## 2 Photometric and Melanopic Relationships among Different Standards
### Radiometric and Photometric Characterization of LEDs  
In this study, 39 commercial light-emitting diodes (LEDs) from NICHIA Corp. (Tokushima, Japan); Bridgelux, Inc. (Fremont, CA, USA); Open Photonics, Inc. (Orlando, FL, USA); Seoul Semiconductor Co., Ltd. (Gyeonggi, South Korea); and SORAA Corporation (Fremont, CA, USA) were characterized and analyzed. These lamps have diverse SPDs and different CCTs (from approximately 2200 K to 6700 K) and CRI \(>\) 80 (Figure 1). Based on photometric principles, their properties were calculated from their SPDs (Table 1).  
Based on the spectral distribution data in Figure 1, EDI (according to CIE S026:2018) and EML (according to WELL) for the different lamps at different CCTs were calculated for equal photopic illuminance (100 lux). These results were estimated at eye level. Based on the same spectral distributions, the circadian light (CL\({}_{\rm A}\)) and circadian stimulus (CS) as described by [PERSON] et al. [14] were also calculated (Table 2). To these calculations, we added calculations for the theoretical A, D65, and equal-energy illuminant, as described by the CIE. Table 2 shows the MAF calculated using Equation (4) from SPD, which is employed to find the melanopic illuminance with the different metrics. Differences among the outcomes occur, first, because of the normalization that is performed in the WELL metric with respect to the equal-energy illuminant, in the CIE metric with respect to the D\({}_{65}\) illuminant, and in the study by [PERSON] et al. with respect to the A illuminant. The WELL values are always higher than those described by the CIE, with a factor 1.104 according to Equations (7) and (10). [PERSON] et al. [14] adopted the function described in Equation (12); its discontinuity is found in Table 2 due to the differences in the definition of luminous efficiency in warm or cool lamps (part of the luminous efficiency has a negative contribution), where the circadian values that correspond to LEDs #16 to #21 (CCT from approximately 4100 K to 3500 K) have a lower melanopic efficiency when the calculations are performed with this metric rather than the other two (Figure 2).  
Figure 1: Spectral power distributions of LEDs divided by Correlated Color Temperature (CCT). (**A**) \(>\)5001 K series, (**B**) 4001–5000 K series, (**C**) 3001–4000 K series, and (**D**) \(<\)3000 K series.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \# & **MAF** & **EDI (lux)** & **EML (lux)** & **Circadian Light (CL\({}_{\text{A}}\)) (lux)** & **Circadian Stimulus (CS)** \\ \hline D\({}_{65}\) (CIE) & 0.906 & 100.00 & 110.40 & 150.98 & 0.196 \\ \hline A (CIE) & 0.449 & 49.59 & 54.75 & 99.99 & 0.139 \\ \hline EQUAL-ENERGY & 0.821 & 90.58  
Regarding CCT, it has been determined that for the same CCT and equal photopic illuminance (100 lux), in general terms EDI and EML linearly increase with an increase in CRI (Figure 3). The same behavior can be observed in the Rea metric, particularly at higher CCTs. At lower CCTs, it is more difficult to determine a fixed rule, perhaps because of the low number of LEDs evaluated with CRI\({}_{90}\) and CRI\({}_{95}\). These characteristics are often observed. However, each lamp must be analyzed in detail, not only by CCT or CRI but also by its SPD. The MAF calculated with Equation (4) has a linear relationship with CCT, and it seems that the two well-correlated parameters can be used as references for the properties of the LEDs.