Phase-shifting interferometry algorithm based on hybrid Kalman ellipse fitting

Lissajous ellipse fitting (LEF) algorithm can recover the 3D shape information of the object surface from the phase shift interferogram. Due to the influence of outliers, noise and short arc fitting, the commonly ellipse fitting algorithm is limited in accuracy and stability. In this paper, a hybrid Kalman ellipse fitting algorithm is proposed. Two sets of simple harmonic motion equation parameters conforming to Lissajous pattern are calculated from fixed or random phase shift interferograms, which are used as the initial values of hybrid Kalman ellipse fitting. The confidence intervals of ellipse parameters are obtained by iteration, and the best coefficient is determined to solve the wrapped phase. In this paper, the results of three-step and four-step LEF are compared with the phase-shifting formula method, and the advantages and disadvantages of different ellipse fitting algorithms are 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 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 better performance than other fitting algorithms.