Method for designing error-resistant phase-shifting algorithm

We present a method for designing error-resistant phase-shifting algorithms to suppress error sources in phase-shifting interferometry. Firstly, the partial-differential processing is applied to the weighted least squares algorithm to obtain error sensitivity equations. Sequentially, bound equations are obtained to minimize error sensitivity. Finally, the bound equations are solved to determine the weights, and the error-resistant phase-shifting algorithms are developed. Aiming at a self-developed interferometer, the proposed method is used to design phase-shifting algorithms which are resistant to given error sources. Theoretical analysis and numerical simulations of the self-designed algorithms compared with a commercial algorithm are completed. Theoretical analysis indicates that the self-designed algorithms meet the desired requirements. Numerical simulations verify the correctness of theoretical analysis. And the comparisons show that the self-designed algorithm is more resistant to error sources that needs to be suppressed. These results verify the proposed method and demonstrate its effectiveness.