## 3 Results  
The SPD and optical power measurement results of each LED were cross-referenced with manufacturers' data to validate whether the LED's behavior aligned with expectations. This validation formed the basis for preliminary analyses of the spectral distribution of the LSTLS and optimization of its SPD. The manufacturers' data of each LED were approximated using Gaussian (Equation (1)) and Lorentz (Equation (2)) functions and compared against measured SPD. Both models provided very suitable values of measure of fit for the SPDs for each LED. The average \(R^{2}\) value for all LEDs did not fall below 0.98 (Table 3). From Table 3, it can be inferred that for LEDs emitting some wavelengths, the fitting is, in general, worse no matter which model is applied. This occurs for some wideband LEDs (540, 575, 615, and 640 nm) and selected narrowband LEDs (590 and 680 nm). The Gaussian function exceeds the Lorentz function in reproducing steep slopes. In contrast, the Lorentz \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{2}{c}{\(R^{2}\)} \\ \hline
**Wavelength** & **FWHM** & **Lorentz** & **Gaussian** \\ \hline
**[nm]** & **[nm]** & **-** & **-** \\ \hline  
Mean & & 0.980 & 0.982 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Coefficients of determination (\(R^{2}\)) for spectral power distributions of LEDs fitted with Gaussian and Lorentz functions. function is more accurate for more gentle slopes (see examples in Figure 1). Additionally, the Gaussian function better models the SPDs with higher asymmetry. For example, for the LED with a peak at 460 nm and FWHM = 25 nm (see Table 1 and Figure 1a), \(R^{2}\) values were 0.942 (Gaussian) and 0.928 (Lorentz). Figure 1c presents the SPDs for the LED with the peak at 640 nm peak, for which the \(R^{2}\) values are 0.968 and 0.958, respectively. Considering the slightly better performance of the Gaussian model, specifically for asymmetric SPDs, it was chosen for the simulations of the LSTLS versions. The selection of LED sets with the criterion of \(R^{2}\) above 0.99 resulted in a number of solutions for each set. In Table 4, the data of the best sets are collected: the \(R^{2}\) value, the number of channels used during optimization of each set, and the number of channels used in a final solution of each set. From the results, it can be inferred that the design of the LSTLS is a non-trivial problem. The A illuminant A LSTLS with a very suitable match of SPD evaluated with the criterion of \(R^{2}\) value may be realized with sets composed of various numbers of channels, where each channel may be composed of various numbers of LEDs of the same type. All SPDs are characterized by a CCT of 2856 K and an \(R^{2}\) value above 0.993. The majority (90%) of the SPDs have an \(R^{2}\) value over 0.997, which suggests an almost perfect fit of the spectra. The analysis of the LSTLS results shows that employing 82 LEDs in each version provides the highest \(R^{2}\) value. Figure 1: Exemplary approximations of the spectral power distributions of LEDs 450 nm (**a**), 540 nm (**b**), 640 nm (**c**) and 740 nm (**d**) using Gaussian and Lorentz functions compared to measurements; error bars, including the radiometric accuracy of the spectroradiometer, are displayed on the chart for the measured curves. The procedure is described in Section 2.3. Figure 2 presents the SPDs of modeled LSTLS versions (numbers according to Table 4). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number of the Version**} & \multirow{2}{*}{**\(R^{2}\)**} & \multirow{2}{*}{**RMSE (mW/nm)**} & \multicolumn{2}{c}{**Number of LED Channels**} \\ \cline{3-5}  & & & **Available** & **Used** \\ \hline
1 & 0.99999 & 0.026 & 82 & 72 \\ \hline
2 & 0.99999 & 0.033 & 82 & 69 \\ \hline
3 & 0.99985 & 0.123 & 43 & 37 \\ \hline
4 &  
In Figure 2b, the spectral power distributions of the modeled LSTLS normalized to the SPD of the illuminant A for 1000 lm of the luminous flux are presented, while in Figure 3, the spectral range is limited to 430 to 690 nm.