# 3D Face Profilometry Based on Galvanometer Scanner with Infrared Fringe Projection in High Speed
## 3 Experiments
### Comparison of Measurement Accuracy in Different Phase Unwrapping Methods  
A static planar surface to evaluate the performance of this measurement system using different temporal phase unwrapping approaches is measured. The standard sample is a plane of marble surface with a 0.18-micron flatness.  
The distance between the plane marble surface and the camera ranged from 555 mm to 635 mm with a step size of 20 mm. On each position, the sinusoidal fringe patterns are projected onto the sample and modulate the surface, then the captured images are used to retrieve the absolute phase map (see Section 2.2) by a four-step phase-shifting method and temporal phase unwrapping algorithm.  
Figure 4: The experimental setup for this FPP measurement system, the projector of galvanometer scanner (MEMS) and digital light projector (DLP) are used to project fringe patterns, respectively. The experimental system uses one projector and one camera. (**a**) Experimental setup; (**b**) DLP projector; (**c**) Projected fringe by DLP; (**d**) MEMS projector; (**e**) Projected fringe by MEMS.  
Figure 5: The galvanometer scanner. (**a**) MEMS device; (**b**) Principle of laser scanner; (**c**) The relationship between current intensity and scanning angle.  
One of the captured fringe images is shown in Figure 6a. Combined with the structured light system calibration parameters, the plane 3D data can be reconstructed.  
Taking the measurement data of the first position as an example, the 3D plane data are reconstructed by using the methods of hierarchical and heterodyne as shown in Figure 6b,c, respectively. The comparisons are performed using the same cross-section of the 3D data, which is shown in Figure 6b,c with the black and red lines, respectively. In order better to see the error distribution, the 3D data of the two lines with the subtraction of their respective fitting line is presented. It can be seen that the measurement results using the method of heterodyne are slightly better than the method of hierarchical, as shown in Figure 6d. However, both datasets have a small curvature, which will be explained in the next section.  
The reconstructed 3D point cloud of the plane marble surface is fitted by a standard plane. The distances between the 3D points and this standard plane are calculated as plane measurement errors for the measurement accuracy evaluation. Figure 6e shows the measurement errors of the plane plate from Figure 6b. The measurement accuracy of the plane at five positions is shown in Table 1. These measurement results demonstrate that the FPP method implemented on this experimental scheme is capable to achieve an accuracy with a 0.2 mm standard deviation. The measurement error using the heterodyne method is smaller than the hierarchical method, so the heterodyne method will be chosen as the temporal phase unwrapping method in this structured light system in the following measurements.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Position**} & \multicolumn{2}{c}{**Standard Deviation (mm)**} \\ \cline{2-3}  & **Heterodyne** & **Hierarchical** \\ \hline
1 & 0.109 & 0.119 \\
2 & 0.125 & 0.130 \\
3 & 0.149 & 0.152 \\
4 & 0.148 & 0.173 \\
5 & 0.165 & 0.180 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The evaluation results of the plate plane.  
Figure 6: The measurement of a standard plane in the first position. (**a**) The one of the captured fringe; (**b**) 3D reconstruction result of the hierarchical method; (**c**) 3D reconstruction result of heterodyne method; (**d**) 3D measurement data of the same cross-section on the plane as shown in (**b,c**) with black and red lines, respectively. The z coordinate is the value of 3D measurement data minus the fitting line; (**e**) Measurement errors of the plane from data analysis as shown in (**b**).