## 3 Results and Discussion
### Critical Point of Interval Time  
Figure 5a,b depicts the relationship between \(r_{eb}\) (on the y-axis) and varying levels of interval time and energy. Figure 5a is derived from a dataset of 90 samples, displaying data for three distinct interval times and five energy levels, resulting in a total of 15 boxes. Within each box, the mean is denoted by a blue diamond. Notably, blue diamonds with the same energy level are connected, forming five distinct lines. Each line connects three means corresponding to the same energy level.  
In contrast, Figure 5b is acquired from a dataset of 48 samples and presents data for two energy levels and four unique interval times, yielding a total of eight boxes. Similarly,  
Figure 5: Box plot of (**a**) 90-sample dataset; (**b**) 48-sample dataset; (**c**) 90-sample dataset with bit, bit/\(\sqrt{2}\), and bit/\(\sqrt{2}\) groups specified. (Note: \"\(\cdots\) notation stands for the power of a number).  
the blue diamond represents the mean within each box. In this figure, two lines connect the means of the same energy level.  
In both figures, there is a clear upward trend, indicating that as both interval time and energy level increase, \(r_{eb}\) tends to also increase.  
To visualize the bit, bit/\(\sqrt{2}\), and bit/\(\sqrt{2}\) group in Figure 5c, the bit represents a line connecting the rightmost blue diamonds for each of the five energy levels. Similarly, the bit/\(\sqrt{2}\) forms another line connecting the five middle blue diamonds for each energy level. Likewise, the bit/\(\sqrt{2}\) is a line connecting the five leftmost blue diamonds of the five energy levels.  
Upon observing Figure 5a, the mean line for the 0.258 mJ energy level shows an increasing trend with interval time. Specifically, \(r_{eb}\) initially rises with interval time, indicating a positive response. However, this effect diminishes as interval time increases, resulting in a decreasing rate of increase in \(r_{eb}\). In contrast, the other energy levels in Figure 5a demonstrate a V-shaped curve. This suggests the presence of an energy threshold \(E_{th}\) for laser ablation, likely situated between 0.258 mJ and 0.288 mJ. Beyond this threshold, prolonging the interval time may not significantly contribute to the recovery of pulse laser energy, thereby limiting \(r_{eb}\) enhancement. For various laser energies, when the energy exceeds 0.258 mJ, there exists a critical value of interval time (ti)c, at which the \(r_{eb}\) value is relatively low. As shown in Table 2, (ti)c is 63.9 s for 0.288 mJ, 70.6 s for 0.318 mJ, 77.4 s for 0.348 mJ, and 84.1 s for 0.378 mJ. The (ti)c were observed in the bit/\(\sqrt{2}\) group.  
In Figure 5b, the mean line for the 0.318 mJ energy level exhibits a pattern similar to that of the 0.258 mJ energy level in Figure 5a. Initially, it rises, but the increase gradually approaches saturation. This is in contrast to the mean line for the 0.318 mJ energy level in Figure 5a, where the line follows a V-shaped curve. In Figure 5b, the mean line for the 0.258 mJ energy level stands out with a sudden spike at an interval time of 57.2 s, creating a distinctive curve not replicated in the other lines of both Figure 5a,b. There is no (ti)c observed from the 48-sample dataset.  
Figure 5b reveals a clear similarity between the behavior of the mean line for the 0.318 mJ energy level and that of the 0.258 mJ energy level in Figure 5a. Both exhibit an initial rise, followed by a gradual saturation effect. This contrasts with the V-shaped trajectory observed for the 0.318 mJ energy level in Figure 5a. A defining characteristic of Figure 5b is the prominent spike exhibited by the mean line for the 0.258 mJ energy level at an interval time of 57.2 s. This distinct behavior is not replicated in any other lines across both figures. Notably, the box plot of the 48-sample dataset yielded no (ti)c observations.