## 3 Simulation of UGR and Illumination Uniformity
### UGR and Uniformity at Beam Angles of 70-120\({}^{\circ}\) at the Same Height  
Table 2 shows the DIALux simulation parameters. It has a luminous flux of 800 lm, reflection factors of desk surface of 50% and desk lamp height of 45 cm. Table 3 shows the variation in the UGR with the beam angle of 70-120\({}^{\circ}\). We can vary the beam angles without changing the height of the desk lamp on the study desk to compare the corresponding UGR values. Figure 2 shows the isoline and color illumination map (lux) of uniformity under different beam angle conditions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Characteristics** \\ \hline \(L0\) (desk length) & 140 cm \\ \(W0\) (desk width) & 80 cm \\ \(L1\) (calculation object length) & 40 cm \\ \(W1\) (calculation object width) & 40 cm \\ \(D1\) (the distance between desk lamp and observer) & 60 cm \\ \(H1\) (the distance between desk surface and observer) & 40 cm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation setup parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Specifications** & **Characteristics** \\ \hline Luminous flux & 800 lumens \\ Reflection factors of desk surface & 50\% \\ Desk lamp height (\(H2\)) & 45 cm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DIALux simulation parameters. Figure 1: Simulation spatial characteristic in software: (**a**) desk luminaire plan and (**b**) side view of desk lamp on study desk. Figure 2 shows the isoline and color illumination map under different beam angles: 70\({}^{\circ}\), 80\({}^{\circ}\), 90\({}^{\circ}\), 100\({}^{\circ}\), 110\({}^{\circ}\), and 120\({}^{\circ}\) respectively. Figure 2c shows the simulation result with a desk lamp beam angle of 90\({}^{\circ}\) in the illumination isoline. This result indicates that the 1000-1400 lux isoline is distributed in most of the space and the \(>\)1000 lux isoline is at the four corners, as indicated by the orange and yellow regions, respectively. The lux isoline changes with a variation in the beam angle. When the beam angle increases, the isoline distribution becomes more uniform because the light exposure range is wider. The simulation results were used to calculate the illumination and uniformity for different beam angles. As shown in Table 4, the uniformity had its maximum value of 0.83 for a beam angle of 120\({}^{\circ}\). The average illumination was 1139 lux for a beam angle of 90\({}^{\circ}\); this was higher than the values for beam angles of 100-120\({}^{\circ}\). The illumination value is greater than 500 lux to comply with the regulations for a desk lamp for a study desk. Figure 3 shows the luminous intensity profile for beam angles of 70-120\({}^{\circ}\). The luminous intensity field for a beam angle of 70\({}^{\circ}\) was the narrowest; with an increase in the beam angle, the luminous intensity field widened. In the determination of the UGR, a narrow beam angle outperformed a wide beam angle. By contrast, in the determination of the illumination uniformity, a wide beam angle was superior to a narrow beam angle. Tables 3 and 4 show the homogenized UGR and uniformity values, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{6}{c}{**Beam Angle**} \\ \cline{2-7}  & **70\({}^{\circ}\)** & **80\({}^{\circ}\)** & **90\({}^{\circ}\)** & **100\({}^{\circ}\)** & **110\({}^{\circ}\)** & **120\({}^{\circ}\)** \\ \hline Average flux (lux) & 1571 & 1322 & 1139 & 998 & 891 & 805 \\ Minimum flux (lux) & 1175 & 1032 & 911 & 810 & 731 & 666 \\ Maximum flux (lux) & 2053 & 1676 & 1414 & 1220 & 1074 & 959 \\ Uniformity & 0.75 & 0.78 & 0.8 & 0.81 & 0.82 & 0.83 \\ \hline \end{tabular}
\end{table} 
Table 4: Illumination and uniformity for beam angles of 70–120\({}^{\circ}\). Figure 4 shows the relationship between UGR and uniformity at various beam angles.