A Formula of the Position Index of a Glare Source in the Visual Field

Abstract 

A Formula of the Position Index of a Glare Source 

in the Visual Field 

Wonwoo Kim 1 and Jeong Tai Kim 1* 

1 Department of Architectural Engineering, Kyung Hee University, 

Yongin 446-701, Korea 

* Corresponding author: J. T. Kim (jtkim@khu.ac.kr) 

Presenting the position index in a formula is very appropriate at this time when computers are 

widely used. However, since the Guth’s position index was limited to the upper visual field 

not the entire visual field, the existing formula of the position index cannot be used on the 

lower visual field. In order to overcome such a limit, it is necessary to create a formula based 

on the position index chart made against the entire visual field. The objective of this study is 

to propose a formula of the position index of a glare source in the whole visual field. The 

glare sensation was measured to create the formula in binocular and monocular vision. The 

results show that there is not a big difference in the level of the discomfort glare sensation 

between the left and right eyes while the lower visual field is more sensitive to the discomfort 

glare then the upper visual field. Based on the BCD luminance distribution in the whole visual 

field obtained through a series of experiments, position index was created, which was then 

turned into a formula. When predicting or evaluating the discomfort glare generated from the 

indoor or outdoor lighting with a computer, this formula would be of great help in easily 

identifying a position index. 

Keywords: Discomfort glare; Formula of the position index; Position index; Light source; 

BCD luminance; Visual field 

1. Introduction 

SHB2010 - 3rd International Symposium on Sustainable Healthy Buildings; Seoul, Korea. 

27 May 2010 

Good lighting requires equal attention to the quantity and quality of the lighting [1]. 

Discomfort glare generating indoors should be removed as it deteriorates the quality of 

lighting. There have been a number of approaches proposed, which can be used to predict and 

evaluate discomfort glare in order to control indoor discomfort glare. VCP (Visual Comfort 

Probability) [2], UGR (Unified Glare Rating) [3] and DGI(Daylight Glare Index) [4] are wellknown 

approaches to the evaluation of discomfort glare. Among others, UGR is the 

239


27 May 2010 

evaluation method that the International Commission on Illumination (CIE) defined as the 

standard to evaluate discomfort glare. 

Existing methods quantify discomfort glare in line with the size of the four physical elements. 

Those four elements are luminance and size of the glare source, background luminance and its 

location in the visual field [5]. The location element of the glare source in the visual field is 

used in order to adjust the change in the discomfort glare from the source deviating from the 

line of sight [6]. Although the light source has the same luminance and size, the light source 

located closer to the line of sight feels brighter than the one located farther away from the line 

of sight. Such phenomenon is well shown in the glare experiments conducted by Luckiesh and 

Holladay [7]. 

In 1925, Luckiesh and Holladay compared the discomfort glare from light source by changing 

its location vertically from the line of sight. They found that the farther the light source moves 

from the line of sight, the brighter the light source should get in order to create the same level 

of glare sensation. This is because of the fact that the location of the light source changes 

within the visual field. This experiment was conducted by making movement in the vertical 

direction only. The current lighting environment reveals that the lighting equipment is 

presented not only in the upper visual field but also in the lower visual field. Therefore it is 

necessary to review the glare sensation for the entire visual field. 

In 1949, Guth measured Borderline between Comfort and Discomfort (BCD) luminance by 

locating a number of light sources in the upper visual field [6]. As a result, they found that the 

farther the light source gets from the line of sight, the higher the luminance of BCD. This 

experiment was, however, confined to the upper visual field only. 

Position index of the glare source suggested by Guth is shown in the chart [6]. However, in 

the VCP, the chart has been converted into numerical formula in order to express the position 

index in a way much easier to understand [8]. Presenting the position index in a formula is 

very appropriate at this time when computers are widely used. However, since the Guth’s 

position index was limited to the upper visual field not the entire visual field, the position index 

used in VCP can be used only for the upper visual field. In other words, this formula cannot be 

used on the lower visual field. In order to overcome such a limit, it is necessary to create a 

formula based on the position index chart made against the entire visual field. 

The purpose of this study is to create a position index chart by measuring the distribution of 

the glare sensation across the entire visual field and turn it into a formula. 

240

2. Position Index of a glare source 

The position index used in the VCP is what Guth suggested in 1949. Guth’s position index 

was created based on the measurements made with 50 subjects aged from 20 to 40. The 

devices used for the measurement included a sphere 1/3 of which was cut out and whose 

diameter is about 203cm, a lamp inside the sphere which created the background luminance, 

and baseline and control light sources. 

The subject was requested to look at the baseline light source located on the line of sight and 

to determine a BCD (Borderline Between Comfort and Discomfort) luminance, which was 

defined as the baseline luminance on which the position index is to be created. After locating 

the test light source on a spot not on the line of sight, the subject was asked to indicate a 

moment when he or she felt that the baseline light source on the line of sight had the same 

luminance with the test light source. Such brightness of the test light source was defined as the 

BCD luminance at the location of the test light source. The light source used was 0.0011sr and 

the luminance of the interior surface of the sphere was uniform at 34cd/㎡. 

In the experiment, the test light source was placed at an interval of 10˚ vertically from the 

line of sight (azimuth 90˚ ), diagonally (azimuth45˚ ), horizontally (azimuth 0˚ ) over the 

upper visual field in order to measure the BCD luminances. Today’s lighting environment has 

lighting equipment found in the lower visual field, so failing to measure the BCD luminance on 

the lower visual field is a critical shortcoming. 

The position index created from the Guth’s experiment can be expressed as follows in Formula 

1 [8]. 

[Formula 1] 


27 May 2010 

Where = angle from vertical of the plane containing the source and the line of sight in 

degrees, = angle between the line of sight and the line from the observer to the source. 

Since the position index of the upper and lower visual fields are not in symmetry [9, 10, 11], 

Formula 1 can be used for the upper visual field only. In order to evaluate discomfort glare 

generated from a light source no matter where the glare source is located on the visual field, 

position index formula that can be applied to the lower visual field is required. 

241 

--

3. Study Approach 


27 May 2010 

First and foremost, the difference in the discomfort glare sensation between using one eye and 

both eyes was studied along with the difference in discomfort glare sensation between the up, 

down, left and right visual field. This examination was required in order to create accurate 

position indices. Then, position index chart was created based on the discomfort glare 

sensation of both eyes, which were to be finally expressed in the form of the position index 

formula. 

3.1. Devices for Experiment 

The glare tester was created for this study (Fig. 1). The glare tester was installed inside a lab 

where no light was allowed to come in from outside as all its windows were completely sealed 

off. The temperature of the lab was maintained at 26 degrees. The glare tester consisted of a 

semi-sphere dome with a diameter of 2 m, a semi-sphere shaped rail inside the dome, an 

incandescent lamp (100 W), and a halogen lamp (100 W). The semi-sphere shaped rail could 

rotate 360° and all the lamps were connected with the dimmer, so their luminance could be 

controlled. 

Test light source could be located on any spot within the scope of the visual field. For this end, 

two test resources were mounted on the rail and they were moved at the speed of 5 

degrees/sec by a power motor. The test light sources were connected with a timer so that the 

time to turn on and off the light could be controlled. 

The interior of the semi-sphere dome was painted white. The background luminance was 

adjustable in the range of 0~350 cd/m 2 . It was 0.0011 sr of the test light source and the 

luminance was adjustable in the range of 0~160,000 cd/m 2 . 

Fig. 1. Glare Tester 

242


27 May 2010 

3.2 How to Conduct the Experiment 

The experiment consisted of the three parts: part 1 measured the limits of the visual field of the 

right and left and both eyes. Part 2 evaluated the BCD luminance of the entire visual field 

while part 3 assessed the BCD luminance on the line of sight. 

Prior to experiment, all the subjects were fully explained of the limits of the visual field, 

concept of the BCD luminance along with the experiment procedures and approaches. 

Exercises were fully conducted. The dimmer was adjusted to set the background luminance of 

the interior of the dome at 34 cd/m 2 . Such background luminance was the same with the one 

applied in the Guth’s experiment. As the background luminance was set, the subject was asked 

to sit in a designated seat in front of the glare tester and then asked put the jaw on jaw holder 

to focus the line of sight on the center of the screen. 

For the experiment part 1, when the visual field limits were measured the luminance of the test 

light source was set at 1,000 cd/m 2 . The visual field limits were measured at the azimuths of 

0°, 45°, 90°, 135°, 180°, − 45°, − 90°, and − 135° (Fig. 2). On each of the azimuths 

chosen, the test light source was moved starting from the location where it was 110° away 

from the line of sight towards the line of sight. While the test light source was moving, the 

subject shouted ‘ Stop’ when the test light source came within the visual field. Upon 

hearing the shout, the experimenter stopped the test light source to record the angle distance 

from the azimuth. Azimuths were selected randomly by the experimenter. The same 

experiment was conducted three times per subject to measure the average, which was to be 

used as the data for analysis. 

In the experiment part 2 where the BCD luminance of the entire visual field was measured, the 

test light source’s luminance was set at 3,000 cd/m 2 , 5,000 cd/m 2 , 10,000 cd/m 2 , and 30,000 

cd/m 2 . Table 1 shows the four types of test light sources used for the experiment. A total of 16 

spots of azimuths were selected: 0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, 157.5°, 180°, − 

22.5°, − 45°, − 67.5°, − 90°, − 112.5°, − 135°, and − 157°. On each of the azimuths 

chosen, the test light source was moved starting from the location where it was 110° away 

from the line of sight towards the inside of the dome. As it was the case for the evaluation of 

the visual field limits, the subject shouted ‘ Stop’ when the subject sensed BCD of the test 

light source. Upon hearing the shout, the experimenter stopped the test light source to record 

the angle distance from the azimuth. Azimuths were selected randomly by the experimenter. 

The subject was exposed to the test light source starting with higher luminance to the lower 

ones. The sequence was planned that way as it was expected that the light source with the 

higher luminance would be stopped at the spot farther from the line of sight compared with the 

light source with lower luminance. This sequence was also designed in order to minimize the 

243


27 May 2010 

case when the light source passed the center of the visual field during experiment. For the 

same subject, BCD luminance was measured for the left, right and both eyes for three times. 

In the experiment part 3 where the BCD luminance was measured on the line of sight, the test 

light source was placed at the center of the dome and the experimenter used a dimmer to 

gradually increase the luminance. In this test, the test light source was set to automatically 

blink every second. When the subject shouted ‘ Stop’ upon feeling BCD sensation of the 

test light source, the experimenter recorded test light source’s luminance. For the same subject, 

BCD luminance was measured for the left, right and both eyes for three times 

The total time consumed to conduct the three experiments per subject was around 4 hours and 

30 minutes. Measurement was done for 20 minutes followed by a 10-minute break. Depending 

on how tired the subject felt in the eyes, experiments were conducted for at least twice or at 

the maximum four times over the period of 2~3 days. Experiment part 1 consisted of 24 

conditions, while part 2 had 192 and part 3 had 9 conditions respectively totaling 225. 

The subjects were graduate students or researchers who studied construction environment. A 

total of 8 subjects joined the experiment: 4 males and 4 females. They aged from 20 to 31 with 

the average being 25.4 years old. 

157.5 

180 

-157.5 

135 

-135 

112.5 

-112.5 

Angular distance [°] 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

90 

-90 

67.5 Radial angle [°] 

Line of sight 

-67.5 

45 

-45 

22.5 

0 

-22.5 

Fig. 2. Angular Distance and Radial Angle in the Visual Field 

Table 1. Conditions of the Test Light Source 

244

Test sources Luminance of 

glare source L 

[cd/m 2 ] 

Size of glare 

Source ω 

[sr] 

I 3000 0.0011 34 

II 5000 0.0011 34 

III 10000 0.0011 34 

IV 30000 0.0011 34 

4. Results of Experiments and Observations 

4.1. Visual field limits 


27 May 2010 

Background 

Luminance Lb 

[cd/m 2 ] 

Fig. 3 shows the visual field limits measured with left, right and both eyes (Experiment part 1). 

Upper visual fields of the left, right and both eyes were 1.52 sr, 1.54 sr and 2.03sr each while 

lower visual fields were 2.04 sr, 1.88 sr and 2.58 sr respectively. The whole visual fields of the 

left, right and both eyes were 3.56 sr, 3.42 sr, 4.61 sr and the area where the left and right eye 

was overlapped was about 2.37 sr. 

The total of the visual field limits of left eye and right eye was similar to that of the visual field 

limits of both eyes. On the whole visual field, the left eye was 77.2% while the right eye was 

74.2%. On the whole visual field, the area where the left and right eye was overlapped was 

about 53.8%. The size of the whole visual field of both eyes was 4.61 sr. In addition, the 

visual field limits of the left and right eyes were in symmetry. 

As for the upper visual field of both eyes, visual field limits were presented at the angle 

distance of about 53˚ when the azimuth was 90˚ . The lower visual field was found to have 

an angle distance of about 67˚ when the azimuth was − 90˚ . The lower visual field 

appeared to be wider than the upper visual field. 

245


27 May 2010 

Fig. 3. Visual Field Limits of Single and Both Eyes 

4.2 BCD luminance of the whole visual field 

Fig. 4, 5, 6,7 are the charts indicating the locations on the visual field of the right and left and 

both eyes that had the same BCD luminance. The sizes of the BCD curves measured using the 

test light source I (3,000 cd/m 2 ) were 0.14 sr, 0.14 sr and 0.22 sr on the upper visual field of 

the right and left and both eyes respectively. They were 0.22 sr, 0.20 sr and 0.38 sr on the 

lower visual field. The whole visual field of the right and left and both eyes was 0.36 sr, 0.34 

sr, and 0.60 sr while the area where the left and right eye was overlapped was approximately 

0.28 sr. 

The sizes of the BCD curves measured using the test light source II (5,000 cd/m 2 ) were 0.28 

sr, 0.27 sr and 0.37 sr on the upper visual field of the right and left and both eyes respectively. 

They were 0.45 sr, 0.47 sr and 0.65 sr on the lower visual field. The whole visual field of the 

right and left and both eyes was 0.73 sr, 0.74 sr, 1.02 sr each, and the area where the left and 

right eye was overlapped was approximately 0.57 sr. 

The sizes of the BCD curves measured using the test light source III (10,000 cd/m 2 ) were 0.65 





246


27 May 2010 

The sizes of the BCD curves measured using the test light source IV (30,000 cd/m 2 ) were 0.78 





Combining all the information on Fig. 4, 5, 6, 7 revealed the three important findings. First, on 

the visual field of the right and left and both eyes, the higher the test light source’s luminance, 

the bigger the BCD curve. This indicates that BCD luminance was higher on the periphery 

than on the center of a visual field. 

Second, the size of the BCD curve of both eyes was the same with that of the BCD curve of 

the left eye on the visual field of the left eye. It was also same with that of the BCD curve of 

the right eye on the visual field of the right eye. This indicates that on the left visual field, the 

left eye reached the BCD sensation earlier, while it was the right eye that did so on the right 

visual field. 

Third, the BCD curves of the left and right eyes were in symmetry and the lower visual field 

had a wider BCD curve than the upper visual field. This indicates that there was not a big 

difference in the level of the discomfort glare sensation of the left and right eyes while the 

lower visual field was more sensitive to the discomfort glare then the upper visual field. 

Fig. 4 BCD Curves Measured Using the Test Light Source I (3,000 cd/m 2 ) 

247


27 May 2010 

Fig. 5. BCD Curves Measured Using the Test Light Source II (5,000 cd/m 2 ) 

Fig. 6. BCD Curves Measured Using the Test Light Source III (10,000 cd/m 2 ) 

Fig. 7. BCD Curves Measured Using the Test Light Source IV (30,000 cd/m 2 ) 

248

4.3 BCD luminance on the line of sight 

Table 2 shows the BCD luminance of the test light source located on the line of sight. The 

average of the BCD luminance values measured on the line of sight was 3337 cd/m 2 for the 

left eye, 4481 cd/m 2 for the right eye, and 5253 cd/m 2 for both eyes. In other words, the BCD 

luminance of the both eyes was 1.6 time higher than the average BCD luminance of the left 

eye, and 1.2 time higher than the average BCD luminance of the right eye. 

BCD luminance of both eyes was 1.9 time higher than what was found in the Guth’s 

experiment (about 2844 cd/m 2 on the average). These results indicate that the BCD luminance 

of Koreans was higher than the BCD luminance in Guth’s experiment. 

Table 2. BCD Luminance on the Line of Sight 

Subject 

No. 


27 May 2010 

Left eye L 

[cd/m 2 ] 

Right eye 

L 

[cd/m 2 ] 

1 3503 4593 6457 

2 2723 4167 7817 

3 6117 7470 4257 

4 3730 5023 6020 

5 2873 2993 5803 

6 2213 3183 3797 

7 2197 3940 2620 

Average 3336 4481 5253 

Both eye L 

[cd/m 2 ] 

5. Turning the Position Index into Formula 

Fig. 8 shows the distribution of the BCD curves measured on both eyes. Fig. 9 shows the 

results of measurements done on a total of 40 people (24 men and 14 women) including those 

8 subjects who participated in this study and preceding ones [b1]. The male subjects were 

aged from 20 to 31 with the average age being at 24.7. 

Line I on the Fig. 8 represents the location of the BCD luminance of 3000 cd/m 2 while Line II 

is the location of the BCD luminance of 5000 cd/m 2 , Line III the BCD luminance of 10000 

cd/m 2 and Line IV BCD luminance of 30000 cd/m 2 . Besides, the dotted line indicates the 

visual field limits and the BCD luminance on the line of sight was 2990 cd/m 2 . 

249


27 May 2010 

The left and right visual field is usually considered to be in symmetry so the locations of the 

BCD curves and visual field limits shown on the left and right eye visual fields on the Fig.8 

were averaged, which are shown in Fig. 9. 

On Fig. 9, with the BCD luminance 2990 cd/m 2 on the line of sight being the Position Index=1, 

the location of Line I is Position Index=1.0, Line II is Position Index=1.7, Line III Position 

Index=3.3, and Line IV Position Index=10. Fig. 9 shows the Position Index chart of the whole 

visual field, which can be presented in terms of a formula as follows: 

Where P= Position index, = angle from vertical of the plane containing the source and the 

line of sight in degrees, = angle between the line of sight and the line from the observer to 

the source. 

Upper Field 

Lower Field 

157.5 

180 

-157.5 

135 

-135 

112.5 

-112.5 

Left 


100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

90 

-90 

Right 

I 


-67.5 

45 

Visual Field 

II 

III 

IV 

-45 

Fig. 8 BCD Curves Measured on Both Eyes 

250 

22.5 

0 

-22.5

Upper Field 

Lower Field 

157.5 

180 

-157.5 

135 

-135 

112.5 

-112.5 

Left 


100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

90 

-90 

P=1 

Right 


-67.5 

45 

Visual Field 

3.3 

1.7 

Fig. 9 BCD Curves based on the Averages of the Left and Right Eyes & Position Index 

6. Conclusion 


27 May 2010 

This research was conducted in order to create a formula of the position index of a glare 

source in the whole visual field. This study evaluated visual field limits of single and both eyes 

plus the BCD luminance within the visual field. Based on the BCD luminance distribution in 

the whole visual field obtained through a series of experiments, position index was created, 

which was then turned into a formula. When predicting or evaluating the discomfort glare 

generated from the indoor or outdoor lighting with a computer, this formula would be of great 

help in easily identifying a position index. 

Analysis of the results of the experiments implemented to create a formula out of the position 

index led to the following findings. 

1. The sum of the visual field limits of left eye and right eye is not much different from the 

visual field limits of both eyes. 

2. On the left visual field, the left eye reaches the BCD sensation earlier, while it is the 

right eye that does so on the right visual field. 

3. There is not a big difference in the level of the discomfort glare sensation between the 

left and right eyes while the lower visual field is more sensitive to the discomfort glare 

then the upper visual field. 

4. The BCD luminance of both eyes is higher than the BCD luminance of a single eye. 

5. 

251 

10 

-45 

22.5 

0 

-22.5


27 May 2010 

Such knowledge described above can be used as important basic data for the evaluation of the 

discomfort glare. 

Acknowledgements 

This research was supported by Basic Science Research Program through the National 

Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and 

Technology (No. 2010-0001867). 

References 

1. CIE ISO8995/CIE S 008/E-2001. Lighting of indoor work places; 1-6. 

2. IESNA. IES Lighting Handbook 1984 Reference Volume. New York: 1984; 9–47. 

3. CIE Technical Report 117. Discomfort Glare in Interior Lighting, CIE, Vienna, 

Austria.; 1995. 

4. Hopkinson RG. Glare from daylighting in buildings. Appl. Ergonom. 1972; 3(1): 206– 

215. 

5. Waters CE, Mistrick RG, Bernecker CA. Discomfort glare from sources of 

nonuniform luminance. J. Illum. Eng. Soc. 1995; 24(2): 73–85. 

6. Luckiesh M, Guth SK. Brightnesses in visual field at borderline between comfort and 

discomfort (BCD), Illum. Eng. 1949; 44: 650-670. 

7. Luckiesh M, Holladay LL. Glare and Visibility, Transactions of the Illuminating 

engineering Society 1925; 20(3): 221-252. 

8. IESNA (2000). IES Lighting Handbook reference & application. Illuminating 

Engineering Society of North America. 3.1-3.38. 

9. T. Iwata and M. Tokura, Position Index for a glare source located below the line of 

vision, Lighting Res Technol 29 (3) (1997), pp. 172–178. 

10. Wonwoo Kim, Hyunjoo Han and Jeong Tai Kim, The position index of a glare source 

at the borderline between comfort and discomfort (BCD) in the whole visual field, 

Building and Environment Volume 44, Issue 5, May 2009, Pages 1017-1023. 

11. J. Wienold and J. Christoffersen, Evaluation methods and development of a new glare 

prediction model for daylight environments with the use of CCD cameras, Energy 

Buildings 38 (2006), pp. 743–757. 

252

A Formula of the Position Index of a Glare Source in the Visual Field

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?