# Uncertainty of UGR Determination

The UGR index value is determined indirectly based on the distribution of luminance. All the indexes used to assess glare were defined in the form of mathematical formulas taking into account the respective lighting parameters and geometrical relationships. In Wolska et al. [2016], an analysis of uncertainties was carried out using the total differential method for formulas used to determine the values of UGR and GR indices. The formula for UGR (Formula (4.2)) can be written in a form depending on a single glare source, taking into account the measured parameters (Formula (10.9)).

where: AUCR - measurement uncertainty (indirect determination of the UGR), Au - uncertainty of measurement of the average luminance of the f-th luminaire (cd/m2), До), - uncertainty of measurement of the solid angle of the /-th luminaire coco, (sr), APj - uncertainty in determining the index P„ AUl - uncertainty of measurement of the average luminance of the background (cd/m2).

The analysis leads to important conclusions regarding the impact of individual parameters on the uncertainty of determining the glare index. Usually the background luminance does not exceed 100 cd/m2. However, it is assumed that discomfort glare may occur only at source luminance exceeding 600 cd/m2 [CIE 1983]. In practice, most often the luminaire’s luminance value is at least 1000 times higher than the background luminance (in the case of LEDs, the multiplier may be much higher). In both cases, the luminance is measured by the same instrument, which means that the values AUi and Au, are the same. Taking into account the relationship between source luminance and background luminance, it can be concluded that the uncertainty of background luminance measurement is a decisive factor. The impact of the uncertainty of measurement of the luminance source is significantly smaller - it can be practically negligible [Wolska et al. 2016; Sawicki et al. 2016b],

# UGR Determination - the Problem of the Angular Size of Glare Sources

The problem of the angular size of glare sources should be considered independently. This is especially important in the analysis of glare from the LEDs commonly used today [Khan et al. 2015]. The rules for determining the UGR index precisely define the angular limits of the observed source. It was assumed that this source should be in the range from 0.0003 sr to 0.1 sr. Therefore, both very small light sources and very large ones are negligible. CIE document [CIE 2002] extended the possibility of using the UGR index for small sources. This was due to the wide use of raster luminaires. The CIE publication assumed that in this case the luminance of the source in the UGR formula should be expressed by the quotient of the luminous intensity of the luminaire in a given direction and the apparent field of the luminous area. At the same time, it was assumed that the apparent luminous area of the source should not be less than 0.005 m2, and the source should be at least 5° above the line of sight.

Research carried out in the 1990s [Flannagan 1999] showed that small light sources with 0.3° or 0.6° angular size which are visible in the field of view do not affect the correct distinguishing of details at all - and therefore do not cause glare. However, it should be taken into account that these tests were carried out using conventional light sources. In contrast, LEDs in the same geometrical conditions can affect glare due to their very high luminance. This was confirmed by later studies; an increase in the luminance of small sources causes an increase in discomfort [Rosenhahn et al. 2004]. Problems related to the size and geometry of the sources are decisive for assessing the impact of LEDs on glare. This is confirmed by different studies [Scheir et al. 2015; Tashiro et al. 2015] in which the authors examined the impact of LED matrices on the glare impression.

In Nonne et al. [2013], the authors analyzed the differences in glare using different light sources: traditional ones and LEDs in different versions. Because LEDs are characterized by a small apparent luminous area, the authors of the study used the UGR formula for small sources and the standard formula. Their conclusion was that the traditional formula provides an assessment which is closer to human perception.

The publication by Eble-Hankins et al. [2009] describes research on the subjective assessment of glare from sources w'ith different non-uniform distribution of luminance, modeled by black and white stripes of different spatial frequency of source. It has been shown that discomfort rises with the increase of spatial frequency. On the other hand, however, a non-uniform stimulus is considered less uncomfortable than a uniform one. The impact of the luminous structure of luminaires with non-uniform luminance on discomfort was also found, especially the luminance of relatively dark parts of the luminaire and the average luminance of the glare source [Funke et al. 2015]. However, there was no effect of distance between LED points inside the luminaire, regardless of the direction of observation of luminance contrasts inside the luminaire [Funke et al. 2015].

The most radical conclusions were reached by the authors of the document by Cai et al. [2013]. The authors stated that all the formulas used so far are inappropriate to assess glare from LEDs. Other studies prove that glare assessment of complex light scenes (with small or large sources, complex luminance distributions) may require fundamental changes in the creation of glare models [CIE 2016b; Clear 2013]. Hence, there are also new proposals for UGR formulas for luminaires with white LEDs using various spatial arrangements in the luminaire. Scheir et al. [2015], Tashiro et al. [2011], and Wagdy et al. [2019] applied machine learning, while Safdar et al. [2018] used a neural response-based model. Research is also being conducted concerning relationships between discomfort glare and physiological responses (pupil diameter, blink rate, and blink amplitude etc.) [Hamedani et al. 2019; Hamedani et al. 2020; Stringham et al. 2011. Lin et al. 2015; Scheir et al. 2019].