## 3 Results and Discussions  
The dose \(D_{E}\) delivered to the IOC sensitive volume by photons and the secondary electrons generated by the incident photons was determined to be 8.373 \(\times\) 10\({}^{-16}\) Gy/photon. The dose \(D_{A}\) delivered to the EBT3 film active layer was determined to be 8.695 \(\times\) 10\({}^{-16}\) Gy/photon with an associated relative error (i.e., the statistical uncertainty) of 0.007. The administrated doses given to the EBT3 film in the experiments were calibrated using \(R=D_{A}/D_{E}=8.695\times 10^{-16}/8.373\times 10^{-16}=1.038\)  
Figure 4: Exposure of EBT3 film to the light source and reflection from the film surface. As \(R\) was close to unity, \(D_{A}\) and \(D_{E}\) were not very different when the photon beam with the continuous energy distribution shown in Figure 1 was employed. The absorption coefficient of the EBT3 film active layer at different administrated X-ray doses obtained from our model is shown in Figure 5. The absorption coefficient increased noticeably for X-ray doses <-600 cGy, but did not change significantly for larger X-ray doses. The insignificant changes in the absorption coefficient for large X-ray doses were due to the formation of a densely cross-linked structure in the exposed EBT3 film active layer, in which significantly more bonds would not form even with a further supply of energy to the monomers. For illustration purposes, snapshots from atomic configurations of the DA monomers [9] before and after the addition of energy from X-ray photons are shown in Figure 6a,b, respectively, which revealed the formation of a densely polymerized system upon exposure of EBT3 films to X-ray. The obtained absorption coefficients were input into the FEM model and the reflected light intensities (\(log(\phi)\)) from the surface of the EBT3 film were obtained as shown in Figure 7. The reflected light intensity decreased with increasing X-ray dose absorbed by the film active layer. Similar to the film absorption coefficient (Figure 5), the reflected light intensity from the EBT3 film surface decreased noticeably for X-ray doses <-600 cGy, but did not change significantly for larger X-ray doses. The latter was explained by the insignificant changes in the absorption coefficients for larger X-ray doses as a result of formation of a densely cross-linked structure in the exposed EBT3 film active layer. Since the \(log(\phi)\) values were obtained from the FEM model, a grid independence test analysis was performed. For the three different grid sizes, namely, 7.68, 5.15, and 3.73 \(\upmu\)m, \(log(\phi)\) did not vary significantly with the X-ray doses. Similar to [3], the _Net ROD_ in our model was defined as _Net ROD = log(\(\phi_{unexposed}\)/\(\phi_{exposed}\))_, where \(\phi_{unexposed}\) and \(\phi_{exposed}\) were reflected light intensities from the films unexposed and exposed to X-ray, respectively. The _Net ROD_ values from the present model were scored over the entire surface of the radiochromic films. The average reflected intensity was determined as the arithmetic mean of the  
Figure 5: Calculated absorption coefficients of EBT3 film active layer versus X-ray dose. Figure 6: Atomic scale configuration of DA monomers: (**a**) before and (**b**) after exposure to X-ray. (Green spheres: carbon atoms; purple spheres: hydrogen atoms; lines: bonding among different atoms in the monomer chains, with more lines representing formation of a denser cluster and thus a denser polymerization.) (Note: A 3D model of polymerization was considered. However, 2D representation of the atomic scale system was used for better visualization) (DA: diacetylene). intensities from the elements in the modeled domain [12; 13; 14]. The experimental data obtained by [PERSON] et al. [10] and the theoretical predictions are shown in Figure 8 for comparison, which showed that the theoretical predictions were very close to the experimental data. The uncertainties shown as shades around the theoretical prediction curves were introduced by the Monte Carlo model.