In fringe-projection profilometry (FPP), the accuracy of phase extraction significantly affects the quality of three-dimensional (3D) reconstruction, whereas the acquisition speed of deformed fringe patterns is directly related to the efficiency of the entire reconstruction process. The light-source-stepping method (LSSM) has been widely investigated owing to its advantages of rapid projection and low cost. However, existing LSSM setups are inevitably accompanied by some errors, e.g., phase-shifting error, light intensity fluctuation error, and high-order harmonics, which significantly reduce the accuracy of phase retrieval. Moreover, most current error-suppression algorithms rely on iterative calculation, where the retrieved phase accuracy is improved at the expense of speed. Hence, this study is conducted to achieve the rapid generation of high-quality phase-shifting fringe patterns based on neural networks, thereby enabling high-precision 3D reconstruction.
In this study, instead of using a normal dual-frequency LSSM setup, a novel technique utilizing two Res-Unet neural networks is proposed to acquire high-quality dual-frequency three-step phase-shifting fringe patterns for 3D measurement. This technique employs high-quality three-step phase-shifting fringe patterns synthesized using the general variable-frequency phase-shifting (GVFPS) algorithm based on our previous study as the ground truth to train the two Res-Unet networks with error-suppression capability. Using the classical three-step phase-shifting and dual-frequency phase unwrapping algorithms in conjunction with system calibration, the measured object’s height can be recovered accurately and efficiently.
The simulation results (Figs. 5 and 7) show that the GVFPS method significantly improves the phase-retrieval accuracy and the high-quality dual-frequency three-step phase-shifting fringe patterns can be generated by integrating it with the two Res-Unet neural networks. Furthermore, the effectiveness of the proposed method was validated by processing fringe patterns captured via a self-designed LSSM setup. In a planar scenario, the root mean square error (RMSE) and peak-to-valley (PV) of the height errors obtained using the classical dual-frequency three-step phase-shifting method and the proposed method are 0.3616 and 0.0773 mm, and 1.4286 and 0.4914 mm, respectively (Fig. 10). Meanwhile, in a plaster statue scenario, the RMSE and PV of the height errors obtained using the classical dual-frequency three-step phase-shifting method and the proposed method are 0.2907 and 0.0972 mm, and 1.6268 and 1.0217 mm, respectively (Fig. 12). Notably, although the Res-Unet neural network and phase-height mapping model adopted in this study can be further improved, they do not affect the validation and demonstration of the effectiveness of the proposed technique. Additionally, the dual-frequency virtual three-step phase-shift method demonstrated via simulations and experiments can be extended to virtual multistep phase-shifting fringe patterns with more frequencies, thereby further improving the testing accuracy of three-dimensional morphologies.
To overcome the disadvantages of the existing dual-frequency LSSM setup, this study proposes a dual-frequency virtual-stepping FPP driven by a neural network, which offers the advantages of low cost, simple and compact structure, as well as rapid acquisition and demodulation of fringe patterns. Simulation and experimental results show that compared with the existing dual-frequency three-step phase-shifting algorithm, the proposed method achieves higher measurement accuracy when projecting only dual-frequency single-frame fringe patterns, with the RMSE reduced by 66.6%.