A fast and precise spatial-carrier phase-shifting algorithm based on the matrix VU factorization strategy that can realize dynamic real-time phase detection is proposed. First, the proposed algorithm divides the spatial-carrier interferogram into four phase-shifting subinterferograms. Second, the matrix VU factorization strategy, an excellent fast iterative algorithm, is used to accurately obtain the measured phase from these subinterferograms. Numerical simulation and experimental comparison verify that this method is an efficient and accurate single-frame phase demodulation algorithm. Meanwhile, the performance of the proposed method is analyzed and discussed for the influencing factors, such as random noise level, carrier-frequency value, and carrier-frequency direction. The results show that the method proposed is a fast and precise phase detection method that provides another effective solution for dynamic real-time phase measurement.
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