Analysis and Compensation of Phase Error Caused by Noise and Nonlinear Response of 3-D Measurement System

For static objects where the fringes are not saturated, the phase accuracy is mainly affected by the unavoidable factors of the introduction of fringe noise and the nonlinear response of the measurement system. The existing noise-induced phase error model is based on a Gaussian noise model, but in fact the noise of the fringe pattern is random. In this work, we establish a new evaluation method that directly converts the noise variance into phase variance, and we compare the anti-noise performance of the three-step and four-step phase-shift methods according to the phase error coefficient. Theoretical and experimental results confirm that the anti-noise performance of the four-step phase-shifting method is 25% higher than that of the three-step phase-shifting method. Subsequently, we also established a phase error model for the nonlinear response of the three-dimensional (3D) measurement system. Since the low measurement efficiency of the existing double N-step phase-shifting (DNPS) method, an improved double N-step phase-shifting (IDNPS) method is proposed. The RMSE of the compensated phase with IDNPS is approximately equal to that with DNPS, but the number of additional fringes with IDNPS is reduced to half that with DNPS. The total time cost of using IDNPS is reduced to 68.5% of using DNPS. Simulations and experiments are conducted to verify the validity of the theoretical analysis results.