## 3 Results and Discussions  
### Model Validation  
When a UV light is projected on the surface of a photocurable resin, the liquid resin is converted into solid from the surface to a certain depth. This depth is called curing depth or \(C_{d}\). The curing depth can be expressed as [20]  
\[C_{d}\ =\ D_{p}\ln(\frac{E}{E_{c}}), \tag{13}\]  
where \(D_{p}\) is penetration depth, \(E\) is given light energy, and \(E_{c}\) is critical light energy. It is seen that curing depth is proportional to natural logarithm of given light energy. This is known as a working curve for a given resin. \(D_{p}\) and \(E_{c}\) are resin specific characteristic parameters. In this study, we use a set of working curves obtained from experiment to validate our simulation model. The details for obtaining a working curve experimentally is given in Appendix B. In simulation, the conversion ratio \(C\) given in Equation (10) is obtained as a continuous field from the initial monomer concentration ([M]\({}_{0}\)) and the monomer concentration ([M]) remaining after the applied energy dose. The value of \(C\) varies between 0 and 1 with 0 being uncured liquid and 1 being fully cured solid. Since a conversion ratio corresponding to the gel point is not readily available from experimental measurement, the conversion ratio value that defines the interface between liquid and cured solid polymer, or 'cut-off' conversion ratio, should be chosen to obtain curing depth from simulation. A various range of cut-off conversion ratios have been reported in literature [21], and we used 5% as a conversion cut-off ratio in this study.  
In order to validate our computational model, we first experimentally obtained working curves of resins having different PI and PA concentrations. The details regarding sample preparation and post-processing procedure are described in Appendix A. PSO was performed on several simulation constants of '\(k_{0}\)', '\(\alpha\)', '\(\alpha\)', '\([\text{O}]_{0}\)', and '\(C\)' to calibrate the computational model. The values of these parameters are reported at a varied range in literature as listed in Table 3. Using RMSE as an objective function, optimization algorithm POS was performed. Table 3 also lists calibrated parameter values after performing PSO. With the calibrated parameters, we performed numerical simulations to obtain working curves for the same resins used in the experiment. Working curves from simulation and experiment are shown in Figure 6 and they show a good agreement. Based on this result, we confirm the validity of our photopolymerization computational model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Parameter** & **Lower/Upper Bounds** & **Calibrated Values** \\ \hline
**Symbol** & **Name** & & \\ \hline \(k_{0}\) & Oxygen inhibition constant & 5–10 \(\times\) 10\({}^{5}\) m\({}^{3}\)/mol/s [25; 26] & 10.02 m\({}^{3}\)/mol/s \\ \(\alpha\) & PI molar absorptivity & 4.6–20 m\({}^{2}\)/mol [21] & 20 m\({}^{2}\)/mol \\ \(\alpha_{\text{a}}\) & PA molar absorptivity & 3680–5520 m\({}^{2}\)/mol [21] & 4591.7 m\({}^{2}\)/mol \\ \([\text{O}]_{0}\) & Initial oxygen concentration & 0.8–1.2 mol/m\({}^{3}\)[26] & 1.03 mol/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: List of calibrating parameters.