Three-Frame Random Phase-Shifting Algorithm Based on VU Decomposition Method and Ellipse Fitting

Abstract To enhance the precision and robustness of the three-frame phase shift technique, a new three-frame random phase-shifting fringe pattern phase demodulation method that combines VU decomposition and ellipse fitting techniques without the need for pre-filtering is proposed. The proposed method first performs VU decomposition on the interferograms to establish two orthogonal components of the fringe pattern. Then, the ellipse fitting method is used to obtain the relevant ellipse coefficients, thereby achieving precise phase demodulation. This method does not require an accurate phase-shifting process, thereby relaxing the stringent requirements on the phase shifter. Compared with traditional algorithms, the proposed method performs better under conditions of non-uniform background intensity and modulation amplitude. Numerical simulation experiments demonstrate that the proposed method maintains good stability across 20 repeated tests. Within the SNR range of 30 to 50 dB, the RMSE of the suggested approach is approximately 0.006 rad. This proves the effectiveness of the algorithm and provides a new approach for the development of three-frame phase-shifting technology.