## 3 Calculation and Simulation Results
### Simulation Results  
Figure 5 shows a graphical representation of the calculation results for four different LED luminaire configurations. On the left, there is a tracing diagram showing random red, green, and blue rays emanating from the LED sources, illustrating the path, and the spread of light in various directions. In the middle, lighting distribution curves are depicted, likely in the form of graphs or charts, demonstrating how the luminous intensity varies in different directions. On the right, there is a 3D distribution curve, which provides a three-dimensional representation of the light spread, showing both the intensity and the spatial distribution of the light from the LED luminaires. As illustrated in Figure 5, the emission angles on plane C90 for all the luminaires are notably narrow, enhancing luminous intensity on distant ceiling areas when aligned correctly. Conversely, the wider emission angles on plane C0 facilitate sufficient overlap in the proximity of the ceiling, ensuring uniform illumination. The colors in Figure 5 are used solely for visualization purposes to differentiate individual light rays within the optical path and do not indicate specific wavelengths or intensities. In the ray tracing diagram for luminaires L1-AL0 and L2-AL6 with only AL in use, it is observed that a segment of the light beam on the right side significantly deviates from the main beam. This deviation could cause glare for the observer unless mitigated by an extra barrier. Upon integrating total internal reflective components, as depicted in luminaires L3 AL-STIR and L4 AL-ATIR, the previously mentioned light beam segments were redirected towards the intended target. This modification not only reduced glare but also improved the overall luminous efficacy of the luminaires. Figure 4: LED luminaire configurations: L1–AL0 with AL segmented into non-refractive (**left**) and refractive (**right**) sections; L2–AL6 with progressively increasing refraction; L3 AL–STIR with two symmetric total internal reflection (STIR) optics; L4 AL–ATIR with a gradient in refraction paired with ATIR optics for enhanced light control. The width of the LED bar is 1 mm. Figure 5: Photometric analysis of luminaires L1–AL0, L2–AL6, L3–AL STIR, and L4–AL ATIR. (**Left**) Ray tracing visualization with RGB light rays illustrating the directional spread of light for each design. (**Middle**) Polar luminous intensity distribution plots showing angle-based light intensity variation, revealing beam shape and spread. (**Right**) 3D polar distribution maps depicting spatial intensity in color-coded format, highlighting regions of high and low intensity. These visualizations enable comparison of each luminaire’s light distribution characteristics, including directionality, uniformity, and intensity control. It is important to note that the lens designs were tailored for practical application, incorporating lens fixation elements at the cost of minor light losses, as can be observed in the tracing diagrams. To navigate this complexity, the ensuing section will introduce the use of rectangular luminous intensity curves as a more efficacious approach for analyzing and evaluating the diverse luminaire configurations. This methodology will facilitate a comprehensive comparison, underpinning a deeper understanding of each design's merits and limitations. Furthermore, the practicality and impact of our design recommendations will be substantiated through case studies, meticulously examining their efficacy in real-world ceiling illumination scenarios. The two lighting researchers [PERSON] and [PERSON] stated in 1978 that at a horizontal illuminance of 1000 lx, a luminance for the ceiling of 200 cd/m\({}^{2}\) and for the walls of 100 cd/m\({}^{2}\) are preferred [24]. At a horizontal illuminance of 500 lx (as defined as a minimum by EN 12464-1:2021 [25]), the above values can be estimated as about 210 cd/m\({}^{2}\) (ceiling) and 70 cd/m\({}^{2}\) (walls).