more saturated under higher illuminances 共Hunt effect兲.
16
Therefore, if an artificial light source increases object satu-
ration 共relative to the reference illuminant兲, the object may
actually appear more like it would when illuminated by real
daylight. This may make the object actually appear more
natural to observers.
The ability to distinguish between similar colors, chro-
matic discrimination is another dimension of color quality
that can deviate from absolute fidelity. The number of ob-
ject colors that a light source permits discrimination be-
tween can be inferred by the gamut area 共of rendered object
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
samples will be larger for some light sources, resulting in
larger gamut areas, than others. When the distance between
samples is larger in a uniform color space, the samples
appear more different from each other 共than when distances
are smaller兲 and an observer would be able to distinguish a
greater number of colors intermediate to the two samples.
In addition to increased chromatic discrimination, larger
object gamut areas have been associated with increased
perceived brightness, enhanced visual clarity, and increased
object color saturation.
17,18
Gamut area is clearly a useful
measure for certain color-quality properties of light sources
and has been proposed as the central component to a num-
ber of proposed color-rendering metrics.
7,19–21
Finally, it was decided a priori that the new metric
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
sodium lamp, R
a
=−47. Color rendering is virtually nonex-
istent with this lamp. A score of zero would effectively
communicate the same message. Negative values simply do
not convey any useful information and have the potential to
confuse users.
The decision to restrict the output of the new metric to
one number is certainly controversial. The argument has
been made that it is impossible to communicate the differ-
ent dimensions of quality with only one number.
22,23
In-
deed, in some cases different dimensions of color quality,
such as fidelity and preference, can be contradictory. A met-
ric to assess a property like color quality inherently con-
denses information. After all, if the goal was to provide all
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-
termine the detailed color-rendering information 共e.g., di-
rection and magnitude of hue, chroma, and lightness shifts兲
of countless object colors. Even with all that information,
most users would still need guidance in how to use the
information to judge the suitability of a light source for a
specific application. The purpose of a metric is to condense
such an immense amount of information into something
manageable and useful. In order to be useful for the great-
est number of users, most of whom have very limited
knowledge of colorimetry, a one-number output is desir-
able. Though most users will not know exactly how the
number was determined or precisely what it means, this is
readily accepted by a majority of people. Throughout the
course of our lives, we use many measurement scales,
whose precise meanings and measurement methodologies
are unknown to us, without concern. Examples of such
measurement scales include shoe sizes, octane ratings of
gasoline, and radio station frequencies. Though most
people do not know precisely how those numbers are de-
termined, they find the scales useful and have a general
understanding of how different outputs relate to each other
共a larger shoe size means a bigger foot兲. However, it was
acknowledged that additional outputs, for expert users
needing specialized information, would be useful and
should be created to supplement the one-number general
output.
3 CQS
Led by these guiding principles, a method for the evalua-
tion of light source color quality was developed through
computational analyses and colorimetric simulations. The
resulting metric was named the CQS, a clear nod to the CRI
but sufficiently different to avoid confusion among users. A
thorough account of the calculations involved in the CQS is
provided here. Readers who are knowledgeable in basic
colorimetry may find the level of detail to be excessive, but
it was deemed important to provide complete enough infor-
mation that even a colorimetry novice could carry out the
calculations. A spreadsheet, with all of the calculations
implemented as well as additional features, such as the dis-
play of simulated sample colors, is also available from the
authors.
3.1 Reference Illuminant
The CQS, like the CRI, is a test-sample method. That is,
color differences 共in a uniform object color space兲 are cal-
culated for a predetermined set of reflective samples when
illuminated by a test source and a reference illuminant. In
essence, through a simulation, the appearance of the object
colors is determined and compared when illuminated by the
test source and the reference illuminant. The reference illu-
minants are the same as those used by the CRI. For test
sources of ⬍5000 K, the reference illuminant is a Planck-
ian radiator at the same CCT as the test source. These cal-
culation procedures are given in CIE’s primary colorimetry
publication
5
but are repeated below. The spectrum of the
Planckian reference illuminant, S
ref
共兲, is calculated by
S
ref
共,T兲 =
L
e,
共,T兲
L
e,
共560 nm,T兲
, 共3兲
where T is the CCT of the test source and L
e,
is the relative
spectral radiance calculated by
L
e,
共,T兲 =
−5
冋
exp
冉
1.4388 ⫻ 10
−2
T
冊
−1
册
−1
. 共4兲
For test sources at 艌5000 K, the reference is a phase of
CIE Daylight illuminant having the same CCT as the test
source. The method for calculating the spectral power dis-
tribution of the daylight illuminant begins with determining
the chromaticity coordinates 共x
D
,y
D
兲 of the illuminant. For
illuminants up to and including 7000 K, x
D
is
Davis and Ohno: Color quality scale
Optical Engineering March 2010/Vol. 49共3兲033602-4
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