## 2 Materials and Methods
### CIE Daylight Model and CCT Determination for a Daylight Spectral Reconstruction
#### 2.3.1 CIE Daylight Model  
In this work, the CIE daylight model was applied as a well-accepted method of daylight spectral reconstruction widely used amongst practitioners and scientists. According to CIE [128], its CCT-dependent formalism is given by:  
\[S_{\text{daylight}}(\lambda)=S_{0}(\lambda)+S_{1}(\lambda)\cdot M_{1}+S_{2}( \lambda)\cdot M_{2}, \tag{9}\]  
where the auxiliary functions \(S_{0}(\lambda)\), \(S_{1}(\lambda)\), and \(S_{2}(\lambda)\) are illustrated in Figure 8. Their function values are tabulated in the corresponding CIE publication [128]. The chromaticity factors \(M_{1}\) and \(M_{2}\) can be calculated from CCT as follows:  
For the CCT range of \(5000\,\text{K}\leq\text{CCT}\leq 7000\,\text{K}\):  
\[X_{\text{D}}=\frac{-4.607\cdot 10^{9}}{\text{CCT}^{3}}+\frac{2.9678\cdot 10^{6} }{\text{CCT}^{2}}+\frac{0.09911\cdot 10^{3}}{\text{CCT}}+0.244063, \tag{10}\]  
For the CCT range of CCT > 7000 K  
\[X_{\text{D}}=\frac{-2.0064\cdot 10^{9}}{\text{CCT}^{3}}+\frac{1.9018\cdot 10^{6} }{\text{CCT}^{2}}+\frac{0.24748\cdot 10^{3}}{\text{CCT}}+0.244063, \tag{11}\]  
\[Y_{\text{D}}=-3\cdot X_{\text{D}}^{2}+2.87\cdot X_{\text{D}}-0.275, \tag{12}\]  
\[M_{1}=\frac{-1.3515-1.7703\cdot X_{\text{D}}+5.9114\cdot Y_{\text{D}}}{0.0241 +0.2562\cdot X_{\text{D}}-0.7341\cdot Y_{\text{D}}}, \tag{13}\]  
\[M_{2}=\frac{0.03-31.4424\cdot X_{\text{D}}+30.0717\cdot Y_{\text{D}}}{0.0241 +0.2562\cdot X_{\text{D}}-0.7341\cdot Y_{\text{D}}}, \tag{14}\]  
\begin{table}
\begin{tabular}{l l l} \hline
**No.** & **Size** & **Content** \\ \hline
1 & 3 \(\times\) 3 & [R G B] \\
2 & 3 \(\times\) 5 & [R G B RGB 1] \\
3 & 3 \(\times\) 7 & [R G B RG RB GB 1] \\
4 & 3 \(\times\) 8 & [R G B RG RB GB RGB 1] \\
5 & 3 \(\times\) 10 & [R G B RG RB GB \(R^{2}\) G\({}^{2}\)\({}^{2}\)\({}^{2}\) 1] \\
6 & 3 \(\times\) 11 & [R G B RG RG RB GB \(R^{2}\) G\({}^{2}\)\({}^{2}\)\({}^{2}\) RGB 1] \\
7 & 3 \(\times\) 14 & [R G B RG RB GB \(R^{2}\) G\({}^{2}\)\({}^{2}\)\({}^{2}\) RGB \(R^{3}\) G\({}^{3}\)\({}^{2}\) 1] \\
8 & 3 \(\times\) 16 & [R G B RG RB GB \(R^{2}\) G\({}^{2}\)\({}^{2}\)\({}^{2}\) RGB \(R^{2}\)G G\({}^{2}\)B \({}^{2}\)R \(R^{3}\) G\({}^{3}\)\({}^{2}\) 3] \\
9 & 3 \(\times\) 17 & [R G B RG RB GB \(R^{2}\) G\({}^{2}\)\({}^{2}\)\({}^{2}\) RGB \(R^{2}\)G G\({}^{2}\)B \({}^{2}\)R \(R^{3}\) G\({}^{3}\)\({}^{2}\) 3] \\
10 & 3 \(\times\) 19 & [R G B RG RB GB \(R^{2}\) G\({}^{2}\)\({}^{2}\)\({}^{2}\)\({}^{2}\) RGB \(R^{2}\)G G\({}^{2}\)B \({}^{2}\)R R2B G2R B2G R3 G3 \({}^{3}\)\({}^{2}\) 3] \\
11 & 3 \(\times\) 20 & [R G B RG RB GB \(R^{2}\) G\({}^{2}\)\({}^{2}\)\({}^{2}\) RGB \(R^{2}\)G G\({}^{2}\)B \({}^{2}\)R R2B G2R B2G R3 \({}^{3}\) G\({}^{3}\)\({}^{2}\) 3 1] \\
12 & 3 \(\times\) 22 & [R G B RG RB GB \(R^{2}\) G\({}^{2}\)\({}^{2}\)\({}^{2}\)\({}^{2}\) RGB \(R^{2}\)G G\({}^{2}\)B \({}^{2}\)R \(R^{2}\)G \(R^{2}\)G \({}^{3}\) G\({}^{3}\)\({}^{2}\) 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 so that the determination of \(S_{\text{daylight}}(\lambda)\) can be traced back to an estimation of the CCT from the color sensor's \(RGB\) readouts. The corresponding algorithmic approach is discussed in the following section.