Vibration-resistant phase retrieval method with contrast compensation for phase-shifting interferometry

Vibration hinders the application of phase-shifting interferometry (PSI) to on-machine test and large-aperture mirror measurement. The investigation of PSI fringe disturbed by vibration indicates that, besides tilt-shifting error, inter- and intra-frame contrast variation is significant. The contrast variation is another dominant error source in phase retrieval of PSI. An inter- and intra-frame contrast compensation method is proposed here to retrieve wavefront phase from interferograms subjected to vibration. The method constructs algebraic equations with interferogram data and solves equations using iterative procedures. Experiments validate its effectiveness and manifest its capability to suppress vibration-induced error over a large frequency region. To enhance the calculation efficiency, a spatial subsampling strategy is proposed. Practical testing shows that subsampling reduces calculation time exponentially and preserves retrieval accuracy and spatial resolution. The proposed method, of which the unique ability is compensating the tilt-shifting error and fringe blur caused by vibration, predicates an effective and low-cost solution for PSI applied in vibration.