## 3 Results and Discussions  
### Selection of Color Components  
It should be noted that the color intensity of a radiochromic film has generally been evaluated with the optical density change (_netOD_) after radiation exposure which is calculated as follows [23; 36]:  
\[netOD(D)=-\log_{10}\frac{PV(D)}{PV(0)} \tag{1}\]  
Figure 2: A scene of reading the EBT-XD film using Nix (**a**) with a smartphone application for reading exclusively the data from Nix via Bluetooth. The measurements of the films in a few hours after irradiation with 160 kV X-rays. Angle dependence of measured color intensities was examined by rotation of Nix with 15\({}^{\circ}\) intervals in a clockwise direction (**b**).  
where \(PV(D)\) represents the pixel's color channel value of the film exposed to radiation at dose \(D\); thus \(PV(0)\) means that of the unirradiated film which is measured before irradiation. The pixel color value is normally obtained for each of the RGB channels (red, green and blue components).  
The authors judged that this way of calculation using the logarithmic functions Equation (1) was too complex in view of practicality and would not fit the aim of the present study, i.e., the development of a simple on-site dosimetry method. Thus, the change in color intensity (\(\Delta I\)) caused by radiation exposure was simply calculated here from the readings obtained with the portable colorimeter as follows:  
\[\Delta I=I(0)-I(D) \tag{2}\]  
where \(I(D)\) is the measured intensity of the respective color channel at \(D\). More concretely, \(I(0)\) was given as the value measured by Nix before irradiation and \(I(D)\) was given as that a few hours after irradiation; it was confirmed that the levels of radiation-induced colorations of EBT-XD had been stable for 24 h after irradiation in all cases. We should note that \(netOD\) would preferably be used in place of \(\Delta I\) if smartphone software which could automatically calculate the netOD value in a simple operation process was available.  
Figure 3 shows the dose responses of the color intensities (RGB, red, green and blue) obtained by Nix with the EBT-XD film irradiated with up to 40 Gy of 160 kV X-rays. The regression curves indicated there were obtained with the following function:  
\[\Delta I=a\times\Big{(}1-e^{(-b\cdot D)}\Big{)}c \tag{3}\]  
where \(a\), \(b\) and \(c\) are the fitting parameters that are empirically determined through regression analyses. As seen in the figure, the red and green components showed good dose responses with small error bars; values of the coefficient of variation (CV) defined as the ratio of the standard deviation to the mean value were less than 3% in all cases. On the other hand, the blue component showed a unique, flat dose response with larger error bars, which indicates a lower sensitivity of this component in radiochromic reactions. As a mixture of the responses of red, green and blue components, the sensitivity of RGB was in the middle of those of these three components.  
Figure 3: Dose dependences of the color intensities of EBT-XD irradiated with 160 kV X-rays at up to 40 Gy as to RGB, red, green and blue components measured with Nix at the angle of 0\({}^{\circ}\).  
While the dose responses of both the red and green components showed convex upward curves, not linear ones, it was considered that a unique radiation dose could be determined directly from each of the measured color intensities as they were monotonically increasing with dose. In a comparison of the red and green components, the red component increased more sharply and reached a saturated status around 10 Gy, while the green component showed a constantly increasing curve up to 40 Gy or higher. This difference qualitatively agrees with the findings in previous studies [21,42] and thus it was judged that these two components would be appropriately used for dose assessment in this dose range (~40 Gy) in case the color intensities of the films be measured by Nix.