## 2 Experiments and Measurement Methods
Next, the sample was shallowly etched with 5% hydrofluoric (HF) acid, which should be undertaken for 10-15 min to fully remove the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Sample**} & \multicolumn{5}{c}{**Grinding Experimental Parameters**} \\ \cline{2-6}  & **Grain Size** & **Cutting** & **Depth of Cut** & **Workpiece** & **Workpiece** \\  & **(\(\upmu\)m)** & **Speed (m/s)** & **(\(\upmu\)m)** & **Rotation Speed** & **Feed Speed** \\  & & & & **(\(\upmu\)m)** & **(\(\upmu\)m)** \\ \hline \#1 & & 19.6 & 1 & & \\ \#2 & & 19.6 & 2 & & \\ \#3 & & 19.6 & 3 & & \\ \#4 & 5 & 19.6 & 4 & 20 & 1 \\ \#5 & & 3.9 & 1 & & \\ \#6 & & 11.7 & 1 & & \\ \#7 & & 19.6 & 1 & & \\ \hline \hlinehydrolytic layer and expose the subsurface defects, which is conducive to microscopic observation. After HF shallow etching, the one-dimensional profile measurement of the surface wedges of the sample was carried out, and the midline profile of the MRF wedges was measured by a high-precision three-dimensional profiler (as shown in Figure 2b) to obtain position information corresponding to different depths. Finally, the samples were placed in the damage precursor multimodal measuring instrument to investigate the laser damage characteristics of each sample at different depths on the subsurface. The instrument contains two test modules, the photothermal weak absorption and the in situ fluorescence confocal imaging. It should be noted that the photothermal weak absorption has a strong correlation with the laser-induced damage threshold of fused silica optics under ultra-violet laser irradiation [27]. By comparing the subsurface photothermal absorption value of fused silica optics, the increase or decrease in the subsurface laser damage performance of fused silica optics can be obtained easily. Hence, photothermal weak absorption analysis as a non-destructive testing method can be used to predict the laser damage performance of ground subsurface [28; 29; 30]. Fluorescence confocal imaging is also a powerful tool to measure low subsurface damage on ground fused silica [31]. The testing steps in the damage precursor multimodal measuring instrument were as follows:  
(1) The photothermal weak absorption was tested in the MRF wedge area on the samples. In the photothermal weak absorption test, the wavelength of the pump laser was 355 nm, the power of the pump light was 4 W, the test mode was transmission mode, the step interval was 50 \(\upmu\)m, and the scanning area was covered with MRF wedges. The accuracy of the test was approximately 0.1 ppm. After setting the test parameters, one can start the module to complete the photothermal weak absorption detection. (2) The in situ fluorescence confocal imaging was conducted along the central axis of MRF wedges on the samples to obtain the evolution of subsurface damage in the depth direction. The fluorescence confocal imaging objective lens had a magnification of 20\(\times\) with a field of view of 120 \(\upmu\)m \(\times\) 120 \(\upmu\)m and the laser power was 40 mW. After setting the test parameters, one can read historical photothermal data from (1) mentioned above and select the positions along the central axis of the MRF wedge for continuous scanning imaging to complete the test. The repeated positioning accuracy was about \(\pm\)1 \(\upmu\)m and the defect detection resolution was approximately 1 \(\upmu\)m. Continuous scanning imaging is constantly updating fluorescence confocal images in real-time in this module. The characterization techniques for the ground subsurface were carried out using two test methods: photothermal weak absorption and fluorescence confocal imaging to obtain laser damage characteristic information, which is helpful for establishing the correlation relationship between subsurface depth, subsurface damage and laser damage characteristics after grinding, ending up with a new subsurface damage depth prediction method based on the laser damage characteristic information proposed. Figure 1: The UPL-450 ultra-precision three-axis grinder.