## 2 Autostereoscopy-Raman Spectrometry-Based Measurement Methodology  
The autostereoscopic 3D metrology method [27] makes use of a micro lens array (MLA) that is incorporated into a single-lens imaging system to capture the raw 3D information of the measured surface in a single snapshot. As a machine vision-based measurement method which uses pixel information as the main medium, the diversity of pixel information distribution (PID) determines the resolution in regard to the matching process. Here, the diversity of PID can be interpreted as certain regional pixel information has pixel values within a large range. In the recording process, the principle of autostereoscopic 3D metrology method system, they use EIs that contain multi-viewpoint stereo information to record spatial targets. As shown in Figure 1, the virtual MLA simulated in computer and a 3D reconstruction algorithm are applied to calculate and rebuild the target in object space. By applying this special digital process, the target 3D information can be obtained quickly and easily, and it is more convenient to handle following measurement data [27; 28]. The 3D target reconstructed by computed depth tomography algorithm (CDTA) is overlapped by a series of sharp depth slices. This process consists of three steps. First, the depth slices are obtained by re-mapping of the pixels from each EI. Second, the clear parts of depth slices are extracted by calculating sharpness function of each pixel. Finally, the clear parts are spliced to realize the reconstruction of the 3D target. Specifically, to obtain image sequence of depth slices is a process of re-mapping the pixels of EIs by virtual MLA. It is an inverse process of recording. It projects each 2D EI onto a special depth plane in object space through optical axis of its respective elemental lens. In the image of a certain depth slice, only the object points belonging to the corresponding depth are clear, while the foreground and background are blurred, because this certain depth is finely focused and other depth planes are defocused. Based on the description of the recording process, the disparity can only be determined by the depth information in the object space. In other words, the disparity of the same depth plane is invariable, and the disparity of different depth planes is variable. In the reconstructed image sequence of depth slices, different points have different focus levels and show as discs of confusion or focus points on a certain slice. The optimum  
Figure 1: Working principle of reconstruction process. focus position of a point in depth can be determined by calculating the maximum focus level of each point. The sharpness function \(F\) is used to evaluate the focus level of a point, and it depends on the gray difference contained in the point and its small local neighborhood, in which the size is generally \(3\times 3\), \(5\times 5\) and \(7\times 7\). As shown in Figure 1, using the \(3\times 3\) neighborhood for example, \(k\in K\), \(K\) is the total number of image sequence, \(I_{k}(i,j)\) is the gray value of pixel \((i,j)\) in \(k\)th slice, \((i,j)\in(x,y)\), and \((x,y)\) means the region of EI. The center distance of consecutive pixels in the horizontal and vertical directions is normalized to \(1\), and the center distance of diagonal direction is normalized to \(\sqrt{2}\). \[ \begin{array}{l}F_{k}(i,j)=[|I_{k}(i,j)-I_{k}(i-1,j)|+|I_{k}(i,j)-I_{k}(i+1,j )|+|I_{k}(i,j)-I_{k}(i,j-1)|+|I_{k}(i,j)-I_{k}(i,j+1)|]+\\ \frac{1}{\sqrt{2}}[|I_{k}(i,j)-I_{k}(i-1,j-1)|+|I_{k}(i,j)-I_{k}(i+1,j-1)|+|I_{ k}(i,j)-I_{k}(i-1,j+1)|+|I_{k}(i,j)-I_{k}(i+1,j+1)|].\end{array}