## 4 Interaction Analysis of Scanning Speed, Pulse Energy, and Repetition Rate
In the weak ablation stage, the femtosecond laser energy applied on the target is small, which has far less effect on the surface modification than on the polishing and melting  
Figure 11: Schematic diagram of fs laser direct writing to produce a single line, where \(l\) is the length of the single line, which is equal to the side length of the sample (10 mm), and V is the volume removed by fs laser ablation, which can be directly extracted from the WL interferometer results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experimental** & **EUV** & **Experimental** & **EUV** & **Experimental** & **EUV** \\
**Condition** & **(\(\upmu\)J/\(\upmu\)m\({}^{3}\))** & **Condition** & **(\(\upmu\)J/\(\upmu\)m\({}^{3}\))** & **Condition** & **(\(\upmu\)J/\(\upmu\)m\({}^{3}\))** \\ \hline
2 mm/s & 0.5723 & 50 \(\upmu\)J & 0.4886 & 500 Hz \(\times\) 200 \(\upmu\)J & 0.858 \\
1.8 mm/s & 0.6071 & 70 \(\upmu\)J & 0.6631 & 10 kHz \(\times\) 10 \(\upmu\)J & 0  
of the diamond coating, so the evolution of the morphologies of the irradiated region is moderate and diamond peaks can always be detected in Raman spectra (Figure 12b). In the stage of intense ablation, the mechanism of fs laser ablation of the diamond coatings is mainly vaporization and phase explosion. Typical LIPSS accompanied by severe graphitization (the diamond peak disappears after 0.78 \(\upmu\)J/\(\upmu\)m\({}^{3}\)) appears in the laser-irradiated regions due to the extensive laser modification and surface roughness Ra increases rapidly with the rise of energy. Moreover, most of the laser energies are absorbed by graphite in the form of heat loss owing to the extremely high absorption coefficient of graphite, thus the ablation of the diamond coating is saturated in this stage. Although EUV can reflect the ablation degree by considering the interaction of scanning speed, pulse energy, and repetition rate as a whole, it is interesting to further detail the significance of each parameter during the interaction progress. A Taguchi array of L\({}_{16}\) (with three factors at four-level, outlined in Table 4) was produced and analyzed using Minitab 19 (Minitab, LLC., State college, Pennsylvania, USA) so that as much useful information as possible can be extracted from a predetermined and limited number of experiments. As can be seen from the response results for the signal-to-noise ratio of Ra and MRR highlighted in Figure 13, repetition rate showed the largest delta for both Ra and MRR, suggesting it has the most significant effect on the two features over the range studied. The scanning speed was found to be the second-ranked factor affecting the surface roughness, but to be the lowest-ranked factor in the MRR response, which means that the scanning speed plays a different role in achieving accuracy and efficiency. As can be seen from Figure 13, we can realize an optimal polishing processing by adopting \(v3\)\(E2\,f3\) (scanning speed 20 mm/s, pulse energy 50 \(\upmu\)J, repetition rate 1 kHz). However, the most efficient parameter set turns out to be \(v2\)\(E4\,f4\) (scanning speed 10 mm/s, pulse energy 120 \(\upmu\)J and repetition rate 2 kHz). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Factors** & **Symbol** & **Unit** & **Level 1** & **Level 2** & **Level 3** & **Level 4** \\ \hline Scanning speed & v & mm/s & 1 & 10 & 20 & 50 \\ Pulse energy & E & \(\upmu\)J & 10 & 50 & 100 & 120 \\ Repetition rate & f & Hz & 100 & 500 & 1000 & 2000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Process parameters and design levels used in the L\({}_{16}\)(4\({}^{3}\)) Taguchi array. Figure 12: Re-plotted curve based on the available data obtained in this work. (**a**) The relationship between the Ra and EUV image inserts shows the corresponding morphologies of EUV connected by a dotted line. (**b**) The correlation between Raman peak position and EUV.