## 4 Interaction Analysis of Scanning Speed, Pulse Energy, and Repetition Rate  
So far, we have discussed the influence of three factors, namely, scanning speed, \(v\), pulse energy, \(E\) and repetition rate, \(f\), on the fs laser ablation results of CVD diamond coating. Among them, the effect of \(v\) is equivalent to that of \(f\), for they determine the effective number of pulses together. In the experiment of scanning speed change, the enhancement of ablation on diamond coating is caused by the strengthening of the incubation effect. In the single pulse energy change experiment, the promotion of ablation arises from the increase of laser fluence. Finally, under the co-affection of pulse energy and repetition rate, the ablation of diamond coating turns into a dynamic equilibrium between cumulative effect and influence of laser fluence, and the ablation degree can be figured out by examining the value  
Figure 10: WL interferometer reconstructed topographies of fs laser-irradiated regions under (**a**) 500 Hz \(\times\) 200 \(\upmu\)J, (**b**)10 kHz \(\times\) 10 \(\upmu\)J, and (**c**)100 kHz \(\times\) 1 \(\upmu\)J. (**d**) Surface roughness Ra and MRR measured under the given conditions. Figure 9: SEM photographs of fs laser-irradiated regions under the interaction of pulse energy and repetition rate. The scanning speed is 1 mm/s. of average laser power. The outcome of actual laser processing is the synergy of the interaction of \(v\), \(p\), and \(f\). In the report of ns laser-induced reduction of graphene oxide, [PERSON] et al. used energy fluences, which represent laser energies applied to unit area, to describe ns laser irradiation effects [31]. Inspired by this, we introduce a parameter embracing all three factors to depict the degree of fs laser ablation. The new parameter represents the fs laser energies applied to unit volume (EUV). Its value is equal to the ratio of single pulse energy to MRR, and can be further calculated by the following equation:  
\[\text{EUV}=\frac{Efl}{Vv}, \tag{2}\]  
where \(l\) is the length of the irradiated region and \(V\) is material volume removed by fs laser irradiation. A schematic diagram of fs laser ablation is drawn in Figure 11. Three factors, \(E\), \(v\), and \(f\), are taken into account in one parameter. Thus, we can simply focus on the EUV to evaluate the influence of fs laser irradiation. The adopted experimental conditions and corresponding EUV are listed in Table 3. The surface roughness Ra and Raman peak positions are re-plotted against EUV in Figure 12.  
Impressively, as can be seen from Figure 12a, no matter how fs laser processing parameters change, the roughness of the material always increases with the increase of EUV. It is obvious that the morphologies of the irradiated regions experienced three stages as the EUV increasing. First, when the EUV is small, the surface of the diamond coating is covered by a layer of re-solidified materials. The edges and corners of the diamond grain of the initial coating surface are polished, and the LIPSS is not obvious because of the re-solidified materials coverage. Second, with the increase of EUV from the initial 0.49 \(\upmu\)J/\(\upmu\)m\({}^{3}\) to 0.79 \(\upmu\)J/\(\upmu\)m\({}^{3}\), the amount of re-solidified materials decreases, instead, there is a large number of white melted slags embed in LIPSS. During this progress, the slope of the fitted EUV-Ra curve is small, indicating a small increasing rate of the surface roughness. After that, the surface morphology of diamond coating begins to change abruptly and presents a typical clear LIPSS. At the same time, the surface roughness Ra increases sharply. These changes suggest that there are two stages of weak ablation and strong ablation in fs laser processing of diamond coatings, the boundary point appears at 0.83 \(\upmu\)J/\(\upmu\)m\({}^{3}\).