## 4 Experimental Setup  
To test the proposed method in real condition, a fringe projection system was set up. The system consisted of a projector (Light Crafter 4500) with resolution of 912 \(\times\) 1140 pixels, and a camera (IOI Flare 2M360-CL) with resolution of 1280 \(\times\) 1024 pixels. A flat board was placed at the closest depth plane of the measured volume, and used as the reference plane. Two isolated objects were selected as the measured objects. Total four patterns, including three phase-shift patterns and one coded pattern, were projected onto the reference plane and the measured objects by the projector, and sequentially captured by the camera.  
Figure 9a-c shows three phase-shift patterns projected onto the reference plane, respectively. Figure 9d shows the corresponding wrapped phase. Figure 9e shows the fringe order, also regarded as the minimum fringe order map \(k_{min}\). Figure 9f shows the absolute phase map also regarded as the minimum phase map \(\Phi_{min}\). Similarly, Figure 10a-c shows the images of three phase-shift patterns projected onto the measured objects, respectively. Figure 10d shows the corresponding wrapped phase map calculated from the three phase-shift patterns. Meanwhile, the average intensity and intensity modulation were calculated. Figure 10e shows the coded pattern with \(N=4\), and Figure 10f shows the corresponding code word map.  
In order to compare the proposed method and [PERSON]'s method, Equations (12) and (14) were both used for computing fringe order. Figure 11a,b shows the fringe order maps recovered by the two methods. As we can see, the proposed method recovered the fringe order map \(\Phi\) correctly; however, [PERSON]'s method led to the wrong fringe order map \(\Phi^{\prime}\) at some areas. There are obvious differences between the two fringe order maps within the two circular areas plotted in Figure 11. The pixels of the  
Figure 8: A 3D reconstruction of the hemisphere. (**a**) The proposed method; (**b**) [PERSON]’s method.  
Figure 9: Images of the reference plane. (**a–c**) Phase-shift patterns; (**d**) wrapped phase map; (**e**) minimum fringe order map \(k_{min}\); (**f**) minimum phase map \(\Phi_{min}\).  
same stripe had the same fringe order \(k\) in Figure 11a. However, the pixels of the same stripe had a different fringe order \(k^{\prime}\) in Figure 11b.  
For better illustration, Figure 12a,b shows the 600 th rows of the two fringe order maps and absolute phase maps. Clearly, \(\Phi-\Phi_{min}<8\pi\) and \(\Phi^{\prime}-\Phi_{min}<2\pi\). This indicates that the maximum depth range of the proposed method is up to \(8\pi\), and that of [PERSON]'s method is only \(2\pi\). Therefore, the proposed method can obtain much larger depth range than [PERSON]'s method. Finally, we reconstructed the 3D shapes of the two isolated objects, as shown in Figure 13.  
Figure 11: Fringe order maps. (**a**) The proposed method; (**b**) [PERSON]’s method.  
Figure 12: The 600 th rows. (**a**) Fringe order maps; (**b**) absolute phase maps.  
Figure 10: Images of the measured objects. (**a**–**c**) Phase-shift patterns; (**d**) wrapped phase map; (**e**) coded pattern; (**f**) code-word map.