## 2 Materials and Methods
### LED Channels' Optimization  
The target spectrum was modeled using various composition versions in the third step. The SPDs of LSTLSs were generated using the Levenberg-Marquardt algorithm LMA, also known as the damped least-squares (DLS) method. This algorithm provided the combined output of multiple LED emitters. Then, the operational parameters of each channel were determined. The simulations aimed to predict the performance of the LED array before physical assembly, providing a basis for subsequent empirical validation.  
The calculations of the target SPD included sets containing 21 to 83 channels, each with a different peak wavelength. Each set consisted of various numbers of chromatic channels and FWHM values (Table 2) with or without additional high CRI (equal to 98) white-light-emitting diode of Sunlike type at 2 various CCTs. It was used to reduce the number of channels and cover the valleys in the output SPD. The research procedure was designed to verify the usability of broadband PC (phosphor-converted) LEDs. This test was performed by replacing narrowband LEDs with peak wavelengths at 640 nm and 650 nm (FWHM = 20 nm) with broadband PC LEDs with peak wavelengths at 640 nm and 650 nm (FWHM = 90 nm). In practice, the feedback control and power supply of a system with a number of channels exceeding 40 present significant challenges. Moreover, such LSTLS would be impractical in photometric layouts, such as with an integrating sphere of limited dimensions. For this research, an additional assumption related to the application was introduced, which limited the area of the LSTLS and excluded the versions with the highest number of channels for practical verification. Therefore, 2 additional sets were selected, among other results, composed of 25 chromatic channels with or without additional Sunlike white-light-emitting diodes, which met the criteria of required matching quality and the surface of the LSTLS.  
\begin{table}
\begin{tabular}{c 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**} & \multicolumn{5}{c}{**Key Differences between Versions**} \\ \cline{6-9}  & & & **Step** **5 nm** & **Step** **10 nm** & **Step** **20 nm** & **Narrowband LEDs** **640 nm and 650 nm** \\ \hline
1 & 82 & No & YES & & & YES \\ \hline
2 & 82 & No & YES & & YES & \\ \hline
3 & 43 & No & & YES & & YES \\ \hline
4 & 43 & No & & YES & YES & \\ \hline
5 & 21 & No & & YES & YES \\ \hline
6 & 21 & No & & YES & YES \\ \hline
7 & 25 & No & & Set of 25 selected LEDs (simulated SPDs of each channel) & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Components of tested versions of LSTLSs.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\lambda_{p}\) [nm] & **FWHM [nm]** & \(\lambda_{p}\) [nm] & **FWHM [nm]** & \(\lambda_{p}\) [nm] & **FWHM [nm]** & \(\lambda_{p}\) [nm] & **FWHM [nm]** \\ \hline
415 & 13 & 515 & 35 & 615 & 20 & 715 & 22 \\
420 & 18 & 520 & 30 & 620 & 15 & 720 & 20 \\
425 & 15 & 525 & 29 & 625 & 16 & 725 & 36 \\
430 & 15 & 530 & 30 & 630 & 15 & 730 & 30 \\
435 & 25 & 535 & 35 & 635 & 20 & 735 & 40 \\
440 & 25 & 540 & 100 & 640 & 90 & 740 & 22 \\
445 & 18 & 545 & 110 & 645 & 16 & 745 & 25 \\
450 & 22 & 550 & 38 & 650 & 90 & 750 & 28 \\
455 & 25 & 555 & 110 & 655 & 17 & 755 & 24 \\
460 & 25 & 560 & 40 & 660 & 17 & 760 & 25 \\
465 & 25 & 565 & 120 & 665 & 20 & 765 & 29 \\
470 & 20 & 570 & 44 & 670 & 20 & 770 & 25 \\
475 & 21 & 575 & 11 & 675 & 20 & 775 & 27 \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._