## 2 Tabular Method for Reducing UGR Calculations, for Every Point on the Room Midline
### Case Study and Illustration of Implementation
#### 2.4.2 Luminaires Equipped with Lenses  
Since in most applications, LED luminous flux must be formed to meet lighting needs, using lenses is one of the approaches for this aim [32]. Therefore, lenses as optical accessories enhance luminous intensity in LED luminaires in the required direction. An LED luminaire with lenses is illustrated in Figure 8.  
Due to the popularity of LED luminaires with lenses, the UGR tabular calculation method proposed in this paper, with demonstrated validity for luminaires with diffusers (uniform luminous intensity distribution) and limitations explained in Section 2.3, is investigated in this case study to estimate efficacy of the method for luminaires with lenses. Although the feasibility of the method was shown in Section 2.3 for luminaires with diffusers (uniform luminous intensity distribution), luminaires equipped with lenses with variety in technical specifications were selected for this case study. The technical specifications of selected luminaires are illustrated in Table S22. For studying eight types of LED luminaires with lenses (luminous intensity distributions of the luminaires are illustrated in Figure 9a-h), UGR at an eye height of 1.2 m from the floor was simulated in DIALux software. The room size is 5H \(\times\) 5H. The observer moves on the room's midline from the left wall to the right wall of the room. For meticulous calculation, UGR is simulated in 0.5 m intervals and the results for all the types of luminaire are divided into luminaires with mild changes and those with drastic changes of UGR during the observer's movement on the room's midline, as illustrated in Figure 10a,b. Mild UGR changes correspond to UGR changes in a range of less than or equal to 6 units when the observer moves along the room's midline. For drastic UGR changes, the range of change is more than 6 units. Figure 8: A sample LED luminaire with lenses. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Luminaire Type** & **A** & **B** & **C** & **D** & **E** & **F** & **G** & **H** \\ \hline
**Deviation of 2D-interpolated or** & & & & & & & & \\
**extrapolated data from average of the** & & & & & & & \\
**simulated UGR as a percentage of 30** & & & & & & & \\
**units of UGR**. & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The deviation of 2D-interpolated or extrapolated UGR average from the simulated UGR average for luminaires A to H.  
As can be seen in Figure 10a,b, the change in UGR values for all LED luminaires with lenses along the midline of the room is more or less similar. They have an alternating behavior with a similar period. Luminaires E and C alternate drastically, while B, G, and F have smoother changes. For each luminaire type, the magnitude and the changes of the values are more or less similar along the observer's path for each UGR curve. Figure 9: _Cont._  
Figure 9: **(a–h)**. (Luminaires types A–H) Luminous intensity distribution of eight luminaires with lenses studied in this research. The points which can be deduced from Figure 10a,b can be summarized as follows:  
* Continuous curve represents lower contrast as UGR is a ratio of luminance (A, B, D, F, G and H). * The average UGR matters (UGR of G < UGR of B). * Discontinuous curve introduces a \"torch\" effect to the design (C and E). * If UGR is not available, there is a chance that its value reaches 30 (E). Figure 10: Eight LED luminaires’ UGR curves (**a**) for luminaires with UGR mild changes (\(\Delta_{max-min}\)UGR \(\leq\) 6), and (**b**) for drastic changes of UGR (\(\Delta_{max-min}\)UGR \(>\) 6) along the room’s midline. (For luminaires described in Figure 9a–h along the room’s midline when the observer’s viewing direction is parallel to the luminaires’ axis). Due to the prevalence of LED luminaires with lenses, it is helpful if methods can be found to calculate UGR for this luminaire type in a reliable manner, with the lowest possible number of calculations, and with acceptable accuracy.