Square Law Dimming: Presumed Perception or Reality? by Craig Bernecker

1. Designers Light Forum
Square Law Dimming:
Presumed Perception or Reality?
Craig A. Bernecker, PH.D., FIES, LC
March 28, 2017

2. Credit(s) earned on completion of
this course will be reported to AIA
CES for AIA members. Certificates of
Completion for both AIA members
and non-AIA members are available
upon request.
This course is registered with AIA CES
for continuing professional
education. As such, it does not
include content that may be deemed
or construed to be an approval or
endorsement by the AIA of any
material of construction or any
method or manner of
handling, using, distributing, or
dealing in any material or product.
___________________________________________
Questions related to specific materials, methods, and
services will be addressed at the conclusion of this
presentation.

3. Learning
Objectives
1. Understand there is a difference between measured light
level and perceived light level when dimming
2. Recognize that the Square Law for dimming is a presumed
relationship between measured light and perceived light
3. Understand the importance of dimming to perceived level
rather than measured level of light
4. Recognize that commissioning a lighting system involves
much more than making certain the lighting controls
operate properly
At the end of the this course, participants will be able to:

4. 4
• Background
• Methodology
• Results
• Conclusion
Square Law Dimming: Presumed
Perception or Reality?

5. 5
• Background
• Methodology
• Results
• Conclusion
Square Law Dimming: Presumed
Perception or Reality?

6. 6
Figure 1. Square Law Dimming Curve [Rea, 2000]

7. 7
Figure 3. A Luminance-Brightness Power Relationship Based on an Exponent of 1/3 [DiLaura et al, 2011, Figure 4.5]

8. 8
Figure 2. The Apparent Magnitude of Electric Shock, Length, and Brightness [Stevens, 1975]

9. 9
Table 1. Representative Exponents of the Power Functions Relating Subjective Magnitude to Stimulus Magnitude [from Stevens, 1975]

10. 10

11. 11
• Background
• Methodology
• Results
• Conclusion
Square Law Dimming: Presumed
Perception or Reality?

12. 12
• School of Constructed Environments Light Lab at Parsons
School of Design (New York, NY)
• Uniform luminance field controlled by a dimming control
system
• Two LED theatrical luminaires with fifty-degree lenses
• Mounted approximately twenty-five feet from a diffuse
neutral color surface (approximately 50% reflectance)
Experimental Set-up

13. 13
Figure 4. Plan View of Experimental Set-up
Experimental Set-up

14. 14
Figure 5. Section View of Experimental Set-up
Experimental Set-up

15. 15
Experimental Set-up

16. 16
Experimental Set-up

17. 17
• Photos of set-up here
Experimental Set-up

18. 18
• Twenty-eight subjects drawn from the student
population at The New School and neighboring
institutions (five total)
• 18 female and 10 male
• Average age = 26, ranging from 18 to 32
• 10 subjects were American; remainder of various other
nationalities
• All participants had either 20/20 or corrected vision to
20/20.
Methodology

19. 19
• Participants seated at a fixed location ≈ 10 feet from the
wall
• Asked to focus at a marked spot on the wall when
making their judgments
• Each subject, tested individually, exposed initially to
lighting at full intensity (100%)
• Asked to rate subsequent levels as a percentage of the
initial level
Procedure

20. 20
• Exposed to 50 different lighting levels divided into two
sets of randomized presentations
• Exposed to the base level of 100% as the basis for
comparison for each presentation
Procedure

21. 21
Figure 7. Frequency Distribution of Dimming Settings
0
2
4
6
8
10
12
14
0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
Frequency
Dimming Setting Range
Dimming Setting Frequency
Procedure

22. 22
• Luminance measurements taken for each dimming
setting from two locations with digital luminance meters
and HDR imaging (to ensure luminance uniformity)
• Luminance meter measurements taken of the same point
on wall where the subject was asked to fix their gaze
• Color temperature measurements were also taken at a
center point on the test wall using a Chroma Meter to
ensure that the color of light was consistent throughout
the presentations.
Procedure

23. 23
Figure 6. Photo of Wall Illuminated to Mid-Range Luminance and Pseudo-Color Map of Its Associated Luminance
20 cd/m2
43 cd/m2
Experimental Set-up

24. 24
• Background
• Methodology
• Results
• Conclusion
Square Law Dimming: Presumed
Perception or Reality?

25. 25
Figure 8. Mean Perceived Levels with Error Bars for the Fifty Dimming Settings
0
20
40
60
80
100
120
0 10 20 30 40 50 60
Mean Perceived Levels (%) with Error Bars for Fifty
Dimming Settings
Results

26. 26
Figure 9. Mean Perceived Lighting Level (%) vs. Actual Dimming Setting
y = 0.9475x + 7.8121
R² = 0.9495
0
20
40
60
80
100
120
0 20 40 60 80 100 120
PerceivedAdjustment(%)
Dimming Setting (%)
Perceived Adjustment vs. Dimming Setting
Results

27. 27
Figure 10. The Relationship Between Dimming Setting and Measured Luminance
y = 10.555x0.5294
R² = 0.9976
0
20
40
60
80
100
120
0 10 20 30 40 50 60 70 80
DimmingSetting
Luminance #2
Dimming Setting vs. Measured Luminance
Results

28. 28
Figure 11. Perceived Level (%) vs. Luminance (meter #2)
y = 16.483x0.428
R² = 0.9426
0
20
40
60
80
100
120
0 10 20 30 40 50 60 70 80
MeanPerceivedLevel(%)
Measured Luminance #2 (cd/m2)
Perceived Level vs. Luminance
Results

29. 29
Figure 12. Perceived Level (%) vs. Luminance (meter #1)
y = 17.238x0.4292
R² = 0.9437
0
20
40
60
80
100
120
0 10 20 30 40 50 60 70
MeanPerceivedLevel(%)
Measured Luminance #1 (cd/m2)
Perceived Level vs. Luminance
Results

30. 30
• Background
• Methodology
• Results
• Conclusion
Square Law Dimming: Presumed
Perception or Reality?

31. 31
• Data clearly present a non-linear relationship between
luminance and perceived level of light (judged as a
percentage of initial level)
• For both sets of luminance measurements, the
relationship between luminance and perceived level of
light follows a power law with an exponent close to 0.43
• Neither Square Law Dimming, nor the brightness power
relationship with an exponent of 0.33 (presented by
Stevens) hold for the data presented in this study
Conclusions

32. 32
• Not inconsistent with some of the other studies
undertaken to determine this relationship
• Although often dealing with object-background
luminance-brightness relationships [Bodmann and La
Toison, 1994] or more complex visual fields with multiple
surfaces [Marsden, 1970], power laws between
luminance and brightness were found with exponents
ranging from 0.35 to 0.6
Conclusions

33. 33
• Wider range of luminances
• Position of the dimmed surface (or source), e.g., overhead
or in front.
• Uniformity of light, i.e., uniform versus non-uniform.
• Surface luminance(s) versus luminance of source versus
luminance of task.
• Color of light (warm versus cool) and/or interaction of
color of light and color of surfaces.
• Culture, age, or gender differences in brightness
perception
To Consider:

34. This concludes The American Institute of Architects Continuing
Education Systems Course