## 3 Results
### Results on Display Characterization
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & \(\gamma_{R}\) & \(\gamma_{G}\) & \(\gamma_{B}\) & \(d_{0,R}\) & \(d_{0,G}\) & \(d_{0,B}\) \\ \hline iPhone 7 & 2.384 & 2.302 & 2.354 & 0.00784 & 0.00784 & 0.00784 \\ \hline iPhone 8 & 2.401 & 2.340 & 2.409 & 0.00784 & 0.00784 & 0.00784 \\ \hline iPhone SE 2020 & 2.402 & 2.336 & 2.438 & 0.00784 & 0.00784 & 0.00784 \\ \hline iPhone 12 & 2.217 & 2.213 & 2.184 & 0.007843 & 0.014955 & 0.026125 \\ \hline iPhone 13 & 2.376 & 2.391 & 2.271 & 0.00784 & 0.00784 & 0.00784 \\ \hline iPhone XS Max & 2.231 & 2.255 & 2.287 & 0.00784 & 0.00784 & 0.00784 \\ \hline iPad 2 & 2.315 & 2.307 & 2.299 & 0.00784 & 0.00784 & 0.00784 \\ \hline iPad 6 th Generation & 2.248 & 2.286 & 2.465 & 0.00784 & 0.00784 & 0.00784 \\ \hline iPad 9 th Generation & 2.249 & 2.284 & 2.349 & 0.00784 & 0.00784 & 0.00784 \\ \hline iPad Pro 2 nd Generation & 2.335 & 2.393 & 2.394 & 0.00784 & 0.00784 & 0.00784 \\ \hline iPad Air 4 th Generation & 2.394 & 2.342 & 2.308 & 0.00784 & 0.00784 & 0.00784 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Tone Rendering Curve parameters for all measured devices. even within the same device, and differ from the standard sRGB model parameters (\(\gamma=2.4\), \(d_{0}=0.0392\)), which assume identical behavior across all three channels. The sRGB model is represented by the black dashed line in Figure 5.  
In total, \(33\)\(\gamma\) parameters were calculated, all ranging from \(2\) to \(3\), with \(28\) values falling below the value \(\gamma=2.4\) from the sRGB method. Only three devices had at least one color channel with \(\gamma_{i}\) (\(i=R,~{}G,~{}B\)) larger than \(2.4\). As shown in Table 3, the channels exceeding \(2.4\) were the blue ones for the three and the red ones for all but one of them. The remaining \(\gamma\) values across devices are all below \(2.4\). To build a generalized model representing all devices characterized, the TRC exponential parameters would be set as \(\gamma_{R}=2.32\pm 0.02\), \(\gamma_{G}=2.314\pm 0.009\) and \(\gamma_{B}=2.34\pm 0.02\). The average values for the \(d_{0,i}\) parameter are slightly higher than \(2/255\). Thus, for practical purposes, it could be assumed that \(d_{0,R}=d_{0,G}=d_{0,B}=2/255\). On the other hand, the values of MDCIM parameters for the iPhone XS Max were also presented at a recent conference [13]. Table 5 shows these values, comparing them with the corresponding values calculated here for the CAAD, as well as the values implicitly assumed when using the sRGB color space. Figure 5: TRCs for the three channels of an iPhone 12 device across the full range of digital values (**a**) and in the region of low digital values (**b**). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **sRGB** &
\begin{tabular}{c} **MDCIM iPhone XS** \\ **Max** \\ \end{tabular} & **CAAD** \\ \hline \multirow{4}{*}{\(R\)} & \(\gamma\) & 2.4 & 2.231 & 2.32 \\  & \(d_{0}\) & 0.04045 & 0.00784 & 0.00784 \\  & \(k_{1}\) & 0.947867 & 0.990441 & 0.989753 \\  & \(k_{2}\) & 0.055 & 0.009559 & 0.010247 \\  & \(\beta\) & 0.077399 & 0.015000 & 0.011436 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimized values for MDCIM parameters based on spectroradiometer data specifically for iPhone XS Max, for average Apple display, and corresponding values assumed in sRGB space.