## 4 Discussion
### Comparison of Ceiling Light Distribution Uniformity  
Calculations were conducted using the Dialux 9.1 software (DIAL GmbH, Bahnhof-sallee 18, 58507 Ludenscheid, Germany) and the relevant IES files for the luminous intensity curves to assess ceiling illumination uniformity and intensity. A virtual room, 6 m long, 4 m wide, and 3 m high, was created for the simulation. Typical materials for the ceiling, wall, and floor were chosen with reflectance values of 85%, 70%, and 60%, respectively, to accurately visualize the ceiling's appearance in the simulation. However, these reflectance values were not factored into the direct illuminance calculations, ensuring that only the direct illumination component was analyzed. Two sets of six luminaires (a total of twelve) were mounted on opposite sides of the room, positioned 0.3 m below the ceiling (\(H\) = 0.3 m). The luminaires were aligned such that their maximum intensity rays formed an 80 deg angle with the vertical. The total LED luminous flux for the simulation was 19,200 lm (12 \(\times\) 1600 lm). Two types of average illuminance \(\overline{E}\) measurements across the ceiling were determined. The first type, \(\overline{E}_{ceiling}^{direct}\), accounted solely for direct light from the light sources to the ceiling, aiding in the comparison of different luminaires for ceiling illumination. The second type, \(\overline{E}_{ceiling}^{total}\), included all light rays--both direct and reflected from surrounding surfaces--offering a realistic view for practical installations that consider the complete interplay of light with the environment. The illuminance uniformity U\({}_{0}\) was employed as a measure of lighting quality, defined by the ratio of minimum to average illuminance \(E_{min}/\overline{E}\). Tube LEDs are commonly utilized for ceiling and wall lighting and act as reference points for evaluating advanced AL-TIR LED luminaires. Figure 8 presents a 3D rendering of the ceiling illuminated by tube LEDs, with the associated illuminance color map shown in Figure 8. Their extensive Lambertian luminous intensity distribution results in a concentration of light near the fixtures, leading to a low direct illuminance uniformity \(U_{TLED}^{direct}\) = 0.25. While tube LEDs offer simplicity and cost-effectiveness, their use in ceiling applications, particularly within decorative ceiling boxes, often results in light being trapped and wasted. Wall-washing LED luminaires, noted for their narrow-spread angles, provide an alternative method for ceiling illumination. Figure 8 illustrates a 3D view of a ceiling lit by NF301 LED (NVC Lighting Inc., Ruhu, Huizhou, Guangdong, China), while Figure 8 displays the corresponding illuminance color map. These LEDs achieve a \(U_{NVCLED}^{direct}\) = 0.56 for direct illumination. Despite the improved U\({}_{0}\), diminished light levels are still discernible in the vicinity of the luminaires. Figure 8,f reveal the lighting impact of the L1-AL0 luminaire equipped with an AL0 lens. The L1-AL0 luminaire's \(U_{AL0}^{direct}\) = 0.57, matching the \(U_{NVCLED}^{direct}\) = 0.56 of the NF301 luminaire and indicating an improved overall lighting intensity. The direct ceiling illuminance \(\overline{E}_{ceiling}^{direct}\) provided by the L1-AL0 luminaire is 366 lx, which exceeds the 292 lx provided by the NF301 luminaires. Figure 9,b present the influence of the L2-AL6 luminaire, featuring an AL6 lens, on ceiling brightness, showcasing a significant rise in direct \(U_{AL6}^{direct}\) to 0.78. The average direct illuminance \(\overline{E}_{ceiling}^{direct}\) for the L2-AL6 luminaire is equivalent to that of the L1-AL0 luminaire, rendering the L2-AL6 design a promising option for widespread production. Figure 9-f illustrate the ceiling illuminated by the L3 AL-STIR and L4 AL-ATIR luminaires, which incorporate ALs with TIR optics. The L3 AL-STIR luminaire combines two symmetric TIR optics with an AL, constituting an AL-STIR system, and achieves a \(U_{NVCLED}^{direct}\) = 0.63.