## 4 Discussion  
To find a way out of the three dilemmas in existing empirical models of subsurface damage prediction, damage precursor multimodal measurement technologies were introduced into the detection of subsurface damage in ultra-precision grinding, and the subsurface damage depth results were different from previous subsurface crack results. It can be seen that the three defect depths generally have a relationship of SSD > SSD(crack) > SSD(cluster). The subsurface damage cluster depth is determined by the cluster crack depth, so it is usually the smallest one. Except for samples #3 and #4, the maximum depth of subsurface damage determined by the damage precursor multimodal tester was generally greater than the subsurface crack depth obtained by microscopic observation. [PERSON], [PERSON] and other scholars also found a similar phenomenon [10; 11]. Having chosen the constant chemical etching rate method and the angle polishing method to measure the subsurface damage depth, [PERSON] found that the former measurement's result was greater than the latter's. He believed that the measurement deviation was caused by the residual stress layer under the crack layer [11]. [PERSON] used the constant chemical etching rate method to measure the existence of a subsurface residual stress layer with a thickness of 10-20 \(\upmu\)m after rough grinding using the #120 grinding wheel and the #80 grinding wheel [10]. However, there is no evidence in their study to suggest that the residual stress layer can cause additional laser absorption, and the residual stress layer actually affects the laser damage performance of optics. Under ultra-precision grinding conditions here, there is also a metamorphic layer under the subsurface crack. The metamorphic layer contains residual stress and even some other damage precursors that will cause additional absorption. The grinding parameters affect the thickness of the metamorphic layer and the crack depth. The thickness of the metamorphic layer is equivalent to the thickness of the subsurface crack, both of which are in the micron range. Hence, it is not comprehensive to characterize the subsurface damage depth only by the maximum crack depth. The subsurface damage layer is constituted by the metamorphic layer and the subsurface crack layer together. The actual subsurface damage layer depth is approximately:  
\[SSD=(1.20\sim 1.95)\times SSD_{(crack)} \tag{1}\]  
\[SSD=(2.00\sim 4.22)\times SSD_{(cluster)} \tag{2}\]  
The introduction of the damage precursor multimodal test method allows for characterization not only including subsurface cracks but also other absorbent damage precursors, resulting in obtaining maximum depths of subsurface defects. It should be noted that the anomalies (SSD less than SSD(crack)) seen in samples #3 and #4 may be due to the limitations of the MRF spot method. The irregular distribution of grinding-induced subsurface damage necessitates a certain scale within characterization methods to obtain relatively accurate maximum damage depth results. While the MRF spot method has a measurement area spanning several millimeters, outcomes obtained through this method only represent local maximum values. As depicted in Figures 3 and 4, there is an exponential decrease in density of grinding-induced subsurface damage as depth increases, indicating that deeper damage is sparse and exhibits randomness. When the depth of the clustered defects is exceeded along the central axis produced by the MRF spot method, the grinding defects are distributed in a sporadic pattern, which is very likely to result in the phenomenon that there are no defects on the central axis, but there are defects in the adjacent regions at similar depths. This caused the small depth of subsurface damage in the damage precursor multimodal measurements for samples #3 and #4. The sporadic distribution of grinding defects at depth makes it very difficult to identify the maximum depth defects, and there is also a risk of significant deviation from the actual subsurface damage depth in the measurement results.