Fig. 1. 3D measurement principle of multifrequency fringe projection profilometry

Fig. 2. Influence of gamma nonlinearity on fringes and phase. (a) Grayscale of fringes obtained from different gamma distortions; (b) ideal and real phases

Fig. 3. gamma distribution

Fig. 4. Fringe patterns and corresponding phase errors under different degrees of defocus. (a) Defocus 0; (b) defocus 1; (c) defocus 2; (d) phase error 0; (e) phase error 1; (f) phase error 2

Fig. 5. Schematic diagrams for solving the phase gradient threshold. (a) Fringe pattern of the standard board; (b) unwrapped phase of the standard board; (c) a column of the unwrapped phase

Fig. 6. Step block phase partitioning. (a) Step block under blank projection; (b) unwrapped phase of the step block; (c) step block Mask1; (d) step block Mask2; (e) step block Mask

Fig. 7. Experimental system

Fig. 8. Results of phase error before and after correction. (a) Comparison of phase errors; (b) local amplification of phase errors

Fig. 9. Step block 3D reconstruction. (a) High-precision ceramic step blocks; (b) original reconstruction point cloud of the step block

Fig. 10. Point cloud results before and after step block correction. (a) Reconstruction result after the global correction; (b) reconstruction result after the regional correction

Fig. 11. Standard sphere reconstruction and fitting results. (a) Standard baseball bat; (b) uncorrected (RMSE is 0.039 mm); (c) Hilbert transformation method (RMSE is 0.031 mm); (d) iterative fitting method for light intensity curve (RMSE is 0.027 mm); (e) global corrected (RMSE is 0.035 mm); (f) regional corrected (RMSE is 0.026 mm)

Fig. 12. Statue reconstruction. (a) Statue; (b) uncorreected; (c) Hilbert transformation method; (d) iterative fitting method for the light intensity curve; (e) global corrected; (f) regional corrected