## 3 Simulation  
In order to explain the effectiveness of the proposed method, a simulation was carried out. Because we only projected red and blue stripes, the response of three channels in the color camera can be described with Equations (4)-(6):  
\[I_{r}(x,y)=\alpha_{rr}I_{pr}(x,y)+\alpha_{br}I_{pb}(x,y) \tag{4}\]  
\[I_{g}(x,y)=\alpha_{rg}I_{pr}(x,y)+\alpha_{bg}I_{pb}(x,y) \tag{5}\]  
\[I_{b}(x,y)=\alpha_{rb}I_{pr}(x,y)+\alpha_{bb}I_{pb}(x,y) \tag{6}\]  
\(I_{r}(x,y)\), \(I_{g}(x,y)\), and \(I_{b}(x,y)\) represent the images of three channels, respectively. \(I_{pr}(x,y)\) and \(I_{pb}(x,y)\) indicate the red and blue stripes we projected. \(\alpha_{rr}\) is the response coefficient of the red channel to the red projection. \(\alpha_{br}\) is the response coefficient of the green channel to the red projection. \(\alpha_{bg}\) is the response coefficient of the green channel to the red projection. \(\alpha_{bg}\) is the response coefficient of the blue channel to the red projection. \(\alpha_{bb}\) is the response coefficient of the blue channel to the blue projection. We set \(\alpha_{rr}\) and \(\alpha_{bb}\) as 0.8; \(\alpha_{rg}\) as 0.2; and \(\alpha_{bg}\), \(\alpha_{br}\), and \(\alpha_{rb}\) as 0.03. The red fringe was vertical and the blue fringe was horizontal so they could be easily distinguished. Figures 3 and 4 show the results. The images measured 1140 \(\times\) 912 pixels, which is consistent with the resolution of the projector we used.  
As shown in Figures 3 and 4, both low-frequency superimposed grating and high-frequency superimposed grating were separated well.  
Using Equations (2) and (3), we unwrapped the wrapped phase. As shown in Figures 5 and 6, the wrapped phase was unwrapped as an absolute phase successfully, and the cross profiles had good linearity. The simulation results revealed that color cross-talk between the red and blue channels did not affect the phase. We then simulated the three-dimensional measurement. The measured object was a hemisphere with a radius of 300 mm, as shown in Figure 7, and the spatial scale of the image was set to 1 mm/pixel. Figure 8 shows the simulation of the phase image captured by the camera, where (a) is the low-frequency phase-shifting image, and (b) is the high-frequency phase-shifting image, and they were all added color crosstalk. Based on the proposed method, we acquired the measurement results from the left (red) and right (blue) projection. We then fit the hemisphere with 3D data.  
Figure 4: High-frequency fringe superposition and separation: (**a**) superimposed fringe; (**b**)red-channel image; (**c**) blue-channel image; (**d**) cross profile of (**b**); (**e**) cross profile of (**c**).  
Figure 3: Low-frequency fringe superposition and separation: (**a**) superimposed fringe; (**b**)red-channel image; (**c**) blue-channel image; (**d**) cross profile of (**b**); (**e**) cross profile of (**c**).  
Figure 5: Red-channel image phase unwrapping: (**a**) low-frequency wrapped phase; (**b**) high-frequency wrapped phase; (**c**) unwrapped phase; (**d**) cross profile of (**a**); (**e**) cross profile of (**b**); (**f**) cross profile of (**c**).  
Figure 6: Blue-channel image phase unwrapping: (**a**) low-frequency wrapped phase; (**b**) high-frequency wrapped phase; (**c**) unwrapped phase; (**d**) cross profile of (**a**); (**e**) cross profile of (**b**); (**f**) cross profile of (**c**).