## 4 Discussion  
### Comparison of Luminous Intensity Distribution Curves  
In Figure 6, the luminous intensity curves for luminaires L1-AL0 and L2-AL6, as well as the ideal luminous intensity curve (K3 LOG) defined by \(k=3\) are illustrated. The luminous intensities of these curves have been normalized, implying that the total fluxes of these luminaires are equivalent. The integral of the luminous intensity values across all the angles, ranging from 0\({}^{\circ}\) to 360\({}^{\circ}\), was calculated and employed as a division factor. The angles at which the maximum luminous intensities occur were aligned to be at 80\({}^{\circ}\), matching the angle of maximum intensity for the ideal luminous intensity curve to facilitate the comparison. The luminous intensities have been adjusted to reflect equal total fluxes across the luminaires, meaning their outputs are comparable. To normalize these curves, the area under the luminous intensity distribution from 0\({}^{\circ}\) to 360\({}^{\circ}\) was calculated and used as a normalization factor. The peak luminous intensities for each curve have been synchronized  
Figure 6: Normalized luminous intensity distribution curves for the L1–AL0 luminaire with AL0 lens, the L2–AL6 luminaire with AL6 lens, and the ideal \(k=3\) curve. The peak intensities are aligned at 80 degrees to compare OUF and uniformity. to occur at 80\({}^{\circ}\) to align with the peak of the ideal luminous intensity curve, enhancing the clarity of comparison. The maximum intensity of the L1-AL0 luminaire with an AL0 lens at this position is only a fourth of the ideal curve's peak intensity. This reduction is attributed to the light that is distributed in less efficient angular regions, specifically from 0\({}^{\circ}\) to 60\({}^{\circ}\), 85\({}^{\circ}\) to 90\({}^{\circ}\), and 190\({}^{\circ}\) to 220\({}^{\circ}\). Conversely, the luminous intensity in the range of 0\({}^{\circ}\) to 60\({}^{\circ}\) for the L1-AL0 luminaire is higher than that of the ideal curve, leading to a less uniform lighting distribution on the ceiling, which will be demonstrated in the forthcoming calculations of ceiling lighting distribution. In Figure 7, the graphical representation showcases the normalized luminous intensity distribution curves for two different luminaires, L3 AL-STIR equipped with an AL-STIR optic and L4 AL-ATIR with an AL-ATIR optic, alongside the luminous intensity curve termed K3 LOG, which is derived using a \(k\)-value of three. The normalization process applied here mirrors that utilized for the L1-AL0 and L2-AL6 luminaires, ensuring that the total light output, quantified as the integral of luminous intensity values over a full 360\({}^{\circ}\) range, is consistent across all the luminaires, thereby enabling a fair comparison of their lighting distribution profiles. From the graph, it is noticeable that both the L3 AL-STIR and L4 AL-ATIR luminaires exhibit peak lighting intensities that are slightly lower than the peak of the ideal K3 LOG curve. This subtle deviation indicates a marginally reduced luminous intensity at the angle of maximum emission when compared to the theoretical optimum modeled by the K3 LOG curve. The inclusion of TIR elements in the luminaire designs, as indicated by the AL-STIR and AL-ATIR nomenclature, appears to have contributed to an improved luminous intensity distribution, drawing it closer to the ideal curve's distribution. The curves for L3 AL-STIR and L4 AL-ATIR also suggest a good alignment with the shape of the K3 LOG curve, particularly around the peak, which implies that the TIR components in their lenses are effective in directing the light towards the target angle. However, the L3 AL-STIR luminaire's curve indicates insufficient lighting intensity from 0\({}^{\circ}\) to approximately 80\({}^{\circ}\), suggesting a lack of illumination in the ceiling's proximal area. Figure 7: Comparison of the normalized luminous intensity curves for the L3 AL–STIR luminaire with AL–STIR lens, L4 AL–ATIR luminaire with AL–ATIR lens, and the ideal \(k\) = 3 curve (K3 LOG).