## 3 Results and Discussion
They include the velocity of the laser beam \(v\), its radius \(w_{0}\), and the repetition rate \(f\), which altogether determine the spatial overlap of laser pulses when the laser beam moves along the trajectory: \(D\sim Ew_{0}f/v\). To find the optimal parameters of laser exposure for given \(w_{0}\) and \(f\), a series of experiments were carried out for different velocities \(v\) and pulse energies \(E\), followed by a cut-width estimation. Figure 3: ZP microsurgery with femtosecond and millisecond laser pulses. Circles demonstrate average cut width \(D_{\text{av}}\) as a function of laser-pulse energy \(E\) for femtosecond laser pulses; velocity \(v=0.01\) mm/s and pulse repetition rate \(f=2.5\) kHz. Open boxes denote hole diameter in the ZP drilled using a millisecond laser pulse with power \(P=47\) mW. Data for \(D_{\text{h}}(E_{\text{ms}})\) are adopted from the open-archive source, Ref [8]. A star stands for parameters considered optimal for the LAH procedure [13]. OB—optical breakdown. Three laser-pulse energies were considered: \(E_{1}=23\) nJ (slightly above the threshold, at which laser cut becomes visible), \(E_{2}=33\) nJ, and \(E_{3}=45\) nJ. Increasing the pulse energy made it possible to raise the velocity relative to the nominal one (\(v=0.01\) mm/s) reported earlier (see \(D_{\text{av}}(E)\) dependence in Figure 3). The embryos with laser cuts performed at \(E_{1}\), \(E_{2}\), and \(E_{3}\), are shown in Figure 4A, B, and C, respectively. The maximum velocity, for which the cut is still visible, increases as the energy of the laser pulses grows. Some additional measurements were made at \(E_{3}=45\) nJ for very low velocities of 0.25 and 0.5 \(\upmu\)m/s in Figure 4C. The pulse repetition rate \(f=2.5\) kHz was kept constant for all the series of experiments. Figure 4: Laser cuts of the zona pellucida for different velocities \(v\). (**A**) \(E_{1}=23\) nJ, \(v=0.001\)–0.01 mm/s\({}_{\text{syn}}\) (**B**) \(E_{2}=33\) nJ, \(v=0.001\)–0.05 mm/s; (**C**) \(E_{3}=45\) nJ, \(v=0.00025\)–0.1 mm/s. Scale bar is 10 \(\upmu\)m.  
Markers (\(\bullet\)) in Figure 5 demonstrate the measured \(D_{\text{av}}\) values obtained for the set of energies \(E_{1}\), \(E_{2}\), and \(E_{3}\) shown in Figure 4. The maximal error bars for each series are shown. The lines represent linear regression \(D=\beta_{0}-\beta_{1}\log(v)\). Coefficients \(\beta_{0}\) and \(\beta_{1}\) are summarized in Table 1.  
The data in Figure 5 demonstrate good agreement with the \(D_{\text{av}}(E)\) values obtained earlier (see Figure 3) for the velocity \(v=0.01\) mm/s (denoted here by \(\circ\)). It can be seen that the desired value of the cut width \(D\) can be obtained for various combinations of laser-pulse energy and velocity. For example, \(D\sim 1.5\) um is achievable by combining \(E\sim 23\) nJ and \(v=0.002\) mm/s; \(E\sim 33\) nJ and \(v=0.025\) mm/s; \(E\sim 45\) nJ and \(v=0.05\) mm/s (for pulse repetition rate \(f=2.5\) kHz and beam waist radius \(\omega_{0}=1.12\) um). These values can be scaled to another pulse repetition rate \(f\) by appropriately changing the velocity \(v\), e.g., for \(f=5\) kHz, halved \(v\) values should be considered (Figure 5). For a beam with radius of \(w_{0}=1.12\) um moving with a velocity of \(v=0.1\) mm/s, it takes \(224\) us to travel a distance equal to its diameter. Five tens of pulses affect nearly the same place. The damage area begins increasing in size, starting from the center of the beam where the intensity is maximal. Each pulse makes the damage area wider. The slower the velocity, the greater the number of pulses affecting the same area. For \(v=0.001\) mm/s, the number of pulses reaches five thousands, and the width of the cut is much greater than that of \(0.1\) mm/s. Further velocity decreases would result in approaching a diameter of a stationary hole formed in the ZP. [PERSON] et al. [32] performed similar investigations of femtosecond laser ablation in agarose and glass samples using a series of laser pulses and a stationary laser beam.