## 3 Results and Discussion  
### Optimal White LED Spectra  
In the study, four luminance levels, including 10, 1, 0.3, and 0.1 cd/m\({}^{2}\) were investigated for both photopic and mesopic vision. Based on the above-mentioned white LED optimization method, the optimal white LED spectra with relatively higher \(L_{mes}\) and \(GV\), highest \(L_{mes}\) and largest \(GV\) denoted as Opt*1, Opt*2, and Opt*3, respectively, were derived for each luminance levels upon the same radiant  
Figure 1: Flow chart of white LED spectrum optimization. quantity condition, and the spectral information is shown in Table 2. The FWHMs of the optimal spectra are 25, 36, and 13 nm for blue, green, and red, except for Opt#2, which is 25, 70, and 70 nm in 10 cd/m\({}^{2}\). The SPDs of optimal white LED under four luminance levels are demonstrated in Figure 2. The results indicate that the peak wavelength of green phosphor shifts to the shorter wavelength with the decrease of luminous level, which follows the transformation of mesopic luminous efficacy function from photopic to scotopic vision. In addition, the peak wavelength located at 450 nm is beneficial to the larger color gamut volume. Table 3 shows the corresponding values of mesopic luminance, gamut volume, and S/P ratio. A trade-off between mesopic luminance and color gamut is quite significant. The photopic/mesopic luminous efficacy of radiation (LER) of equal energy white light is about 181, 206, 230, 259 lm/W for 10, 1, 0.3, and 0.1, cd/m\({}^{2}\), respectively. In the aspect of the S/P ratio, the optimal spectra with a higher \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**cd/m\({}^{2}\)**} & \multicolumn{3}{c}{**Peak Wavelength (nm)**} & \multicolumn{3}{c}{**Density Ratios**} \\ \cline{2-7}  & **Opt\#1** & **Opt\#2** & **Opt\#3** & **Opt\#1** & **Opt\#2** & **Opt\#3** \\ \hline
10 & 450, 545, 610 & 450, 550, 585 & 450, 530, 615 & 0.4, 0.5, 1.0 & 0.4, 1.0, 0.9 & 0.6, 0.5, 1.0 \\
1 & 450, 535, 610 & 455, 550, 605 & 450, 530, 615 & 0.3, 0.4, 1.0 & 0.1, 0.2, 0.6 & 0.6, 0.5, 1.0 \\
0.3 & 450, 530, 615 & 455, 550, 605 & 450, 510, 635 & 0.6, 0.5, 1.0 & 0.1, 0.2, 0.6 & 0.2, 0.3, 0.8 \\
0.1 & 450, 515, 615 & 465, 510, 605 & 450, 515, 620 & 0.4, 0.5, 0.9 & 0.3, 0.5, 1.0 & 0.4, 0.5, 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information of optimal spectra. Figure 2: Optimal spectral power distributions (SPDs) for four lighting conditions: (a) 10 cd/m\({}^{2}\), (b) 1 cd/m\({}^{2}\), (c) 0.3 cd/m\({}^{2}\), (d) 0.1 cd/m\({}^{2}\). S/P ratio can raise the mesopic luminance and also extend the color gamut volume with a decrease in luminance. In other words, they are more appropriate for application in mesopic vision. The outcome is in accordance with the previous study [14]. Figure 3 shows the color gamut of optimal spectra in the CIE LAB color space under each lighting condition. The information of optimal spectra inclusive of LER, CRI, \(R_{\text{f}}\), \(R_{\text{g}}\), CCT, and Duv is presented in Table 4. LER(\(m\)) can be described as Equation (14), where LER\({}_{\text{mes}}(m)\) is calculated only when the luminance L\({}_{\text{p}}\) is below 5 cd/m\({}^{2}\). Otherwise, LER\({}_{\text{p}}\) is used to represent the LER. R\({}_{\text{f}}\) and R\({}_{\text{g}}\) are the fidelity and gamut index defined from IES TM-30-15 to evaluate color rendition. At present, the majority of the white LED spectrum is optimized based on luminous efficiency and color rendering index mostly in the photopic vision, which shows a wider color gamut than in mesopic vision. However, the conventional color rendering properties such as CRI and IES TM-30-15 cannot express the color variation with the  
Figure 3: Illustration of color gamut of optimal SPDs.