## 2 Measurement Principle  
The 3D-DIC technique is generally believed to be one of the most effective full field strain/surface shape measurement methods [33; 41; 34]. Although 3D surface deformation measurement can be easily achieved using 3D-DIC method with satisfactory accuracy, the direct application of such a technique to the measurement of anodes in LIBs is still challenging, because the traditional 3D-DIC method depends on binocular vision technique using various imaging devices. Commonly used methods of 3D reconstruction with a single imaging device, such as structured light projection (SLP) and laser scanning can simply measure the 3D surface shape instead of 3D deformation. To achieve genuine 3D deformation determination, extra in-plane displacement measurement must be introduced and combined. In the current study, the authors employ such a strategy by combining the in-plane (2D) DICmethod with laser scanning using an LCSM system. The imaging principle of the system is illustrated in Figure 1.  
As shown in Figure 1, an LCSM system has the ability to offer grey level images of 256 bits describing the in-plane features and to scan the electrode surface describing the surface shape, simultaneously. However, the in-plane displacement distribution obtained by the DIC method and the 3D surface shape by laser scanning are coupled. The key issue here is to decouple such information. The decoupling process can be described as follows:  
1. Images of 256 bit grey-level in laser mode and the surface shape data of the tested electrode are simultaneously captured with an LCSM before the electrode deforms, expressed as \(I(x,y)\) and \(Z(x,y)\), respectively. Note that \(I(x,y)\) which denotes the grey-level values distribution and \(Z(x,y)\) which denotes the height values distribution are the functions of the in-plane coordinate values \((x,y)\).
2. Images of 256 bit grey-level (in color mode) and the surface shape data (in laser mode) of the tested the electrode are simultaneously captured after the electrode deforms, expressed as \(I^{\prime}(x,y)\) and \(Z^{\prime}(x,y)\), respectively.
3. In-plane displacement distribution of the electrode surface can be determined with color mode images by DIC technique. The displacement along two mutually perpendicular directions can be expressed as \(u(x,y)\) and \(v(x,y)\), respectively.
4. The 3D surface is shifted back to its original location (before it deforms) by subtracting the in-plane displacement distribution values, rewritten as \(Z^{\prime}(x-u,y-v)\).
5. Decoupled out-of-plane displacement by subtracting \(Z(x,y)\) from \(Z^{\prime}(x-u,y-v)\). The decoupled out-of-plane displacement is written as \(w(x,y)\).  
Through the above five steps, a genuine 3D deformation measurement is achieved. The overall measurement principle can be summarized and illustrated in Figure 2.  
The measurement principle, the algorithm and other details of the traditional DIC/3D DIC technique have been discussed in a series of articles [33; 34; 41]. Hence, in the current study the relevant contents of DIC are not repeated.  
The theoretical error of the 3D deformation calculated according to the method shown in Figure 2 is as follows: displacement sensitivity is about 0.005 to 0.05 pixels, and strain sensitivity is about 50 to 100 microstrains.  
Figure 1: Imaging principles of the LCSM for in-plane images and surface shape.