Color-dulling solid-state sources of light
Artūras Žukauskas,1,* Rimantas Vaicekauskas,2 and Michael Shur3
1
Institute of Applied Research, Vilnius University, Saulėtekio al. 9-III, LT-10222 Vilnius, Lithuania
Department of Computer Science, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
3
Department of Electrical, Computer, and System Engineering, Rensselaer Polytechnic Institute, 110 8th Street,
Troy, New York 12180, USA
*arturas.zukauskas@ff.vu.lt
2
Abstract: The spectral power distributions (SPDs) of solid-state sources
were optimized for rendering the highest number of colors with a
perceptually noticeable reduction in chroma (dulling) while maintaining the
hue distortion below an acceptable threshold. Statistical color rendition
indices derived from the analysis of color-shift vectors of 1269 Munsell
samples were used in the objective functions for the optimization of SPDs
of the color-dulling sources. The starting optimization point was the SPD
composed of narrow yellow and blue (YB) emissions, which both dulls
colors and distorts hues. Two methods were applied to reduce the huedistorting effect of the narrow-band YB source. The first method,
broadening the spectral bands, yields SPDs similar to that of a dichromatic
white light-emitting diode (LED) with the partial conversion of narrowband blue electroluminescence to wide-band yellow photoluminescence.
The second method, multiplying the spectral bands, results in the SPDs
similar to those of trichromatic clusters of red, yellow, and blue (RYB) and
amber, green, and blue (AGB) LEDs.
©2012 Optical Society of America
OCIS codes: (110.2945) Illumination design; (330.1690) Color; (330.1715) Color, rendering
and metamerism; (230.3670) Light-emitting diodes.
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1. Introduction
Solid-state lighting technology offers high versatility in composing the spectral power
distribution (SPD) of light sources by combining direct and phosphor-converted emission
from light-emitting semiconductor chips [1–4]. Such versatility results in the light sources
with very different color rendition quality. Generally, color rendition properties of solid-state
sources of light can be classified in terms of high fidelity, color saturating, and color dulling
[5]. The basic approach to the optimization of the SPD of high-fidelity solid-state lamps,
which make objects appear “natural,” relies on the minimization of color shifts in respect of a
reference illuminant [6–8]. Such lamps have SPDs balanced throughout the entire visible
spectrum. The SPDs of color-saturating light sources improve color discrimination and make
objects appear “vivid”. Such sources can be optimized through the maximization of the color
shift components directed toward increased chroma [9]. Typical color-saturating sources use
the blends of narrow-band red, green, and blue (RGB) emissions with the deficiency of
spectral power in the “yellow” (530-610 nm) region [5].
Some solid-sate sources of light reduce chroma of many colors, i.e. make illuminated
objects appear dull [5,10–12]. Commonly, reduced chroma is believed to have perceptually
negative impact and color dulling is considered as an unwanted property of lamps. However
for numerous applications, reduced chroma is actually advantageous. For example, colordulling light sources might be useful for presenting certain natural objects, such as butter [13],
for displaying art in similar fashion to low-light conditions such as churches and caves [14],
and for meeting color preferences of some cultural/national, professional, gender, and age
groups [15]. Furthermore, color-dulling blends can be used for the designing of light sources
with tunable color rendition properties such as a “color-rendition engine,” which is controlled
using a weighted sum of color-saturating and color-dulling SPDs [16,17].
A well known color-dulling blend is the composition of narrow-band yellow and blue
(YB) lights [18]. Such a blend has the highest possible luminous efficacy of radiation (LER)
[19,20]. However, the narrow-band YB blend severely distorts hues, making all red and green
colors lost [18]. Color-dulling white phosphor-conversion LEDs and 2-, 3-, and 4-component
colored-LED clusters [5,10–12] also distort hues. However, there is no systematic approach
to composing the SPDs of color-dulling light sources with a trade-off between the color
dulling ability and the hue distortion.
The goal of this work is to provide the basic principles for composing the SPDs of colordulling solid-state sources of light with an acceptable hue-distorting ability. Our approach to
the optimization of the color-dulling blends of colored components trades-off the abilities of a
light source to reduce chroma and to distort hues. The trade-off is implemented through
broadening and splitting the spectral components of the narrow-band YB blend.
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2. Optimization approach
The optimization approach used in this work assesses SPDs by two color rendition
characteristics that measure the color-dulling effect and hue-distorting effect, respectively.
The two criteria of optimization used are the Color Dulling Index (CDI) and Hue Distortion
Index (HDI) obtained from the statistical analysis of color-shift vectors [5,21] for 1269
Munsell samples [22]. When the reference illuminant is replaced by a simulated SPD, each of
1269 color-shift vectors are analyzed in respect of the triple just-perceivable chromaticity
difference (three-step MacAdam ellipse). The CDI is defined as the percentage of test color
samples that have color-shift vectors with projections exceeding triple just perceivable
reduction of chroma. The HDI is defined as the percentage of test color samples that have
color-shift vectors with projections exceeding triple just perceivable difference of hue. The
simulated SPDs were also characterized by LER and the General Color Rendering Index (Ra),
as well as by two gamut-area indices based on the chromaticity shifts of 8 test color samples
in the U*V*W* color space (GAI) [23] and on the chromaticity shifts of 15 test color samples
in the CIELAB color space, (Qg) [24], respectively.
The reference illuminants used were the blackbody illuminants with correlated color
temperatures (CCTs) of 3000 K and 4500 K (for warm-white and cool-white lamps,
respectively) and the daylight phase illuminant with a CCT of 6500 K (for daylight lamps).
The starting point for the optimization was a YB illuminant with the SPD composed of
two narrow spectral bandwidth Gaussian shapes. The full width at half magnitude (FWHM)
used in this work was 30 nm, which is an average bandwidth of direct-emission LEDs. Such
an illuminant has both high CDI and high HDI (around 80% in the CCT range of 3000-6500
K), i.e. it both dulls colors and severely distorts hues of the illuminated objects. The following
two methods were applied to reduce the hue-distorting effect. The first method is broadening
the spectral bands resulting in SPDs similar to those of phosphor-conversion LEDs. The
second method is splitting the spectral lines into three 30-nm wide bands resulting in SPDs
similar to those of trichromatic clusters of colored direct-emission LEDs.
The solution of optimization problems yielded the SPDs with the highest CDI and with an
acceptable HDI value (not exceeding a certain value, HDImax). The optimization objective was
CDI, while the condition HDI ≤ HDImax served as a constraint. Within the first method, the
variables of the objective function are the peak wavelengths, λ1 and λ2, bandwidths, ∆1 and ∆2,
and relative radiant fluxes, Φ1 and Φ2, of the two bands:
F ( λ1 , λ2 , ∆1 , ∆ 2 , Φ1 , Φ 2 ) = CDI HDI ≤ HDI
max
.
(1)
Within the second method, the bandwidths are fixed, and the variables of the objective
function are peak wavelengths and relative radiant fluxes of the three bands:
F ( λ1 , λ2 , λ3 , Φ1 , Φ 2 , Φ 3 ) = CDI HDI ≤ HDI
max
.
(2)
In both cases, the objective function has six variables that satisfy three color-mixing
equations [25]. The optimization domain, where these objective functions are maximized, is
the parametric space with 3 degrees of freedom. The maximization of such objective
functions was performed using a computer routine, which performs stochastic searching on a
three-dimensional parametric surface [6].
3. Results and discussion
3.1 Band broadening
Maximizing the objective function given by Eq. (1) has shown that the variation of HDImax
results in unstable behavior of the short-wavelength (blue) component, ∆1, within a range of
30-150 nm. Such a jitter indicates the insensitivity of the color-dulling effect to ∆1 ;
moreover, the solutions with wide blue components have about 10% lower LER than those
with the 30-nm wide bandwidth. In order to mitigate this effect, we examined the behavior of
the maxima of the objective function with additional constraints on the bandwidths
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100
CCT=3000 K (a)
Color rendition indices
80
120
60
40
90
20
120
60
40
90
∆2
CDI
GAI
Qg
Ra
20
0
30
(d)
600
120
60
40
90
20
60
60
0
30
-20
(e)
600
450
550
150
80
60
0
CCT=6500 K (c)
150
80
-20
Peak wavelengths (nm)
100
CCT=4500 K (b)
150
30
-20
(f)
600
450
450
λ1
λ2
550
400
550
400
400
LER
500
350
450
300
0
20
40
60
80
500
500
350
350
450
450
300
300
0
20
40
60
80
0
20
40
60
80
Maximal acceptable hue distortion index
Luminous efficacy of radiation (lm/W)
100
Long-wavelength band width (nm)
introduced. Constraining the width of the blue component to the initial value of 30 nm
resulted in almost the same values of maximized CDI as in the case of unconstrained
bandwidth and in the highest values of LER. However, constraining the width of the yellow
component bandwidth to 30 nm resulted in noticeably lower (by up to 10%) values of the
maximized CDI. In the latter case, the SPD also had lower values of LER. Therefore, our
further analysis of the two-component SPDs of color-dulling light sources is restricted to
broadening the yellow band, while maintaining the blue band at the initial width of 30 nm.
Such SPDs can be implemented within dichromatic white LEDs with partial conversion of
narrow-band blue electroluminescence from a semiconductor chip to broad-band yellow
photoluminescence from a phosphor converter.
Figures 1(a), (b), and (c) show the maximized CDI (magenta triangles) and the width of
the yellow band (yellow circles) as functions of HDImax for the three values of CCT. Also
shown are the dependences of gamut-area indices GAI (red line) and Qg (green line) as well
as of Ra (black line). At the highest values of acceptable HDI of about 80%, the width of the
yellow component is 30 nm and the CDI attains values of 77-81% depending on CCT. With
decreasing the value of acceptable HDI to 10-20%, the yellow component gradually broadens
to about 150 nm, and the CDI drops to about 40%. At the same time, the reduced CDI results
in an increase of the gamut-area indices and Ra.
Fig. 1. (a), (b), and (c) Dependences of the maximized CDI (magenta triangles) and the width
of the yellow band (yellow circles) on the maximal acceptable HDI for the two-component
SPDs at CCTs of 3000 K, 4500 K, and 6500 K, respectively. The red, green, and black lines
show the variation of GAI, Qg, and Ra . (d), (e), and (f) Corresponding dependences of the peak
wavelengths of the two components (yellow and blue squares) and LER (pink lines).
Figures 1(d), (e), and (f) show the corresponding variation of the peak positions of the two
bands and of LER. With increasing the acceptable HDI, the peak position of the shortwavelength component remains around 460-470 nm. The long-wavelength component shifts
from about 605 nm to approximately 580 nm for the CCT of 3000 K and remains almost
constant around 565 nm for the CCT of 6500 K. At the same time, the LER tends to decrease
from 395 to 480 lm/W at high acceptable HDIs to about 300 lm/W at low acceptable HDIs.
The obtained CDI vs. HDImax dependences are the optimal boundaries (Pareto fronts) that
delineate the fundamental trade-off between the color-dulling ability and hue-distortion effect
of dichromatic yellow-blue light sources. For designing practical color-dulling light sources,
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one needs to set an acceptable value of HDI that preserves perceptually reduced chroma for a
considerable fraction of color samples. For instance, an acceptable value of HDI can be set to
50%, which is the characteristic of a common phosphor-conversion dichromatic
InGaN/Y3Al5O12:Ce3+ white LED [5].
Table 1 presents the parameters of the selected dichromatic color-dulling light sources
with the SPDs containing a broadened long-wavelength (yellow) component. The first three
lines in Table 1 show the optimization results for HDImax = 50% for the three values of CCT.
The CDI has values in the range of 61-74% depending on the CCT. The corresponding
gamut-area indices are in the ranges of 36-69 and 58-72 for GAI and Qg, respectively, and the
LER is in the range of 337-418 lm/W. The general CRI of these light sources is in the range
of 39 to 65; however, the latter index cannot serve as an indicator of the color-dulling ability,
since a reduced Ra can be also a characteristic of the light sources with increased colorsaturating ability [5,9,17].
Table 1. Parameters of Selected Dichromatic Color-dulling Light Sources with
Broad Yellow Band
CCT
CDI
(K)
3000
74
4500
64
6500
61
6042
53
*Average values
HDI
Ra
GAI
Qg
50
50
50
50
39
57
65
71
36
57
69
85
58
69
72
90
LER
(lm/W)
418
371
337
325
λ1
(nm)
473
468
465
451*
∆1
(nm)
30
30
30
18
Φ1
0.211
0.311
0.371
0.274
λ2
(nm)
584
577
570
577*
∆2
(nm)
64
80
91
121
Φ2
0.789
0.689
0.629
0.726
The bottom row in Table 1 shows the parameters of a common phosphor-conversion
dichromatic white LED [5]. Such an LED has a somewhat reduced CDI in comparison with
the optimal daylight counterpart. Also, it exhibits a lower LER and higher gamut-area indices
and Ra. Nevertheless, this type of an LED can be considered as a typical dichromatic colordulling solid-state light source with a broadened long-wavelength component. The colordulling ability of such an LED can be maximized by the shifting of the both components to
longer wavelengths and by the narrowing of the yellow component.
3.2 Band splitting
Maximizing the objective function presented by Eq. (2) yields SPDs composed of three
narrow (30 nm wide) components. Such SPDs can be implemented within trichromatic
clusters of colored LEDs.
Figures 2(a), (b), and (c) show the maximized CDI (magenta triangles) as a function of
HDImax for the three values of CCT, respectively. Also shown are the dependences of gamutarea indices GAI (red line) and Qg (green line) as well as of Ra (black line). At the highest
values of acceptable HDI of 60-70%, the CDI attains values of 74-81% depending on CCT.
Note that these values of CDI are attained with a smaller percentage of test color samples
with distorted hue than in the case of the two-component SPDs considered in the previous
section. With decreasing the value of acceptable HDI to 10-20%, the CDI drops to about 20%
and the gamut-area indices and Ra increase. The color rendition indices displayed in Figs.
2(a), (b), and (c) have a discontinuity at the values of HDImax in the range of 20-30%.
Figures 2(d), (e), and (f) show the corresponding variation of the peak positions of the
three bands and of LER. These dependences exhibit the same discontinuity as the color
rendition indices. This discontinuity can be linked to the existence of two types of color
dulling trichromatic LED clusters. The first type, red-yellow-blue (RYB), clusters yield the
highest values of CDI at higher acceptable HDIs. With increasing the acceptable HDI, the
peak position of the short-wavelength component in the RYB clusters remains around 470
nm. The mid-wavelength component shifts from about 550 nm to 570-580 nm and the longwavelength component shifts from about 610 nm to 670 nm or even higher. The LER of the
RYB clusters tends to decrease as the acceptable HDI increases. Such a behavior of LER is
opposite to that of the YB SPDs with a broadened yellow component (see Figs. 1(d), (e), and
(f)).
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100
100
Color rendition indices
CCT=3000 K (a)
CCT=6500 K (c)
80
80
80
60
60
60
40
40
20
20
(d)
700
Peak wavelengths (nm)
CCT=4500 K (b)
λ1
λ2
700
400
650
40
CDI
GAI
Qg
Ra
20
λ3
LER
(e)
650
350
600
550
250
450
350
600
300
500
250
450
0
20
40
60
80
400
650
300 550
500
(f)
700
400
350
600
550
300
500
250
450
0
20
40
60
80
0
20
40
60
80
Luminous efficacy of radiation (lm/W)
100
Maximal acceptable hue distortion index
Fig. 2. (a), (b), and (c) Dependences of the maximized CDI (magenta triangles) on the
maximal acceptable HDI for the SPDs composed of three 30-nm wide components at CCTs of
3000 K, 4500 K, and 6500 K, respectively. The red, green, and black lines show the variation
of GAI, Qg, and Ra . (d), (e), and (f) Corresponding dependences of the peak wavelengths of
the three components (red, yellow, and blue squares) and LER (pink lines).
The second type, amber-green-blue (AGB), clusters yield the highest values of CDI at the
lower acceptable HDIs. With increasing the acceptable HDI, the peak position of the shortwavelength component in the AGB clusters remains at slightly shorter wavelengths around
460 nm. The mid-wavelength and long-wavelength components peak at about 520-535 nm
and 590-600 nm, respectively. The LER of the AGB clusters tends to increase with HDImax
and is higher than that of the RYB counterparts due to the absence of the red component,
which has low luminous efficacy.
The obtained CDI vs. HDImax dependences are the Pareto fronts that delineate the
fundamental trade-off between the color-dulling ability and hue-distortion effect of
trichromatic light sources with the SPDs composed of narrow bands. Once again, for practical
color-dulling trichromatic light sources, an acceptable value of HDI can be set to 50%.
Table 2 presents the parameters of the selected trichromatic color-dulling light sources
with the SPDs containing narrow-band components. The first three rows in Table 2 show the
results of the optimization of RYB SPDs for HDImax = 50% for the three values of CCT.
Depending on the CCT, the CDI has values in the range of 66-79%, somewhat higher than
those for the dichromatic SPDs (see Table 1). The corresponding gamut-area indices are in
the ranges of 36-70 and 60-73 for GAI and Qg, respectively, and the LER is in the range of
322-354 lm/W that is somewhat below that of the dichromatic SPDs. The general CRI is in
the range of 41 to 69.
Currently, the optimal RYB clusters are not practical because of the lack of efficient
yellow LEDs. Alternatively, AGB clusters are easy to compose of commercially available
AlGaInP amber and InGaN green and blue LEDs that have peak wavelengths very close to
those shown in Figs. 2(d), (e), and (f). The bottom three rows in Table 2 show the parameters
of a common AGB cluster [5] for the three values of CCT. The CDI of such a cluster (5167%) is somewhat reduced in comparison with that of the corresponding optimal RYB
counterparts. However, such an AGB cluster exhibits a somewhat higher LER. Another
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option is using a phosphor-conversion amber LED within the AGB cluster [17]. In this case,
the CDI has an even lower value (49% at a CCT of 4500 K).
Table 2. Parameters of Selected Trichromatic Color-dulling Light Sources with
Narrow Bands
CCT
(K)
3000
4500
6500
3000
4500
6500
CDI
HDI
Ra
GAI
Qg
79
69
66
67
57
51
50
50
50
49
48
43
41
61
69
28
51
63
36
59
70
33
57
70
60
70
73
54
66
72
LER
(lm/W)
322
354
326
446
394
355
λ1
(nm)
478
472
471
452
452
452
Φ1
0.194
0.338
0.433
0.154
0.265
0.346
λ2
(nm)
575
564
559
523
523
523
Φ2
0.446
0.419
0.367
0.228
0.296
0.320
λ3
(nm)
649
625
621
591
591
591
Φ3
0.360
0.243
0.200
0.618
0.439
0.334
3.3 Color-shift vector distributions
The above solution of the optimization problem yielded two basic types of the color-dulling
SPDs: a dichromatic composition of narrow-band blue and wide-band yellow components
and a trichromatic composition of narrow-band red, yellow, and blue, or (within some limits)
of amber, green, and blue components. (Our estimates show that no substantial improvement
of the color-dulling effect results from further increasing the number of narrow-band
components.) This section describes the distributions of the color-shift vectors for the two
types of color-dulling light sources.
Figures 3(a) and (c) show the SPDs of the selected dichromatic and trichromatic colordulling light sources with the same acceptable hue-distortion ability (HDImax = 50%) for the
CCT of 4500 K. Both SPDs have very similar blue components peaking at 468 nm and 472
nm, respectively. When converting from the dichromatic to the trichromatic SPD, the 80 nm
wide yellow band with the peak at 577 nm asymmetrically splits into two narrow bands
peaking at 564 nm and 625 nm, respectively. Such splitting results in a somewhat higher CDI
and a lower LER.
Figures 3(b) and (d) show the corresponding distributions of the color-shift vectors in
respect of a blackbody radiator estimated for 218 Munsell samples of value /6. The
distributions are presented within the a*−b* chromaticity plane of the CIELAB color space;
arrows schematically show the vectors that are estimated to have perceptual noticeable
chromaticity distortions [21]; circles correspond to the test color samples rendered with high
fidelity (i.e. with color shifts smaller than triple just perceivable alteration of chromaticity).
One can see that splitting the broad long-wavelength band into two narrow bands results in
some increase of the number of test color samples with reduced chroma. However, the
splitting has almost no effect on the pattern of the distribution of the color-shift vectors. The
samples with low chroma (in the centre of the diagrams) are rendered with high fidelity,
whereas with increasing chroma, chromaticity distortions become more prominent following
a characteristic four-pole regularity [21,26]. A small number of yellow and violet test color
samples with increased chroma and a considerably larger number of red and green samples
with reduced chroma have small hue distortions. In the four in-between hue regions (orange,
yellow-green, blue, and purple), the color shift vectors exhibit gradual turning with hue
showing a conversion from reduced chroma to distorted hue and further to increased chroma.
For the CCTs of 3000 K and 6500 K, the color-shift vector distributions (not shown) have
similar properties.
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(C) 2012 OSA
Received 22 Feb 2012; revised 10 Apr 2012; accepted 10 Apr 2012; published 13 Apr 2012
23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 9761
CDI=64%
HDI=50%
LER=371 lm/W
(b)
60
40
20
0
-20
-40
-60
(c)
CDI=69%
HDI=50%
LER=354 lm/W
(d)
60
40
20
0
b* chromaticity coordinate
Spectral power (arb. units)
(a)
-20
-40
-60
400
500
600
700
Wavelength (nm)
-60 -40 -20 0 20 40 60
a* chromaticity
coordinate
Fig. 3. Optimized model SPDs of color-dulling dichromatic (a) and trichromatic (b) light
sources with HDImax = 50% at a CCT of 4500 K. (b) and (d) Corresponding distributions of the
color-shift vectors for 218 Munsell samples of value /6 in the a*−b* chromaticity plane of the
CIELAB color space. Open points, samples that have colors rendered with high fidelity;
arrows, schematic chromaticity shifts of samples that have color distortions, such as increased
or decreased saturation as well as distorted hue (the magnitude of each vector is normalized to
the size of the individual MacAdam ellipse as in [21]).
4. Summary
We have established the fundamental trade-offs between the color-dulling ability and huedistortion effect of dichromatic and trichromatic light sources. This allowed for finding the
optimal SPDs of solid-state sources that render the highest number of dulled colors while
maintaining the hue distortion below an acceptable threshold. Two basic types of colordulling SPDs have been found: a dichromatic composition of narrow-band blue and wideband yellow components and a trichromatic composition of narrow-band red, yellow, blue
and or, with some limitation, of amber, green, and blue components. The color-dulling light
source of the first type can be implemented using dichromatic white LEDs with partial
conversion of narrow-band blue electroluminescence from a semiconductor chip to broadband yellow photoluminescence from phosphor converter. The color-dulling light source of
the second type can be implemented as a trichromatic RYB or AGB cluster of colored LEDs.
Acknowledgments
The work at VU was funded in part by a grant from the Research Council of Lithuania (No.
MIP-73/2010). The work at RPI was supported primarily by the Engineering Research
Centers Program (ERC) of the National Science Foundation under NSF Cooperative
Agreement No. EEC-0812056 and in part by New York State under NYSTAR contract
C090145.
#163475 - $15.00 USD
(C) 2012 OSA
Received 22 Feb 2012; revised 10 Apr 2012; accepted 10 Apr 2012; published 13 Apr 2012
23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 9762