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Spatial brightness perception of trichromatic stimuli.


Inquiries into the human visual system have occurred for centuries, and in the last hundred years, numerical quantifications that describe photoreception for vision were established. The most widespread measures of photoreception are the CIE Standard Observers for photometry and colorimetry. The former is employed to characterize photometric concepts such as luminous flux and illuminance. The latter is employed to characterize colorimetric concepts such as correlated color temperature (CCT) and the CIE color rendering index (CRI), and it underlies more complex colorimetric concepts such as CIE color appearance models (for example, CIECAM02). Despite the proven utility of CIE photometry and colorimetry, many studies have shown that lumen-based metrics are not entirely consistent with human brightness perception [See, for example: Berman and others, 1990, 1992; Boyce and others, 2003; Bullough and others, 2011; Fotios and Houser, 2007; Houser and Hu, 2004; Houser and others, 2004, 2009; Hu and others, 2006; Rea and others, 2011; Smith and Rea, 1979; Thornton, 1992a-c; Vidovszky-Nemeth and Schanda, 2011; Vrabel and others, 1995]. Seeking to explain these differences, many models of vision and brightness perception have been proposed [See, for example: Berman and Liebel, 1996; Csuti and Schanda, 2008; Fairchild, 2005; Houser, 2001; Judd, 1955; Rea and others, 2011; Thornton, 1998, 1999].

The genesis for the hypotheses described herein can be traced to studies by Thornton [Thornton, 1992a-c, 1997] and Houser and his colleagues [Houser and Hu, 2004; Houser and others, 2004], who conducted experiments on the brightness perception of metameric stimuli with a focus on tri-band illuminants emphasizing the spectral regions at or near 450, 530, and 610 nm. Thornton termed these the "prime color" spectral regions and suggested that they represent underlying and invariant peaks of human visual sensitivity. Thornton's experiments, and those of Houser and his colleagues, utilized adjustment techniques (that is, Maxwell method brightness matching) to produce visual matches to daylight fluorescent lamplight. They concluded that the use of prime color components increases the potential for maximum brightness perception per watt of optical radiation in addition to maximizing the brightness to luminance ratio.

This is of practical significance given the desire to reduce the energy consumed by lighting without degrading lighting quality. One aspect of lighting quality in particular--the perception of spatial brightness--is emphasized here. A draft definition of spatial brightness was recently proposed by the IES Visual Effects of Lamp Spectral Distribution committee:

"Spatial brightness describes a visual sensation to the magnitude of the ambient lighting within an environment, such as a room or lighted street. Generally, the ambient lighting creates atmosphere and facilitates larger visual tasks such as safe circulation and visual communication. This brightness percept encompasses the overall sensation based on the response of a large part of the visual field extending beyond the fovea. It may be sensed or perceived while immersed within a space, or when a space is observed remotely but fills a large part of the visual field. Spatial brightness does not necessarily relate to the brightness of any individual objects or surfaces in the environment, but may be influenced by the brightness of these individual items."

In addition, we were interested in possible age-related differences in the perception of spatial brightness. It is known that the eye-brain system changes with age [Weale, 1988; Turner and Mainster, 2008; DiLaura and others, 2011], yet we do not know of any past studies on spatial brightness as a function of age. If any model of brightness perception is to be more fully embraced for the spectral design of light sources, it will need to be shown that the spectral considerations are comparable for young and old observers.


The study reported here was conducted to test the effect of both spectrum and age on spatial brightness perception using direct comparison; participants were required to make a forced choice between pairs of stimuli composed of three primaries. Forty subjects evenly divided into two age groups evaluated pairs of lighting conditions presented sequentially with unlimited alternations by choosing which of the pair appeared brighter. Two distinct sets of four spectral power distributions (SPDs) were created by varying the peak wavelength of either the blue or the red primary of a red, green, blue (RGB) light-emitting diode (LED) source.



The primary independent variable was SPD. Two sets of four SPDs were created using a spectrally tunable source [Telelumen, Undated]. For all eight SPDs, RGB light emitting diodes (LEDs) were mixed to create white light matching the chromaticity of a blackbody radiator at 3500 K as close as possible--actual measures at the observers' eyes were 3500 K [+ or -] 20 K, with [D.sub.uv] ranging from 0.0002 to 0.0011. Thus, all stimuli were metamers based on the International Commission on Illumination (CIE) 1931 2[degrees] Standard Observer (that is, colorimetric metamers). Metamerism usually refers to the phenomenon in which sources that are spectrally different appear the same; in this case, it refers to stimuli that are numerically the same according to the CIE system of colorimetry despite being spectrally different.

One set of four SPDs varied the peak wavelength of the blue primary while holding the peak wavelengths of the green and red primaries constant (blue series). Another set of four SPDs was created by varying the peak wavelength of the red primary while holding the peak wavelengths of the blue and green primaries constant (red series). The SPDs are shown in Fig. 1. The gamut areas created by the eight primary sets are shown in Fig. 2. The spectrally tunable source used an integrating chamber and two diffusing elements to ensure an equal luminous intensity distribution for all eight conditions, regardless of the primaries in use. There was no perceptible difference in luminance distribution for the different stimuli.



The peak wavelengths of the nominally blue primaries in the blue series were measured to be 435, 448, 461, and 480 nm, whereas the green and red primaries had peak wavelengths of 535 and 623 nm, respectively. These four SPDs are referred to as A, B, C, and D. The peak wavelengths of the nominally red primaries in the red series were measured to be 602, 616, 635, and 661 nm, whereas the blue and green primaries had peak wavelengths of 448 and 535 nm, respectively. These four SPDs are labeled as W, X, Y, and Z. The blue and red primaries represent the full range of LEDs that might be employed in an RGB architectural lighting system. The properties of the 10 total primaries used in this experiment are shown in Fig. 3. These values were obtained by measuring each LED when operating alone; small differences in output associated with the different drive current necessary for each combination were observed, but for consistency and clarity the values are always notated using the standalone measurement. SPDs were measured using a StellarNet EPP2000C spectrometer, which the manufacturer claims has an optical resolution of 3 nm, is accurate to less than 0.25 nm, and has a repeatability of less than 0.05 nm. Measurements were output from 360 to 830 nm, recorded in 0.25 nm increments. The remote integrating sphere for this apparatus was oriented vertically and positioned on a tripod at the location of the observers' eyes.
Fig. 3. Peak wavelength, FWHM, and CIE 1931 chromaticity coordinates
of the ten LEDs used as primaries, when operated alone. Minor
differences in output occurred when the LEDs were operated in
combination to create the eight stimuli.

Peak          Full     1931 CIE Chromaticity
Wavelength   Width        Coordinates
(nm)          Half

                                 x              y

435              22                  0.167  0.024
448              24                  0.156  0.034
461              2H                  0.143  0.062
480              30                  0.110  0.18S
493              34                  0.094  0.377
535              43                  0.265  0.668
602              16                  0.604  0.3S2
616              13                  0.650  0.338
623             1 8                  0.674  0.321
635              19                  0.689  0.301
661              19                  0.711  0.281

The primaries were mixed using custom control software. Target chromaticity coordinates of (0.4053, 0.3907) in the CIE 1931 chromaticity diagram--the chromaticity of a blackbody radiator at 3500 K--and a target illuminance at the eye of 555 lx, were used to calibrate the eight stimuli. These targets were chosen because they are within the range of architectural illumination, with the illuminance being sufficiently high as to easily avoid any mesopic effects. The drive currents necessary to produce stimuli matching these requirements was programmed prior to the experiment. SPDs were measured with the spectrometer as described above and output to text with a range of 360 to 830 nm using 1 nm increments. Illuminance was measured using a Minolta T-10 illuminance meter with a current NIST traceable calibration and the equivalence of the eight stimuli was verified with the spectrometer. Figure 4 illustrates the location of the measurement devices.


Because the output of LEDs varies with the temperature of the p-n junction, the luminaire cycled the eight stimuli in 5-second intervals for at least one hour prior to the first subject of a session beginning the procedure. The same warm-up procedure was followed for the final calibration of the stimuli before the experiment began. It was found that the output was approximately stable at this point. Due to both the instability of the light output and tolerance of the measurement devices, the properties of the stimuli varied over time. Nevertheless, careful calibration and procedural consistency kept this variability to a minimum. A quantitative description of each stimulus is given in Fig. 5. These values were calculated from the average of SPD measurements taken at the beginning and end of the experiment (that is, immediately before the first subject participated and immediately after the last subject participated). Additionally, spot measurements were taken on a regular basis to confirm the stimuli were within a tight tolerance. Illuminance was measured at 554 [+ or -] 2 lx, whereas chromaticity was measured at (0.405 [+ or -] 0.002, 0.391 [+ or -] 0.002). Both chromaticity and illuminance varied evenly across all SPDs rather than disparately, resulting in consistently matched stimuli despite minor changes in measured values.
                         Blue                          Red Series
                       Series                        (448-535-XXX)

                          A       B      C      D            W

Peak Wavelength of         435    448    461    480            602
Variable Primary

1931 CIE Chromaticity    0.405  0.406  0.406  0.405          0.405
X Coordinate

1931 CIE Chromaticity    0.393  0.393  0.393  0.392          0.392
Y Coordinate

Watts                     1.50   1.49   1.53   1.68           1.29

Luminous Efficacy of       369    373    362    329            429

Circadian Stimulus       0.086  0.093  0.112  0.161          0.081

CS/w *100                 5.74   6.26   7.32   9.57           6.25

S/P Ratio                 1.45   1.53   1.70   2.14           1.30

P *(S/P)0.5                666    686    722    811            631

Correlated Color          3513   3503   3503   3513           3514
Temperature (CCT)

Color Rendering Index     73.2   78.1   77.6   62.8           55.7

Color Discrimination      84.4   81.8   76.7   65.5           53.0
Index (CDI)

Farnsworth Munsell        80.3   78.6   75.2   67.0           51.7
Gamut Area (FMG)

Illuminance (lux)          554    554    553    554            553

[V.sub.M] ([lambda])       556    555    554    554            555

[V.sub.10]([lambda])       577    580    587    607            578

[V.sub.b.2]                766    766    769    777            710

[V.sub.b.10]               795    802    818    864            740

VSRS Ranks, 18-25            1      2      4      3              4

VSRS Ranks, 50+Group         1    2 *      4    2 *              4

                         X      Y      Z

Peak Wavelength of       616    635    661
Variable Primary

1931 CIE Chromaticity  0.405  0.405  0.405
X Coordinate

1931 CIE Chromaticity  0.391  0.392  0.391
Y Coordinate

Watts                   1.41   1.70   2.94

Luminous Efficacy of     392    326    188

Circadian Stimulus     0.091  0.097  0.100

CS/w *100               6.45   5.71   3.42

S/P Ratio               1.49   1.60   1.67

P *(S/P)0.5              675    701    716

Correlated Color        3520   3512   3519
Temperature (CCT)

Color Rendering Index   84.3   56.5   27.8

Color Discrimination    75.4   91.4  100.2
Index (CDI)

Farnsworth Munsell      72.7   87.4   97.2
Gamut Area (FMG)

Illuminance (lux)        553    553    553

[V.sub.M] ([lambda])     555    555    555

[V.sub.10]([lambda])     580    581    575

[V.sub.b.2]              751    789    816

[V.sub.b.10]             785    826    854

VSRS Ranks, 18-25          3      2      1

VSRS Ranks, 50+Group       3      2      1

Fig. 5. Colorimetric, photometric, and other quantitative
properties of the eight RGB LED mixtures.

2.1.2 AGE

A second independent variable was subject age. Forty subjects were recruited, evenly divided between a younger and an older age group, in order to investigate the effect of the aging eye on brightness perception. Subjects in the younger age group ranged from 20 to 24 years of age, with an average of 21.8 years and standard deviation of 1.37 years. Subjects in the older group ranged from 50 to 63 years of age, with an average of 56.2 years and a standard deviation of 4.07 years. The younger group included 12 males and 8 females, whereas the older group included 5 males and 15 females. One subject in the older group was completely colorblind, according to the 24 Plate Ishihara Color Vision Test; the remainder scored as color normal. Data from the colorblind subject was is included in this analysis; a separate analysis was performed with the data removed, but the results were not significantly different. No subjects had prior knowledge of the stimuli presented to them.


Stimulus pairs were presented in a rapid-sequential sequence, with each stimulus appearing for 5 seconds with a dark period of 0.01 seconds in between. The sequence alternated for a minimum of 30 seconds before a judgment was made. This alternation sequence results in the observer experiencing mixed chromatic adaptation [Fairchild and Reniff, 1995]. Rapid-sequential ranking is an accepted method for evaluating brightness perception, and has been used in several previous experiments [McNelis and others, 1985; Berman and others, 1990; Vrabel and others, 1995; Houser and others, 2009]. It produces results that are comparable to side-by-side comparison methods [Houser and others, 2009; Fotios and Cheal, 2010]. Interval bias, an effect of presentation order, can result in unintended preference for the first or second stimulus [Klein, 2001; Yeshurun and others, 2008]. This effect was reduced by utilizing multiple alternations and was counterbalanced by presenting stimulus pairs in both orders. Null condition trials were recorded to evaluate the extent of the interval bias.


The dependent variable was perceived brightness. Subjects were asked to choose which of the two stimuli in each pair appeared brighter. This was a forced choice. If the subject declared that they were equal, the experimenter instructed him or her that some of the judgments might be difficult, but that an honest assessment of which of the pair appeared brighter was required.


The four conditions in each series result in 16 permutations of stimulus pairs, including four pairs of null condition trials where the two stimuli were the same. Each permutation was assigned a comparison number and each subject evaluated the combinations in a computer-generated random order. The 12 permutations with mixed stimuli were comprised of six pairs of stimuli that were presented in two orders--for example, AB and BA. Presenting the stimuli in both orders counterbalanced any order bias. During analysis, each of the six pairs of counterbalanced stimuli was combined as a single condition, resulting in six unique, non-null condition comparisons.


The stimuli were presented in a viewing booth constructed of medium density fiberboard, which also supported the luminaire (Fig. 4). The inside of the booth was 0.81 m wide, 0.41 m deep, and 1.04 m tall. The front side of the booth was partially enclosed, with the bottom 0.61 m open to allow the observer to view the surfaces but not the luminaire itself. The luminaire was mounted in the center of the top surface, with a circular hole allowing the lens and cylindrical diffuser to penetrate into the booth. The side and bottom surfaces extended 0.39 m out towards the observer. A chin-forehead rest was mounted at this point, centered on the opening, with eye height approximately 0.41 m above the bottom surface of the booth.

All visible surfaces were painted with Behr Premium Plus Ultra Paint and Primer in One, Ultra Pure White Interior Flat Enamel. This high reflectance paint has a relatively even reflectance distribution across the visible spectrum. The exact distribution is not critical to the experiment as the stimulus was measured at the eye.

The Telelumen luminaire was connected to a computer through a local area network. Custom software provided by Telelumen was used to establish settings for the four stimuli. The settings for each stimulus were saved and combined into 16 script files, one for each comparison. The script files were opened and played in a predetermined sequence by the experimenter.


This study was approved by the Penn State University Institutional Review Board.

Upon arrival, subjects read a brief description of the experiment and signed an informed consent form. The Keystone Visual Skills Test and 24 Plate Ishihara Color Vision Test were then administered; no volunteer was excluded from the experiment based on the results of these tests, or for any other reason. Each subject also completed a general information survey that included information such as sex, age, and known visual impairments.

Following vision testing, the subject was escorted to the viewing booth and provided with general instructions. Once the subject was comfortable, the room lights were turned off and the experiment proceeded with two practice comparisons to ensure comprehension of the task. After answering any questions, the experiment continued with the presentation of the 16 comparisons for either the blue or red series, then the other series. The series presented first was alternated between subjects to counterbalance any order effect.

For each pair of stimuli the experimenter loaded a script that alternated the light in the booth every 5 seconds with a dark period of 0.01 seconds between each alternation. This 0.01 second dark period was implemented to provide the subject with a visual cue that the stimuli were changing; this signal was particularly important for the null condition trials. The experimenter also spoke aloud "A, B, A, B..." as the settings changed. The subject was instructed to wait for at least three alternations--A-B-A-B-A-B--before providing a response, but was allowed to observe as many alternations as desired. Once a response was given, the script was stopped and the judgment was recorded. The experimenter then loaded the next script, which also provided a brief dark period of less than 0.5 seconds during downloading.


Subjects' choices of either A or B were recorded during the experiment and later converted to binary digits (0 or 1) for analysis. Inverse combinations (for example, AB and BA) were combined as a single condition. Because both inverse combinations were seen by all subjects, the number of observations for each combination is twice the number of subjects. For all statistical analyses, the number of subjects was used rather than number of observations because the observations were dependent. Essentially, the two observations per pair of inverse combinations have been averaged.


With null condition trials, or the presentation of two identical stimuli, random chance suggests an even number of choices for the first and second stimulus. Figure 6 shows the results of the four null condition trials seen by all subjects for each series. In the blue series, subjects chose the second stimulus in the BB null condition trial 75 percent of the time, regardless of age group. This was statistically significant at the [alpha] = 0.05 level according to the Z-test for proportions--a normal approximation to the binomial test--for each group individually (p = 0.025) and for the combined group (p = 0.002). In the red series, no trials resulted in subjects selecting one stimulus with significantly greater frequency, individually or combined.
Fig. 6. Results of the null condition trials. Shaded, bold values
represent results that are statistically different from 50/50 at
the [alpha] = 0.05 level according to the Ztest for proportions
(normal approximation to binomial test).

Choice  Combo   Blue Series                    Combo    Red Series
               (XXX-535-623)                          (448-535-XXX)

                  Younger     Older  Combined            Younger

First   AA               30%    45%       38%  WW               45%

Second                   70%    55%       63%                   55%

First   BB               25%    25%       25%  XX               45%

Second                   75%    75%       75%                   55%

First   CC               55%    50%       53%  YY               35%

Second                   45%    50%       48%                   65%

First   DD               60%    70%       65%  zz               35%

Second                   40%    30%       35%                   65%

First   TOTAL            43%    48%       45%  TOTAL            39%

Second                   58%    53%       55%                   61%


        Older  Combined

First     60%       53%

Second    40%       48%

First     65%       55%

Second    35%       45%

First     35%       35%

Second    65%       65%

First     35%       35%

Second    65%       65%

First     49%       44%

Second    51%       56%

Although both series show a tendency for subjects to select the second stimulus (55 percent for the blue series, 56 percent for the red series), this overall inclination is not statistically different from random chance (p = 0.527 and p = 0.477, respectively). This helps to establish reliability of the data. Regardless, all pairs of mixed stimuli were presented in both orders to counterbalance any interval bias.


The effect of SPD on brightness perception was examined by evaluating the pairs of mixed stimuli. Figure 7 provides the percentage of choices for each comparison, for both age groups and with the age groups combined. A Z-test for proportions was performed on each comparison as an approximation for the binomial test. Comparisons with a p-value less than [alpha] = 0.05 are shaded. This analysis method considers each comparison independently. Alternatively, Fig. 8 displays the results of Variance Stable Rank Sums (VSRS) analyses that were completed for each age group and each series. VSRS is an adaptation of two-way analysis of variance by ranks developed by Dunn-Rankin [Dunn-Rankin and others, 2004] that has been used in previous lighting research [Quellman and Boyce, 2002; Houser and others, 2009]. VSRS ranks the stimuli using all comparisons, with larger differences in rank indicating a greater perceptual difference. With four stimuli and 20 subjects, a difference of at least 20.98 is required to achieve statistical significance at the [alpha] = 0.05 level.
Fig. 7. Results of the mixed condition trials, with each pairing
representing a combination of both presentation orders. Shaded, bold
values represent results that are statistically different from 50/50
at the [alpha] = 0.05 level according to the Z test for proportions.
Red, underlined values indicate combinations where the proportions
for the younger and older groups were significantly different at the
[alpha] = 0.05 level.

Combo    Blue Series                    Combo      Red Series
        (XXX-S35-623)                            (44S-535-XXX)

           Younger     Older  Combined              Younger     Older

[435]A            93%    45%       69%  [602] W             3%    15%
[448]B             8%    55%       31%  [616] X            98%    85%
[435]A            98%    83%       90%  [602] W             5%    15%
[461]C             3%    18%       10%  [635] Y            95%    85%
[435]A            63%    50%       56%  [602] W             3%     5%
[480]D            38%    50%       44%  [661] Z            98%    95%
[448]B            90%    80%       85%  [616] X             8%    15%
[461]C            10%    20%       15%  [635] Y            93%    85%
[448]B            60%    40%       50%  [616] X             8%    15%
[480]D            40%    60%       50%  [661] Z            93%    85%
[461]C            55%    35%       45%  [635] Y             3%     5%
[480]D            45%    65%       55%  [661] Z            98%    95%



[435]A        9%
[448]B       91%
[435]A       10%
[461]C       90%
[435]A        4%
[480]D       96%
[448]B       11%
[461]C       89%
[448]B       11%
[480]D       89%
[461]C        4%
[480]D       96%

Fig. 8. Ranks (R,) and results of the variance stable rank sums
tests. Shaded, bold values represent comparisons that are
significantly different at the [alpha] = 0.05 level, which
requires a difference in rank of at least 20.98. Comparisons
with a rank difference of at least 25.42 are different with
significance exceeding the [alpha] = 0.01 level.

              Blue Series

                      A     B     C     D

   [R.sub.i]         50.5  31.5  13.5  24.5

A       50.5            -
B       31.5         19.0     -
C       13.5         37.0  18.0     -
D       24.5         26.0   7.0  11.0     -

                A     B    c    D

   [R.sub.i]  35.5    35  14.5  35

A       35.5     -
B         35   0.5
C       14.5  21.0  20,5     -
D         35   0.5   0.0  20.5   -

                    Red Series

                W         X       Y     Z

   [R.sub.i]   1.5          22    40  56.5

W        1.5     -
X         22  20.5           -
Y         40  38.5        18.0     -
Z       56.5  55.0        34.5  16.5     -

                W     X     Y    Z

   [R.sub.i]     5    25    39  51

W          5     -
X         25  20.0     _
Y         39  34.0  14.0     -
Z         51  46.0  26.0  12.0   -

The results from the red series are very clear. Participants overwhelmingly felt that the stimulus with the longer wavelength red primary was brighter. Figure 7 shows that each comparison had one stimulus that was favored with statistical significance, based on the Z-test for proportions. The rank order of the VSRS also indicates a preference for a longer wavelength red primary; however statistical significance at [alpha] = 0.05 was only achieved for nonconsecutively ranked stimuli.

The results from the blue series do not exhibit a clear pattern and the choices for several comparisons were not conclusive. For the older group, stimuli A, B, and D are ranked as having approximately equal brightness according to VSRS analysis. Stimulus C is significantly different from stimulus A, but falls just short of reaching significance when compared to stimuli B and D. When evaluated with the Z-test for proportions, the older group found statistically significant differences only for stimulus pairs AC and BC. The younger group found stimulus A to be significantly brighter than stimuli C and D, according to the VSRS analysis. Analysis with the Z-test for proportions indicates younger subjects found stimulus A to be significantly brighter than stimuli C and D, in addition to finding stimulus B significantly brighter than stimulus C.


While there was little difference in choice between the two groups for the red series, the results from the blue series are notable. In all combinations involving stimulus A, which has a blue primary with a peak wavelength at 435 nm, the older group chose stimulus A as brighter less times than the younger group. The combination with the greatest difference was AB, where younger subjects chose A 93 percent of the time compared to just 45 percent for the older group (p = 0.003, Z-test for two proportions). Combining all six mixed condition comparisons, younger subjects were more likely to choose the stimulus with a blue primary having a shorter peak wavelength (76 percent) than were the older subjects (55 percent) with statistical significance (p = 0.001).

Examining the number of times subjects in each group had a split decision--that is, chose the opposite stimulus for the inverse presentation--reveals differences in the difficulty of the evaluations for younger and older subjects. There were 240 total decisions for each series, 120 per group. For the red series, the overall group had 15 split decisions (6 percent), with 7 being made by the younger group and 8 being made by the older group. For the blue series, the overall group had 40 split decisions (17 percent), with 15 for the younger group (13 percent) and 25 for the older group (21 percent). When evaluated within a given series, the difference in split decisions between age groups does not reach significance. However, the difference in split decisions for the red series and blue series for the overall group is significant (p = 0.001), as is the difference between the number of split decisions for the older group (p = 0.003). The difference in number of split decisions between the red series and blue series for the younger group is not significant.


In this experiment, two sets of four fixed stimuli were evaluated via forced choice. The stimuli were colorimetric metamers--they were measured to have equal luminance and equal chromaticity coordinates--within a small tolerance. However, the stimuli were not visual metamers, confirmed in descriptions provided by observers when informally questioned after finishing the procedure. This is the conceptual inverse of the method used by Thornton [1992a] and Houser and Hu [2004], where the power of the primaries was modified by the observers to create a visual match to a reference, and thus by assumed translation to all other sets of trichromatic stimuli.

These two methods, choice and matching, have distinct advantages and disadvantages. Requiring only a choice simplifies the task for the observer and presents an experience similar to everyday life. When stimuli are compared directly in this manner, however, the magnitude of differences remains unknown. Visual matching is a more difficult task for observers, but allows for analysis that is more complex, such as establishing ratios of brightness to luminance and brightness to watts of optical radiation. Furthermore, color difference can be examined by calculating the chromaticity of the reference and test stimuli when matched.

Because the stimuli in this experiment were compared and not matched, it is not possible to determine brightness per watt or brightness to luminance ratios. This does not make the data less meaningful, however. The choice method allows for a direct test of predictors such as cirtopic to photopic (C/P) ratio, CCT, visual efficiency functions, or prime color theory. It also demonstrates the effect of metameric mismatches on brightness perception. Stimuli composed of three spectral primaries and mixed to equal chromaticity and equal luminance do not appear equally bright.


When matched at a constant chromaticity and constant luminance, a variable third primary requires the least amount of power when at a prime color, as was seen with the stimuli in this experiment (Fig. 1). This relationship was first documented by Thornton, who then showed that the same relationship holds when brightness perception is held constant instead of luminance. This relationship is a direct correlate of untransformed color matching functions (CMFs)--such as the CIE 1931 RGB CMFs--which show that the human visual system is most sensitive to energy at the peaks of the three functions. These peaks coincide with the prime color regions. What cannot be implied absolutely, however, is that a triplet of prime color primaries maximizes the lumens per watt of optical radiation (a.k.a., luminous efficiency of radiation, LER) or perceived brightness per watt.

Computer optimizations show that LER is maximized with a bimodal distribution, with primaries at approximately 450 and 580 nm, depending on the specific chromaticity desired. Note that this relationship is limited to stimuli near the blackbody locus and within a practical range of CCTs. Thornton [1992a] demonstrated that this relationship holds when luminance is replaced by perceived brightness. The same relationship is seen in the LER values calculated for the stimuli in this experiment (Fig. 5). When the blue primary is varied, the peak LER occurs for stimulus B with a blue primary at 448 nm. When the red primary is varied, the peak LER occurs for stimulus W with a red primary at 602 nm--the red primaries did not vary over a wide enough range for LER to reach its absolute maximum. Implied in this bimodal distribution is the ineffectiveness of energy in the 500 nm region, which provides little contribution to luminance--or the achromatic channel of brightness perception--and requires significantly more energy than a shorter wavelength primary to result in a color match. It is important to remember that while they are efficacious, bichromatic mixtures do not make practical light sources due to very poor color rendition properties.


Figure 5 lists values computed for various lighting metrics, many of which have been considered correlates for spatial brightness perception. By design, CCT was equivalent within the tolerance of calibration. Hu and colleagues [2006] demonstrated that lamps with very different CCTs could appear equally bright, whereas this experiment demonstrates that stimuli with the same CCT can elicit different perceptions of brightness. The fact that the stimuli appeared different in color illustrates another error in using CCT as a correlate for brightness perception: two lamps with the same CCT can have not only different chromaticity coordinates but also a very different appearance.

The most advanced models of brightness perception available today--color appearance models (CAMs)--cannot be used to predict the results of this experiment, and are therefore not included in Fig. 5. CAMs rely on tristimulus values as the primary input, in addition to adapting conditions and other related criteria. The eight stimuli used in this experiment were designed to have equivalent tristimulus values. Though visually different, they are identical according to CAMs and thus theoretically should elicit equal perceptions of spatial brightness.

The stimuli in this experiment were established as producing equal illuminance using the CIE 2[degrees] standard observer (V([lambda])), despite the fact that the experimental conditions were known to be outside the range for which V([lambda]) is strictly applicable. This concession was made to account for the overwhelming use of V([lambda]) within the lighting industry. Several more recent--and perhaps more applicable--visual efficiency functions were examined during the analysis, but none consistently predicted the rank order of the stimuli according to the subjects. These included [V.sub.M]([lambda]), [V.sub.10]([lambda]), [V .sub.b,2]([lambda]), and [V.sub.b,10]([lambda]) [CIE, 1999]. The [V.sub.b,2]([lambda]) and [V.sub.b,10]([lambda]) functions were able to predict the red series, but the prediction for the blue series was substantially different from the observed result; this was similar to other different types of predictors.

Thornton [1992b] demonstrated a clear relationship between CRI and prime color theory. Therefore, it is possible to use CRI as an indicator of adherence to prime color theory for trichromatic stimuli. Like many correlations, any relationship between CRI and perceived brightness does not imply causation. This is especially true for this experiment, since the viewing booth was painted white and no chromatic objects were present. Furthermore, though peaks for maximum CRI, and to a lesser extent maximum color discrimination index (CDI), fall within prime color regions, neither of these metrics accurately predict color perception of highly structured SPDs, such as the ones in this experiment [Ohno, 2004; Davis and Ohno, 2005; Royer and others, 2011]. Regardless, CRI was a poor predictor of perceived brightness. Although CRI was highest for the stimuli with primaries closest to the prime color regions, those stimuli were not judged the brightest.

Of all the color quality metrics, CDI had the highest correlation with brightness perception. CDI is maximized when the blue and red primaries are shifted to shorter and longer wavelengths, respectively. In the red series, brightness perception clearly increased as the wavelength of the red primary increased. A similar though less definitive trend exists for the blue series. No physiological explanation exists for this correlation; the dataset is too small to imply causation. The one stimulus seemingly out of order with the CDI ranking is stimulus D, with a blue primary at 480 nm. It is notable that this coincides with the peak sensitivity of intrinsically photosensitive retinal ganglion cells (ipRGCs), though there are other potential explanations for this occurrence. Rod intrusion is not likely an explanation because the illuminance at the eye (554 lx) and luminances of the booth surfaces (165-195 cd/[m.sup.2]) were high [Thornton and Fairman, 1998; Trezona, 1996]. However, stimulus D was notably one of the most chromatic in appearance. Because ipRGCs are not thought to respond to short bursts of light, it is unlikely they would contribute directly to brightness perception in this experiment. Regardless of the duration of exposure, Vidovszky-Nemeth and Schanda [2011] found that the influence of ipRGCs on the brightness perception of an achromatic target to be negligible.

Several theoretical estimates of brightness perception based on scotopic [Berman and others, 1990; Berman, 1992; Berman and Liebel, 1996] or cirtopic photoreception [Berman, 2008] are shown in Fig. 5. If limited to the red series, these measures would be an accurate predictor of the rank order of perceptual brightness. However, they are very poor predictors for the blue series, almost predicting the inverse of perception. Although individual variation is large, the color difference in the stimuli appeared to be sequential for both series. The progression was more subtle for the red series, moving from slightly pink to more achromatic in appearance as the wavelength of the red primary increased. The progression of the blue series was more pronounced, moving from achromatic or cool in appearance to yellow-green or warm in appearance. (3) Several observers made unsolicited comments about the color difference. These progressions in color appearance are not unprecedented, however. The bowtie effect demonstrated by Thornton [1992a] indicates that stimuli with primaries near 480-500 nm (called the "anti-prime" region) will have the largest difference between chromaticity coordinates and appearance. This was also the case in this experiment.

It is notable that the area of greatest difference between chromaticity coordinates and perceived color is in the 480 -500 and 580 nm regions. These regions are also the crossover points for the chromatic channels in the opponent signals model [Hurvich, 1981]. It is plausible that individual differences in these crossover points result in a different response than is predicted by a Standard Observer, which is an average response.


Thornton [1992a] demonstrated that at equal perceived brightness, a purely prime color source would have a lower measured luminance than a purely anti-prime source when matched to the same reference. This relationship is less clear if two of the primaries are at prime color wavelengths and one is not, as was sometimes the case for this experiment.

It is difficult to characterize the results of this experiment in terms of prime color theory, which would predict W or X to be brighter than Y or Z. This was not the case. However, based on the format of the data from this experiment, it is impossible to evaluate whether or not stimuli comprised of prime color primaries elicit greater brightness perception per watt because both watts and brightness perception were changing simultaneously. In the red series, the stimuli that appeared brighter were also radiating more watts of optical power. It is plausible, and supported by past research [Hu and Houser, 2006], that humans are more sensitive to long wavelengths than is characterized with the CMFs (CIE 1931 2 [degrees]) used in this experiment. (4) Given the forced choice methodology used in this study, even small errors in the CMFs could manifest as a consistent trend.

The results of the blue series were less conclusive, and the predictors were less distinct, making comparisons to the predictions of prime color theory even more tenuous. Driven by the difference for older observers, the level of difficulty in making judgments of brightness was significantly higher for the blue series compared to the red series. The exact cause of this difference is speculatory; however, in comparing the numerous visual efficiency functions that have been proposed to augment V([lambda]), there is typically greater difference in the shortwavelength region. Further, the blue series included primaries extending into the anti-prime region (approximately 480-500 nm), whereas the red series did not. This may have introduced other chromatic affects, as previously described.

One of the downsides of the choice method of evaluating colorimetric metamers is that in addition to different brightness, stimuli also appear different in color. The Helmholtz-Kohlrausch effect refers to the phenomenon of colored stimuli appearing brighter than nominally white stimuli of the same luminance, which has been documented in numerous experiments [Wyszecki and Stiles, 1982]. In these cases, the brightness to luminance ratio was derived for stimuli of very different chromaticity and appearance. For this experiment, the stimuli had matching chromaticity coordinates but still appeared different in color. Though it is not the typical scenario for which the Helmholtz-Kohlrausch effect is prescribed, it is possible that the disparate color appearance of the stimuli influenced judgments. Of particular note is stimulus D, with a blue primary peaking at 480 nm, which was likely the most chromatic appearing of the blue series stimuli. It was ranked out of sequence, appearing brighter than stimulus C. The results of the red series are similar to what was documented by MacAdam [1950]. When the quantity of optical radiation from the red primary was reduced, the mixture changed color and appeared brighter. In this experiment, a similar trend occurred when the red primary was shifted to a longer wavelength: the mixture changed color and appeared brighter.


Vision changes with age. Acuity, brightness perception, and color perception are all altered by physical changes to the components of the eye and these changes may interact with each other to produce compound effects. Changes in spectral retinal illumination as a function of age, which are most pronounced in the short-wavelength region of the visible spectrum, can be seen in Fig. 9. With the proliferation of LEDs providing many opportunities to utilize specific primaries in commercial lamps, identifying the consequences of using a very shortwavelength blue primary is important.

The AB comparison, with the peak wavelength of the blue primary varying between 435 and 448 nm, exhibited a statistically significant difference between the two age groups. It is plausible that the decrease in transmission of the lens with age, specifically for short-wavelength energy, is responsible for this disparity. Though these findings require additional research with more specific aims, they support the current effort of the CIE to develop CMFs for specific age groups [CIE, 2006; Csuti and Schanda, 2008].


Several observers provided an unsolicited description of different stimuli appearing to originate from a different location, often more overhead, or elicit a greater sensation of peripheral brightness. This was typically noted for the red series. This specific effect is undocumented. The stimuli originated from the same luminaire, which included a diffusing lens. Within tight tolerances, the luminance distributions were as identical as reasonably possible. Further investigation is warranted.


Lamp manufacturers must make choices about spectral primaries based on colorimetric and photometric properties, such as chromaticity and luminance. While other experimental methods may provide better data for developing relationships that can be mathematically modeled, the forced choices made in this experiment provide broad trends. This experiment indicated that at equal chromaticity and luminance, perceived brightness will vary as a function of spectral content.

The exact relationship between SPD and spatial brightness perception is elusive, but brightness perception should be among the factors that are considered when selecting primaries for an RGB LED system, or any other type of light source. Furthermore, while it is not possible to rule out contributions from ipRGCs, it is unlikely that they contribute to the difference in brightness perception noted for the stimuli in this experiment, due to the mechanics of their response to optical radiation. Finally, the results suggest that the choice of red primary in an RGB system is more important to brightness perception than the choice of blue primary, at least within the ranges and intervals studied.

The continued development of models of human vision--and specifically models of brightness perception--would be beneficial to the lighting industry as a whole. Although this experiment used RGB LEDs, it is important that models and metrics are appropriate for all types of sources--spectral tuning is a technology-neutral concept. Developing new lamps with specific capabilities to optimally stimulate the human visual and/or nonvisual systems has the potential to provide energy savings, improved visual environments, and improved health.


Eight tri-band illuminants were created to have chromaticity coordinates equivalent to that of blackbody radiation at 3500 K. These stimuli were colorimetric metamers, but they were not visual metamers to real human observers. The stimuli were divided into two sets of four illuminants each, a blue series (whereby the peak wavelength of blue primary was varied and the peak wavelength of the green and red primaries were unchanged) and a red series (whereby the peak wavelength of the red primary was varied and the peak wavelength of the green and blue primaries were unchanged). Twenty participants less than 24 years of age and twenty participants greater than 50 years of age made assessments of brightness using a forced choice protocol, from which we conclude:

1. Light stimuli measured to be identical according to CIE photometry and colorimetry do not appear equally bright or the same color to either younger or older subjects.

2. Age may affect brightness perception when short-wavelength primaries are used, especially those with peak wavelengths shorter than 450 nm.

3. Scotopic to Photopic or Cirtopic to Photopic ratio theory, prime color theory, correlated color temperature, photometry, color quality metrics, linear brightness models, and color appearance models all failed to predict or correctly order the difference in the participants' perception of brightness.

Past measures of spatial brightness have not considered illuminants that are as highly structured, metameric, and discontinuous as those employed in this experiment. Further, no studies have been conducted to examine the performance of existing measures relative to this increasingly prevalent form of optical stimulus. Since such spectra are now physically realizable, and entirely plausible for general illumination, there is now a more pressing need to understand how people perceive such spectra. It is evident that different SPDs that are nominally equal will require different quantities of optical radiation, and thus consume more or less power. This presents a spectral tuning opportunity, where a practical goal is to optimize spatial brightness perception per watt of optical radiation.


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Michael P. Royer (1) * PhD and Kevin W. Houser (2) PhD, PE

(1.) Pacific Northwest National Laboratory; (2.) Department of Architectural Engineering, The Pennsylvania State University

* Corresponding author: Michael Royer, E-mail:

(3.) These observations are based on the perception of the experimenter. It is possible that perception varied from subject to subject.

(4.) Despite the full field of view used in this experiment, the CIE 1931 2 [degrees] CMFs were employed since they are related to V([lambda]), which is the current basis for quantifying light in architectural applications. The flaws of misapplying V([lambda]) to circumstances outside the purview of its original development are well documented [e.g., Houser 2001].

[c] 2012 The Illuminating Engineering Society of North America

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Date:Oct 1, 2012
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