# Online Phase Measurement Profilometry for a Fast-Moving Object
## 3 Experiment and Analysis
Figure 5: Low-resolution deformed patterns and super-resolution reconstructions: (**a**) Reference; (**b**) _I\({}^{\prime\prime}\)_14 with matching points; (**c**) Reconstruction by averaging; (**d**) Reconstruction by MAP; (**e**) Enlargement of rectangular area in (**c**); (**f**) Enlargement of rectangular area in (**d**). In the same way, high-resolution deformed patterns of the other four work stations can also be obtained, and the reconstructed results are shown in Figure 6. Figure 6a shows five frames of high-resolution deformed patterns reconstructed by the averaging method, and Figure 6c shows five high-resolution deformed patterns reconstructed by the proposed method, which are \({{}^{\prime}}{{}^{\prime}}{{}_{1}}{{}^{\prime}}{{}_{2}},{{}^{\prime}}{{}^{\prime}}{{} _{3}},{{}^{\prime}}{{}^{\prime}}{{}_{4}},{{}^{\prime}}{{}_{5}}\). In Figure 6a,c, the marked dotted line shows that the position of the object in each frame is not the same. We adopt optical flow [24] to obtain equivalent deformed patterns, and the results are shown in Figure 6b,d. The pixel size of Figure 6b,d is 458 \(\times\) 512, and in Figure 6b,d, the position of the object in each frame is the same. Figures 6e and 6f are, respectively, the experimental results of PMP 3D reconstruction using Figure 6b,d. From Figure 6e,f, it can be seen that the reconstructed result by the proposed method is better than that by the averaging method, and the phase information is more complete. At the same time, in order to better analyze the measuring results of the proposed method, the measuring result of eight-step PMP [25] is taken as the quasi truth value, and the eight-step PMP is taken for the same but stationary object. Figure 7 shows the 255 th column sectional view of the reconstructed 3D profile of the object with different methods. Figure 6: Experimental results for “face” model, pixel size of Figure 6a,c is 512 \(\times\) 512, pixel size of (**b,d**) is 458 \(\times\) 512: (**a**) High-resolution deformed patterns by averaging; (**b**) Equivalent deformed patterns by averaging; (**c**) High-resolution deformed patterns by the proposed method; (**d**) Equivalent deformed patterns by the proposed method; (**e**) Object reconstruction by averaging; (**f**) Object reconstruction by the proposed method. Figure 7b is the enlargement of Figure 7a forehead (rectangular area). The dot-and-dash line is the result of the eight-step PMP, the dotted line is the result of the averaging method, and the solid line is the result of the proposed method. As can be seen from Figure 7a, the reconstructed result of the proposed method is closer to that of the eight-step PMP, and better than that of the averaging method. As can be seen from the details shown in Figure 7b, the results of the proposed method are also very close to those of the eight-step PMP. The reconstructed result of the proposed method is better than that of the averaging method, either in the whole or in the detail. The experimental results indicate that the proposed method can improve the resolution while preserving the details of the object. In order to further verify the applicability of the proposed method, this experiment used a more complex model, a \"snail\" model, and the speed of the object is 0.5 m/s, super-resolution \(q\) = 2, the max num of the iterators \(m\) is 200. The experimental data and the results of the comparison experiment are shown in Figure 8. Figure 8a, Figure 8b, and Figure 8c are one frame of the high-resolution deformed patterns obtained by the averaging method, proposed method and eight-step PMP, respectively. Figure 8d-f show the corresponding wrapped phases, and they are obtained by calculating all equivalent deformed patterns, and through phase unwrapping and height mapping, the reconstructed results are shown in Figure 8g-i. It also can be seen that motion blur in Figure 8b is less than that in Figure 8a; The wrapped phase in Figure 8e is clearer than that in Figure 8d and is closer to that in Figure 8f.