## 3 Indoor Lighting Simulations
### Lighting for Elderly Individuals  
The age-dependent spectral correction factor for lens transmission k(\(\lambda\),\(\gamma\)) defined for an observer of age Y is a parameter that should be considered to address nonvisual effects of light in lighting designs in which the age of the user is a key factor [32]. This value is defined as k(\(\lambda\),32 years) = 1, and the higher that the age is, the lower the value. This correction factor enables us to estimate the real transmission factor of the eye, the lens in particular, and to determine how much light passes through the pupil and reaches the retina. Table 6 shows the calculations for 4 LEDs whose characteristics are provided in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\#} & \(\mathbf{k_{mel,trans}}\) & \(\mathbf{k_{mel,trans}}\) & \(\mathbf{k_{mel,trans}}\) & \(\mathbf{k_{mel,trans}}\) \\ \cline{2-5}  & **(10 Years)** & **(32 Years)** & **(45 Years)** & **(75 Years)** \\ \hline
4 & \(1.118\) & \(1.000\) & \(0.889\) & \(0.598\) \\ \hline
15 & \(1.111\) & \(1.000\) & \(0.895\) & \(0.615\) \\ \hline
24 & \(1.103\) & \(1.000\) & \(0.901\) & \(0.635\) \\ \hline
32 & \(1.099\) & \(1.000\) & \(0.906\) & \(0.653\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Age-dependent correction factor for lens transmission at four ages calculated for four LEDs.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Wall Reflectance 80\%, Rotation around**} & \multicolumn{2}{c}{**Table**} & \multicolumn{2}{c}{**Table**} \\ \cline{2-5}  & **a Horizontal Axis** & \multicolumn{2}{c}{**(Reflectance 60\%)**} & \multicolumn{2}{c}{**(Reflectance 0\%)**} \\ \cline{2-5}  & **Photopic Illuminance (lux)** & **E\textundersundersunders** & **E\textundersundersunders** & **E\textundersundersunders** & **E\textundersundersunders** \\ \hline \multirow{3}{*}{\(0^{\circ}\)} & Intensive & 330 & 269 & 276 & 216 \\ \cline{2-5}  & Lambertian & 407 & 401 & 357 & 348 \\ \cline{2-5}  & Extensive & 430 & 429 & 373 & 370 \\ \hline \multirow{3}{*}{\(45^{\circ}\)} & Intensive & 291 & 284 & 95 & 92 \\ \cline{2-5}  & Lambertian & 318 & 312 & 124 & 120 \\ \cline{2-5}  & Extensive & 336 & 324 & 124 & 121 \\ \hline \multirow{3}{*}{\(60^{\circ}\)} & Intensive & 319 & 309 & 82 & 80 \\ \cline{2-5}  & Lambertian & 329 & 318 & 94 & 88 \\ \cline{2-5}  & Extensive & 353 & 336 & 95 & 90 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Relationship between vertical illuminance at the eye-level plane (120 cm) with a wall reflectance of 80% and angular variation with respect to the horizontal axis.  
Figure 6: Graphical representation of the angular variation of the vision axis with respect to the horizontal axis; vertical illuminance at the eye-level plane (120 cm); wall reflectance of 80%.  
The higher the CCT is, the lower the \(\rm{k_{mel,trans}}\). This phenomenon combined with the age of the subject creates a wide spectrum of possibilities that must be considered in lighting projects. As described below, Equations (7), (10), and (12) were defined at the corneal plane or entrance of the pupil (EP). Now, they must be modified to determine how much melanopic illuminance reaches the retina:  
\[\rm{EML_{Retina}}=\rm{EML_{EP}}\times\rm{k_{mel,trans}}\rightarrow\rm{EML_{EP}}= \frac{\rm{EML_{Retina}}}{\rm{k_{mel,trans}}}, \tag{13}\]  
\[\rm{EDI_{Retina}}=\rm{EDI_{EP}}\times\rm{k_{mel,trans}}\rightarrow\rm{EDI_{EP} }=\frac{\rm{EDI_{Retina}}}{\rm{k_{mel,trans}}}, \tag{14}\]  
\[\rm{CL_{A-Retina}}=\rm{CL_{A-EP}}\times\rm{k_{mel,trans}}\rightarrow\rm{CL_{A- EP}}=\frac{\rm{CLA_{-Retina}}}{\rm{k_{mel,trans}}}, \tag{15}\]  
where \(\rm{EML_{Retina}}\), \(\rm{EDI_{Retina}}\), and \(\rm{CL_{A-Retina}}\) are the effective values required by their respective standards--for example, illumination levels in different hospital areas, schools, or residential homes--and that should be considered in lighting projects.