## 4 Discussion
### Comparison of Ceiling Light Distribution Uniformity
Notably, the L4 AL-ATIR luminaire, which integrates an AL with asymmetric TIR elements (AL-ATIR), attains the highest uniformity with a \(U_{ALATIR}^{direct}\) = 0.83 and an average illuminance of 429 lx, as depicted in (c) and (d). These findings align with the analysis of rectangular luminous intensity curves in Figure 7, which juxtaposes the AL-ATIR with the ideal K3 LOG curve. The inability of the L4 AL-ATIR luminaire to reach perfect direct illuminance uniformity \(U_{ital}^{direct}=1\) may be attributed to factors such as the intricacies of the optical design and the physical dimensions of the LED packages. Moreover, the necessity for complex thermal management with smaller LED packages makes them less viable for HCL applications. The findings from the ceiling illumination analysis are consolidated in Table 1. \(\overline{E}_{ceiling}^{direct}\) denotes the average direct illuminance on the ceiling. Direct optical utilization factor (DOUF) represents the ratio of direct luminous flux to total flux; \(\overline{E}_{ceiling}^{total}\) signifies the average total illuminance on the ceiling, factoring in the reflected light from surrounding surfaces. Notably, the total optical utilization factor (TOUF) can exceed 100% due to the substantial contribution from reflected light. In summary, we selected the tube LED as a reference configuration due to its popularity and widespread use as a standard luminaire. The NFLED was chosen for its reputation as one of the top-performing wall-washing luminaires. The AL0 and AL6 LED luminaires were included based on their use in previous projects, allowing for direct and straightforward  
Figure 8: Comprehensive 3D renderings and illuminance color maps for diverse LED luminaire configurations illustrating their effects on direct ceiling illumination: (**a**,**b**) feature 12 tube LEDs with a direct illuminance uniformity \(U_{TLED}^{direct}\) of 0.25; (**c**,**d**) display 24 NVC NF301 LEDs achieving a \(U_{NVCLED}^{direct}\) of 0.56 for improved uniformity; (**e**,**f**) show ceiling illumination by an AL0 LED (L1–AL0 luminaire) with a \(U_{AL0}^{direct}\) of 0.57.  
comparison. Finally, the AL-STIR LED was included based on recent advancements proposed by [PERSON] et al. [19] in asymmetric lighting design. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Luminaires**} & \multirow{2}{*}{**Optics**} & \multicolumn{2}{c}{**Illuminance**\(\begin{subarray}{c}\text{{\emph{-direct}}}\\ \text{{\emph{Engine}}}\text{{\emph{(k)}}}\end{subarray}\)} & \multirow{2}{*}{**Dir. Util.**} & \multirow{2}{*}{**Factor DOUF**} & \multicolumn{2}{c}{**Direct Uniform**} & \multicolumn{2}{c}{**Illuminance**\(\begin{subarray}{c}\text{{\emph{-total}}}\\ \text{{\emph{Engine}}}\text{{\emph{(k)}}}\end{subarray}\)} & \multirow{2}{*}{**Total Uniform**} & \multirow{2}{*}{**Total Util.**} \\  & & \(E_{\text{\emph{Engine}}}\text{{\emph{(k)}}}\) & & & & & \\ \hline \(12\times\) TLED & Diffuser & 252 & 36\% & 0.25 & 483 & 0.42 & 70\% \\ \hline \(24\times\) NF301 & Sym. Lens & 292 & 43\% & 0.56 & 404 & 0.76 & 57\% \\ \hline \(12\times\) L1-AL0 & AL0 Lens & 366 & 53\% & 0.64 & 606 & 0.75 & 88\% \\ \hline \(12\times\) L2-AL6 & AL6 Lens & 362 & 53\% & 0.78 & 556 & 0.90 & 81\% \\ \hline \(12\times\) L3-AL STIR & AL STIR & 354 & 51\% & 0.63 & 487 & 0.87 & 71\% \\ \hline \(12\times\) L4-AL ATIR & AL ATIR & 429 & 63\% & 0.83 & 700 & 0.91 & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ceiling illumination analysis results. Figure 9: Three-dimensional renderings and illuminance color maps of advanced AL LED luminaires demonstrating their impact on ceiling illumination: (**a,b**) AL6 LED configuration provides a uniformity \(U_{AL6}^{direct}\) of 0.78, depicting efficient light distribution; (**c,d**) AL–STIR LED setup, achieving a uniformity \(U_{INVLED}^{direct}\) of 0.63, combines optics for balanced illumination; (**e,f**) AL–ATIR LED arrangement reaches the highest uniformity \(U_{ALATIR}^{direct}\) of 0.83, showcasing optimal uniformity and intensity control across the ceiling.