibration.