## 3 Results and Discussion
### Optical Experimental Setup and Results
The diameter of the laser beam waist \(w_{f}\) can be calculated [9] by  
\[\rm d_{f}=\frac{4.\lambda.f.M^{2}}{d_{0}.\pi} \tag{5}\]  
where \(\lambda\) is the laser wavelength, \(f\) defines the focal length of the f-theta lens, d\({}_{0}\) is the laser beam diameter on the lens (1/e\({}^{2}\)), and M\({}^{2}\) is the beam quality of the laser. Subsequently, a diffraction-limited spot radius of d\({}_{\rm f}\) = 10 \(\mu\)m. Then, the Rayleigh length of \(Z_{\rm f}\) = 229 \(\mu\)m can be calculated by substituting into the below Equation (6) [40]  
\[Z_{\rm f}=\frac{\pi.\left(\frac{\rm d_{f}}{2}\right)^{2}}{\lambda} \tag{6}\]  
The minimum and maximum beam diameters were collected in the workpiece's range of \(\pm\)25 mm to ensure the f-theta lens's safety. Laser-beam-quality conditions need to be met to evaluate the beam quality of the ablations and measure the working length. According to the ISO standards, a beam ellipticity (the ratio of d minor to d major at the z position) of more than 87% is regarded as circular. The ablation threshold for silicon was calculated for the used 210 fs laser source. Static pulse ablations with power varying from 30% to 60% are shown in Figure 10.  
The results of laser power measurement and laser energy are shown in Figure 11a,b. The ablation fluence can be determined from 0.165 \(\mu\)J/cm\({}^{2}\) to 1.884 \(\mu\)J/cm\({}^{2}\) in the attenuator transmission range of 20% to 65%. The ablation threshold can be determined according to [PERSON]'s method [41] because the required fluence must be higher than the ablation threshold. A plot of the [PERSON] method for determining the ablation threshold is shown in Figure 11c. Thereby, we can see that the ablation threshold value for silicon is 0.026 \(\mu\)J/cm\({}^{2}\). From [PERSON]'s plot and images of the ablation, 30% of the laser source power was selected for the experimental setup to compare the roundness of static pulsed ablation using the proposed 1D system with the conventional 2D system, when scanning along the \(Y\)-axis. To determine the gaussian beam intensity profile, 11 equidistant positions were selected with a pitch of 5 mm at different galvanometer deflections in a range of \(\pm\)25 mm, as depicted in Figure 12a. Five holes are drilled at each position with equal spacing of 20 \(\mu\)m. Figure 12b shows the image captured by Thorlab's CCD camera system with five drilled holes at the center of the silicon wafer. At the non-deflection position of the galvanometer's deflection, an ablation with an average diameter of 10.3 \(\mu\)m (the mean value between the maximum and minimum diameters of the laser beam spot diameter), and an average via-hole roundness of 95.4%, can be achieved. The roundness can change due to the oscillation characteristics of the laser beam at different measurement times and by the influence of power loss over long periods of use. Figure 12c depicts the process of measuring and collecting spot sizes at different locations to calculate the roundness of the experimental setup. Figure 10: Optical microscopy image of typical static pulse ablations with power variation from 30%, 40%, 50%, and 60% of laser source power. To determine the effective working length of the proposed 1D scanning system using two galvanometer scanners, compared to the conventional 2D scanning system, the roundness of the silicon ablation was determined at different galvanometer deflection positions in the focal plane of the f-theta lens. To evaluate the roundness of the spots, the  
Figure 11: (**a**) Output laser power, (**b**) laser energy, and (**c**) ablation threshold plot for silicon using laser fluences of F = 0.165 \(\upmu\)J/cm\({}^{2}\)–1.884 \(\upmu\)J/cm\({}^{2}\) in the attenuator transmission range of 20% to 65%. Figure 12: Experiment to investigate the roundness of ablations through camera images and microscopic measurements: (**a**) ablation position, (**b**) the number of ablation, and (**c**) ablation measurements.