## 4 Discussion  
The measured spectra for the designed supply currents have worse performance according to the \(R^{2}\) measure--it is 0.992 (RMSE = 0.891 mW/nm) for SPD no. 8 and 0.991 (RMSE = 0.951 mW/nm) for SPD no. 22, which is caused by the changes in the SPD of the components for various operation points. During the characterization of LEDs, variations in their spectral parameters were observed (\(\lambda_{p}\) and FWHM) in response to changes in current intensity. The spectral shifts are not similar for all types of LEDs--the most significant shifts are observed for two spectral ranges (435-550 nm and 660-780 nm). These shifts are notably more pronounced for blue and green light compared to red light. Moreover, the shift occurs toward shorter wavelengths for LEDs emitting blue and green light, whereas for LEDs emitting red light, it occurs toward longer wavelengths. Additionally, the test results revealed a non-uniform effect of power supply on the changes in FWHM. These effects are the main reason for the discrepancies between simulated and measured SPDs, but a detailed analysis of this effect is not the merit of this research. The accuracy of the simulations of the LSTLS could be improved if the models of changes for each LED were included during simulations. This is the main limitation of this research. However, its aim was not to model accurately the LSTLS but to analyze the most widely used criterion for the quality of spectral matching.  
The \(R^{2}\) measure is widely applied for curve-fitting purposes. We applied it to evaluate the components and the system. Additionally, we calculated the RMSE values as another popular quality measure. It provides an average discrepancy of the final SPD per nanometer; therefore, both measures are similar in that both provide averaged data. They also lead to similar conclusions, as higher \(R^{2}\) usually means lower RMSE with very small discrepancies from this rule (see Table 4). That makes it difficult to assess the quality of the spectral matching of LSTLSs, which depends on the selection of LED channels and their operation conditions, as they affect the SPD of each component of LSTLSs, even if the temperature is constant. As presented in this research, similar mismatch error values may be obtained for different SPDs where the mismatch occurs in various spectral bands. That may be observed, for example, in Figure 6, which presents the SPDs of two measured LSTLS solutions, which are characterized by similar values of \(R^{2}\). However, the discrepancies between the target spectrum and the obtained ones occur in various spectral ranges--the central region (red circle) overlaps with the region, where the V(\(\lambda\)) curve has the highest values. In contrast, the border region (green circle) is less important from the point of view of photometry.  
Figure 6: Spectral power distributions of measured SPDs of LSTLSs.  
Similar doubts can be drawn for the evaluation of components used in the LSTLS for photometric applications. For example, for LEDs presented in Figure 1a,c, the values of \(R^{2}\) were noticeably lower for LEDs with a peak at 460 nm while higher in the case of 640 nm. In spite of that, comparing their spectra, it can be inferred that in the first case, the peak and FWHM were accurately modeled. The biggest differences occurred outside the central part of the SPD. The opposite situation was for the LED with the peak at 640 nm; although the region with the highest share of the optical power density was not very well simulated, the \(R^{2}\) value was higher. These effects suggest that it might be useful to search for other measures for the evaluation of spectral matching of SPDs of the components and LSTLS systems in specific applications, which could improve the accuracy of their modeling and facilitate the selection of the best solution. Specifically, responsivity curves adequate for the application area could be considered design criteria for the LSTLS [36].