Phase-shifting interferometry algorithm based on hybrid Kalman ellipse fitting

Based on the Lissajous ellipse fitting (LEF) algorithm, the 3D morphology information of the object surface can be recovered from the phase-shifting interferograms. Due to the influence of outliers, noise and short arc fitting, the commonly-used ellipse fitting algorithm is limited in accuracy and stability. Therefore, a hybrid Kalman ellipse fitting algorithm was proposed. Two sets of simple harmonic motion equation parameters conforming to Lissajous pattern were calculated from fixed or random phase-shifting interferograms, which were used as the initial values of hybrid Kalman ellipse fitting. The confidence intervals of ellipse parameters were obtained by iteration, and the optimal coefficient was determined to solve the wrapped phase. The results of three-step and four-step LEF were compared with that of phase-shifting formula method, and the advantages and disadvantages of different ellipse fitting algorithms were analyzed. When the phase shift is a random value, the RMS value of the three-step LEF error is 0.052 4 rad, which is 20.36% lower than that of the formula method. When the phase shift is 90°, the RMS value of the three-step LEF error is 0.045 8 rad, which is 30.39% lower than that of the formula method, and the four-step LEF error is similar to the formula method. Simulation and experiments show that the proposed algorithm has better stability and performance than other fitting algorithms.