A Fast Self-Correction Method for Nonlinear Sinusoidal Fringe Images in 3-D Measurement

Phase-shifting profilometry (PSP) is a method used to establish the pixel correspondence between a projector and a camera using phase-shifting fringe patterns. Due to the nonlinear intensity response of the captured images, nonlinear errors will be induced into the calculated phase and thus decrease the accuracy of 3-D measurement. In this article, we propose a fast self-correction algorithm to reduce the nonlinear phase error without the need for additional projections or precalibration. In this study, we derived an average intensity expression of the captured fringe images that contain the nonlinear response parameters. We can establish a set of equations with the known projection fringe information and unknown nonlinear parameters based on the captured fringe images at different frequencies used in the multifrequency heterodyne algorithm. Based on the equation set, the nonlinear response parameters can be solved for each pixel in the captured images, and the inverse function of the system response can thus be obtained and used to correct the actual nonlinear gray value. This pointwise correction algorithm can reduce the nonlinear phase error corresponding to different frequency fringe images without increasing the number of projections and with no excessive calculation time. Furthermore, this method can use small-pitch fringe patterns to improve the measurement accuracy while maintaining the reliability of the phase unwrapping. Experimental results show that the proposed method can eliminate the nonlinear phase error, improve phase unwrapping robustness, and achieve a high measurement quality for fast 3-D measurement through PSP.