## 3 Materials and Methods
### Experimental Design  
The effects of the energy density of water jet-guided laser \(I\), cleaning speed \(v\), cleaning line spacing \(L\)2 and laser pulse frequency \(f\) on the cleaning effect of water jet-guided quasi-continuous laser were studied by single-factor experiments. To achieve the purpose of efficient cleaning, a single cleaning process was adopted in this study. Figure 3 is a schematic diagram of the water jet-guided laser cleaning path. The surface cleaning area of the sample is a square of 10 mm \(\times\) 10 mm, and the laser spot overlap is according to the \"S\" path. The transverse overlap rate between the water jet-guided laser spots is set to \(\gamma_{1}\), and the longitudinal overlap rate is set to \(\gamma_{2}\). The transverse spot overlap rate is mainly determined by the laser pulse frequency and spot moving speed, while the longitudinal overlap rate is determined by the cleaning line spacing set by the computer control program.  
Figure 2: Schematic diagram of water jet-guided quasi-continuous laser cleaning equipment.  
The transverse spot overlap rate can be expressed as [33]:  
\[\gamma_{1}=\left(1-\frac{v}{f\times D}\right)\times 100\% \tag{1}\]  
The longitudinal spot overlap rate can be expressed as follows:  
\[\gamma_{2}=\left(1-\frac{L_{2}}{D}\right)\times 100\% \tag{2}\]  
The energy density of a water jet-guided laser is closely related to the laser power and laser pulse frequency. The laser energy density \(I\) can be expressed as follows:  
\[I=\frac{E}{S}=\frac{4E}{\pi\times D^{2}}=\frac{4\times P}{\pi\times D^{2} \times f} \tag{3}\]  
where \(E\) is the energy of a single pulse, \(S\) is the cross-sectional area of the water beam fiber, \(P\) is the average cleaning power of the water jet-guided laser, and \(D\) is the diameter of the water beam fiber.  
To quantitatively assess the surface quality of the water jet-guided laser cleaning area, the collected pictures of the cleaned area are binarized. Figure 4a,b show photos of the sample surface after water jet-guided laser cleaning and its binarized image, respectively. In addition to most of the silver-white areas that are clean, there are also some areas that appear yellow, brown, and black, namely residual resin-based coating and over-cleaning ablation marks. The cleanliness \(\eta\) was introduced as an important indicator to assess the quality of water jet-guided laser cleaning, which is expressed as follows:  
\[\eta=\frac{N_{c}}{N} \tag{4}\]  
where \(N\) is the total number of pixel points for calculating the binarized processed image, and \(N_{c}\) is the number of pixel points for calculating the white area (original substrate surface).  
Figure 3: Schematic diagram of the water jet-guided laser cleaning path.  
The cleaning rate \(U_{s}\) is introduced as an important indicator for evaluating the cleaning efficiency of the water jet-guided laser, and its expression is [34]:  
\[U_{s}=\frac{S_{c}}{t}=\frac{v^{2}}{fN_{t}} \tag{5}\]  
where \(S_{c}\) is the surface area of the sample cleaned by the water jet-guided laser, \(t\) is the cleaning time, and \(N_{t}\) is the minimum number of cleanings when cleanliness \(\eta\) reaches 90%.