## 3 Simulation of UGR and Illumination Uniformity
### UGR and Uniformity at Beam Angle of 90\({}^{\circ}\) for Different Desk Lamp Heights  
Table 5 shows the variation in the UGR with the desk lamp height for a beam angle of 90\({}^{\circ}\). We can modulate desk lamp height without changing the beam angle of the desk lamp to compare UGR. Figure 5 shows the isoline and color illumination map (lux) of uniformity for different desk lamp heights with a beam angle of 90\({}^{\circ}\). Figure 4: UGR and uniformity for beam angles of 70–120\({}^{\circ}\). Figure 3: Luminous intensity field profile for beam angles of 70–120\({}^{\circ}\). Figure 5: Isoline and color illumination map (lux) with different light source heights: (**a**) 35 cm, (**b**) 40 cm, (**c**) 41 cm, (**d**) 42 cm, (**e**) 43 cm, (**f**) 44 cm, (**g**) 45 cm, (**h**) 46 cm, (**i**) 47 cm, (**j**) 48 cm, and (**k**) 50 cm. \begin{table}
\begin{tabular}{c c c} \hline
**Beam Angle Degree** & **Desk Lamp Height \(H2\) (cm)** & **UGR** \\ \hline
90 & 35 & \(<\)10 \\
90 & 40 & \(<\)10 \\
90 & 41 & \(<\)10 \\
90 & 42 & 13.1 \\
90 & 43 & 15 \\
90 & 44 & 16.3 \\
90 & 45 & 17.4 \\
90 & 46 & 19.2 (fail) \\
90 & 47 & 20.7 (fail) \\
90 & 48 & 21.8 (fail) \\
90 & 50 & 23.5 (fail) \\ \hline \end{tabular}
\end{table} 
Table 5: Relationship between UGR and desk lamp height. Figure 5 shows the isoline and color illumination map (lux) with different light source heights: 35, 40, 41, 42, 43, 44, 45, 46, 47, 48, and 50 cm, respectively. Figure 5g shows the lux isolines simulated using a 45 cm high desk lamp; 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 simulation results were used to calculate the illumination uniformity for different desk lamp heights. To comply with the regulations for a study desk, a desk lamp height of 50 cm resulted in the highest uniformity, and a height of 35 cm resulted in the highest average flux. Tables 5 and 6 present the homogenized UGR and uniformity values, respectively. Figure 6 shows the variation in the UGR and the uniformity with the desk lamp height. For a beam angle of 90\({}^{\circ}\) and desk lamp height of 45 \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Beam Angle Degree** & **Desk Lamp Height**\(H2\) **(cm)** & **Rotation Angle (\(\theta\))** & **UCR** \\ \hline
90 & 45 & 5\({}^{\circ}\) & \(<\)10 \\
90 & 45 & 4\({}^{\circ}\) & \(<\)10 \\
90 & 45 & 3\({}^{\circ}\) & 12.1 \\
90 & 45 & 2\({}^{\circ}\) & 14.4 \\
90 & 45 & 1\({}^{\circ}\) & 16.1 \\
90 & 45 & 0\({}^{\circ}\) & 17.4 \\
90 & 45 & \(-1^{\circ}\) & 19.4 (fail) \\
90 & 45 & \(-2^{\circ}\) & 21.2 (fail) \\
90 & 45 & \(-3^{\circ}\) & 22.6 (fail) \\
90 & 45 & \(-4^{\circ}\) & 23.6 (fail) \\
90 & 45 & \(-5^{\circ}\) & 24.5 (fail) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Relationship between UGR and rotation angle. Figure 7 shows isoline and color illumination map (lux) with different desk lamp rotation angles \(5^{\circ},4^{\circ},3^{\circ},2^{\circ},1^{\circ},0^{\circ},-1^{\circ},-2^{\circ}, -3^{\circ},-4^{\circ}\), and \(-5^{\circ}\), respectively. Figure 7f shows the lux isolines simulated using a desk lamp rotation angle of \(0^{\circ}\); the 1000-1400 lux isoline and the \(>\)1000 lux isoline are at the four corners, similar to the situation resulting from a rotation angle of \(1^{\circ}\), as indicated by the orange and yellow regions, respectively. The simulation results were used to calculate the illumination and uniformity for different desk lamp rotation angles, as shown in Table 8. For a desk lamp rotation angle of \(0^{\circ}\), the uniformity achieved the maximum value of 0.8. For the determination of the illumination and uniformity, a rotation angle of \(0^{\circ}\) was better than other rotation angles. Tables 7 and 8 show the homogenized UGR and uniformity values, respectively. Figure 8 shows the variation in the UGR and the uniformity with the rotation angle.