# Online Phase Measurement Profilometry for a Fast-Moving Object
## 3 Experiment and Analysis  
In order to verify the feasibility and practicability of the proposed method, an online 3D measurement experimental system is built. As shown in Figure 3, the projector used in this experiment is PLED-W200 DLP, and the image collector is a SDI-C2010M camera, the highest frame rate of this camera is 60 fps when the image pixel size is 1920 \(\times\) 1080; in order to adapt the fast speed, we increase the frame rate to 100 fps while the pixel size is decreased to 256 \(\times\) 256. During this measurement, the object is driven from left to right by the electric translation platform Y100 SC01 at a fast speed, Through the previous experimental calibration, we measured that the relationship between pixels and the motion distance is approximately 1.245 mm/pixel. The entire image acquisition process is:  
1. The designed 5 frames of sinusoidal gratings with a shifting phase of \(2/5\pi\) are combined into a repeated video. 2. The projector projects the video onto the object. 3. Start the electric translation platform at a given speed. 4. Turn on the DLP frame synchronization signal to trigger the camera, thus achieving synchronous acquisition. 5. After 0.2 s, turn off the DLP frame synchronization. In this experiment, the frame rate of the video is 25 fps, and the frame rate of the camera is 100 fps. Thus, at the same work station, 4 frames (\(K\) = 4) of deformed patterns are captured. The image acquisition is real time, data processing is post-processing, and the data processing includes super-resolution reconstruction, obtaining equivalent deformed patterns and PMP 3D reconstruction. Because the iterative solution of the super-resolution reconstruction takes some time, and iteration time is related to hardware and data process mode, in future, we will use a better computer or adapt graphics processing unit (GPU) acceleration to speed up data processing. The proposed method is compared with the averaging method, and the experimental data are shown in Figure 4. Figure 4a is a measured object, which is a \"face\" model, and in this experiment, the speed of the object is 0.2 m/s. Figure 4b is a set of low-resolution deformed patterns captured at the first work station, which are \(I^{\prime\prime}\)11, \(I^{\prime\prime}\)12, \(I^{\prime\prime}\)13, \(I^{\prime\prime}\)14, and the pixel size is 256 \(\times\) 256. Figure 3: Experimental system. The reconstructed deformed patterns are shown in Figure 5, Figure 5a is _I\({}^{\prime\prime}\)_11, and it is regarded as a reference frame. The process of pixel matching is in Figure 5a,b. The points marked in Figure 5a are the selected feature points of _I\({}^{\prime\prime}\)_11, the other points marked in Figure 5b are the matching points of _I\({}^{\prime\prime}\)_14. The difference between the two set of points represents the movement of the \"face\". Then the estimated motion matrix, blur matrix and down-sampling matrix are used for subsequent iterations. In this experiment, the super-resolution factor \(q\) is 2, the max number of iterations \(m\) is 200. Figure 5c,d are the reconstructed results of the averaging method and MAP, respectively, and their pixel size is 512 \(\times\) 512. By comparison, it can be seen that the deformed pattern reconstructed by MAP is clearer, and there is no large motion blur. At the same time, compared with the original low-resolution deformed pattern, the deformed pattern reconstructed by MAP has a good effect on noise suppression. Figure 5e,f are the enlargements of the rectangular areas of Figure 5c,d, respectively. Compared with Figure 5e, Figure 5f has a clearer edge, which further indicates that noise is reduced effectively using MAP. Figure 4: Measured data of “face” model: (**a**) Measured object; (**b**) A set of deformed patterns.