## 2 Materials and Methods
### Evaluation of the Investigated Models  
The quality of spectral matching was assessed through the most frequently used R-squared (\(R^{2}\)) and root mean square error (RMSE) values, which quantify the goodness of fit between the simulation data and the target [35]:  
\[R^{2}=1-\frac{\sum_{\lambda=380}^{780}(A_{\lambda}-M)^{2}}{\sum_{\lambda=380}^{780 }(P_{\lambda}-M)^{2}}, \tag{3}\]  
where \(P_{\lambda}\)--spectral power density of the source for the wavelength \(\lambda\), \(A_{\lambda}\)--spectral power density of the target SPD for the wavelength \(\lambda\), and \(M\)--mean value of the spectral power density for the target SPD.  
\[RMSE=\sqrt{\frac{\sum_{\lambda=380}^{780}(A_{\lambda}-P_{\lambda})^{2}}{N}}, \tag{4}\]  
where \(P_{\lambda}\)--spectral power density of the source for the wavelength \(\lambda\), \(A_{\lambda}\)--spectral power density of the target SPD for the wavelength \(\lambda\), and \(N\) = the number of data points.  
Equations (3) and (4) are used to compare the spectral deviation between the modeled (in stage 1) and measured SPDs of LEDs and between the designed LSTLS and the illuminant A at the third stage of this research.  
The experimental validation of the simulated LED systems was conducted using a well-calibrated photometric setup. This included a spectroradiometer GL Spectis 1.0 Touch with an integrating sphere GL OPTI SPHERE 205 mm (GL Opic, Puszczykowo, Poland) to independently measure the SPD, optical power, and luminous flux of each LED emitter. These data were used to evaluate the accuracy of spectral modeling of LEDs selected for practical tests and the quality of predicting the SPD of the LSTLS. The setup was designed to replicate standard photometric testing environments with controlled ambient conditions to minimize external influences. Each LED was mounted on a metal-core printed circuit board (MCPCB) and then on an oversized heat sink. The ambient and heat sink temperatures were constant (20 \({}^{\circ}\)C).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Version No.**} & \multirow{2}{*}{\begin{tabular}{c} **Number of** \\ **Chromatic Channels** \\ \end{tabular} } & \multirow{2}{*}{**White LED**} & \multirow{2}{*}{\begin{tabular}{c} **Step** \\ **5 nm** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Step** \\ **10 nm** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Step** \\ **20 nm** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Step** \\ **640 nm and 650 nm** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Narrowband LEDs** \\ **640 nm and 650 nm** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Wideband LEDs** \\ **640 nm and 650 nm** \\ \end{tabular} } \\ \hline
8 & 25 & No & \multicolumn{4}{c}{Set of 25 selected LEDs (measurements)} \\ \hline
9 & 82 & 2700 K & YES & \multicolumn{4}{c}{YES} \\ \hline
10 & 82 & 2700 K & YES & \multicolumn{4}{c}{YES} \\ \hline
11 & 43 & 2700 K & \multicolumn{4}{c}{YES} & \multicolumn{4}{c}{YES} \\ \hline
12 & 43 & 2700 K & \multicolumn{4}{c}{YES} & \multicolumn{4}{c}{YES} \\ \hline
13 & 21 & 2700 K & \multicolumn{4}{c}{YES} & \multicolumn{4}{c}{YES} \\ \hline
14 & 21 & 2700 K & \multicolumn{4}{c}{YES} & \multicolumn{4}{c}{YES} \\ \hline
15 & 82 & 3000 K & YES & \multicolumn{4}{c}{YES} \\ \hline
16 & 82 & 3000 K & YES & \multicolumn{4}{c}{YES} \\ \hline
17 & 43 & 3000 K & \multicolumn{4}{c}{YES} & \multicolumn{4}{c}{YES} \\ \hline
18 & 43 & 3000 K & \multicolumn{4}{c}{YES} & \multicolumn{4}{c}{YES} \\ \hline
19 & 21 & 3000 K & \multicolumn{4}{c}{YES} & \multicolumn{4}{c}{YES} \\ \hline
20 & 21 & 3000 K & \multicolumn{4}{c}{YES} & \multicolumn{4}{c}{YES} \\ \hline
21 & 25 & 3000 K & \multicolumn{4}{c}{Set of 26 selected LEDs (simulated SPDs of each channel)} \\ \hline
22 & 25 & 3000 K & \multicolumn{4}{c}{Set of 26 selected LEDs (measurements)} \\ \hline \hline \end{tabular}
\end{table}
Table 2: \(Cont.\)