Fig. 1. Top view of schematic diagram of dual-frequency light-source-stepping method (LSSM)

Fig. 2. Diagrams of the overall system structure and algorithm workflow. (a) Acquisition of dual-frequency single-frame fringe patterns; (b) generation of dual-frequency three-step phase-shifting fringe patterns based on neural networks; (c) 3D reconstruction

Fig. 3. Simulation of LED light source array and planar grating. (a) LED light source array with errors; (b) planar Ronchi grating model

Fig. 4. Simulated high-frequency three-step phase-shifting fringe patterns with errors and the corresponding spectrum. (a1)‒(a3) High-frequency fringe patterns; (a4) normalized intensity curves along the red dashed line in Figs. 4(a1)‒(a3); (b) spectrum of Fig. 4(a1); (c) spectrum cross-sectional line in the center row of Fig. 4(b)

Fig. 5. Absolute phase maps (in radian) of simulated fringe patterns on the reference plane. (a) Absolute phase map obtained by the traditional dual-frequency three-step phase-shifting method; (b) absolute phase map obtained by GVFPS method; (c) phase demodulation error curves along cross-section marked by the red dashed lines

Fig. 6. Three-step phase-shifting fringe deformed patterns output by Res-Unet and their reference ground truth. (a1)‒(a4) Three-step phase-shifting fringe deformed patterns output by the Res-Unet and the normalized intensity curves along the red dashed line; (b1)‒(b4) three-step phase-shifting fringe deformed patterns of the reference ground truth and the normalized intensity curves along the red dashed line

Fig. 7. Absolute phase and the corresponding residual error maps (in radian) of the simulated peak-valley-like object obtained by the traditional dual-frequency three-step phase-shifting method and the proposed method. (a)(c) Traditional dual-frequency three-step phase-shifting method; (b)(d) proposed method; (e) phase demodulation error curves along cross-section marked by the red dashed lines

Fig. 8. Experimental testing device. (a) Overall setup diagram; (b) side view of dual-frequency LSSM projector

Fig. 9. Comparison of fringe patterns for a planar object. (a1)‒(a3) Output of the pre-trained Res-Unet; (a4) normalized intensity curves along the red dashed line; (b1)‒(b3) reference ground truth fringe patterns; (b4) normalized intensity curves along the red dashed line

Fig. 10. Height maps of the planar object obtained by different methods. (a) Height map obtained by the traditional dual-frequency three-step phase-shifting method; (b) height map obtained by the proposed method; (c) comparison curves of height errors along the red dashed lines

Fig. 11. Comparison of fringe patterns for a plaster statue. (a1)‒(a3) Output of the pre-trained Res-Unet; (a4) normalized intensity curves along the red dashed line; (b1)‒(b3) the reference ground truth fringe patterns; (b4) normalized intensity curves along the red dashed line

Fig. 12. Height and corresponding error maps of the plaster statue obtained by different methods. (a)(c) Traditional three-step phase-shifting method; (b)(d) proposed method; (e) comparison curves of height errors along the red dashed lines

Table 1. Architecture and parameters of the Res-Unet neural network