Optical Engineering 49共3兲, 033602 共March 2010兲

Color quality scale

Wendy Davis Abstract. The color rendering index 共CRI兲 has been shown to have de-
Yoshi Ohno ficiencies when applied to white light-emitting-diode–based sources. Fur-
National Institute of Standards and Technology thermore, evidence suggests that the restricted scope of the CRI unnec-
100 Bureau Drive, MS 8442 essarily penalizes some light sources with desirable color qualities. To
Gaithersburg, Maryland 20899-8442 solve the problems of the CRI and include other dimensions of color
E-mail: wendy.davis@nist.gov quality, the color quality scale 共CQS兲 has been developed. Although the
CQS uses many of elements of the CRI, there are a number of funda-
mental differences. Like the CRI, the CQS is a test-samples method that
compares the appearance of a set of reflective samples when illuminated
by the test lamp to their appearance under a reference illuminant. The
CQS uses a larger set of reflective samples, all of high chroma, and
combines the color differences of the samples with a root mean square.
Additionally, the CQS does not penalize light sources for causing in-
creases in the chroma of object colors but does penalize sources with
smaller rendered color gamut areas. The scale of the CQS is converted
to span 0–100, and the uniform object color space and chromatic adap-
tation transform used in the calculations are updated. Supplementary
scales have also been developed for expert users. © 2010 Society of Photo-
Optical Instrumentation Engineers. 关DOI: 10.1117/1.3360335兴

Subject terms: colorimetry; color rendering; light-emitting diodes.

Paper 090748PR received Sep. 28, 2009; revised manuscript received Jan. 8,
2010; accepted for publication Jan. 13, 2010; published online Mar. 30, 2010.

1 Introduction illumination by the test source and the reference illuminant

is computed in CIE 1964 W*U*V* uniform color space.
Color rendering is defined by the International Commission The Special CRI 共Ri兲 is calculated for each reflective
on Illumination 共CIE兲 as the “effect of an illuminant on the sample 共i兲 by
color appearance of objects by conscious or subconscious
comparison with their color appearance under a reference Ri = 100 − 4.6⌬Ei . 共1兲
illuminant.”1 The CIE color rendering index2 共CRI兲 is
widely used and the only internationally accepted metric The General CRI 共Ra兲 is simply the average of Ri for the
for assessing the color-rendering performance of light first eight samples, all of which have low to moderate chro-
sources. The CRI was developed in the middle of the twen- matic saturation 关shown in Fig. 1共a兲兴
tieth century to evaluate the color-rendering performance of
then-new fluorescent lamps. Recent momentum to commer- 8
1
cialize lamps using light-emitting diodes 共LEDs兲 for gen- Ra = 兺 Ri . 共2兲
eral illumination is exposing some shortcomings of the 8 i=1
CRI, some of which are particularly prominent when ap- A perfect score of 100 represents no color differences in
plied to LEDs.3,4 These observations have led to the devel- any of the eight samples under the test source and reference
opment of a color quality scale 共CQS兲, which aspires to illuminant.
solve the problems of the CRI, be applicable to all light The CRI has a number of shortcomings and problems.
source technologies, and evaluate aspects of color quality The uniform color space used to calculate color differences
beyond color rendering. is outdated and no longer recommended for use. The red
In the calculation of the CRI, the color appearance of 14 region of this color space is particularly nonuniform. In-
reflective samples is calculated when illuminated by a ref- stead, the CIE currently recommends CIE 1976 L*a*b*
erence illuminant and the test light source. The simulated
共CIELAB兲 and CIE 1976 L*u*v* 共CIELUV兲5 for calculat-
color of the 14 samples, when illuminated by a CIE Day-
ing object color differences. The chromatic adaptation
light illuminant of 6500 K 共D65兲, is shown in Fig. 1.
transform used by the CRI is also considered obsolete and
For the CRI calculations, the reference illuminant is a
inadequate. The Von Kries chromatic adaptation correction
Planckian radiator 共if ⬍5000 K兲 or a CIE Daylight illumi-
has been shown to perform poorer than other available
nant 共if 艌5000 K兲, matched to the correlated color tem-
models, such as the Colour Measurement Committee’s
perature 共CCT兲 of the test source. After accounting for
Chromatic Adaptation Transform of 2000 共CMCCAT2000兲
chromatic adaptation with a Von Kries correction, the dif-
and the CIE’s Chromatic Adaptation Transform 共CIE
ference in color appearance 共⌬Ei兲 for each sample between
CAT02兲.6
The CRI method specifies that the CCT of the reference
0091-3286/2010/$25.00 © 2010 SPIE illuminant be matched to that of the test source, which as-

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 Davis and Ohno: Color quality scale

Fig. 1 Simulated color appearance of 14 CRI reflective samples when illuminated by D65. The eight
samples used in the calculation of Ra are in the top row.

sumes complete chromatic adaptation to any light source two-dimensional 共a* , b*兲 CIELAB plot: the origin repre-
CCT. This assumption fails at extreme CCTs, however. For sents a neutral gray, the distance from the origin represents
example, a 2000-K 共very reddish兲 blackbody source would object chroma 共similar to saturation兲, and the angle repre-
achieve a CRI Ra = 100. However, the colors of objects il- sents object hue. The gray line connecting the circles shows
luminated by such a source would appear distorted. the object colors under the reference illuminant, and the
None of the eight reflective samples used in the compu- black line connecting the squares shows them when illumi-
tation of Ra are highly saturated. This can be problematic, nated by the test source. The positive a*-axis roughly cor-
especially for red-green-blue 共RGB兲 white LEDs with responds to red hues, and it is clear that the chroma of
strong peaks and pronounced valleys in their spectra. Color reddish objects is markedly decreased under the test source.
rendering of saturated colors can be very poor even when In this case, the fact that the CRI uses relatively desaturated
rendering of desaturated colors is good, which would result
in a high Ra value. RGB LEDs have the potential to be
highly energy efficient, but poor color rendering would in-
hibit their market acceptance. Developers of these light
sources need an effective metric to evaluate the color ren-
dering of RGB LED sources and LED luminaires.
The eight Special Color Rendering Indices are combined
by a simple averaging to obtain the General Color Render-
ing Index. This makes it possible for a lamp to score quite
well, even when it renders one or two colors very poorly.
Again, RGB LEDs are at an increased risk of being affected
by this problem, because their unique spectra are more vul-
nerable to poor rendering in only certain areas of color
space. These problems also apply to phosphor-type white
LEDs if narrowband phosphors are used, as most fluores-
cent lamps currently use, as well as any other current or
future light source employing narrowband radiation.
Finally, the very definition of color rendering is limiting.
Color rendering is a measure of only the fidelity of object
colors under the source of interest, and any deviation of
object color appearance from under a blackbody or daylight
illuminant is considered bad. Because of this constraint, all
shifts in perceived object hue, saturation, and lightness re-
sult in equal decrements of the Ra score. In practical appli-
cation, however, increases in the chromatic saturation of
reflective objects, observed when certain sources illuminate
certain surfaces, are considered desirable. Increases in satu-
ration yield better visual clarity and enhance perceived
brightness.7,8
A couple of computational examples from white LED
simulations3 illustrate the deficiencies and limitations of the
CRI. First, consider an RGB LED with peaks at 466, 538,
and 603 nm. Its spectrum is shown in Fig. 2共a兲. This source
would have a CCT of 3300 K and would receive a CRI Ra
of 80. This Ra is generally considered rather high, and most
users would trust that the source is a good color renderer. Fig. 2 共a兲 Spectrum of RGB LED with peaks at 466, 538, and
603 nm. 共b兲 CIELAB plot of color rendering performance with 15
However, this RGB LED would render saturated red and saturated reflective samples. The gray circles plot sample color un-
purple object colors very poorly, as shown in the CIELAB der the reference illuminant, and the black squares show sample
plot of 15 saturated object colors in Fig. 2共b兲. This is a color under the test source.

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 Davis and Ohno: Color quality scale

The CQS was modeled after the CRI to the extent that
was reasonably possible without sacrificing metric perfor-
mance. The CRI has been used in the lighting industry for
decades, and in spite of its problems, many users have been
content with it. The decision to develop a new metric that
has “the look and feel” of the familiar CRI not only pro-
vided a useful starting point for the development of the
CQS, but hopefully will aid in industry adoption.
Though a major motivation for the replacement of the
CRI is its relatively poor performance with some LED light
sources, the CQS was developed to evaluate color quality
for all types of light sources. The comparison of lighting
products of differing technologies will only be possible if
all light sources are evaluated with the same metric. Fur-
thermore, the goal was established to maintain consistency
of average scores with the CRI for fluorescent lamps. This
was a practical consideration, because the CRI is widely
used and accepted among fluorescent lamp manufacturers.
It was anticipated that a new metric with widely disparate
outputs could suffer from a lack of market acceptance and
use.
Unlike the CRI, which only considers the fidelity of ob-
ject colors under the test source, the new metric would seek
to integrate other dimensions of color quality. Evidence has
accumulated over the years that object colors that actually
deviate from perfect fidelity often “look better” to people.
That is, certain shifts in hue or chroma of object colors are
preferred by observers. This was the basis of the Flattery
Index, a metric proposed by Judd in 1967.9 He compiled
the results of previous psychology studies to determine the
preferred color shifts for common objects. For example, the
Fig. 3 共a兲 Spectrum of RGB LED with peaks at 455, 534, and
616 nm. 共b兲 CIELAB plot of color rendering performance with 15 preferred color of Caucasian skin is redder and more satu-
saturated reflective samples. The gray circles plot sample color un- rated than true fidelity.10 The colors of green leaves and
der the reference illuminant, and the black squares show sample grass are preferred to appear less yellow and slightly more
color under the test source. saturated than they really are.11 These findings were also
the basis for the proposed Color Preference Index 共CPI兲.12
More recent research has indicated that object colors are
reflective samples and combines the Special Color Render- often remembered as being slightly more saturated than
ing Indices by averaging leads to an inappropriately high Ra they really are,13 suggesting that humans’ idealized or pre-
score. ferred object colors have a higher chromatic saturation than
The spectrum of a slightly different RGB LED is shown the real objects. A later proposal suggested combining ele-
in Fig. 3共a兲. In this case, the peaks are at 455, 534, and ments of the CPI and CRI into a single CPI-CRI.14
616 nm and the CCT would also be 3300 K. However, the The illuminance of the lit environment has a profound
CRI Ra for this RGB LED would be only 67, a fairly low effect on object colors, but cannot reasonably be integrated
score that many users may not consider suitable for certain into a color-quality metric, which needs to be applicable to
color-important applications. However, the CIELAB plot in individual light sources, independent of their ultimate ap-
Fig. 3共b兲 reveals that the primary deviations in object color plications. Even if it is known that a given light bulb emits
caused by the test source are increases in object chroma for 3000 lumens, it is not known how far away from the user
green, turquoise, orange, and red colors. In real life, this the bulb will be installed or whether it will be installed with
light source would not appear very bad to most users and, other light sources. As a practical matter, illuminance can-
in some cases, would be preferred. This RGB LED source not be integrated into a color-quality metric. However, it is
illustrates the potential benefits of increasing the scope of a reasonable to assume that the environments in which the
new metric from the strict definition of color rendering to artificial light sources are used will be substantially dimmer
include other dimensions of color quality. than outdoor daylight conditions. Indoor artificial lighting
environments are commonly 50–500 lux, while daylight
outdoors can be up to 100,000 lux. If daylight is considered
2 Guiding Principles to be humans’ “ultimate reference illuminant,” as an over-
A number of basic tenets directed the development of the whelming portion of human evolution relied on daylight as
CQS. They are based on both practical and theoretical con- the primary light source, then it could also be concluded
siderations. To fully understand the reasoning behind the that objects illuminated by daylight are the most natural
different elements of the CQS, a brief description of these looking. The perceived hues of colors are dependent on
guiding principles is warranted. illuminance 共Bezold–Brucke effect兲,15 and colors appear

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 Davis and Ohno: Color quality scale

more saturated under higher illuminances 共Hunt effect兲.16 are unknown to us, without concern. Examples of such
Therefore, if an artificial light source increases object satu- measurement scales include shoe sizes, octane ratings of
ration 共relative to the reference illuminant兲, the object may gasoline, and radio station frequencies. Though most
actually appear more like it would when illuminated by real people do not know precisely how those numbers are de-
daylight. This may make the object actually appear more termined, they find the scales useful and have a general
natural to observers. understanding of how different outputs relate to each other
The ability to distinguish between similar colors, chro- 共a larger shoe size means a bigger foot兲. However, it was
matic discrimination is another dimension of color quality acknowledged that additional outputs, for expert users
that can deviate from absolute fidelity. The number of ob- needing specialized information, would be useful and
ject colors that a light source permits discrimination be- should be created to supplement the one-number general
tween can be inferred by the gamut area 共of rendered object output.
colors兲 of the light source. For instance, if one selects a set
of reflective samples and plots them in CIELAB with dif-
ferent light sources as the illuminants, the spacing between 3 CQS
samples will be larger for some light sources, resulting in Led by these guiding principles, a method for the evalua-
larger gamut areas, than others. When the distance between tion of light source color quality was developed through
samples is larger in a uniform color space, the samples computational analyses and colorimetric simulations. The
appear more different from each other 共than when distances resulting metric was named the CQS, a clear nod to the CRI
are smaller兲 and an observer would be able to distinguish a but sufficiently different to avoid confusion among users. A
greater number of colors intermediate to the two samples. thorough account of the calculations involved in the CQS is
In addition to increased chromatic discrimination, larger provided here. Readers who are knowledgeable in basic
object gamut areas have been associated with increased colorimetry may find the level of detail to be excessive, but
perceived brightness, enhanced visual clarity, and increased it was deemed important to provide complete enough infor-
object color saturation.17,18 Gamut area is clearly a useful mation that even a colorimetry novice could carry out the
measure for certain color-quality properties of light sources calculations. A spreadsheet, with all of the calculations
and has been proposed as the central component to a num- implemented as well as additional features, such as the dis-
ber of proposed color-rendering metrics.7,19–21 play of simulated sample colors, is also available from the
Finally, it was decided a priori that the new metric authors.
would yield a one-number output between zero and 100.
The CRI can generate outputs with large negative numbers
for very poor test sources. For instance, for a low-pressure 3.1 Reference Illuminant
sodium lamp, Ra = −47. Color rendering is virtually nonex- The CQS, like the CRI, is a test-sample method. That is,
istent with this lamp. A score of zero would effectively color differences 共in a uniform object color space兲 are cal-
communicate the same message. Negative values simply do culated for a predetermined set of reflective samples when
not convey any useful information and have the potential to illuminated by a test source and a reference illuminant. In
confuse users. essence, through a simulation, the appearance of the object
The decision to restrict the output of the new metric to colors is determined and compared when illuminated by the
one number is certainly controversial. The argument has test source and the reference illuminant. The reference illu-
been made that it is impossible to communicate the differ- minants are the same as those used by the CRI. For test
ent dimensions of quality with only one number.22,23 In- sources of ⬍5000 K, the reference illuminant is a Planck-
deed, in some cases different dimensions of color quality, ian radiator at the same CCT as the test source. These cal-
such as fidelity and preference, can be contradictory. A met- culation procedures are given in CIE’s primary colorimetry
ric to assess a property like color quality inherently con- publication5 but are repeated below. The spectrum of the
denses information. After all, if the goal was to provide all Planckian reference illuminant, Sref共␭兲, is calculated by
possible information about how a given light source would
render object colors, then one could use the spectral power
distribution of the source and colorimetric formulae to de- Le,␭共␭,T兲
termine the detailed color-rendering information 共e.g., di- Sref共␭,T兲 = , 共3兲
Le,␭共560 nm,T兲
rection and magnitude of hue, chroma, and lightness shifts兲
of countless object colors. Even with all that information, where T is the CCT of the test source and Le,␭ is the relative
most users would still need guidance in how to use the spectral radiance calculated by
information to judge the suitability of a light source for a

冋 冉 冊 册
specific application. The purpose of a metric is to condense
such an immense amount of information into something 1.4388 ⫻ 10−2 −1

manageable and useful. In order to be useful for the great- Le,␭共␭,T兲 = ␭−5 exp −1 . 共4兲
␭T
est number of users, most of whom have very limited
knowledge of colorimetry, a one-number output is desir- For test sources at 艌5000 K, the reference is a phase of
able. Though most users will not know exactly how the CIE Daylight illuminant having the same CCT as the test
number was determined or precisely what it means, this is source. The method for calculating the spectral power dis-
readily accepted by a majority of people. Throughout the tribution of the daylight illuminant begins with determining
course of our lives, we use many measurement scales, the chromaticity coordinates 共xD , y D兲 of the illuminant. For
whose precise meanings and measurement methodologies illuminants up to and including 7000 K, xD is

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 Davis and Ohno: Color quality scale

Fig. 4 Simulated color appearance of 15 CQS reflective samples when illuminated by D65.

− 4.6070 ⫻ 109 2.9678 ⫻ 106 0.09911 ⫻ 103 4/14, and 7.5 RP 4/12. The reflectance factors for these
xD = + + samples are given in Appendix A. Although it was shown
共Tcp兲3 共Tcp兲2 Tcp
earlier that light sources can perform poorly with saturated
+ 0.244063. 共5兲 reflective samples even when they perform well with de-
saturated samples, extensive computational testing has re-
For illuminants with CCT of ⬎7000 K, xD is vealed that the inverse is never true. That is, there is no
light source spectrum that would render saturated colors
− 2.0064 ⫻ 109 1.9018 ⫻ 106 0.24748 ⫻ 103
xD = + + well, but perform poorly with desaturated colors. This is
共Tcp兲3 共Tcp兲2 Tcp related to some of the intrinsic properties of reflective ob-
+ 0.237040. 共6兲 jects. Desaturated colors have a higher broad baseline re-
flectance than saturated colors. In essence, that baseline is
The y coordinate 共y D兲 is calculated by white/gray. Of course, white is relatively “easy” for a
white-light source to render, because the light itself is
2
y D = − 3.000xD + 2.870xD − 0.275. 共7兲 white. Highly saturated objects lack the relatively high
broad baseline, and most of their reflected light is from a
The relative spectral power distribution of the daylight ref- much smaller segment of the visible spectrum. Therefore,
erence illuminant, Sref共␭兲, is calculated with the CQS sample set is limited to only saturated colors. The
simulated color appearance of these samples, when illumi-
Sref共␭兲 = S0共␭兲 + M 1S1共␭兲 + M 2S2共␭兲, 共8兲 nated by D65, is shown in Fig. 4.
where S0共␭兲, S1共␭兲, and S2共␭兲 are functions of wavelength The next step in calculating the CQS is to determine the
and are given in Table T.2 of Ref. 5. M 1 and M 2 are mul- tristimulus values 共X, Y, and Z兲 of each reflective sample 共i兲
tiplication factors determined as follows: when illuminated by the reference illuminant. In the fol-
lowing calculations, Ri共␭兲 is the spectral reflectance factor
− 1.3515 − 1.7703xD + 5.9114y D of reflective sample i,
M1 = , 共9兲
0.0241 + 0.2562xD − 0.7341y D

M2 =
0.0300 − 31.4424xD + 30.0717y D
. 共10兲
Xi,ref = kref 冕
␭
Sref共␭兲Ri共␭兲x̄共␭兲d␭, 共11兲
0.0241 + 0.2562xD − 0.7341y D
Because the tables of S0共␭兲, S1共␭兲, and S2共␭兲 are avail-
able only at 5-nm intervals, the calculation of the CQS 共as
well as the CRI兲 uses wavelength intervals of 5 nm, which
is sufficient. Smaller intervals normally would not produce
Y i,ref = kref 冕
␭
Sref共␭兲Ri共␭兲ȳ共␭兲d␭, 共12兲

meaningfully different results, but if smaller interval calcu-

lations are desired in order to match the wavelength inter-

冕
val of spectral distribution measurement of the test source,
then the S0共␭兲, S1共␭兲, and S2共␭兲 values should be interpo- Zi,ref = kref Sref共␭兲Ri共␭兲z̄共␭兲d␭, 共13兲
lated using Lagrange, cubic spline, or other recommended ␭
interpolation method.24 Calculation at intervals of ⬎5 nm
should not be used. where

冒冕
3.2 Tristimulus Values
There are 15 reflective samples used in the CQS calcula-
tions, all of which are currently commercially available kref = 100 Sref共␭兲ȳ共␭兲d␭. 共14兲
␭
Munsell samples, of the following hue value/chroma desig-
nations: 7.5 P 4/10, 10 PB 4/10, 5 PB 4/12, 7.5 B 5/10, 10
BG 6/8, 2.5 BG 6/10, 2.5 G 6/12, 7.5 GY 7/10, 2.5 GY A similar set of calculations is performed for the samples
8/10, 5 Y 8.5/12, 10 YR 7/12, 5 YR 7/12, 10 R 6/12, 5 R when illuminated by the test source.

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 Davis and Ohno: Color quality scale

Xi,test = ktest 冕
␭
Stest共␭兲Ri共␭兲x̄共␭兲d␭, 共15兲 Zw,test = ktest 冕 ␭
Stest共␭兲R共␭兲z̄共␭兲d␭. 共24兲

Then, the tristimulus values are transformed into R, G, and

Y i,test = ktest 冕 Stest共␭兲Ri共␭兲ȳ共␭兲d␭, 共16兲

B values

冢 冣 冢 冣
␭ Ri,test Xi,test
Gi,test = M Y i,test , 共25兲

Zi,test = ktest 冕␭
Stest共␭兲Ri共␭兲z̄共␭兲d␭, 共17兲
Bi,test Zi,test

冢 冣 冢 冣
Rw,ref Xw,ref
where Gw,ref = M Y w,ref , 共26兲

冒冕
Bw,ref Zw,ref
ktest = 100 Stest共␭兲ȳ共␭兲d␭. 共18兲

冢 冣 冢 冣
␭
Rw,test Xw,test
These integral calculations are done numerically at 5-nm Gw,test = M Y w,test , 共27兲
intervals. Bw,test Zw,test
where
3.3 Chromatic Adaptation Transform

冢 冣
0.7982 0.3389 − 0.1371
Even though the CCT of the reference illuminant is
matched to that of the test source, the chromaticity coodi- M = − 0.5918 1.5512 0.0406 . 共28兲
nates are likely different, because the test source chroma- 0.0008 0.0239 0.9753
ticity rarely falls exactly on the Planckain locus or Daylight
locus. Thus, a chromatic adaptation transform is necessary Next, the “corresponding” R, G, and B 共Ri,test,c, Gi,test,c,
to compensate for these types of differences in light color, Bi,test,c兲 values are determined for each sample i,
as was also applied in CRI. A current chromatic adaptation
transform procedure was adopted in CQS. Ri,test,c = Ri,test␣共Rw,ref/Rw,test兲, 共29兲
After calculation of the tristimulus values of the illumi-
nated samples, these values are corrected for chromatic ad-
Gi,test,c = Gi,test␣共Gw,ref/Gw,test兲, 共30兲
aptation. The CMCCAT200025 is applied. The tristimulus
values of a perfect diffuser illuminated by the reference
illuminant 共Xw,ref, Y w,ref, Zw,ref兲 and by the test source Bi,test,c = Bi,test␣共Bw,ref/Bw,test兲, 共31兲
共Xw,test, Y w,test, Zw,test兲 are first calculated as the white refer-
ences. For a perfect diffuser, R共␭兲 ⬅ 1. where

␣ = Y w,test/Y w,ref . 共32兲

Xw,ref = kref 冕␭
Sref共␭兲R共␭兲x̄共␭兲d␭, 共19兲 Readers familiar with CMCCAT2000 may note the ab-
sence of the variables for the lumninances of adapting
fields 共LA1 and LA2兲 and degree of adaptation 共D兲. Because

冕
the luminances are not knowable in this situation, they were
Y w,ref = kref Sref共␭兲R共␭兲ȳ共␭兲d␭, 共20兲 assumed to be high and identical 共e.g., 500 cd/ m2兲, which
␭ makes the degree of adaptation equal to 1. As these values
cancelled out, they do not appear in Eqs. 共29兲–共32兲.
The corresponding tristimulus values 共Xi,test,c, Y i,test,c,

Zw,ref = kref 冕 ␭
Sref共␭兲R共␭兲z̄共␭兲d␭, 共21兲
Zi,test,c兲 after chromatic adaptation correction are then cal-
culated,

冢 冣 冢 冣
Xi,test,c Ri,test,c
and
Y i,test,c = M −1 Gi,test,c , 共33兲

Xw,test = ktest 冕 ␭
Stest共␭兲R共␭兲x̄共␭兲d␭, 共22兲
Zi,test,c
where
Bi,test,c

冢 冣
1.076450 − 0.237662 0.161212

Y w,test = ktest 冕 ␭
Stest共␭兲R共␭兲ȳ共␭兲d␭, 共23兲
M −1
= 0.410964 0.554342
0.034694 .
− 0.010954 − 0.013389 1.024343
共34兲

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 Davis and Ohno: Color quality scale

3.4 CIE 1976 L*a*b* Coordinates In a similar manner, the difference in chroma between
The uniform object color space used in the CQS calcula- the two illumination conditions, reference and test, is cal-
culated as follows:
tions is CIE 1976 L*a*b*; thus, these coordinates are cal-
culated for each of the reflective samples 共i兲 when illumi-
⌬Cab,i
* = C* *
− Cab,i,ref . 共46兲
* , a* , b* 兲. The
nated by the reference illuminant 共Li,ref i,ref i,ref
ab,i,test

calculation procedures are given in CIE’s primary colorim- The color difference between illumination by the refer-
etry publication,5 but are repeated as follows: ence illuminant and test source for each sample is given by

* = 116
Li,ref 冉 冊
Y i,ref
Y w,ref
1/3
− 16, 共35兲
* = 关共⌬L*兲2 + 共⌬a*兲2 + 共⌬b*兲2兴1/2 .
⌬Eab,i i i i
共47兲

冋冉 冊 冉 冊 册
3.5 Application of the Saturation Factor
1/3 1/3
Xi,ref Y i,ref Rather than simply calculating the color difference of each
* = 500
ai,ref − , 共36兲
Xw,ref Y w,ref reflective sample as above, a saturation factor is introduced
in the calculations of the CQS. The saturation factor serves

* = 200
bi,ref 冋冉 冊 冉 冊 册
Y i,ref
Y w,ref
1/3
−
Zi,ref
Zw,ref
1/3
. 共37兲
to negate any contribution to the color difference that arises
from an increase in object chroma from test source illumi-
nation 共relative to the reference illuminant兲. As discussed
earlier, evidence suggests that increases in object chroma,
Note that, in the definition of CIELAB,5 the formulae are
as long as they are not excessive, are not detrimental to
different depending on the values of 共X / Xn兲, 共Y / Y n兲, and
color quality and may even be beneficial. Taking the middle
共Z / Zn兲. These conditional formulae are needed only to cor- ground, with the implementation of the saturation factor, a
rect the results for very low reflectance samples. It has been test source that increases object chroma is not penalized,
computationally verified that such conditional formulae are but is also not rewarded. The color difference for each
not needed for the 15 color samples used in CQS, thus the sample 共i兲 illuminated by the test source and reference il-
simple formulae above are sufficient for accurate calcula- luminant are calculated, with the integration of the satura-
tion for these samples. tion factor 共⌬Eab,i,sat
* 兲 is calculated by
This procedure is repeated to calculate the coordinates
for each sample 共i兲 illuminated by the test source 共Li,test* ,
⌬Eab,i,sat
* = ⌬Eab,i
* if ⌬Cab,i
* 艋 0, 共48兲
ai,test, bi,test兲.
* *

* = 116
Li,test 冉 冊
Y i,test,c
Y w,test
1/3
− 16, 共38兲
⌬Eab,i,sat
* = 关共⌬Eab,i
* 兲2 − 共⌬C* 兲2兴1/2
ab,i
if ⌬Cab,i
* ⬎ 0. 共49兲

冋冉 冊 冉 冊 册
3.6 Root Mean Square
1/3 1/3
Xi,test,c Y i,test,c All the previous mathematical steps are performed for each
* = 500
ai,test − , 共39兲
Xw,test Y w,test of the reflective samples. In the calculation of the General
Color Quality Scale 共Qa兲, the color differences from all 15

* = 200
bi,test 冋冉 冊 冉 冊 册
Y i,test,c
Y w,test
1/3
−
Zi,test,c
Zw,test
1/3
. 共40兲
samples are considered. If the color differences were
merely combined by averaging all 15 color differences,
then the Qa score could be still relatively high even if one
From these coordinates, the chroma of each sample un- or two color samples show very large color differences.
der the reference illuminant 共Cab,ref* 兲 and test source This situation is entirely possible with the notable peaks
and valleys of RGB LEDs, which can render a couple of
共Cab,test
* 兲 is calculated as follows:
object colors poorly, while performing well for all other
* = 关共a* 兲2 + 共b* 兲2兴1/2 , object colors. To ensure that poor rendering of even a few
Ci,ref i,ref i,ref
共41兲 object colors has a significant impact on the General Color
Quality Scale, the color differences are combined by root
* = 关共a* 兲2 + 共b* 兲2兴1/2 .
Ci,test 共42兲 mean square 共rms兲,

冑
i,test i,test
15
The differences of the coordinates 共⌬L* , ⌬a* , ⌬b*兲 be- 1
tween illumination by the reference illuminant and test ⌬Erms = 兺 共⌬Eab,i,sat
15 i=1
* 兲2 . 共50兲
source for each sample are calculated as follows:

⌬Li* = Li,test
* − L* ,
i,ref
共43兲 3.7 Scaling Factor
The “rms average” CQS score is calculated by
⌬ai* = ai,test
* − a* , 共44兲
i,ref Qa,rms = 100 − 3.1 ⫻ ⌬Erms . 共51兲
The 3.1 in Eq. 共51兲 is the scaling factor, similar to the
⌬bi* = bi,test
* − b* .
i,ref
共45兲 value 4.6 used in the calculation of CRI 关Eq. 共1兲兴. The

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 Davis and Ohno: Color quality scale

Fig. 6 CCT factor 共MCCT兲 as a function of color temperature for

reference illuminants ⱕ3500 K.

exhibit decreased chromatic discrimination performance.

This factor is calculated only from the gamut area of the
reference source and given by

Fig. 5 The 0–100 scale function 共dashed兲 used to convert original

M CCT = T3共9.2672 ⫻ 10−11兲 − T2共8.3959 ⫻ 10−7兲
scores 共solid兲. + T共0.00255兲 − 1.612 共for T ⬍ 3500 K兲, 共53兲

scaling factor for the CRI was selected such that a halo- M CCT = 1 共for T 艌 3500 K兲, 共54兲
phosphate warm white lamp would receive a Ra value of where T is the CCT of the test light source. The derivation
51.26 The scaling factor for the CQS was selected so that of this equation is given in Appendix B, which need not be
the average of the General Color Quality Scales 共Qa兲 for a repeated by the users of the CQS. As shown in Fig. 6, the
set of CIE standard fluorescent lamp spectra 共F1–F12兲5 is CCT factor has little impact on white-light sources of prac-
equal to the average output of the CRI 共Ra = 75.1兲 for these tical CCT range 共less than two Qa points are lost for
sources. Though the average scores remain the same for sources T ⬎ 2800 K兲 but will penalize the light sources hav-
these representative fluorescent lamp spectra, scores for in- ing much lower CCTs.
dividual lamps are not identical. This selection was in-
tended to maintain a certain degree of consistency between 3.10 General CQS
the CRI and CQS in real use and minimize the changes of Finally, the General CQS 共Qa兲 is calculated as follows:
values from CRI to CQS for traditional light sources.
Qa = M CCTQa,0–100 . 共55兲
3.8 0–100 Scale Conversion
The CRI can give negative values, which is not desired.
Because the basic structure of the calculations are the same 3.11 Special CQS
for the CRI and CQS, the CQS would also yield negative Similar to the CRI, the CQS values for individual test
results for very poor color-rendering sources. To avoid oc- samples are calculated to allow more detailed evaluation of
currences of such negative numbers, a mathematical func- color quality. Using the same scaling factor, the 0–100 con-
tion, as follows, is implemented version formula, and the CCT factor described above, the
Special CQS 共Qi兲 for each reflective sample i is calculated
Qa,0–100 = 10 ln兵exp共Qa,rms/10兲 + 1其. 共52兲 by
The input and output relationship of this formula is Qi,PRE = 100 − 3.1 ⫻ ⌬Eab,i,sat
* , 共56兲
shown in Fig. 5. As shown in the figure, only scores lower
than ⬃30 are affected by this conversion and higher values
are scarcely affected. Because such low scores only apply Qi,0–100 = 10共ln exp共Qi,PRE/10兲 + 1兲, 共57兲
to lamps with truly poor color quality, the linearity of the
scale at the very bottom is deemed unimportant.
Qi = M CCTQi,0–100 . 共58兲
3.9 CCT Factor
One final multiplication factor addresses the fact that the 4 Additional Scales
reference illuminant 共with its CCT matched to that of the Though it was emphasized that the CQS must have a one-
test source兲 always has a perfect score 共 = 100兲 for any CCT. number output, it is acknowledged that certain applications
This variable, called the CCT factor, was devised to penal- 共e.g., quality control in factories兲 will require more specific
ize lamps with extremely low CCTs, which have smaller information about the color-rendering properties of light
gamut areas 共and, therefore, render fewer object colors兲 and sources. Therefore, for expert users, three additional indices

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 Davis and Ohno: Color quality scale

共described below兲 are made available from the CQS calcu-

lations. These additional scales are also calculated in the
CQS spreadsheet available from the authors.

4.1 Color Fidelity Scale Qf

The Color Fidelity Scale 共Qf兲 is intended to evaluate the
fidelity of object color appearances 共compared to the refer-
ence illuminant of the same CCT and illuminance兲, similar
to the function of CRI Ra. Qf is calculated using exactly the
same procedures as the CQS Qa, except that it excludes the
saturation factor; thus, the equations in Section 3.5 are
skipped and the following is used in all cases regardless of
the direction of sample chroma shifts:
Fig. 7 Comparison of Qa 共gray squares兲 and Ra 共black diamonds兲
for several traditional lamps including fluorescent and other dis-
⌬E* ab,i,sat
= ⌬Eab,i
* . 共59兲 charge lamps. Qf 共black triangles兲, Qp 共gray circles兲, and Qg 共black
dashes兲 are also shown.
As was done for Qa, the scores of Qf are scaled so that the
average score for the 12 reference fluorescent lamp spectra
共F1–F12 in Ref. 5兲 is the same as that for CRI Ra 共thus, for
CQS Qa兲. The scaling factor for Qf in Eq. 共51兲 is changed In some cases, RGB white-light spectra can have large
to 2.93. gamut areas by increasing object chroma in the red and
green regions. Larger gamut areas are always accompanied
by corresponding hue shifts. Thus, by looking at the rela-
4.2 Color Preference Scale Qp tive gamut area Qg and knowing the type of light source,
Although the General CQS Qa was designed to indicate the one can develop a reasonable estimate of the shape of
overall color quality of a light source, the Color Preference 共a* , b*兲 plot profile for the 15 samples. Note that gamut
Scale 共Qp兲 places additional weight on preference of object area does not necessarily correlate well with color prefer-
color appearance. This metric is based on the notion that ence or color discrimination performance when it is much
increases in chroma are generally preferred and should be larger than that of the reference illuminant.
rewarded. Qp is calculated using exactly the same proce-
dures as the CQS Qa, except that it rewards light sources 5 Comparison of the CQS and CRI
for increasing object chroma; thus, Eq. 共51兲 in Section 3.7
Although there are several improvements in the CQS over
is replaced by
the CRI, one of the most significant changes is the inclu-

冋 1
Qa,rms = 100 − 3.78 ⫻ ⌬Erms − 兺 ⌬Cab
15 i=1
15
* · K共i兲 ,
册 共60兲
sion of the saturation factor, which is effective when light
sources enhance object chroma. Because traditional light
sources 共incandescent and discharge lamps兲 mostly do not
enhance chroma 共except the neodymium lamp兲 and because
where Qa is scaled so that the scores for fluorescent lamps will be
similar to Ra, the scores of Qa for traditional lamps are
K共i兲 = 1 *
for Cab,test 艌 Cab,ref
* , 共61兲 generally very close to Ra. Figure 7 shows the comparison
of Qa and Ra 共as well as Qf, Qp, and Qg兲 for several tradi-
tional lamps, including fluorescent and other discharge
K共i兲 = 0 *
for Cab,test ⬍ Cab,ref
* . 共62兲
lamps. The differences are within three points for fluores-
As was done for Qa, the scores of Qp are rescaled 共scaling cent lamps and five points for all these lamps. On the other
factor of 3.78兲 so that the average score for the 12 reference hand, the CQS shows much larger differences for neody-
fluorescent lamp spectra 共F1–F12 in Ref. 5兲 is the same as mium lamps and some RGB LED model spectra, as shown
that for CRI Ra. in Fig. 8, which shows differences up to 20 points. In ad-
dition to RGB LED spectra that enhance object chroma,
Fig. 8 shows some RGB LED spectra that have relatively
4.3 Gamut Area Scale Qg poor color rendering for saturated colors and are scored
The Gamut Area Scale 共Qg兲 is calculated as the relative lower by the CQS than the CRI. The data for the light
gamut area formed by the 共a* , b*兲 coordinates of the 15 sources in Fig. 7 and 8 are shown in Table 1. This demon-
samples illuminated by the test light source in the CIELAB strates that though the CQS does not deviate substantially
object color space. Qg is normalized by the gamut area of from the Ra scores for traditional lamps 共this is a require-
D65 multiplied by 100; therefore, its scaling is different ment for acceptance from the lighting industry兲, it appro-
from Qa, Qf, and Qp and can be Ⰷ100. See Appendix B for priately treats the chroma-enhancing RGB white LED
the equations to calculate the gamut area formed by the 15 sources and problematic LED sources.
samples. Note that the chromatic adaptation transform to
D65 共used in the derivation of the CCT factor兲 is not used 6 Conclusions
in Qg. Qg is calculated directly from the 共a* , b*兲 coordi- Throughout the development of the calculations of the
nates calculated in Section 3.4. CQS, computational testing of the performance of the met-

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 Davis and Ohno: Color quality scale

lower score is far more appropriate and communicates to

users how this particular RGB LED performs at color ren-
dering compared to other lamps.
The RGB LED shown in Fig. 3 would receive a Ra of
only 67 despite its reasonable overall color quality. In this
case, the CQS would give this light source a Qa of 79.
Though the 12 point score increase is notable, the CQS still
penalizes this chroma-enhancing source for its hue shifts.
Simulations have shown that all light spectra that enhance
object chroma also induce comparable hue shifts. There-
fore, a chroma-enhancing source will never receive a Qa of
100. The purpose of the saturation factor is not to favor
Fig. 8 Comparison of Qa 共gray squares兲 and Ra 共black diamonds兲
chroma-enhancing sources, but merely to limit the extent to
for several RGB LED model spectra. Qf 共black triangles兲, Qp 共gray which they are penalized. This RGB LED illustrates that
circles兲, and Qg 共black dashes兲 are also shown. this objective is met by the CQS. A similar example is the
neodymium lamp, which is given CQS Qa = 88, an 11-point
increase from CRI Ra = 77.
ric provided feedback as to whether elements of the calcu- The new metric will serve not only RGB LEDs but also
lations were effective at enabling the CQS to meet its goals phosphor-type white LEDs, which are presently more
共discussed in Section 2兲. dominant in lighting products. Currently available white
Let us revisit the RGB LED shown in Fig. 2. As dis- LEDs use broadband phosphors, but it is foreseen that
cussed earlier, this source would receive an Ra score of 80, phosphor LEDs will employ narrowband phosphors in the
though it performs very poorly for saturated red and purple future, which would have the same problems with CRI as
reflective samples. Due in large part to the saturated set of the RGB LEDs. Fluorescent lamps followed such a path of
reflective samples and the rms combination of color differ- development. They were initially developed using broad-
ences, the Qa score for this RGB LED would be 73. This

Table 1 Detailed information on light sources used for Figs. 7 and 8.

Lamp Details CCT Ra Qa Qf Qp Qg

Incan. 2812 100 98 98 98 98

CW-FL F34/CW/RS/EW 4196 59 61 62 57 76

WW-FL F34T12WW/RS/EW 3011 50 54 54 53 76

TriPh-FL 1 F32T8/TL841 3969 85 83 83 84 98

TriPh-FL 2 F32T8/TL850 5072 86 85 84 88 101

Mercury H38JA-100/DX 3725 53 53 50 62 87

MH MHC100/U/MP/4K 4167 92 92 92 94 100

SHPS SDW-T 100W/LV 2508 85 80 77 87 102

RGB LED 共470-525-630兲 Simulation 3018 31 55 44 79 111

RGB LED 共464-538-613兲 Simulation 3300 80 85 81 92 108

RGB LED 共467-548-616兲 Simulation 3300 90 82 81 84 101

RGB LED 共464-562-626兲 Simulation 3300 59 78 71 94 121

RGB LED 共457-540-605兲 Simulation 3300 80 74 73 77 95

RGB LED 共455-547-623兲 Simulation 3300 73 79 73 92 116

RGB LED 共473-545-616兲 Simulation 3304 85 77 78 73 90

Neodym. Incandescent type 2757 77 88 82 99 112

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 Davis and Ohno: Color quality scale

band phosphors but currently employ primarily narrowband test, validate, and improve the performance of the CQS are
phosphors for improved energy efficiency and color render- underway. This is a necessary step to ultimately assess and
ing. verify the performance of this metric.
Though the approach for developing the CQS relied Appendix A. Spectral Reflectance Factors for 15
heavily on computational analyses, visual experiments to CQS Samples

Wavelength 7.5P 10PB 5PB 7.5B 10BG 2.5BG 2.5G 7.5GY

共nm兲 4/10 4/10 4/2 5/10 6/8 6/10 6/12 7/10

380 0.1086 0.1053 0.0858 0.079 0.1167 0.0872 0.0726 0.0652

385 0.138 0.1323 0.099 0.0984 0.1352 0.1001 0.076 0.0657
390 0.1729 0.1662 0.1204 0.1242 0.1674 0.1159 0.0789 0.0667
395 0.2167 0.2113 0.1458 0.1595 0.2024 0.1339 0.0844 0.0691
400 0.2539 0.2516 0.1696 0.1937 0.2298 0.1431 0.0864 0.0694
405 0.2785 0.2806 0.1922 0.2215 0.2521 0.1516 0.0848 0.0709
410 0.2853 0.2971 0.2101 0.2419 0.2635 0.157 0.0861 0.0707
415 0.2883 0.3042 0.2179 0.2488 0.2702 0.1608 0.0859 0.0691
420 0.286 0.3125 0.2233 0.2603 0.2758 0.1649 0.0868 0.0717
425 0.2761 0.3183 0.2371 0.2776 0.2834 0.1678 0.0869 0.0692
430 0.2674 0.3196 0.2499 0.2868 0.2934 0.1785 0.0882 0.071
435 0.2565 0.3261 0.2674 0.3107 0.3042 0.1829 0.0903 0.0717
440 0.2422 0.3253 0.2949 0.3309 0.3201 0.1896 0.0924 0.0722
445 0.2281 0.3193 0.3232 0.3515 0.3329 0.2032 0.0951 0.0737
450 0.214 0.3071 0.3435 0.3676 0.3511 0.212 0.0969 0.0731
455 0.2004 0.2961 0.3538 0.3819 0.3724 0.2294 0.1003 0.0777
460 0.1854 0.2873 0.3602 0.4026 0.4027 0.2539 0.1083 0.0823
465 0.1733 0.2729 0.3571 0.4189 0.4367 0.2869 0.1203 0.0917
470 0.1602 0.2595 0.3511 0.4317 0.4625 0.317 0.1383 0.1062
475 0.1499 0.2395 0.3365 0.4363 0.489 0.357 0.1634 0.1285
480 0.1414 0.2194 0.3176 0.4356 0.5085 0.3994 0.1988 0.1598
485 0.1288 0.1949 0.2956 0.4297 0.5181 0.4346 0.2376 0.1993
490 0.1204 0.1732 0.2747 0.4199 0.5243 0.4615 0.2795 0.2445
495 0.1104 0.156 0.2506 0.4058 0.5179 0.4747 0.3275 0.2974
500 0.1061 0.1436 0.2279 0.3882 0.5084 0.4754 0.3671 0.3462
505 0.1018 0.1305 0.2055 0.366 0.4904 0.4691 0.403 0.3894
510 0.0968 0.1174 0.1847 0.3433 0.4717 0.4556 0.4201 0.418
515 0.0941 0.1075 0.1592 0.3148 0.4467 0.4371 0.4257 0.4433
520 0.0881 0.0991 0.1438 0.289 0.4207 0.4154 0.4218 0.4548
525 0.0842 0.0925 0.1244 0.2583 0.3931 0.3937 0.409 0.4605
530 0.0808 0.0916 0.1105 0.234 0.3653 0.3737 0.3977 0.4647
535 0.0779 0.0896 0.0959 0.2076 0.3363 0.3459 0.3769 0.4626
540 0.0782 0.0897 0.0871 0.1839 0.3083 0.3203 0.3559 0.4604
545 0.0773 0.0893 0.079 0.1613 0.2808 0.2941 0.3312 0.4522
550 0.0793 0.0891 0.0703 0.1434 0.2538 0.2715 0.3072 0.4444
555 0.079 0.0868 0.0652 0.1243 0.226 0.2442 0.2803 0.4321
560 0.0793 0.082 0.0555 0.1044 0.2024 0.2205 0.2532 0.4149
565 0.0806 0.0829 0.0579 0.0978 0.1865 0.1979 0.2313 0.4039
570 0.0805 0.0854 0.0562 0.091 0.1697 0.18 0.2109 0.3879
575 0.0793 0.0871 0.0548 0.0832 0.1592 0.161 0.1897 0.3694
580 0.0803 0.0922 0.0517 0.0771 0.1482 0.1463 0.1723 0.3526
585 0.0815 0.0978 0.0544 0.0747 0.1393 0.1284 0.1528 0.3288
590 0.0842 0.1037 0.0519 0.0726 0.1316 0.1172 0.1355 0.308

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 Davis and Ohno: Color quality scale

Wavelength 7.5P 10PB 5PB 7.5B 10BG 2.5BG 2.5G 7.5GY

共nm兲 4/10 4/10 4/2 5/10 6/8 6/10 6/12 7/10

595 0.0912 0.1079 0.052 0.0682 0.1217 0.1045 0.1196 0.2829

600 0.1035 0.1092 0.0541 0.0671 0.1182 0.0964 0.105 0.2591
605 0.1212 0.1088 0.0537 0.066 0.1112 0.0903 0.0949 0.2388
610 0.1455 0.1078 0.0545 0.0661 0.1071 0.0873 0.0868 0.2228
615 0.1785 0.1026 0.056 0.066 0.1059 0.0846 0.0797 0.2109
620 0.2107 0.0991 0.056 0.0653 0.1044 0.0829 0.0783 0.2033
625 0.246 0.0995 0.0561 0.0644 0.1021 0.0814 0.0732 0.1963
630 0.2791 0.1043 0.0578 0.0653 0.0991 0.0805 0.0737 0.1936
635 0.3074 0.1101 0.0586 0.0669 0.1 0.0803 0.0709 0.1887
640 0.333 0.1187 0.0573 0.066 0.098 0.0801 0.0703 0.1847
645 0.3542 0.1311 0.0602 0.0677 0.0963 0.0776 0.0696 0.1804
650 0.3745 0.143 0.0604 0.0668 0.0997 0.0797 0.0673 0.1766
655 0.392 0.1583 0.0606 0.0693 0.0994 0.0801 0.0677 0.1734
660 0.4052 0.1704 0.0606 0.0689 0.1022 0.081 0.0682 0.1721
665 0.4186 0.1846 0.0595 0.0676 0.1005 0.0819 0.0665 0.172
670 0.4281 0.1906 0.0609 0.0694 0.1044 0.0856 0.0691 0.1724
675 0.4395 0.1983 0.0605 0.0687 0.1073 0.0913 0.0695 0.1757
680 0.444 0.1981 0.0602 0.0698 0.1069 0.093 0.0723 0.1781
685 0.4497 0.1963 0.058 0.0679 0.1103 0.0958 0.0727 0.1829
690 0.4555 0.2003 0.0587 0.0694 0.1104 0.1016 0.0757 0.1897
695 0.4612 0.2034 0.0573 0.0675 0.1084 0.1044 0.0767 0.1949
700 0.4663 0.2061 0.0606 0.0676 0.1092 0.1047 0.081 0.2018
705 0.4707 0.212 0.0613 0.0662 0.1074 0.1062 0.0818 0.2051
710 0.4783 0.2207 0.0618 0.0681 0.1059 0.1052 0.0837 0.2071
715 0.4778 0.2257 0.0652 0.0706 0.1082 0.1029 0.0822 0.2066
720 0.4844 0.2335 0.0647 0.0728 0.1106 0.1025 0.0838 0.2032
725 0.4877 0.2441 0.0684 0.0766 0.1129 0.1008 0.0847 0.1998
730 0.4928 0.255 0.0718 0.0814 0.1186 0.1036 0.0837 0.2024
735 0.496 0.2684 0.0731 0.0901 0.1243 0.1059 0.0864 0.2032
740 0.4976 0.2862 0.0791 0.1042 0.1359 0.1123 0.0882 0.2074
745 0.4993 0.3086 0.0828 0.1228 0.1466 0.1175 0.0923 0.216
750 0.5015 0.3262 0.0896 0.1482 0.1617 0.1217 0.0967 0.2194
755 0.5044 0.3483 0.098 0.1793 0.1739 0.1304 0.0996 0.2293
760 0.5042 0.3665 0.1063 0.2129 0.1814 0.133 0.1027 0.2378
765 0.5073 0.3814 0.1137 0.2445 0.1907 0.1373 0.108 0.2448
770 0.5112 0.3974 0.1238 0.2674 0.1976 0.1376 0.1115 0.2489
775 0.5147 0.4091 0.1381 0.2838 0.1958 0.1384 0.1118 0.2558
780 0.5128 0.4206 0.1505 0.2979 0.1972 0.139 0.1152 0.2635
785 0.5108 0.423 0.1685 0.3067 0.2018 0.1378 0.1201 0.2775
790 0.5171 0.4397 0.1862 0.3226 0.2093 0.1501 0.1253 0.2957
795 0.5135 0.4456 0.2078 0.3396 0.2161 0.1526 0.1313 0.3093
800 0.5191 0.4537 0.2338 0.3512 0.2269 0.1646 0.1393 0.3239
805 0.5191 0.4537 0.2338 0.3512 0.2269 0.1646 0.1393 0.3239
810 0.5191 0.4537 0.2338 0.3512 0.2269 0.1646 0.1393 0.3239
815 0.5191 0.4537 0.2338 0.3512 0.2269 0.1646 0.1393 0.3239
820 0.5191 0.4537 0.2338 0.3512 0.2269 0.1646 0.1393 0.3239
825 0.5191 0.4537 0.2338 0.3512 0.2269 0.1646 0.1393 0.3239
830 0.5191 0.4537 0.2338 0.3512 0.2269 0.1646 0.1393 0.3239

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 Davis and Ohno: Color quality scale

Wavelength 2.5GY 5Y 10YR 5YR 10R 5R 7.5RP

共nm兲 8/10 8.5/12 7/12 7/12 6/12 4/14 4/12

380 0.0643 0.054 0.0482 0.0691 0.0829 0.053 0.0908

385 0.0661 0.0489 0.0456 0.0692 0.0829 0.0507 0.1021
390 0.0702 0.0548 0.0478 0.0727 0.0866 0.0505 0.113
395 0.0672 0.055 0.0455 0.0756 0.0888 0.0502 0.128
400 0.0715 0.0529 0.0484 0.077 0.0884 0.0498 0.1359
405 0.0705 0.0521 0.0494 0.0806 0.0853 0.0489 0.1378
410 0.0727 0.0541 0.0456 0.0771 0.0868 0.0503 0.1363
415 0.0731 0.0548 0.047 0.0742 0.0859 0.0492 0.1363
420 0.0745 0.0541 0.0473 0.0766 0.0828 0.0511 0.1354
425 0.077 0.0531 0.0486 0.0733 0.0819 0.0509 0.1322
430 0.0756 0.0599 0.0501 0.0758 0.0822 0.0496 0.1294
435 0.0773 0.0569 0.048 0.0768 0.0818 0.0494 0.1241
440 0.0786 0.0603 0.049 0.0775 0.0822 0.048 0.1209
445 0.0818 0.0643 0.0468 0.0754 0.0819 0.0487 0.1137
450 0.0861 0.0702 0.0471 0.0763 0.0807 0.0468 0.1117
455 0.0907 0.0715 0.0486 0.0763 0.0787 0.0443 0.1045
460 0.0981 0.0798 0.0517 0.0752 0.0832 0.044 0.1006
465 0.1067 0.086 0.0519 0.0782 0.0828 0.0427 0.097
470 0.1152 0.0959 0.0479 0.0808 0.081 0.0421 0.0908
475 0.1294 0.1088 0.0494 0.0778 0.0819 0.0414 0.0858
480 0.141 0.1218 0.0524 0.0788 0.0836 0.0408 0.0807
485 0.1531 0.1398 0.0527 0.0805 0.0802 0.04 0.0752
490 0.1694 0.1626 0.0537 0.0809 0.0809 0.0392 0.0716
495 0.1919 0.1878 0.0577 0.0838 0.0838 0.0406 0.0688
500 0.2178 0.2302 0.0647 0.0922 0.0842 0.0388 0.0678
505 0.256 0.2829 0.0737 0.1051 0.0865 0.0396 0.0639
510 0.311 0.3455 0.0983 0.123 0.091 0.0397 0.0615
515 0.3789 0.4171 0.1396 0.1521 0.092 0.0391 0.0586
520 0.4515 0.4871 0.1809 0.1728 0.0917 0.0405 0.0571
525 0.5285 0.5529 0.228 0.1842 0.0917 0.0394 0.0527
530 0.5845 0.5955 0.2645 0.1897 0.0952 0.0401 0.0513
535 0.6261 0.6299 0.2963 0.1946 0.0983 0.0396 0.0537
540 0.6458 0.6552 0.3202 0.2037 0.1036 0.0396 0.0512
545 0.6547 0.6661 0.3545 0.2248 0.115 0.0395 0.053
550 0.6545 0.6752 0.395 0.2675 0.1331 0.0399 0.0517
555 0.6473 0.6832 0.4353 0.3286 0.1646 0.042 0.0511
560 0.6351 0.6851 0.4577 0.3895 0.207 0.041 0.0507
565 0.6252 0.6964 0.4904 0.4654 0.2754 0.0464 0.0549
570 0.6064 0.6966 0.5075 0.5188 0.3279 0.05 0.0559
575 0.5924 0.7063 0.5193 0.5592 0.3819 0.0545 0.0627
580 0.5756 0.7104 0.5273 0.5909 0.425 0.062 0.0678
585 0.5549 0.7115 0.5359 0.6189 0.469 0.0742 0.081
590 0.5303 0.7145 0.5431 0.6343 0.5067 0.0937 0.1004
595 0.5002 0.7195 0.5449 0.6485 0.5443 0.1279 0.1268
600 0.4793 0.7183 0.5493 0.6607 0.5721 0.1762 0.1595
605 0.4517 0.7208 0.5526 0.6648 0.5871 0.2449 0.2012
610 0.434 0.7228 0.5561 0.6654 0.6073 0.3211 0.2452
615 0.4169 0.7274 0.5552 0.6721 0.6141 0.405 0.2953
620 0.406 0.7251 0.5573 0.6744 0.617 0.4745 0.3439

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 Davis and Ohno: Color quality scale

Wavelength 2.5GY 5Y 10YR 5YR 10R 5R 7.5RP

共nm兲 8/10 8.5/12 7/12 7/12 6/12 4/14 4/12

625 0.3989 0.7274 0.562 0.6723 0.6216 0.5335 0.3928

630 0.3945 0.7341 0.5607 0.6811 0.6272 0.5776 0.4336
635 0.3887 0.7358 0.5599 0.6792 0.6287 0.6094 0.4723
640 0.3805 0.7362 0.5632 0.6774 0.6276 0.632 0.4996
645 0.3741 0.7354 0.5644 0.6796 0.6351 0.6495 0.5279
650 0.37 0.7442 0.568 0.6856 0.6362 0.662 0.5428
655 0.363 0.7438 0.566 0.6853 0.6348 0.6743 0.5601
660 0.364 0.744 0.5709 0.6864 0.6418 0.6833 0.5736
665 0.359 0.7436 0.5692 0.6879 0.6438 0.6895 0.5837
670 0.3648 0.7442 0.5657 0.6874 0.6378 0.6924 0.589
675 0.3696 0.7489 0.5716 0.6871 0.641 0.703 0.5959
680 0.3734 0.7435 0.5729 0.6863 0.646 0.7075 0.5983
685 0.3818 0.746 0.5739 0.689 0.6451 0.7112 0.6015
690 0.3884 0.7518 0.5714 0.6863 0.6432 0.7187 0.6054
695 0.3947 0.755 0.5741 0.6893 0.6509 0.7214 0.6135
700 0.4011 0.7496 0.5774 0.695 0.6517 0.7284 0.62
705 0.404 0.7548 0.5791 0.6941 0.6514 0.7327 0.6287
710 0.4072 0.7609 0.5801 0.6958 0.6567 0.7351 0.6405
715 0.4065 0.758 0.5804 0.695 0.6597 0.7374 0.6443
720 0.4006 0.7574 0.584 0.7008 0.6576 0.741 0.6489
725 0.3983 0.7632 0.5814 0.702 0.6576 0.7417 0.6621
730 0.3981 0.7701 0.5874 0.7059 0.6656 0.7491 0.6662
735 0.399 0.7667 0.5885 0.7085 0.6641 0.7516 0.6726
740 0.4096 0.7735 0.5911 0.7047 0.6667 0.7532 0.6774
745 0.4187 0.772 0.5878 0.7021 0.6688 0.7567 0.6834
750 0.4264 0.7739 0.5896 0.7071 0.6713 0.76 0.6808
755 0.437 0.774 0.5947 0.7088 0.6657 0.7592 0.6838
760 0.4424 0.7699 0.5945 0.7055 0.6712 0.7605 0.6874
765 0.4512 0.7788 0.5935 0.7073 0.6745 0.7629 0.6955
770 0.4579 0.7801 0.5979 0.7114 0.678 0.7646 0.7012
775 0.4596 0.7728 0.5941 0.7028 0.6744 0.7622 0.6996
780 0.4756 0.7793 0.5962 0.7105 0.6786 0.768 0.7023
785 0.488 0.7797 0.5919 0.7078 0.6823 0.7672 0.7022
790 0.5066 0.7754 0.5996 0.7112 0.6806 0.7645 0.7144
795 0.5214 0.781 0.5953 0.7123 0.6718 0.7669 0.7062
800 0.545 0.7789 0.5953 0.7158 0.6813 0.7683 0.7075
805 0.545 0.7789 0.5953 0.7158 0.6813 0.7683 0.7075
810 0.545 0.7789 0.5953 0.7158 0.6813 0.7683 0.7075
815 0.545 0.7789 0.5953 0.7158 0.6813 0.7683 0.7075
820 0.545 0.7789 0.5953 0.7158 0.6813 0.7683 0.7075
825 0.545 0.7789 0.5953 0.7158 0.6813 0.7683 0.7075
830 0.545 0.7789 0.5953 0.7158 0.6813 0.7683 0.7075

Appendix B. Calculation of CCT Factor CIELAB was designed for best performance with D65, and
The CCT factor is based on the relative gamut area of the the gamut areas of a wide range of CCTs can be more
reference illuminant as a function of its CCT. First, the accurately evaluated using this conversion.
X , Y , Z tristimulus values of the 15 reflective samples under Then, the gamut area of the 15 CQS samples in CIELAB
the reference illuminant are converted to their color appear- 共a , b*兲 space 共see Section 3.4兲 is calculated for the refer-
*
ance under D65 using CMCCAT2000 chromatic adaptation ence illuminant at the given CCT. The gamut area is di-
transform23 共see Section 3.3兲. This is done because vided into 15 triangles 共S兲, each of which is formed by two

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 Davis and Ohno: Color quality scale

Table 2 Gamut areas and CCT factors 共MCCT兲 for a number of CIELAB units兲. If the gamut area of the reference illumi-
CCTs. nant is greater than that of D65, the multiplication factor is
simply set to 1,
CCT 共K兲 Gamut Area MCCT
M CCT = 1 if G 艌 8210, 共69兲
1000 1579 0.19

1500 5293 0.65 G

M CCT = if G ⬍ 8210. 共70兲
2000 7148 0.87
8210
The results of the CCT factor calculations are shown in
2500 7858 0.96
Table 2 for a number of CCT values. It only needs to be
2856 8085 0.99 calculated for CCTs of ⬍3500 K. A curve fit to the points
for illuminants of ⬍4000 K in Table 2, as shown in Fig. 6,
3000 8144 0.99 was obtained with a third-order polynomial with R2
= 0.9999
3500 8267 1.00
M CCT = T3共9.2672 ⫻ 10−11兲 − T2共8.3959 ⫻ 10−7兲
4000 8322 1.00
+ T共0.00255兲 − 1.612, 共71兲
5000 8354 1.00
where T is the CCT of the reference illuminant. This func-
6000 8220 1.00 tion fits the data well, and this polynomial can be used to
determine the CCT factor for sources of ⬍3500 K, elimi-
6500 8210 1.00
nating the need for Eqs. 共63兲–共70兲.
7000 8202 1.00
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 Davis and Ohno: Color quality scale

Res. Appl. 33, 192–200 共2008兲. Yoshi Ohno is the group leader of Optical
24. CIE 167: 2005, “Recommended practice for tabulating spectral data Sensor Group, Optical Technology Division
for use in color computations” 共2005兲. of NIST. His group is responsible for main-
25. C. J. Li, M. R. Luo, B. Rigg, and R. W. G. Hunt, “CMC 2000
chromatic adaptation transform: CMCCAT2000,” Color Res. Appl. taining national standards of the candela,
27, 49–58 共2002兲. lumen, and color scales. He serves as the
26. J. Schanda and N. Sándor, “Colour rendering, past-present-future,” in director of CIE Division 2 and active in many
Proc. of Int. Lighting and Colour Conf., pp. 76–85, SANCI, Cape national and international committees in
Town, South Africa 共2003兲.
ANSI, IESNA, CIE, CIPM, and IEC on opti-
cal metrology and standardization of solid
Wendy Davis is a vision scientist in the Op- state lighting.
tical Technology Division at the National In-
stitute of Standards and Technology 共NIST兲.
She joined NIST soon after completing her
PhD in vision science at the University of
California, Berkeley, in 2004. Dr. Davis and
her colleagues in colorimetry and photom-
etry are currently establishing a permanent
Vision Science Program at NIST. Her cur-
rent main research focus is the develop-
ment of a color quality metric, suitable for
both solid state lighting, and traditional lamps.

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