## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Energy** & \(\mathbf{E_{1}}\) **= 23 nJ** & \(\mathbf{E_{2}}\) **= 33 nJ** & \(\mathbf{E_{3}}\) **= 45 nJ** \\ \hline \(\beta_{0}\) & \(-0.27\pm 0.13\) & \(0.01\pm 0.21\) & \(0.10\pm 0.08\) \\ \(\beta_{1}\) & \(0.33\pm 0.02\) & \(0.34\pm 0.04\) & \(0.42\pm 0.01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Linear regression coefficients. Figure 5: Cut width \(D_{\text{av}}\) as a function of velocity \(v\) for a set of laser-pulse energies. Pulse repetition rate \(f=2.5\) kHz; beam radius \(\omega_{0}=1.12\) μm. \(D_{\text{av}}(E)\) represents the data from Figure 3. The whiskers represent the \(\Delta D\) averaged over the number of measurements in the series. Laser energy is deposited into the media when the laser intensity in the focal region exceeds the intensity threshold for nonlinear absorption. Radial intensity distribution is given by the equation  
\[I(r)=\frac{P_{0}}{\pi\omega_{0}^{2}}e^{-(r/\omega_{0})^{2}}. \tag{2}\]  
For a given laser energy \(E\), the intensity meets the threshold at a defined transverse \(r_{\text{th}}\) radius (the sample is damaged within the \(r_{\text{th}}=D/2\)):  
\[I(r_{\text{th}})=\frac{0.94E}{\pi\omega_{0}^{2}}e^{-(r_{\text{th}}/\omega_{0}) ^{2}}=I_{\text{th}}. \tag{3}\]  
Using the relation for average power \(P_{\text{avg}}=E\cdot f\), [PERSON] et al. [32] derive an equation for the radius of damaged area (shown as a blue curve in Figure 3):  
\[r_{\text{th}}(P_{\text{avg}})=\omega_{0}\sqrt{\ln\frac{0.94E}{\tau\pi\omega_{0 }^{2}I_{\text{th}}}}=\omega_{0}\sqrt{\ln\frac{0.94P_{\text{avg}}}{\tau f\pi \omega_{0}^{2}I_{\text{th}}}}. \tag{4}\]  
Finding the analytical expression for the cut width \(D\) as a function of two variables (energy \(E\) and the velocity \(v\)) is of practical interest. Using linear regression for \(\log v\) according to Figure 5 and a square root function in Equation (4) for energy \(E\), the functional of the following form can be written as  
\[D(E,v)=\big{(}a-b\log v\big{)}\big{(}c\sqrt{\ln E}+d\big{)}. \tag{5}\]  
Adjustment of the parameters was performed in the numeric computing environment Matlab R2021b (MathWorks, Natick, MA, USA) using the _fittype_ function. For the energy values \(E\) (in nI) and the velocity of the laser beam \(v\) (in mm/s), the coefficients were found to be \(a=0.177\), \(b=1.19\), \(c=1.989\), and \(d=-3.076\). The approximation error of the experimental data by the constructed surface (Figure 6) did not exceed 0.15 mm, and the coefficient of determination \(R^{2}=0.9861\). The function presented is valid for energies between 19 and 52 nJ and for velocities in the range of 0.00025 and 0.1 mm/s. When choosing the optimal combination of laser-exposure parameters, the following considerations should be followed. In configuration with a stationary laser beam and a moving microscope stage with an embryo in a Petri dish, velocities \(v>0.03\) mm/s are unsuitable due to the high acceleration experienced by the embryo at the beginning of the movement and the high risk of displacement from its initial position (an embryo lies freely at the bottom of the dish and is not anchored). On the other hand, velocities \(v<0.001\) mm/s significantly increase the dissection time, as well as the total time the embryos stay outside the incubator. Thus, the choice of parameters should begin with setting the desired width of the zona pellucida cut. To minimize the thermal impact, the lowest energy values should be chosen for the specified cut width \(D\), taking into account the above restrictions on the allowable velocities in the range \(v=(0.001\)-\(0.03)\) mm/s in accordance with the dependencies shown in Figures 4 and 5. The popularity of femtosecond yytterbium lasers has grown substantially over the past decade. They provide pulses 250-500 fs long, with energies of up to several tens of microjoules. The fibre format of such a laser makes it compact compared to conventional femtosecond ones and provides low maintenance.