## 3 Experiments and Analysis
### Experiments and Analysis  
Many experiments measuring the 3D shape of many objects with the proposed method were carried out. Figure 4 shows one of the experimental results. Here, the face model shown in Figure 4a is used to be measured. Figure 4b shows the color fringe pattern that is caused by a reference plane, which is shown in Figure 3, captured by color camera, and the single-frame color deformed pattern of the measured object is shown in Figure 4c. The three-frame monochromatic fringe patterns demodulated in tricolor channels of the single-frame captured color fringe pattern are shown in Figure 4d-f and the three-frame monochromatic deformed patterns demodulated in tricolor channels of the single-frame captured color deformed pattern are shown as Figure 4g-i. Due to the overlapping among tricolor channels, the issues of the existence of sensitivity differences and color crosstalk are unavoidable. The experimental data show that the above issues exist and seriously introduce some errors in phase resolution. Thus, we need to correct the monochromatic phase-shifting deformed patterns before calculating the phase to reduce the errors introduced by the existences of sensitivity differences and color crosstalk. The existences of sensitivity differences and color crosstalk among these monochromatic phase-shifting deformed patterns are corrected by the proposed method. The reference plane background image before gray imbalance correction is shown in Figure 5a; the reference plane background image after gray imbalance correction is shown in Figure 5b; the background image of the measured object before gray imbalance correction is shown in Figure 5c; and the background image of the object after gray imbalance correction is shown in Figure 5d. After comparison and analysis, we found that, by using the proposed method to correct the background, the errors caused by the existence of sensitivity differences and color crosstalk are further reduced. It must be pointed out that some blurriness in the corrected background image of measured object is caused because of the filtering process. Therefore, the proposed method has some disadvantages in measuring sharp objects. Figure 3: Experimental system. Figure 6a shows the corresponding wrapped phase calculated by these monochromatic deformed patterns after correction. The reconstructed result of the measured face model is shown in Figure 6b. It is clearly shown that the 3D shape of measured face model is well restored, and this reconstructed result proves the feasibility of the proposed method in measurement of 3D shape. The restored result by the eight-step PMP was chosen as the quasi-truth value to analyze measurement accuracy of the proposed method. Then, a comparison experiment between the traditional color PMP and the proposed method was carried out. Figure 4: Experimental data: (**a**) measured object; (**b**) color fringe pattern; (**c**) color deformed pattern; (**d**–**f**) the demodulated monochromatic fringe patterns of R, G, and B; and (**g**–**i**) the demodulated monochromatic deformed patterns of R, G, and B.  
Figure 5: Gray imbalance correction: (**a**) reference plane background image before correction; (**b**) reference plane background image after correction (**c**) background image of the measured object before correction; and (**d**) background image of the measured object after correction. Figure 7 shows the 547 th column data of the reconstructed result by these methods. The reconstructed result of measured face model by the eight-step PMP is shown as a dotted line in Figure 7. The reconstructed result of measured object by the traditional single-shot color PMP is shown as a chain line in Figure 7. The reconstructed result of measured object by the proposed method is shown as a solid line in Figure 7. It is obvious that the reconstructed 3D shapes of the measured object with all three methods are well achieved. As is known, the large-step PMP has very high efficiency and measuring accuracy.