Four-step phase-shifting nonlinear error self-correction method

In structured light projection three-dimensional measurement systems, the phase error caused by the nonlinear response of the projector greatly affects measurement accuracy. We propose a phase self-correction method for the commonly used four-step phase-shifting method. In fringe projection profilometry, the phase error of the fringe harmonics exhibits periodic characteristics. To compensate for this phase error, we only need to obtain the phase shifted by half a period with respect to the phase error. Therefore, we introduce an additional phase based on the compensation formula to address the nonlinear error in the four-step phase-shifting method. Then, to make the additional phase compensation to the uncorrected original phase, we shift the additional phase by a certain pixel displacement. Finally, by combining the shifted additional phase with the four-step phase-shifting phase, we can eliminate the nonlinear error. This method effectively reduces the impact of the projector’s gamma effect on the measurement results and is simple to implement without complex pre-processing. Multiple experiments have verified the feasibility and reliability of the proposed method. The experimental results show that the proposed method can effectively eliminate nonlinear errors in measurement systems.