## 3 Conclusions  
In this paper, a comprehensive investigation was performed on the efficacy of the proposed easy-to-use and calculation-reducing method for UGR calculation for LED luminaires. UGR as a metric for evaluation of indoor lighting user visual discomfort is introduced in related standards, and advised UGR values should be observed by indoor lighting designers. Indoor lighting designers must simulate their designation to find out whether it meets the standard limits or not. The proposed method makes it possible to find by referral to the UGR table given by the manufacturer, or by an interpolation or extrapolation of the table numbers, the UGR of points on the room's midline. Efficacy and validation limits of the proposed method were mathematically proved and discussed in detail. Since LED luminaires have attracted great attention, it is crucial that approaches be found to calculate UGR while consuming less time and energy. For luminaires with diffusers or uniform luminous intensity distribution, the tabular method was proved, calculated, and simulated. The results confirmed the validity of this method.  
For luminaires with lenses, as in the method proof anticipated, the tabular method failed to model the UGR accurately. It can be based on non-uniform luminous intensity distribution of these types of luminaires. Further research is needed for modelling and finding a fast and easy-to-use way to calculate UGR for LED luminaires with lenses.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12073462/s1](https://www.mdpi.com/article/10.3390/app12073462/s1)]([https://www.mdpi.com/article/10.3390/app12073462/s1](https://www.mdpi.com/article/10.3390/app12073462/s1)).  
Conceptualization, R.A. and D.K.; methodology, R.A. and D.K.; software, R.A. and D.K.; validation, D.K.; formal analysis, R.A. and D.K.; investigation, R.A. and D.K.; resources, D.K.; data curation, R.A. and D.K.; writing--original draft preparation, R.A.; writing--review and editing, D.K.; visualization, R.A. and D.K.; supervision, D.K.; project administration, D.K.; funding acquisition, D.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c 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 data** & & & & & & & & & \\
**average from average of the simulated** & & & & & & & & \\
**UGR as a percentage of 30 units of** & & & & & & & & \\
**UGR**. & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: The deviation of 2D-interpolated or extrapolated data average from average of the simulated UGR as a percentage of 30 units of UGR for luminaires A to H.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \multicolumn{5}{c}{**Difference between Proposed Method and Simulation Results as a Percentage of 30 Units of UGR**} \\ \hline
**Luminaire Type** & & & & & & & & \\
**Observer Distance from Movement** & & & & & & & & \\
**Starting Point (m)** & & & & & & & & \\ \hline
**2** & 13.33\% & 36.5\% & 12.17\% & 17.00\% & 24.33\% & 10.27\% & 10.67\% & 0.60\% \\
**4** & & 3.33\% & 23.33\% & 7.67\% & 20.33\% & - * & 13.67\% & 10.67\% & 17.43\% \\
**6** & & 5.50\% & 2.50\% & 10.33\% & 20.27\% & - * & 13.00\% & 13.33\% & 10.77\% \\ \hline \hline \end{tabular}  
* Difference is incalculable since simulation software according to UGR exceeding of 30 units limit does not calculate the UGR.  
\end{table}
Table 7: The deviation of 2D-interpolated or extrapolated UGR table data from the simulated UGR as a percentage of 30 units of UGR for luminaires A to H.