## 2 Tabular Method for Reducing UGR Calculations, for Every Point on the Room Midline
### Case Study and Illustration of Implementation  
#### 2.4.1 Luminaires Equipped with Diffusers (Uniform Luminous Intensity Distribution)  
First, eight types of LED luminaire with diffusers are studied. The luminous intensity distribution for all the eight luminaire types can be seen in Figure 6a-h. Although feasibility of the method is shown in Section 2.3 for luminaires with diffusers (uniform luminous intensity distribution), luminaires with variety in technical specification were selected for practical investigation of the method's efficacy. The technical specifications of selected luminaires are illustrated in Table S5. For studying eight types of LED luminaires with diffusers, UGR at the eye height of 1.2 m is simulated in DIALux software. The room size is 5H \(\times\) 5H and the observer moves on the room's midline from the left wall to the right wall parallel to the luminaires' axis. For meticulous calculation, UGR is simulated each 0.5 m of the observer's path. Detailed results for all the types of luminaire are integrated and illustrated in Figure 7.  
As can be seen in Figure 7, UGR changes for all LED luminaires with diffusers along the midline of the room were more or less similar. They started with a value which decreased after passing each row of the luminaires perpendicular to the observer's viewing direction (moving path). After reaching the last two meters, the decrement became such that the UGR was under 10 units of UGR and was not given by the simulation software. Due to the prevalence of LED luminaires with diffusers, it is helpful to find methods to calculate UGR for this type of luminaire in a reliable manner, with the smallest possible number of calculations, and with acceptable accuracy. In this research, a tabular approach is proposed for the estimation of the UGR of LED luminaires with diffusers, as well as conventional luminaire types with uniform luminous intensity distribution for UGR calculation reduction with acceptable accuracy. Figure 6: _Cont._  
Figure 6: (**a-h**) (Luminaires types A–H) Luminous intensity distribution of the eight types of luminaires with diffusers studied in this research. For luminaires, manufacturers usually publish UGR calculating tables for obtaining UGR in the worst case, which corresponds to the midpoints of the walls. An example of a UGR table (luminaire with diffuser type A's UGR table) is illustrated in Supplementary Table S1. By accurate investigation of the curves in Figure 7 along with UGR tables published by manufacturers of eight types of LED luminaires with diffusers, a relation between them can be understood. As explained before, the proposed method uses each number in the UGR table related to a room with dimensions corresponding to the observer's position on a room midline. The X dimensions for two rooms are equal, but the Y dimension of the second (corresponding smaller) room is equal to the observer's distance from the opposite-side wall in the observer's field of view in the main room. As showed mathematically in Section 2.3, the method works properly. For further validation of the method, examples for luminaires with luminous intensity distributions as in Figure 6a-h will be examined. By examining eight luminaires A to H and using two sets of the table data for X = 2H and 4H as well as Y = 2H, 3H, 4H, and 6H (as within the red border in Supplementary Table S1 and illustrated in Supplementary Tables S6-S13) for 2D interpolation or extrapolation, the similarities between the results of simulation and the proposed method for the mentioned types of luminaires are checked and confirmed (Tables S14-S21). X dimensions (2H and 4H) are selected since the room dimension 5H is near these two values and the ranges of Y from 2H, 3H, 4H, and 6H correspond to 4 m, 6 m, 8 m, and 12 m, respectively, which properly cover the observer's distance from 10 to 0 m from the opposite-side wall.