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 hue-distorting 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 narrow-band 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 OSA
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 . 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 . 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 .
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, color-dulling light sources might be useful for presenting certain natural objects, such as butter , for displaying art in similar fashion to low-light conditions such as churches and caves , and for meeting color preferences of some cultural/national, professional, gender, and age groups . 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 . 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 . 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 color-dulling 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.
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 . 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)  and on the chromaticity shifts of 15 test color samples in the CIELAB color space, (Qg) , 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, Δ1 and Δ2, and relative radiant fluxes, Φ1 and Φ2, of the two bands:
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:
In both cases, the objective function has six variables that satisfy three color-mixing equations . 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 .
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, Δ1, within a range of 30-150 nm. Such a jitter indicates the insensitivity of the color-dulling effect to Δ1 ; 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 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.
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 short-wavelength 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, 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 .
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 color-saturating ability [5,9,17].
The bottom row in Table 1 shows the parameters of a common phosphor-conversion dichromatic white LED . 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 color-dulling solid-state light source with a broadened long-wavelength component. The color-dulling 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 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 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 long-wavelength 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)).
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 short-wavelength 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  for the three values of CCT. The CDI of such a cluster (51-67%) is somewhat reduced in comparison with that of the corresponding optimal RYB counterparts. However, such an AGB cluster exhibits a somewhat higher LER. Another option is using a phosphor-conversion amber LED within the AGB cluster . In this case, the CDI has an even lower value (49% at a CCT of 4500 K).
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 color-dulling 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 ; 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.
We have established the fundamental trade-offs between the color-dulling ability and hue-distortion 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 color-dulling SPDs have been found: a dichromatic composition of narrow-band blue and wide-band 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 broad-band 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.
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.
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