Research Article Optimization of Multiband White-Light ...downloads.hindawi.com/archive/2015/263791.pdfis paper describes an ee ctive approach for the optimization of multiband spectra
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Research ArticleOptimization of Multiband White-Light Illuminants forSpecified Color Temperatures
Snjezana Soltic1 and Andrew Neil Chalmers2
1Manukau Institute of Technology Private Bag 94006 Manukau 2241 New Zealand2Auckland University of Technology Institute of Biomedical Technologies Private Bag 92006 Auckland 1142 New Zealand
Correspondence should be addressed to Andrew Neil Chalmers achalmerautacnz
Received 21 January 2015 Accepted 19 April 2015
Academic Editor Xian An Cao
Copyright copy 2015 S Soltic and A N ChalmersThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper describes an effective approach for the optimization of multiband spectra to produce prospective white-light spectrahaving specific color temperatures The optimization process employs a genetic algorithm known as differential evolution whichaims to minimize the color rendering differences between a prospective white-light spectrum and its corresponding referenceilluminant Color rendering is assessed by calculating the CIEDE2000 color difference (ΔE
00) for 14 CIE test colors under the two
sources Optimized white-light spectra were matched to three CIE standard illuminants that is A (2856K) D50
(5003K) andD65
(6504K) Optimal solutions for three- and four-band 25 and 50 nm Gaussian spectra are presented and analyzed togetherwith mixed 4-LED spectra that were optimized in the same way In all cases the simulated sources were shown to provide colorrendering of such quality that ΔE00av le 224 units Such white-light sources would likely find wide acceptance in numerous lightingapplications
1 Introduction
It is now firmly established that by tuning the spectralintensities of light-emitting diodes (LEDs) which emit differ-ent bands of radiation a white-light spectrum characterizedby good color rendering and efficacy can be designedLED spectra have been simulated [1ndash4] and spectra of realLEDs digitized for use [4ndash8] Typically the color renderingproperties of thewhite-light spectrumare expressed using thecolor rendering index (CRI) recommended in CommissionInternationale de lrsquoEclairage (CIE) publication 133 [9] andefficacy in terms of the luminous efficacy of radiation whichis the ratio of luminous flux to radiant flux (LER lmrad-W)
The performance of any given mixture is governed by thenumber of bands [7] and their shape [10] as well as the peakemission wavelengths (120582
119894) and bandwidths (Δ
119894) of each of
the bands used [5 6] Starting with a trichromatic mixture ofldquoRedrdquo ldquoGreenrdquo and ldquoBluerdquo bands the color rendering can beimproved by the addition of an ldquoAmberrdquo band Any further
additional band (119899 gt 4) increases the complexity of themixing process and the control of the white-point with onlymarginal performance benefits [7] It is shown that if thepeak wavelengths and bandwidths of available LEDs couldbe freely manipulated then it would be possible to producethree-LED sources with excellent white-light spectra [5]
Our earlier work used an approach that focused purelyon the best achievable combination of CRI and LER Thecorrelated color temperature (CCT) was an uncontrolledvariable in the process and the random CCTs that resultedwere predominantly in the 3000ndash4000K range It has becomeapparent however that lighting manufacturers are desirousof spectral designs for light sources that can achieve specifictarget CCT values [11] The marketing of light sources isevidently based upon a primary specification of CCT withCRI and LER (while still of high importance) coming assecondary parameters
We have therefore designed a new optimization processwhich puts CCT at the center of the process and then
Hindawi Publishing CorporationAdvances in OptoElectronicsVolume 2015 Article ID 263791 10 pageshttpdxdoiorg1011552015263791
2 Advances in OptoElectronics
proceeds to optimize color rendering while maintaining aclose tolerance to the target CCT value We selected threeCCT values to illustrate the effectiveness of our process
Our approach excludes the physical processes that areneeded for the conversion of input energy (most oftenelectrical) into radiant energy Our focus is rather on thedistribution of energy within the radiant spectrum sincethis determines both the color and efficacy properties of aspectrumAs in our earlierwork the optimization processwasbased on the differential evolution algorithm as describedin Section 2 and it is now based on the minimization ofcolor differences expressed in the CIEDE2000 equation [12]currently recommended for computation of perceived colordifferences between color pairs The results are presented inSection 3 It is demonstrated that white-light spectra with adesired CCT and both good color rendering and efficacy arefeasible using three or four bands
2 Method
The optimization tool is a Matlab implementation of thepopulation-based differential evolution (DE) algorithm [13]where a population of possible solutions is evaluated usinga fitness function The search for an optimal solution startswith a population of 119875 randomly created solution vectors119878V1 119878V119895 119878V119875 each vector representing a candidatemixed light spectrum where some characteristics of theindividual bands in the candidate spectrum for exampleintensities are randomized As new solutions are created andevaluated only the fitter solutions are moved to the nextgeneration [7]
The basis of the selection process in our algorithm is thecolor difference of specific surface colors as they appear underthe candidate spectrum and under the reference spectrumof the same CCT In each new generation the offspringsolutions are evaluated using a fitness function (119891fit) basedon the color differenceΔ119864
00calculated using the CIEDE2000
color difference formula Hence the algorithm searches fora spectrum with the lowest color differences The optimumsolution is determined after having performed 119866 (typically1000) cycles of the evaluations that is the best solution incycle 119866 is accepted as the best white-light spectrum
Thus the intent is to minimize the average color differ-ence Δ119864
00(Avg) for a set of color samples The color samples(Table 1) are the 14 test samples specified in CIE133 [9]Samples 1 to 8 have low to moderate chromatic saturationSamples 9 to 12 represent saturated red yellow green andblue and Samples 13 and 14 represent light human complex-ion and green foliage respectivelyThe CIE test color samplesare used since they constitute a well known and widely usedset
After the completion of each DE run the performanceof each optimized solution is assessed using the CIE generalcolor rendering index 119877
119886 determined as per [9] and the
lowest color rendering value 119877min together with the LERFurthermore the Δ119864
00119894for each test sample is tabulated
(Tables 2 3 4 and 5) together with the color differencesdecomposed into chromatic differences [14] in terms of
Table 1 The 14 CIE test colors [9]
Number Style name Brief description1 75 R 64 Light grayish red2 5 Y 64 Dark grayish yellow3 5 GY 68 Strong yellow green4 25 G 66 Moderate yellowish green5 10 BG 64 Light bluish green6 5 PB 68 Light blue7 25 P 68 Light violet8 10 P 68 Light reddish purple9 45 R 413 Strong red10 5 Y 810 Strong yellow11 45 G 58 Strong green12 3 PB 311 Strong blue13 5 YR 84 Light yellowish pink14 5 GY 44 Moderate olive green
0010203040506070809
1
400 450 500 550 600 650 700
Rela
tive i
nten
sity
460 640590525
120582 (nm)
Figure 1 Spectral power distributions of real LEDs used in theoptimized mixtures The peak wavelengths (nm) are given aboveeach spectrum
Δ119862119886119887
lowast Δ119867119886119887
lowast and Δ119871lowast Positive (negative) differences meanthat the color test samples illuminated by the optimized spec-trum have more (less) of that variable than when illuminatedby the reference illuminantThe closeness of the chromaticitymatches to the target CCTs has been computed in the CIE(1199061015840V1015840) chromaticity space [14]These data are included on the
grounds of the importance of this parameter to the potentialusers in the lighting industry To gauge the significance of ourcomputedΔ(1199061015840V1015840) color differences the color difference in the(1199061015840V1015840) diagram between 5000K and 6500K on the Planckianlocus is Δ(1199061015840V1015840) sim 002 and between 2700K and 3000K thedifference is Δ(1199061015840V1015840) sim 001
21 Optimization of Real LEDMixtures Here a solution (119878V119895)is the spectrum of the light produced by a mixture of either3 or 4 real LEDs being a selected subset of the Luxeon range[15] (Figure 1) The optimization starts with a population ofrandomly created solution vectors where the intensities (119868
119894)
of the individual LED spectra are randomizedThe results arepresented in Section 31
22 Optimization of Synthetic LED Spectra Represented byGaussian Functions The above mentioned method is usedwith modification to optimize mixtures of Gaussian bandswhere each band (119878
119894) is simulated over a specific bandwidth
within the wavelength range of 120582 from 380 to 780 nm (in1 nm increments) The properties of each Gaussian band areexpressed in what follows
119878119894 (120582) = 119868119894119890
minus(120582minus120582119894)221205752
120575 =Δ119894
2radic2 ln 2
(1)
where 119868119894120582119894 andΔ
119894represent peak intensity peakwavelength
and spectral bandwidth (or full-width at half-maximumFWHM) respectively and (2) represents the compositespectrum of 119899 bands each having the same value of FWHMbandwidth
119878V119895 =
119899
sum
1119878119894(120582) (2)
with 119899 chosen to be either 3 or 4 as explained in the Section 3The optimization starts with a population of randomly
created solution vectors where the intensities and the peakwavelengths of the individual Gaussian bands are random-ized while their spectral bandwidths are kept constantTwo bandwidths have been investigated 25 nm and 50 nmrepresenting ldquotypicalrdquo LED spectral bandwidths
3 Results
31 Real LEDMixtures We explored the feasibility of obtain-ing LED-based sources to match illuminants A D
50 and D
65
using a set of real LEDs with the spectral power distributionsshown in Figure 1 The choice was made to focus on theoptimization of 4-band spectra as previous work [3 5 7 8 10]indicated that mixing only the blue green and red wouldresult in spectra with poor color rendering An exceptionoccurs if the red band can be broadened or the red peakwavelength lowered [3 5]
The optimized 4-band spectra are shown in Figure 2Table 2 shows that the spectra are acceptable standard illu-minant simulators having average color differences below1 Δ11986400
unit and CIE color rendering index 119877119886ge 93
The Δ(1199061015840V1015840) color differences are below 0004 and could beconsidered subthreshold for white light
Overall the changes in lightness of the test colors areconsistent regardless of the correlated color temperatureSamples 3 7ndash10 and 14 become lighter and the remainderbecome darker (Table 2) This is thought to be due to thepeaks and valleys in the combined spectra resulting from theparticular 4 LED spectra selected for the experiment
The color differences are lowest for the Illuminant Asimulation where 11 samples (1ndash10 12ndash14) have both Δ119862
119886119887
lowast
andΔ119867119886119887
lowast below 5 units and the Sample 11 chroma differenceis just above 5 units (Δ119862
119886119887
lowast
(11)A = 561) For the Illuminant Asimulations the greatest change in hue is observed for Sample12 (strong blue Δ119867
119886119887
lowast
(12)A = minus395) and the highest change
in lightness is observed for Sample 3 (strong yellow green)which becomes slightly darker (Δ119871lowast
(3)A = minus076)The Illuminant D simulations show significant increases
in the color errors for Sample 12 (Δ119862119886119887
lowast
(12)D50 = 701Δ119867119886119887
lowast
(12)D50 = minus878 and Δ119862119886119887
lowast
(12)D65 = 955Δ119867119886119887
lowast
(12)D65 = minus1021)
32 Optimization of Gaussian Bands Optimized spectra areshown in Figures 3 4 and 5 with the values of the peakwavelengths given above each diagram
321 Illuminant A Figure 3 and Table 3 show the results ofthe optimization of the Illuminant A simulators showing that3-band and 4-bandGaussianmixtures scored satisfactorily inthe CRI metric (119877
119886ge 84) All simulators have a higher LER
(ge318 lmrad-W) than real Illuminant A (LERA = 156 lmrad-W)The spectra are named S
1 S2 and S
3 where S
1represents
the 25 nm 3-band spectrum S2represents the 50 nm 3-band
spectrum and S3represents the 25 nm 4-band spectrumThe
Δ(1199061015840V1015840) color differences are below 0006 for S
2and S3
As expected the lower color errors (hence better colorrendering) are obtained by either employing wider Gaussianbands (S
2) or using an additional 4th band (S
3) However a
wider red band and the additional amber band reduced LER(from416 lmrad-W to 357 and 318 lmrad-W) by introducingmore radiated power at wavelengths where the119881(120582) functionhas low valuesThe 25 nm 3-band spectrum (S
1) exhibits very
poor rendering of blue (Sample 12 strong blue 11987712= 119877min =
24) (Table 3(a))Simulators S
2and S
3render all color samples better
than S1 including the problematic saturated Samples 9ndash12
However poor scoreswere recorded for Sample 9 (strong red)in S2 and for Sample 12 (strong blue) in both S
2and S3
Figure 3 shows the spectral power distributions of theIlluminant A simulations The Gaussian peaks follow thegeneral trend of the Illuminant A spectrumThe low emissionin the blue region helps explain the problematic rendering ofthe strong blue sample shown in Table 3
Based on these results the S1mixture would be an
unsatisfactory simulator of Illuminant A while the S2and S3
mixtures would be acceptable for noncritical uses
322 Illuminant D50 The results for Illuminant D
50are
shown in Figure 4 and Table 4 The spectra are named S4
S5 and S
6 where S
4represents the 25 nm 3-band spectrum
S5represents the 50 nm 3-band spectrum and S
6represents
the 25 nm 4-band spectrum The LER of the spectra isge323 lmrad-W (versus the lower LER of real Illuminant D
50
at 207 lmrad-W) and color rendering 119877119886ge 85 Spectrum S
4
has a particularly bad effect on the chroma and hue of thestrong blue (Sample 12) (Δ119862
As expected the color shifts and the differences inlightness are smaller for S
5and S
6 that is wider individual
bands and 4-bandmixture result in better white-light spectraIn particular the best color rendering expressed in termsof Δ119862
119886119887
lowast and Δ119867119886119887
lowast is for S6where the color errors are
all below 4 units Also S6introduces the lowest changes
6 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
A
0
02
04
06
08
1
380 480 580 680 780
0
02
04
06
08
1
380 480 580 680 780
120582 (nm)
120582 (nm)
120582 (nm)
D50
D65
Figure 2 Optimized 4-LED relative spectral power distributions
in lightness Table 4 reveals considerable improvements inmatching Illuminant D
50by widening the individual bands
or by introducing the 4th band The Δ(1199061015840V1015840) value of 00050for S5is considered just-noticeable and Δ(1199061015840V1015840) = 00019 for
S6is below the noticeable threshold
323 Illuminant D65 Simulators for Illuminant D
65
(Figure 5 and Table 5) follow the same general trends as forD50 and the mixture with wider spectral bands (S
8) and
the mixture with 4 bands (S9) gave higher 119877
119886values and
lower LER values than the 25 nm 3-band mixture The colorrendering in terms of CIE CRI is highly satisfactory 119877
119886ge 87
and the strong blue sample again exhibits the poorest colorrendering (119877
12(S7) = 119877min = 38) The chromaticities of thesimulations are very near to the chromaticity of IlluminantD65 Δ(1199061015840V1015840) lt 0006 in all experiments The LER of the
spectra is ge299 lmrad-W (versus the LER of real IlluminantD65at 204 lmrad-W)Optimized spectrum S
7introduces larger color errors
(Δ11986400av = 224) than any other in this paper In particular the
blue sample has both hue and chroma differences greater than16 units (Table 5(a)) This aspect was somewhat unexpectedand is thought to be due to the spectral discrepanciesbetween the simulated spectra and real D
65 particularly at
the wavelength extremities Further evidence is given by thefact that strong red (Sample 9) gives the next-worst 119877
119894in
Table 5(a)
33 Comparison of Peak Wavelengths It is instructive tocompare our optimized Gaussian peak wavelengths withthe peak wavelengths of the set of real LEDs all of whichare collated in Table 6 The real LEDs are labeled as ldquoBluerdquo
Advances in OptoElectronics 7
0
02
04
06
08
1
380 480 580 680 780
470 548 614
0
02
04
06
08
1
380 480 580 680 780
471 548 621
0
02
04
06
08
1
380 480 580 680 780
468 643589533
120582 (nm) 120582 (nm)
120582 (nm)
Figure 3 Optimized relative spectral power distributions (S1 S2 S3) for Illuminant A
In most of the spectra the blue Gaussian band wasbetween about 470 nm and 460 nm Exceptions are S
6and S9
the 4-band D50
and D65
simulators in which the optimizermoved the blue and green bands to lower wavelengths toaccommodate the amber bandThe green peaks in the 3-bandmixtures were optimized toward the peak of the 119881
120582curve
(120582 = 555 nm) thus producing the spectra with improved LERvalues as compared with the corresponding optimized LEDmixtures
It was consistently observed that the optimized wave-lengths for the red band were between about 610 nm to620 nm However the 4-band Illuminant A simulator S
3 has
the red band at 120582119877(S3) = 643 nm We ascribe that to the fact
that the amber band was optimized to 120582119860(S3) = 589 nm as
compared with 120582119860(S6) = 555 nm and 120582
119860(S9) = 558 nm for theD simulators The result was the noticeable improvement inthe rendering of test Sample 9 with source S
3
8 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
468 611542
0
02
04
06
08
1
380 480 580 680 780
470 619544
0
02
04
06
08
1
380 480 580 680 780
451 614555502
120582 (nm) 120582 (nm)
120582 (nm)
Figure 4 Optimized relative spectral power distributions (S4 S5 S6) for Illuminant D50
It was noteworthy in nearly all our results that the strongred (Sample 9) and strong blue (Sample 12) were badlyaffected by the truncation of the extrema of the synthesizedspectra
4 Conclusions
We have demonstrated that it is possible to simulate the CIEstandard illuminants A D
50 and D
65by mixing multiband
LED and Gaussian spectra The overall performance of theGaussian-based mixtures was better than the LED-basedcounterparts due to the freedom to select the most suitablepositions in the spectrum for the peak wavelengths in theGaussian mixtures
The simulation results show that 3-band Gaussian Illumi-nant A simulators could have CRI above 84 and LER double
that of Illuminant A Well designed 3-band Gaussian D50
and D65
simulators may have both CRI ge 85 and LER ge315 lmrad-W 4-band simulators improve color rendering bydistributing the bands in the visible spectrum
Our optimization techniques as described do not needto be constrained by the choice of test color samples colordifference formulae target spectrum or choice of standardobserver This is demonstrated in this paper where wehave shown how our previously published algorithm can bemodified to apply new color difference techniques to newobjectives in this case the achievement of specific sourceCCT targets
It should be noted that the spectra presented here areresults of simulations and further work is required toinvestigate the practical implementation of those spectra andto evaluate them in ldquoreal liferdquo situations
Advances in OptoElectronics 9
0
02
04
06
08
1
380 480 580 680 780
464 609539
0
02
04
06
08
1
380 480 580 680 780
460 538 615
0
02
04
06
08
1
380 480 580 680 780
449 498 618558
120582 (nm) 120582 (nm)
120582 (nm)
Figure 5 Optimized relative spectral power distributions (S7 S8 S9) for Illuminant D65
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors wish to acknowledge the support provided forthis work by the Technology Development Centre of theManukau Institute of Technology
References
[1] T Erdem S Nizamoglu X W Sun and H V Demir ldquoAphotometric investigation of ultra-efficient LEDs with highcolor rendering index and high luminous efficacy employingnanocrystal quantumdot luminophoresrdquoOptics Express vol 18no 1 pp 340ndash347 2010
[2] G He L Zheng and H Yan ldquoLED white lights with high CRIand high luminous efficacyrdquo in LED and Display Technologiesvol 7852 of Proceedings of SPIE 2010
[3] Y Ohno ldquoSpectral design considerations for white LED colorrenderingrdquoOptical Engineering vol 44 no 11 Article ID 1113022005
[4] A Zukauskas R Vaicekauskas F Ivanauskas R Gaska and MS Shur ldquoOptimization of white polychromatic semiconductorlampsrdquoApplied Physics Letters vol 80 no 2 pp 234ndash236 2002
[5] E Taylor P R Edwards and R W Martin ldquoColorimetry andefficiency of white LEDs spectral width dependencerdquo PhysicaStatus Solidi A Applications and Materials Science vol 209 no3 pp 461ndash464 2012
[6] R S Berns ldquoDesigning white-light LED lighting for the displayof art a feasibility studyrdquo Color Research and Application vol36 no 5 pp 324ndash334 2011
[7] S Soltic and A N Chalmers ldquoDifferential evolution for theoptimisation of multi-band white LED light sourcesrdquo LightingResearch amp Technology vol 44 no 2 pp 224ndash237 2012
10 Advances in OptoElectronics
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006
proceeds to optimize color rendering while maintaining aclose tolerance to the target CCT value We selected threeCCT values to illustrate the effectiveness of our process
Our approach excludes the physical processes that areneeded for the conversion of input energy (most oftenelectrical) into radiant energy Our focus is rather on thedistribution of energy within the radiant spectrum sincethis determines both the color and efficacy properties of aspectrumAs in our earlierwork the optimization processwasbased on the differential evolution algorithm as describedin Section 2 and it is now based on the minimization ofcolor differences expressed in the CIEDE2000 equation [12]currently recommended for computation of perceived colordifferences between color pairs The results are presented inSection 3 It is demonstrated that white-light spectra with adesired CCT and both good color rendering and efficacy arefeasible using three or four bands
2 Method
The optimization tool is a Matlab implementation of thepopulation-based differential evolution (DE) algorithm [13]where a population of possible solutions is evaluated usinga fitness function The search for an optimal solution startswith a population of 119875 randomly created solution vectors119878V1 119878V119895 119878V119875 each vector representing a candidatemixed light spectrum where some characteristics of theindividual bands in the candidate spectrum for exampleintensities are randomized As new solutions are created andevaluated only the fitter solutions are moved to the nextgeneration [7]
The basis of the selection process in our algorithm is thecolor difference of specific surface colors as they appear underthe candidate spectrum and under the reference spectrumof the same CCT In each new generation the offspringsolutions are evaluated using a fitness function (119891fit) basedon the color differenceΔ119864
00calculated using the CIEDE2000
color difference formula Hence the algorithm searches fora spectrum with the lowest color differences The optimumsolution is determined after having performed 119866 (typically1000) cycles of the evaluations that is the best solution incycle 119866 is accepted as the best white-light spectrum
Thus the intent is to minimize the average color differ-ence Δ119864
00(Avg) for a set of color samples The color samples(Table 1) are the 14 test samples specified in CIE133 [9]Samples 1 to 8 have low to moderate chromatic saturationSamples 9 to 12 represent saturated red yellow green andblue and Samples 13 and 14 represent light human complex-ion and green foliage respectivelyThe CIE test color samplesare used since they constitute a well known and widely usedset
After the completion of each DE run the performanceof each optimized solution is assessed using the CIE generalcolor rendering index 119877
119886 determined as per [9] and the
lowest color rendering value 119877min together with the LERFurthermore the Δ119864
00119894for each test sample is tabulated
(Tables 2 3 4 and 5) together with the color differencesdecomposed into chromatic differences [14] in terms of
Table 1 The 14 CIE test colors [9]
Number Style name Brief description1 75 R 64 Light grayish red2 5 Y 64 Dark grayish yellow3 5 GY 68 Strong yellow green4 25 G 66 Moderate yellowish green5 10 BG 64 Light bluish green6 5 PB 68 Light blue7 25 P 68 Light violet8 10 P 68 Light reddish purple9 45 R 413 Strong red10 5 Y 810 Strong yellow11 45 G 58 Strong green12 3 PB 311 Strong blue13 5 YR 84 Light yellowish pink14 5 GY 44 Moderate olive green
0010203040506070809
1
400 450 500 550 600 650 700
Rela
tive i
nten
sity
460 640590525
120582 (nm)
Figure 1 Spectral power distributions of real LEDs used in theoptimized mixtures The peak wavelengths (nm) are given aboveeach spectrum
Δ119862119886119887
lowast Δ119867119886119887
lowast and Δ119871lowast Positive (negative) differences meanthat the color test samples illuminated by the optimized spec-trum have more (less) of that variable than when illuminatedby the reference illuminantThe closeness of the chromaticitymatches to the target CCTs has been computed in the CIE(1199061015840V1015840) chromaticity space [14]These data are included on the
grounds of the importance of this parameter to the potentialusers in the lighting industry To gauge the significance of ourcomputedΔ(1199061015840V1015840) color differences the color difference in the(1199061015840V1015840) diagram between 5000K and 6500K on the Planckianlocus is Δ(1199061015840V1015840) sim 002 and between 2700K and 3000K thedifference is Δ(1199061015840V1015840) sim 001
21 Optimization of Real LEDMixtures Here a solution (119878V119895)is the spectrum of the light produced by a mixture of either3 or 4 real LEDs being a selected subset of the Luxeon range[15] (Figure 1) The optimization starts with a population ofrandomly created solution vectors where the intensities (119868
119894)
of the individual LED spectra are randomizedThe results arepresented in Section 31
22 Optimization of Synthetic LED Spectra Represented byGaussian Functions The above mentioned method is usedwith modification to optimize mixtures of Gaussian bandswhere each band (119878
119894) is simulated over a specific bandwidth
within the wavelength range of 120582 from 380 to 780 nm (in1 nm increments) The properties of each Gaussian band areexpressed in what follows
119878119894 (120582) = 119868119894119890
minus(120582minus120582119894)221205752
120575 =Δ119894
2radic2 ln 2
(1)
where 119868119894120582119894 andΔ
119894represent peak intensity peakwavelength
and spectral bandwidth (or full-width at half-maximumFWHM) respectively and (2) represents the compositespectrum of 119899 bands each having the same value of FWHMbandwidth
119878V119895 =
119899
sum
1119878119894(120582) (2)
with 119899 chosen to be either 3 or 4 as explained in the Section 3The optimization starts with a population of randomly
created solution vectors where the intensities and the peakwavelengths of the individual Gaussian bands are random-ized while their spectral bandwidths are kept constantTwo bandwidths have been investigated 25 nm and 50 nmrepresenting ldquotypicalrdquo LED spectral bandwidths
3 Results
31 Real LEDMixtures We explored the feasibility of obtain-ing LED-based sources to match illuminants A D
50 and D
65
using a set of real LEDs with the spectral power distributionsshown in Figure 1 The choice was made to focus on theoptimization of 4-band spectra as previous work [3 5 7 8 10]indicated that mixing only the blue green and red wouldresult in spectra with poor color rendering An exceptionoccurs if the red band can be broadened or the red peakwavelength lowered [3 5]
The optimized 4-band spectra are shown in Figure 2Table 2 shows that the spectra are acceptable standard illu-minant simulators having average color differences below1 Δ11986400
unit and CIE color rendering index 119877119886ge 93
The Δ(1199061015840V1015840) color differences are below 0004 and could beconsidered subthreshold for white light
Overall the changes in lightness of the test colors areconsistent regardless of the correlated color temperatureSamples 3 7ndash10 and 14 become lighter and the remainderbecome darker (Table 2) This is thought to be due to thepeaks and valleys in the combined spectra resulting from theparticular 4 LED spectra selected for the experiment
The color differences are lowest for the Illuminant Asimulation where 11 samples (1ndash10 12ndash14) have both Δ119862
119886119887
lowast
andΔ119867119886119887
lowast below 5 units and the Sample 11 chroma differenceis just above 5 units (Δ119862
119886119887
lowast
(11)A = 561) For the Illuminant Asimulations the greatest change in hue is observed for Sample12 (strong blue Δ119867
119886119887
lowast
(12)A = minus395) and the highest change
in lightness is observed for Sample 3 (strong yellow green)which becomes slightly darker (Δ119871lowast
(3)A = minus076)The Illuminant D simulations show significant increases
in the color errors for Sample 12 (Δ119862119886119887
lowast
(12)D50 = 701Δ119867119886119887
lowast
(12)D50 = minus878 and Δ119862119886119887
lowast
(12)D65 = 955Δ119867119886119887
lowast
(12)D65 = minus1021)
32 Optimization of Gaussian Bands Optimized spectra areshown in Figures 3 4 and 5 with the values of the peakwavelengths given above each diagram
321 Illuminant A Figure 3 and Table 3 show the results ofthe optimization of the Illuminant A simulators showing that3-band and 4-bandGaussianmixtures scored satisfactorily inthe CRI metric (119877
119886ge 84) All simulators have a higher LER
(ge318 lmrad-W) than real Illuminant A (LERA = 156 lmrad-W)The spectra are named S
1 S2 and S
3 where S
1represents
the 25 nm 3-band spectrum S2represents the 50 nm 3-band
spectrum and S3represents the 25 nm 4-band spectrumThe
Δ(1199061015840V1015840) color differences are below 0006 for S
2and S3
As expected the lower color errors (hence better colorrendering) are obtained by either employing wider Gaussianbands (S
2) or using an additional 4th band (S
3) However a
wider red band and the additional amber band reduced LER(from416 lmrad-W to 357 and 318 lmrad-W) by introducingmore radiated power at wavelengths where the119881(120582) functionhas low valuesThe 25 nm 3-band spectrum (S
1) exhibits very
poor rendering of blue (Sample 12 strong blue 11987712= 119877min =
24) (Table 3(a))Simulators S
2and S
3render all color samples better
than S1 including the problematic saturated Samples 9ndash12
However poor scoreswere recorded for Sample 9 (strong red)in S2 and for Sample 12 (strong blue) in both S
2and S3
Figure 3 shows the spectral power distributions of theIlluminant A simulations The Gaussian peaks follow thegeneral trend of the Illuminant A spectrumThe low emissionin the blue region helps explain the problematic rendering ofthe strong blue sample shown in Table 3
Based on these results the S1mixture would be an
unsatisfactory simulator of Illuminant A while the S2and S3
mixtures would be acceptable for noncritical uses
322 Illuminant D50 The results for Illuminant D
50are
shown in Figure 4 and Table 4 The spectra are named S4
S5 and S
6 where S
4represents the 25 nm 3-band spectrum
S5represents the 50 nm 3-band spectrum and S
6represents
the 25 nm 4-band spectrum The LER of the spectra isge323 lmrad-W (versus the lower LER of real Illuminant D
50
at 207 lmrad-W) and color rendering 119877119886ge 85 Spectrum S
4
has a particularly bad effect on the chroma and hue of thestrong blue (Sample 12) (Δ119862
As expected the color shifts and the differences inlightness are smaller for S
5and S
6 that is wider individual
bands and 4-bandmixture result in better white-light spectraIn particular the best color rendering expressed in termsof Δ119862
119886119887
lowast and Δ119867119886119887
lowast is for S6where the color errors are
all below 4 units Also S6introduces the lowest changes
6 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
A
0
02
04
06
08
1
380 480 580 680 780
0
02
04
06
08
1
380 480 580 680 780
120582 (nm)
120582 (nm)
120582 (nm)
D50
D65
Figure 2 Optimized 4-LED relative spectral power distributions
in lightness Table 4 reveals considerable improvements inmatching Illuminant D
50by widening the individual bands
or by introducing the 4th band The Δ(1199061015840V1015840) value of 00050for S5is considered just-noticeable and Δ(1199061015840V1015840) = 00019 for
S6is below the noticeable threshold
323 Illuminant D65 Simulators for Illuminant D
65
(Figure 5 and Table 5) follow the same general trends as forD50 and the mixture with wider spectral bands (S
8) and
the mixture with 4 bands (S9) gave higher 119877
119886values and
lower LER values than the 25 nm 3-band mixture The colorrendering in terms of CIE CRI is highly satisfactory 119877
119886ge 87
and the strong blue sample again exhibits the poorest colorrendering (119877
12(S7) = 119877min = 38) The chromaticities of thesimulations are very near to the chromaticity of IlluminantD65 Δ(1199061015840V1015840) lt 0006 in all experiments The LER of the
spectra is ge299 lmrad-W (versus the LER of real IlluminantD65at 204 lmrad-W)Optimized spectrum S
7introduces larger color errors
(Δ11986400av = 224) than any other in this paper In particular the
blue sample has both hue and chroma differences greater than16 units (Table 5(a)) This aspect was somewhat unexpectedand is thought to be due to the spectral discrepanciesbetween the simulated spectra and real D
65 particularly at
the wavelength extremities Further evidence is given by thefact that strong red (Sample 9) gives the next-worst 119877
119894in
Table 5(a)
33 Comparison of Peak Wavelengths It is instructive tocompare our optimized Gaussian peak wavelengths withthe peak wavelengths of the set of real LEDs all of whichare collated in Table 6 The real LEDs are labeled as ldquoBluerdquo
Advances in OptoElectronics 7
0
02
04
06
08
1
380 480 580 680 780
470 548 614
0
02
04
06
08
1
380 480 580 680 780
471 548 621
0
02
04
06
08
1
380 480 580 680 780
468 643589533
120582 (nm) 120582 (nm)
120582 (nm)
Figure 3 Optimized relative spectral power distributions (S1 S2 S3) for Illuminant A
In most of the spectra the blue Gaussian band wasbetween about 470 nm and 460 nm Exceptions are S
6and S9
the 4-band D50
and D65
simulators in which the optimizermoved the blue and green bands to lower wavelengths toaccommodate the amber bandThe green peaks in the 3-bandmixtures were optimized toward the peak of the 119881
120582curve
(120582 = 555 nm) thus producing the spectra with improved LERvalues as compared with the corresponding optimized LEDmixtures
It was consistently observed that the optimized wave-lengths for the red band were between about 610 nm to620 nm However the 4-band Illuminant A simulator S
3 has
the red band at 120582119877(S3) = 643 nm We ascribe that to the fact
that the amber band was optimized to 120582119860(S3) = 589 nm as
compared with 120582119860(S6) = 555 nm and 120582
119860(S9) = 558 nm for theD simulators The result was the noticeable improvement inthe rendering of test Sample 9 with source S
3
8 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
468 611542
0
02
04
06
08
1
380 480 580 680 780
470 619544
0
02
04
06
08
1
380 480 580 680 780
451 614555502
120582 (nm) 120582 (nm)
120582 (nm)
Figure 4 Optimized relative spectral power distributions (S4 S5 S6) for Illuminant D50
It was noteworthy in nearly all our results that the strongred (Sample 9) and strong blue (Sample 12) were badlyaffected by the truncation of the extrema of the synthesizedspectra
4 Conclusions
We have demonstrated that it is possible to simulate the CIEstandard illuminants A D
50 and D
65by mixing multiband
LED and Gaussian spectra The overall performance of theGaussian-based mixtures was better than the LED-basedcounterparts due to the freedom to select the most suitablepositions in the spectrum for the peak wavelengths in theGaussian mixtures
The simulation results show that 3-band Gaussian Illumi-nant A simulators could have CRI above 84 and LER double
that of Illuminant A Well designed 3-band Gaussian D50
and D65
simulators may have both CRI ge 85 and LER ge315 lmrad-W 4-band simulators improve color rendering bydistributing the bands in the visible spectrum
Our optimization techniques as described do not needto be constrained by the choice of test color samples colordifference formulae target spectrum or choice of standardobserver This is demonstrated in this paper where wehave shown how our previously published algorithm can bemodified to apply new color difference techniques to newobjectives in this case the achievement of specific sourceCCT targets
It should be noted that the spectra presented here areresults of simulations and further work is required toinvestigate the practical implementation of those spectra andto evaluate them in ldquoreal liferdquo situations
Advances in OptoElectronics 9
0
02
04
06
08
1
380 480 580 680 780
464 609539
0
02
04
06
08
1
380 480 580 680 780
460 538 615
0
02
04
06
08
1
380 480 580 680 780
449 498 618558
120582 (nm) 120582 (nm)
120582 (nm)
Figure 5 Optimized relative spectral power distributions (S7 S8 S9) for Illuminant D65
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors wish to acknowledge the support provided forthis work by the Technology Development Centre of theManukau Institute of Technology
References
[1] T Erdem S Nizamoglu X W Sun and H V Demir ldquoAphotometric investigation of ultra-efficient LEDs with highcolor rendering index and high luminous efficacy employingnanocrystal quantumdot luminophoresrdquoOptics Express vol 18no 1 pp 340ndash347 2010
[2] G He L Zheng and H Yan ldquoLED white lights with high CRIand high luminous efficacyrdquo in LED and Display Technologiesvol 7852 of Proceedings of SPIE 2010
[3] Y Ohno ldquoSpectral design considerations for white LED colorrenderingrdquoOptical Engineering vol 44 no 11 Article ID 1113022005
[4] A Zukauskas R Vaicekauskas F Ivanauskas R Gaska and MS Shur ldquoOptimization of white polychromatic semiconductorlampsrdquoApplied Physics Letters vol 80 no 2 pp 234ndash236 2002
[5] E Taylor P R Edwards and R W Martin ldquoColorimetry andefficiency of white LEDs spectral width dependencerdquo PhysicaStatus Solidi A Applications and Materials Science vol 209 no3 pp 461ndash464 2012
[6] R S Berns ldquoDesigning white-light LED lighting for the displayof art a feasibility studyrdquo Color Research and Application vol36 no 5 pp 324ndash334 2011
[7] S Soltic and A N Chalmers ldquoDifferential evolution for theoptimisation of multi-band white LED light sourcesrdquo LightingResearch amp Technology vol 44 no 2 pp 224ndash237 2012
10 Advances in OptoElectronics
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006
22 Optimization of Synthetic LED Spectra Represented byGaussian Functions The above mentioned method is usedwith modification to optimize mixtures of Gaussian bandswhere each band (119878
119894) is simulated over a specific bandwidth
within the wavelength range of 120582 from 380 to 780 nm (in1 nm increments) The properties of each Gaussian band areexpressed in what follows
119878119894 (120582) = 119868119894119890
minus(120582minus120582119894)221205752
120575 =Δ119894
2radic2 ln 2
(1)
where 119868119894120582119894 andΔ
119894represent peak intensity peakwavelength
and spectral bandwidth (or full-width at half-maximumFWHM) respectively and (2) represents the compositespectrum of 119899 bands each having the same value of FWHMbandwidth
119878V119895 =
119899
sum
1119878119894(120582) (2)
with 119899 chosen to be either 3 or 4 as explained in the Section 3The optimization starts with a population of randomly
created solution vectors where the intensities and the peakwavelengths of the individual Gaussian bands are random-ized while their spectral bandwidths are kept constantTwo bandwidths have been investigated 25 nm and 50 nmrepresenting ldquotypicalrdquo LED spectral bandwidths
3 Results
31 Real LEDMixtures We explored the feasibility of obtain-ing LED-based sources to match illuminants A D
50 and D
65
using a set of real LEDs with the spectral power distributionsshown in Figure 1 The choice was made to focus on theoptimization of 4-band spectra as previous work [3 5 7 8 10]indicated that mixing only the blue green and red wouldresult in spectra with poor color rendering An exceptionoccurs if the red band can be broadened or the red peakwavelength lowered [3 5]
The optimized 4-band spectra are shown in Figure 2Table 2 shows that the spectra are acceptable standard illu-minant simulators having average color differences below1 Δ11986400
unit and CIE color rendering index 119877119886ge 93
The Δ(1199061015840V1015840) color differences are below 0004 and could beconsidered subthreshold for white light
Overall the changes in lightness of the test colors areconsistent regardless of the correlated color temperatureSamples 3 7ndash10 and 14 become lighter and the remainderbecome darker (Table 2) This is thought to be due to thepeaks and valleys in the combined spectra resulting from theparticular 4 LED spectra selected for the experiment
The color differences are lowest for the Illuminant Asimulation where 11 samples (1ndash10 12ndash14) have both Δ119862
119886119887
lowast
andΔ119867119886119887
lowast below 5 units and the Sample 11 chroma differenceis just above 5 units (Δ119862
119886119887
lowast
(11)A = 561) For the Illuminant Asimulations the greatest change in hue is observed for Sample12 (strong blue Δ119867
119886119887
lowast
(12)A = minus395) and the highest change
in lightness is observed for Sample 3 (strong yellow green)which becomes slightly darker (Δ119871lowast
(3)A = minus076)The Illuminant D simulations show significant increases
in the color errors for Sample 12 (Δ119862119886119887
lowast
(12)D50 = 701Δ119867119886119887
lowast
(12)D50 = minus878 and Δ119862119886119887
lowast
(12)D65 = 955Δ119867119886119887
lowast
(12)D65 = minus1021)
32 Optimization of Gaussian Bands Optimized spectra areshown in Figures 3 4 and 5 with the values of the peakwavelengths given above each diagram
321 Illuminant A Figure 3 and Table 3 show the results ofthe optimization of the Illuminant A simulators showing that3-band and 4-bandGaussianmixtures scored satisfactorily inthe CRI metric (119877
119886ge 84) All simulators have a higher LER
(ge318 lmrad-W) than real Illuminant A (LERA = 156 lmrad-W)The spectra are named S
1 S2 and S
3 where S
1represents
the 25 nm 3-band spectrum S2represents the 50 nm 3-band
spectrum and S3represents the 25 nm 4-band spectrumThe
Δ(1199061015840V1015840) color differences are below 0006 for S
2and S3
As expected the lower color errors (hence better colorrendering) are obtained by either employing wider Gaussianbands (S
2) or using an additional 4th band (S
3) However a
wider red band and the additional amber band reduced LER(from416 lmrad-W to 357 and 318 lmrad-W) by introducingmore radiated power at wavelengths where the119881(120582) functionhas low valuesThe 25 nm 3-band spectrum (S
1) exhibits very
poor rendering of blue (Sample 12 strong blue 11987712= 119877min =
24) (Table 3(a))Simulators S
2and S
3render all color samples better
than S1 including the problematic saturated Samples 9ndash12
However poor scoreswere recorded for Sample 9 (strong red)in S2 and for Sample 12 (strong blue) in both S
2and S3
Figure 3 shows the spectral power distributions of theIlluminant A simulations The Gaussian peaks follow thegeneral trend of the Illuminant A spectrumThe low emissionin the blue region helps explain the problematic rendering ofthe strong blue sample shown in Table 3
Based on these results the S1mixture would be an
unsatisfactory simulator of Illuminant A while the S2and S3
mixtures would be acceptable for noncritical uses
322 Illuminant D50 The results for Illuminant D
50are
shown in Figure 4 and Table 4 The spectra are named S4
S5 and S
6 where S
4represents the 25 nm 3-band spectrum
S5represents the 50 nm 3-band spectrum and S
6represents
the 25 nm 4-band spectrum The LER of the spectra isge323 lmrad-W (versus the lower LER of real Illuminant D
50
at 207 lmrad-W) and color rendering 119877119886ge 85 Spectrum S
4
has a particularly bad effect on the chroma and hue of thestrong blue (Sample 12) (Δ119862
As expected the color shifts and the differences inlightness are smaller for S
5and S
6 that is wider individual
bands and 4-bandmixture result in better white-light spectraIn particular the best color rendering expressed in termsof Δ119862
119886119887
lowast and Δ119867119886119887
lowast is for S6where the color errors are
all below 4 units Also S6introduces the lowest changes
6 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
A
0
02
04
06
08
1
380 480 580 680 780
0
02
04
06
08
1
380 480 580 680 780
120582 (nm)
120582 (nm)
120582 (nm)
D50
D65
Figure 2 Optimized 4-LED relative spectral power distributions
in lightness Table 4 reveals considerable improvements inmatching Illuminant D
50by widening the individual bands
or by introducing the 4th band The Δ(1199061015840V1015840) value of 00050for S5is considered just-noticeable and Δ(1199061015840V1015840) = 00019 for
S6is below the noticeable threshold
323 Illuminant D65 Simulators for Illuminant D
65
(Figure 5 and Table 5) follow the same general trends as forD50 and the mixture with wider spectral bands (S
8) and
the mixture with 4 bands (S9) gave higher 119877
119886values and
lower LER values than the 25 nm 3-band mixture The colorrendering in terms of CIE CRI is highly satisfactory 119877
119886ge 87
and the strong blue sample again exhibits the poorest colorrendering (119877
12(S7) = 119877min = 38) The chromaticities of thesimulations are very near to the chromaticity of IlluminantD65 Δ(1199061015840V1015840) lt 0006 in all experiments The LER of the
spectra is ge299 lmrad-W (versus the LER of real IlluminantD65at 204 lmrad-W)Optimized spectrum S
7introduces larger color errors
(Δ11986400av = 224) than any other in this paper In particular the
blue sample has both hue and chroma differences greater than16 units (Table 5(a)) This aspect was somewhat unexpectedand is thought to be due to the spectral discrepanciesbetween the simulated spectra and real D
65 particularly at
the wavelength extremities Further evidence is given by thefact that strong red (Sample 9) gives the next-worst 119877
119894in
Table 5(a)
33 Comparison of Peak Wavelengths It is instructive tocompare our optimized Gaussian peak wavelengths withthe peak wavelengths of the set of real LEDs all of whichare collated in Table 6 The real LEDs are labeled as ldquoBluerdquo
Advances in OptoElectronics 7
0
02
04
06
08
1
380 480 580 680 780
470 548 614
0
02
04
06
08
1
380 480 580 680 780
471 548 621
0
02
04
06
08
1
380 480 580 680 780
468 643589533
120582 (nm) 120582 (nm)
120582 (nm)
Figure 3 Optimized relative spectral power distributions (S1 S2 S3) for Illuminant A
In most of the spectra the blue Gaussian band wasbetween about 470 nm and 460 nm Exceptions are S
6and S9
the 4-band D50
and D65
simulators in which the optimizermoved the blue and green bands to lower wavelengths toaccommodate the amber bandThe green peaks in the 3-bandmixtures were optimized toward the peak of the 119881
120582curve
(120582 = 555 nm) thus producing the spectra with improved LERvalues as compared with the corresponding optimized LEDmixtures
It was consistently observed that the optimized wave-lengths for the red band were between about 610 nm to620 nm However the 4-band Illuminant A simulator S
3 has
the red band at 120582119877(S3) = 643 nm We ascribe that to the fact
that the amber band was optimized to 120582119860(S3) = 589 nm as
compared with 120582119860(S6) = 555 nm and 120582
119860(S9) = 558 nm for theD simulators The result was the noticeable improvement inthe rendering of test Sample 9 with source S
3
8 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
468 611542
0
02
04
06
08
1
380 480 580 680 780
470 619544
0
02
04
06
08
1
380 480 580 680 780
451 614555502
120582 (nm) 120582 (nm)
120582 (nm)
Figure 4 Optimized relative spectral power distributions (S4 S5 S6) for Illuminant D50
It was noteworthy in nearly all our results that the strongred (Sample 9) and strong blue (Sample 12) were badlyaffected by the truncation of the extrema of the synthesizedspectra
4 Conclusions
We have demonstrated that it is possible to simulate the CIEstandard illuminants A D
50 and D
65by mixing multiband
LED and Gaussian spectra The overall performance of theGaussian-based mixtures was better than the LED-basedcounterparts due to the freedom to select the most suitablepositions in the spectrum for the peak wavelengths in theGaussian mixtures
The simulation results show that 3-band Gaussian Illumi-nant A simulators could have CRI above 84 and LER double
that of Illuminant A Well designed 3-band Gaussian D50
and D65
simulators may have both CRI ge 85 and LER ge315 lmrad-W 4-band simulators improve color rendering bydistributing the bands in the visible spectrum
Our optimization techniques as described do not needto be constrained by the choice of test color samples colordifference formulae target spectrum or choice of standardobserver This is demonstrated in this paper where wehave shown how our previously published algorithm can bemodified to apply new color difference techniques to newobjectives in this case the achievement of specific sourceCCT targets
It should be noted that the spectra presented here areresults of simulations and further work is required toinvestigate the practical implementation of those spectra andto evaluate them in ldquoreal liferdquo situations
Advances in OptoElectronics 9
0
02
04
06
08
1
380 480 580 680 780
464 609539
0
02
04
06
08
1
380 480 580 680 780
460 538 615
0
02
04
06
08
1
380 480 580 680 780
449 498 618558
120582 (nm) 120582 (nm)
120582 (nm)
Figure 5 Optimized relative spectral power distributions (S7 S8 S9) for Illuminant D65
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors wish to acknowledge the support provided forthis work by the Technology Development Centre of theManukau Institute of Technology
References
[1] T Erdem S Nizamoglu X W Sun and H V Demir ldquoAphotometric investigation of ultra-efficient LEDs with highcolor rendering index and high luminous efficacy employingnanocrystal quantumdot luminophoresrdquoOptics Express vol 18no 1 pp 340ndash347 2010
[2] G He L Zheng and H Yan ldquoLED white lights with high CRIand high luminous efficacyrdquo in LED and Display Technologiesvol 7852 of Proceedings of SPIE 2010
[3] Y Ohno ldquoSpectral design considerations for white LED colorrenderingrdquoOptical Engineering vol 44 no 11 Article ID 1113022005
[4] A Zukauskas R Vaicekauskas F Ivanauskas R Gaska and MS Shur ldquoOptimization of white polychromatic semiconductorlampsrdquoApplied Physics Letters vol 80 no 2 pp 234ndash236 2002
[5] E Taylor P R Edwards and R W Martin ldquoColorimetry andefficiency of white LEDs spectral width dependencerdquo PhysicaStatus Solidi A Applications and Materials Science vol 209 no3 pp 461ndash464 2012
[6] R S Berns ldquoDesigning white-light LED lighting for the displayof art a feasibility studyrdquo Color Research and Application vol36 no 5 pp 324ndash334 2011
[7] S Soltic and A N Chalmers ldquoDifferential evolution for theoptimisation of multi-band white LED light sourcesrdquo LightingResearch amp Technology vol 44 no 2 pp 224ndash237 2012
10 Advances in OptoElectronics
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006
22 Optimization of Synthetic LED Spectra Represented byGaussian Functions The above mentioned method is usedwith modification to optimize mixtures of Gaussian bandswhere each band (119878
119894) is simulated over a specific bandwidth
within the wavelength range of 120582 from 380 to 780 nm (in1 nm increments) The properties of each Gaussian band areexpressed in what follows
119878119894 (120582) = 119868119894119890
minus(120582minus120582119894)221205752
120575 =Δ119894
2radic2 ln 2
(1)
where 119868119894120582119894 andΔ
119894represent peak intensity peakwavelength
and spectral bandwidth (or full-width at half-maximumFWHM) respectively and (2) represents the compositespectrum of 119899 bands each having the same value of FWHMbandwidth
119878V119895 =
119899
sum
1119878119894(120582) (2)
with 119899 chosen to be either 3 or 4 as explained in the Section 3The optimization starts with a population of randomly
created solution vectors where the intensities and the peakwavelengths of the individual Gaussian bands are random-ized while their spectral bandwidths are kept constantTwo bandwidths have been investigated 25 nm and 50 nmrepresenting ldquotypicalrdquo LED spectral bandwidths
3 Results
31 Real LEDMixtures We explored the feasibility of obtain-ing LED-based sources to match illuminants A D
50 and D
65
using a set of real LEDs with the spectral power distributionsshown in Figure 1 The choice was made to focus on theoptimization of 4-band spectra as previous work [3 5 7 8 10]indicated that mixing only the blue green and red wouldresult in spectra with poor color rendering An exceptionoccurs if the red band can be broadened or the red peakwavelength lowered [3 5]
The optimized 4-band spectra are shown in Figure 2Table 2 shows that the spectra are acceptable standard illu-minant simulators having average color differences below1 Δ11986400
unit and CIE color rendering index 119877119886ge 93
The Δ(1199061015840V1015840) color differences are below 0004 and could beconsidered subthreshold for white light
Overall the changes in lightness of the test colors areconsistent regardless of the correlated color temperatureSamples 3 7ndash10 and 14 become lighter and the remainderbecome darker (Table 2) This is thought to be due to thepeaks and valleys in the combined spectra resulting from theparticular 4 LED spectra selected for the experiment
The color differences are lowest for the Illuminant Asimulation where 11 samples (1ndash10 12ndash14) have both Δ119862
119886119887
lowast
andΔ119867119886119887
lowast below 5 units and the Sample 11 chroma differenceis just above 5 units (Δ119862
119886119887
lowast
(11)A = 561) For the Illuminant Asimulations the greatest change in hue is observed for Sample12 (strong blue Δ119867
119886119887
lowast
(12)A = minus395) and the highest change
in lightness is observed for Sample 3 (strong yellow green)which becomes slightly darker (Δ119871lowast
(3)A = minus076)The Illuminant D simulations show significant increases
in the color errors for Sample 12 (Δ119862119886119887
lowast
(12)D50 = 701Δ119867119886119887
lowast
(12)D50 = minus878 and Δ119862119886119887
lowast
(12)D65 = 955Δ119867119886119887
lowast
(12)D65 = minus1021)
32 Optimization of Gaussian Bands Optimized spectra areshown in Figures 3 4 and 5 with the values of the peakwavelengths given above each diagram
321 Illuminant A Figure 3 and Table 3 show the results ofthe optimization of the Illuminant A simulators showing that3-band and 4-bandGaussianmixtures scored satisfactorily inthe CRI metric (119877
119886ge 84) All simulators have a higher LER
(ge318 lmrad-W) than real Illuminant A (LERA = 156 lmrad-W)The spectra are named S
1 S2 and S
3 where S
1represents
the 25 nm 3-band spectrum S2represents the 50 nm 3-band
spectrum and S3represents the 25 nm 4-band spectrumThe
Δ(1199061015840V1015840) color differences are below 0006 for S
2and S3
As expected the lower color errors (hence better colorrendering) are obtained by either employing wider Gaussianbands (S
2) or using an additional 4th band (S
3) However a
wider red band and the additional amber band reduced LER(from416 lmrad-W to 357 and 318 lmrad-W) by introducingmore radiated power at wavelengths where the119881(120582) functionhas low valuesThe 25 nm 3-band spectrum (S
1) exhibits very
poor rendering of blue (Sample 12 strong blue 11987712= 119877min =
24) (Table 3(a))Simulators S
2and S
3render all color samples better
than S1 including the problematic saturated Samples 9ndash12
However poor scoreswere recorded for Sample 9 (strong red)in S2 and for Sample 12 (strong blue) in both S
2and S3
Figure 3 shows the spectral power distributions of theIlluminant A simulations The Gaussian peaks follow thegeneral trend of the Illuminant A spectrumThe low emissionin the blue region helps explain the problematic rendering ofthe strong blue sample shown in Table 3
Based on these results the S1mixture would be an
unsatisfactory simulator of Illuminant A while the S2and S3
mixtures would be acceptable for noncritical uses
322 Illuminant D50 The results for Illuminant D
50are
shown in Figure 4 and Table 4 The spectra are named S4
S5 and S
6 where S
4represents the 25 nm 3-band spectrum
S5represents the 50 nm 3-band spectrum and S
6represents
the 25 nm 4-band spectrum The LER of the spectra isge323 lmrad-W (versus the lower LER of real Illuminant D
50
at 207 lmrad-W) and color rendering 119877119886ge 85 Spectrum S
4
has a particularly bad effect on the chroma and hue of thestrong blue (Sample 12) (Δ119862
As expected the color shifts and the differences inlightness are smaller for S
5and S
6 that is wider individual
bands and 4-bandmixture result in better white-light spectraIn particular the best color rendering expressed in termsof Δ119862
119886119887
lowast and Δ119867119886119887
lowast is for S6where the color errors are
all below 4 units Also S6introduces the lowest changes
6 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
A
0
02
04
06
08
1
380 480 580 680 780
0
02
04
06
08
1
380 480 580 680 780
120582 (nm)
120582 (nm)
120582 (nm)
D50
D65
Figure 2 Optimized 4-LED relative spectral power distributions
in lightness Table 4 reveals considerable improvements inmatching Illuminant D
50by widening the individual bands
or by introducing the 4th band The Δ(1199061015840V1015840) value of 00050for S5is considered just-noticeable and Δ(1199061015840V1015840) = 00019 for
S6is below the noticeable threshold
323 Illuminant D65 Simulators for Illuminant D
65
(Figure 5 and Table 5) follow the same general trends as forD50 and the mixture with wider spectral bands (S
8) and
the mixture with 4 bands (S9) gave higher 119877
119886values and
lower LER values than the 25 nm 3-band mixture The colorrendering in terms of CIE CRI is highly satisfactory 119877
119886ge 87
and the strong blue sample again exhibits the poorest colorrendering (119877
12(S7) = 119877min = 38) The chromaticities of thesimulations are very near to the chromaticity of IlluminantD65 Δ(1199061015840V1015840) lt 0006 in all experiments The LER of the
spectra is ge299 lmrad-W (versus the LER of real IlluminantD65at 204 lmrad-W)Optimized spectrum S
7introduces larger color errors
(Δ11986400av = 224) than any other in this paper In particular the
blue sample has both hue and chroma differences greater than16 units (Table 5(a)) This aspect was somewhat unexpectedand is thought to be due to the spectral discrepanciesbetween the simulated spectra and real D
65 particularly at
the wavelength extremities Further evidence is given by thefact that strong red (Sample 9) gives the next-worst 119877
119894in
Table 5(a)
33 Comparison of Peak Wavelengths It is instructive tocompare our optimized Gaussian peak wavelengths withthe peak wavelengths of the set of real LEDs all of whichare collated in Table 6 The real LEDs are labeled as ldquoBluerdquo
Advances in OptoElectronics 7
0
02
04
06
08
1
380 480 580 680 780
470 548 614
0
02
04
06
08
1
380 480 580 680 780
471 548 621
0
02
04
06
08
1
380 480 580 680 780
468 643589533
120582 (nm) 120582 (nm)
120582 (nm)
Figure 3 Optimized relative spectral power distributions (S1 S2 S3) for Illuminant A
In most of the spectra the blue Gaussian band wasbetween about 470 nm and 460 nm Exceptions are S
6and S9
the 4-band D50
and D65
simulators in which the optimizermoved the blue and green bands to lower wavelengths toaccommodate the amber bandThe green peaks in the 3-bandmixtures were optimized toward the peak of the 119881
120582curve
(120582 = 555 nm) thus producing the spectra with improved LERvalues as compared with the corresponding optimized LEDmixtures
It was consistently observed that the optimized wave-lengths for the red band were between about 610 nm to620 nm However the 4-band Illuminant A simulator S
3 has
the red band at 120582119877(S3) = 643 nm We ascribe that to the fact
that the amber band was optimized to 120582119860(S3) = 589 nm as
compared with 120582119860(S6) = 555 nm and 120582
119860(S9) = 558 nm for theD simulators The result was the noticeable improvement inthe rendering of test Sample 9 with source S
3
8 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
468 611542
0
02
04
06
08
1
380 480 580 680 780
470 619544
0
02
04
06
08
1
380 480 580 680 780
451 614555502
120582 (nm) 120582 (nm)
120582 (nm)
Figure 4 Optimized relative spectral power distributions (S4 S5 S6) for Illuminant D50
It was noteworthy in nearly all our results that the strongred (Sample 9) and strong blue (Sample 12) were badlyaffected by the truncation of the extrema of the synthesizedspectra
4 Conclusions
We have demonstrated that it is possible to simulate the CIEstandard illuminants A D
50 and D
65by mixing multiband
LED and Gaussian spectra The overall performance of theGaussian-based mixtures was better than the LED-basedcounterparts due to the freedom to select the most suitablepositions in the spectrum for the peak wavelengths in theGaussian mixtures
The simulation results show that 3-band Gaussian Illumi-nant A simulators could have CRI above 84 and LER double
that of Illuminant A Well designed 3-band Gaussian D50
and D65
simulators may have both CRI ge 85 and LER ge315 lmrad-W 4-band simulators improve color rendering bydistributing the bands in the visible spectrum
Our optimization techniques as described do not needto be constrained by the choice of test color samples colordifference formulae target spectrum or choice of standardobserver This is demonstrated in this paper where wehave shown how our previously published algorithm can bemodified to apply new color difference techniques to newobjectives in this case the achievement of specific sourceCCT targets
It should be noted that the spectra presented here areresults of simulations and further work is required toinvestigate the practical implementation of those spectra andto evaluate them in ldquoreal liferdquo situations
Advances in OptoElectronics 9
0
02
04
06
08
1
380 480 580 680 780
464 609539
0
02
04
06
08
1
380 480 580 680 780
460 538 615
0
02
04
06
08
1
380 480 580 680 780
449 498 618558
120582 (nm) 120582 (nm)
120582 (nm)
Figure 5 Optimized relative spectral power distributions (S7 S8 S9) for Illuminant D65
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors wish to acknowledge the support provided forthis work by the Technology Development Centre of theManukau Institute of Technology
References
[1] T Erdem S Nizamoglu X W Sun and H V Demir ldquoAphotometric investigation of ultra-efficient LEDs with highcolor rendering index and high luminous efficacy employingnanocrystal quantumdot luminophoresrdquoOptics Express vol 18no 1 pp 340ndash347 2010
[2] G He L Zheng and H Yan ldquoLED white lights with high CRIand high luminous efficacyrdquo in LED and Display Technologiesvol 7852 of Proceedings of SPIE 2010
[3] Y Ohno ldquoSpectral design considerations for white LED colorrenderingrdquoOptical Engineering vol 44 no 11 Article ID 1113022005
[4] A Zukauskas R Vaicekauskas F Ivanauskas R Gaska and MS Shur ldquoOptimization of white polychromatic semiconductorlampsrdquoApplied Physics Letters vol 80 no 2 pp 234ndash236 2002
[5] E Taylor P R Edwards and R W Martin ldquoColorimetry andefficiency of white LEDs spectral width dependencerdquo PhysicaStatus Solidi A Applications and Materials Science vol 209 no3 pp 461ndash464 2012
[6] R S Berns ldquoDesigning white-light LED lighting for the displayof art a feasibility studyrdquo Color Research and Application vol36 no 5 pp 324ndash334 2011
[7] S Soltic and A N Chalmers ldquoDifferential evolution for theoptimisation of multi-band white LED light sourcesrdquo LightingResearch amp Technology vol 44 no 2 pp 224ndash237 2012
10 Advances in OptoElectronics
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006
22 Optimization of Synthetic LED Spectra Represented byGaussian Functions The above mentioned method is usedwith modification to optimize mixtures of Gaussian bandswhere each band (119878
119894) is simulated over a specific bandwidth
within the wavelength range of 120582 from 380 to 780 nm (in1 nm increments) The properties of each Gaussian band areexpressed in what follows
119878119894 (120582) = 119868119894119890
minus(120582minus120582119894)221205752
120575 =Δ119894
2radic2 ln 2
(1)
where 119868119894120582119894 andΔ
119894represent peak intensity peakwavelength
and spectral bandwidth (or full-width at half-maximumFWHM) respectively and (2) represents the compositespectrum of 119899 bands each having the same value of FWHMbandwidth
119878V119895 =
119899
sum
1119878119894(120582) (2)
with 119899 chosen to be either 3 or 4 as explained in the Section 3The optimization starts with a population of randomly
created solution vectors where the intensities and the peakwavelengths of the individual Gaussian bands are random-ized while their spectral bandwidths are kept constantTwo bandwidths have been investigated 25 nm and 50 nmrepresenting ldquotypicalrdquo LED spectral bandwidths
3 Results
31 Real LEDMixtures We explored the feasibility of obtain-ing LED-based sources to match illuminants A D
50 and D
65
using a set of real LEDs with the spectral power distributionsshown in Figure 1 The choice was made to focus on theoptimization of 4-band spectra as previous work [3 5 7 8 10]indicated that mixing only the blue green and red wouldresult in spectra with poor color rendering An exceptionoccurs if the red band can be broadened or the red peakwavelength lowered [3 5]
The optimized 4-band spectra are shown in Figure 2Table 2 shows that the spectra are acceptable standard illu-minant simulators having average color differences below1 Δ11986400
unit and CIE color rendering index 119877119886ge 93
The Δ(1199061015840V1015840) color differences are below 0004 and could beconsidered subthreshold for white light
Overall the changes in lightness of the test colors areconsistent regardless of the correlated color temperatureSamples 3 7ndash10 and 14 become lighter and the remainderbecome darker (Table 2) This is thought to be due to thepeaks and valleys in the combined spectra resulting from theparticular 4 LED spectra selected for the experiment
The color differences are lowest for the Illuminant Asimulation where 11 samples (1ndash10 12ndash14) have both Δ119862
119886119887
lowast
andΔ119867119886119887
lowast below 5 units and the Sample 11 chroma differenceis just above 5 units (Δ119862
119886119887
lowast
(11)A = 561) For the Illuminant Asimulations the greatest change in hue is observed for Sample12 (strong blue Δ119867
119886119887
lowast
(12)A = minus395) and the highest change
in lightness is observed for Sample 3 (strong yellow green)which becomes slightly darker (Δ119871lowast
(3)A = minus076)The Illuminant D simulations show significant increases
in the color errors for Sample 12 (Δ119862119886119887
lowast
(12)D50 = 701Δ119867119886119887
lowast
(12)D50 = minus878 and Δ119862119886119887
lowast
(12)D65 = 955Δ119867119886119887
lowast
(12)D65 = minus1021)
32 Optimization of Gaussian Bands Optimized spectra areshown in Figures 3 4 and 5 with the values of the peakwavelengths given above each diagram
321 Illuminant A Figure 3 and Table 3 show the results ofthe optimization of the Illuminant A simulators showing that3-band and 4-bandGaussianmixtures scored satisfactorily inthe CRI metric (119877
119886ge 84) All simulators have a higher LER
(ge318 lmrad-W) than real Illuminant A (LERA = 156 lmrad-W)The spectra are named S
1 S2 and S
3 where S
1represents
the 25 nm 3-band spectrum S2represents the 50 nm 3-band
spectrum and S3represents the 25 nm 4-band spectrumThe
Δ(1199061015840V1015840) color differences are below 0006 for S
2and S3
As expected the lower color errors (hence better colorrendering) are obtained by either employing wider Gaussianbands (S
2) or using an additional 4th band (S
3) However a
wider red band and the additional amber band reduced LER(from416 lmrad-W to 357 and 318 lmrad-W) by introducingmore radiated power at wavelengths where the119881(120582) functionhas low valuesThe 25 nm 3-band spectrum (S
1) exhibits very
poor rendering of blue (Sample 12 strong blue 11987712= 119877min =
24) (Table 3(a))Simulators S
2and S
3render all color samples better
than S1 including the problematic saturated Samples 9ndash12
However poor scoreswere recorded for Sample 9 (strong red)in S2 and for Sample 12 (strong blue) in both S
2and S3
Figure 3 shows the spectral power distributions of theIlluminant A simulations The Gaussian peaks follow thegeneral trend of the Illuminant A spectrumThe low emissionin the blue region helps explain the problematic rendering ofthe strong blue sample shown in Table 3
Based on these results the S1mixture would be an
unsatisfactory simulator of Illuminant A while the S2and S3
mixtures would be acceptable for noncritical uses
322 Illuminant D50 The results for Illuminant D
50are
shown in Figure 4 and Table 4 The spectra are named S4
S5 and S
6 where S
4represents the 25 nm 3-band spectrum
S5represents the 50 nm 3-band spectrum and S
6represents
the 25 nm 4-band spectrum The LER of the spectra isge323 lmrad-W (versus the lower LER of real Illuminant D
50
at 207 lmrad-W) and color rendering 119877119886ge 85 Spectrum S
4
has a particularly bad effect on the chroma and hue of thestrong blue (Sample 12) (Δ119862
As expected the color shifts and the differences inlightness are smaller for S
5and S
6 that is wider individual
bands and 4-bandmixture result in better white-light spectraIn particular the best color rendering expressed in termsof Δ119862
119886119887
lowast and Δ119867119886119887
lowast is for S6where the color errors are
all below 4 units Also S6introduces the lowest changes
6 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
A
0
02
04
06
08
1
380 480 580 680 780
0
02
04
06
08
1
380 480 580 680 780
120582 (nm)
120582 (nm)
120582 (nm)
D50
D65
Figure 2 Optimized 4-LED relative spectral power distributions
in lightness Table 4 reveals considerable improvements inmatching Illuminant D
50by widening the individual bands
or by introducing the 4th band The Δ(1199061015840V1015840) value of 00050for S5is considered just-noticeable and Δ(1199061015840V1015840) = 00019 for
S6is below the noticeable threshold
323 Illuminant D65 Simulators for Illuminant D
65
(Figure 5 and Table 5) follow the same general trends as forD50 and the mixture with wider spectral bands (S
8) and
the mixture with 4 bands (S9) gave higher 119877
119886values and
lower LER values than the 25 nm 3-band mixture The colorrendering in terms of CIE CRI is highly satisfactory 119877
119886ge 87
and the strong blue sample again exhibits the poorest colorrendering (119877
12(S7) = 119877min = 38) The chromaticities of thesimulations are very near to the chromaticity of IlluminantD65 Δ(1199061015840V1015840) lt 0006 in all experiments The LER of the
spectra is ge299 lmrad-W (versus the LER of real IlluminantD65at 204 lmrad-W)Optimized spectrum S
7introduces larger color errors
(Δ11986400av = 224) than any other in this paper In particular the
blue sample has both hue and chroma differences greater than16 units (Table 5(a)) This aspect was somewhat unexpectedand is thought to be due to the spectral discrepanciesbetween the simulated spectra and real D
65 particularly at
the wavelength extremities Further evidence is given by thefact that strong red (Sample 9) gives the next-worst 119877
119894in
Table 5(a)
33 Comparison of Peak Wavelengths It is instructive tocompare our optimized Gaussian peak wavelengths withthe peak wavelengths of the set of real LEDs all of whichare collated in Table 6 The real LEDs are labeled as ldquoBluerdquo
Advances in OptoElectronics 7
0
02
04
06
08
1
380 480 580 680 780
470 548 614
0
02
04
06
08
1
380 480 580 680 780
471 548 621
0
02
04
06
08
1
380 480 580 680 780
468 643589533
120582 (nm) 120582 (nm)
120582 (nm)
Figure 3 Optimized relative spectral power distributions (S1 S2 S3) for Illuminant A
In most of the spectra the blue Gaussian band wasbetween about 470 nm and 460 nm Exceptions are S
6and S9
the 4-band D50
and D65
simulators in which the optimizermoved the blue and green bands to lower wavelengths toaccommodate the amber bandThe green peaks in the 3-bandmixtures were optimized toward the peak of the 119881
120582curve
(120582 = 555 nm) thus producing the spectra with improved LERvalues as compared with the corresponding optimized LEDmixtures
It was consistently observed that the optimized wave-lengths for the red band were between about 610 nm to620 nm However the 4-band Illuminant A simulator S
3 has
the red band at 120582119877(S3) = 643 nm We ascribe that to the fact
that the amber band was optimized to 120582119860(S3) = 589 nm as
compared with 120582119860(S6) = 555 nm and 120582
119860(S9) = 558 nm for theD simulators The result was the noticeable improvement inthe rendering of test Sample 9 with source S
3
8 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
468 611542
0
02
04
06
08
1
380 480 580 680 780
470 619544
0
02
04
06
08
1
380 480 580 680 780
451 614555502
120582 (nm) 120582 (nm)
120582 (nm)
Figure 4 Optimized relative spectral power distributions (S4 S5 S6) for Illuminant D50
It was noteworthy in nearly all our results that the strongred (Sample 9) and strong blue (Sample 12) were badlyaffected by the truncation of the extrema of the synthesizedspectra
4 Conclusions
We have demonstrated that it is possible to simulate the CIEstandard illuminants A D
50 and D
65by mixing multiband
LED and Gaussian spectra The overall performance of theGaussian-based mixtures was better than the LED-basedcounterparts due to the freedom to select the most suitablepositions in the spectrum for the peak wavelengths in theGaussian mixtures
The simulation results show that 3-band Gaussian Illumi-nant A simulators could have CRI above 84 and LER double
that of Illuminant A Well designed 3-band Gaussian D50
and D65
simulators may have both CRI ge 85 and LER ge315 lmrad-W 4-band simulators improve color rendering bydistributing the bands in the visible spectrum
Our optimization techniques as described do not needto be constrained by the choice of test color samples colordifference formulae target spectrum or choice of standardobserver This is demonstrated in this paper where wehave shown how our previously published algorithm can bemodified to apply new color difference techniques to newobjectives in this case the achievement of specific sourceCCT targets
It should be noted that the spectra presented here areresults of simulations and further work is required toinvestigate the practical implementation of those spectra andto evaluate them in ldquoreal liferdquo situations
Advances in OptoElectronics 9
0
02
04
06
08
1
380 480 580 680 780
464 609539
0
02
04
06
08
1
380 480 580 680 780
460 538 615
0
02
04
06
08
1
380 480 580 680 780
449 498 618558
120582 (nm) 120582 (nm)
120582 (nm)
Figure 5 Optimized relative spectral power distributions (S7 S8 S9) for Illuminant D65
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors wish to acknowledge the support provided forthis work by the Technology Development Centre of theManukau Institute of Technology
References
[1] T Erdem S Nizamoglu X W Sun and H V Demir ldquoAphotometric investigation of ultra-efficient LEDs with highcolor rendering index and high luminous efficacy employingnanocrystal quantumdot luminophoresrdquoOptics Express vol 18no 1 pp 340ndash347 2010
[2] G He L Zheng and H Yan ldquoLED white lights with high CRIand high luminous efficacyrdquo in LED and Display Technologiesvol 7852 of Proceedings of SPIE 2010
[3] Y Ohno ldquoSpectral design considerations for white LED colorrenderingrdquoOptical Engineering vol 44 no 11 Article ID 1113022005
[4] A Zukauskas R Vaicekauskas F Ivanauskas R Gaska and MS Shur ldquoOptimization of white polychromatic semiconductorlampsrdquoApplied Physics Letters vol 80 no 2 pp 234ndash236 2002
[5] E Taylor P R Edwards and R W Martin ldquoColorimetry andefficiency of white LEDs spectral width dependencerdquo PhysicaStatus Solidi A Applications and Materials Science vol 209 no3 pp 461ndash464 2012
[6] R S Berns ldquoDesigning white-light LED lighting for the displayof art a feasibility studyrdquo Color Research and Application vol36 no 5 pp 324ndash334 2011
[7] S Soltic and A N Chalmers ldquoDifferential evolution for theoptimisation of multi-band white LED light sourcesrdquo LightingResearch amp Technology vol 44 no 2 pp 224ndash237 2012
10 Advances in OptoElectronics
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006
Figure 2 Optimized 4-LED relative spectral power distributions
in lightness Table 4 reveals considerable improvements inmatching Illuminant D
50by widening the individual bands
or by introducing the 4th band The Δ(1199061015840V1015840) value of 00050for S5is considered just-noticeable and Δ(1199061015840V1015840) = 00019 for
S6is below the noticeable threshold
323 Illuminant D65 Simulators for Illuminant D
65
(Figure 5 and Table 5) follow the same general trends as forD50 and the mixture with wider spectral bands (S
8) and
the mixture with 4 bands (S9) gave higher 119877
119886values and
lower LER values than the 25 nm 3-band mixture The colorrendering in terms of CIE CRI is highly satisfactory 119877
119886ge 87
and the strong blue sample again exhibits the poorest colorrendering (119877
12(S7) = 119877min = 38) The chromaticities of thesimulations are very near to the chromaticity of IlluminantD65 Δ(1199061015840V1015840) lt 0006 in all experiments The LER of the
spectra is ge299 lmrad-W (versus the LER of real IlluminantD65at 204 lmrad-W)Optimized spectrum S
7introduces larger color errors
(Δ11986400av = 224) than any other in this paper In particular the
blue sample has both hue and chroma differences greater than16 units (Table 5(a)) This aspect was somewhat unexpectedand is thought to be due to the spectral discrepanciesbetween the simulated spectra and real D
65 particularly at
the wavelength extremities Further evidence is given by thefact that strong red (Sample 9) gives the next-worst 119877
119894in
Table 5(a)
33 Comparison of Peak Wavelengths It is instructive tocompare our optimized Gaussian peak wavelengths withthe peak wavelengths of the set of real LEDs all of whichare collated in Table 6 The real LEDs are labeled as ldquoBluerdquo
Advances in OptoElectronics 7
0
02
04
06
08
1
380 480 580 680 780
470 548 614
0
02
04
06
08
1
380 480 580 680 780
471 548 621
0
02
04
06
08
1
380 480 580 680 780
468 643589533
120582 (nm) 120582 (nm)
120582 (nm)
Figure 3 Optimized relative spectral power distributions (S1 S2 S3) for Illuminant A
In most of the spectra the blue Gaussian band wasbetween about 470 nm and 460 nm Exceptions are S
6and S9
the 4-band D50
and D65
simulators in which the optimizermoved the blue and green bands to lower wavelengths toaccommodate the amber bandThe green peaks in the 3-bandmixtures were optimized toward the peak of the 119881
120582curve
(120582 = 555 nm) thus producing the spectra with improved LERvalues as compared with the corresponding optimized LEDmixtures
It was consistently observed that the optimized wave-lengths for the red band were between about 610 nm to620 nm However the 4-band Illuminant A simulator S
3 has
the red band at 120582119877(S3) = 643 nm We ascribe that to the fact
that the amber band was optimized to 120582119860(S3) = 589 nm as
compared with 120582119860(S6) = 555 nm and 120582
119860(S9) = 558 nm for theD simulators The result was the noticeable improvement inthe rendering of test Sample 9 with source S
3
8 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
468 611542
0
02
04
06
08
1
380 480 580 680 780
470 619544
0
02
04
06
08
1
380 480 580 680 780
451 614555502
120582 (nm) 120582 (nm)
120582 (nm)
Figure 4 Optimized relative spectral power distributions (S4 S5 S6) for Illuminant D50
It was noteworthy in nearly all our results that the strongred (Sample 9) and strong blue (Sample 12) were badlyaffected by the truncation of the extrema of the synthesizedspectra
4 Conclusions
We have demonstrated that it is possible to simulate the CIEstandard illuminants A D
50 and D
65by mixing multiband
LED and Gaussian spectra The overall performance of theGaussian-based mixtures was better than the LED-basedcounterparts due to the freedom to select the most suitablepositions in the spectrum for the peak wavelengths in theGaussian mixtures
The simulation results show that 3-band Gaussian Illumi-nant A simulators could have CRI above 84 and LER double
that of Illuminant A Well designed 3-band Gaussian D50
and D65
simulators may have both CRI ge 85 and LER ge315 lmrad-W 4-band simulators improve color rendering bydistributing the bands in the visible spectrum
Our optimization techniques as described do not needto be constrained by the choice of test color samples colordifference formulae target spectrum or choice of standardobserver This is demonstrated in this paper where wehave shown how our previously published algorithm can bemodified to apply new color difference techniques to newobjectives in this case the achievement of specific sourceCCT targets
It should be noted that the spectra presented here areresults of simulations and further work is required toinvestigate the practical implementation of those spectra andto evaluate them in ldquoreal liferdquo situations
Advances in OptoElectronics 9
0
02
04
06
08
1
380 480 580 680 780
464 609539
0
02
04
06
08
1
380 480 580 680 780
460 538 615
0
02
04
06
08
1
380 480 580 680 780
449 498 618558
120582 (nm) 120582 (nm)
120582 (nm)
Figure 5 Optimized relative spectral power distributions (S7 S8 S9) for Illuminant D65
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors wish to acknowledge the support provided forthis work by the Technology Development Centre of theManukau Institute of Technology
References
[1] T Erdem S Nizamoglu X W Sun and H V Demir ldquoAphotometric investigation of ultra-efficient LEDs with highcolor rendering index and high luminous efficacy employingnanocrystal quantumdot luminophoresrdquoOptics Express vol 18no 1 pp 340ndash347 2010
[2] G He L Zheng and H Yan ldquoLED white lights with high CRIand high luminous efficacyrdquo in LED and Display Technologiesvol 7852 of Proceedings of SPIE 2010
[3] Y Ohno ldquoSpectral design considerations for white LED colorrenderingrdquoOptical Engineering vol 44 no 11 Article ID 1113022005
[4] A Zukauskas R Vaicekauskas F Ivanauskas R Gaska and MS Shur ldquoOptimization of white polychromatic semiconductorlampsrdquoApplied Physics Letters vol 80 no 2 pp 234ndash236 2002
[5] E Taylor P R Edwards and R W Martin ldquoColorimetry andefficiency of white LEDs spectral width dependencerdquo PhysicaStatus Solidi A Applications and Materials Science vol 209 no3 pp 461ndash464 2012
[6] R S Berns ldquoDesigning white-light LED lighting for the displayof art a feasibility studyrdquo Color Research and Application vol36 no 5 pp 324ndash334 2011
[7] S Soltic and A N Chalmers ldquoDifferential evolution for theoptimisation of multi-band white LED light sourcesrdquo LightingResearch amp Technology vol 44 no 2 pp 224ndash237 2012
10 Advances in OptoElectronics
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006
In most of the spectra the blue Gaussian band wasbetween about 470 nm and 460 nm Exceptions are S
6and S9
the 4-band D50
and D65
simulators in which the optimizermoved the blue and green bands to lower wavelengths toaccommodate the amber bandThe green peaks in the 3-bandmixtures were optimized toward the peak of the 119881
120582curve
(120582 = 555 nm) thus producing the spectra with improved LERvalues as compared with the corresponding optimized LEDmixtures
It was consistently observed that the optimized wave-lengths for the red band were between about 610 nm to620 nm However the 4-band Illuminant A simulator S
3 has
the red band at 120582119877(S3) = 643 nm We ascribe that to the fact
that the amber band was optimized to 120582119860(S3) = 589 nm as
compared with 120582119860(S6) = 555 nm and 120582
119860(S9) = 558 nm for theD simulators The result was the noticeable improvement inthe rendering of test Sample 9 with source S
3
8 Advances in OptoElectronics
0
02
04
06
08
1
380 480 580 680 780
468 611542
0
02
04
06
08
1
380 480 580 680 780
470 619544
0
02
04
06
08
1
380 480 580 680 780
451 614555502
120582 (nm) 120582 (nm)
120582 (nm)
Figure 4 Optimized relative spectral power distributions (S4 S5 S6) for Illuminant D50
It was noteworthy in nearly all our results that the strongred (Sample 9) and strong blue (Sample 12) were badlyaffected by the truncation of the extrema of the synthesizedspectra
4 Conclusions
We have demonstrated that it is possible to simulate the CIEstandard illuminants A D
50 and D
65by mixing multiband
LED and Gaussian spectra The overall performance of theGaussian-based mixtures was better than the LED-basedcounterparts due to the freedom to select the most suitablepositions in the spectrum for the peak wavelengths in theGaussian mixtures
The simulation results show that 3-band Gaussian Illumi-nant A simulators could have CRI above 84 and LER double
that of Illuminant A Well designed 3-band Gaussian D50
and D65
simulators may have both CRI ge 85 and LER ge315 lmrad-W 4-band simulators improve color rendering bydistributing the bands in the visible spectrum
Our optimization techniques as described do not needto be constrained by the choice of test color samples colordifference formulae target spectrum or choice of standardobserver This is demonstrated in this paper where wehave shown how our previously published algorithm can bemodified to apply new color difference techniques to newobjectives in this case the achievement of specific sourceCCT targets
It should be noted that the spectra presented here areresults of simulations and further work is required toinvestigate the practical implementation of those spectra andto evaluate them in ldquoreal liferdquo situations
Advances in OptoElectronics 9
0
02
04
06
08
1
380 480 580 680 780
464 609539
0
02
04
06
08
1
380 480 580 680 780
460 538 615
0
02
04
06
08
1
380 480 580 680 780
449 498 618558
120582 (nm) 120582 (nm)
120582 (nm)
Figure 5 Optimized relative spectral power distributions (S7 S8 S9) for Illuminant D65
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors wish to acknowledge the support provided forthis work by the Technology Development Centre of theManukau Institute of Technology
References
[1] T Erdem S Nizamoglu X W Sun and H V Demir ldquoAphotometric investigation of ultra-efficient LEDs with highcolor rendering index and high luminous efficacy employingnanocrystal quantumdot luminophoresrdquoOptics Express vol 18no 1 pp 340ndash347 2010
[2] G He L Zheng and H Yan ldquoLED white lights with high CRIand high luminous efficacyrdquo in LED and Display Technologiesvol 7852 of Proceedings of SPIE 2010
[3] Y Ohno ldquoSpectral design considerations for white LED colorrenderingrdquoOptical Engineering vol 44 no 11 Article ID 1113022005
[4] A Zukauskas R Vaicekauskas F Ivanauskas R Gaska and MS Shur ldquoOptimization of white polychromatic semiconductorlampsrdquoApplied Physics Letters vol 80 no 2 pp 234ndash236 2002
[5] E Taylor P R Edwards and R W Martin ldquoColorimetry andefficiency of white LEDs spectral width dependencerdquo PhysicaStatus Solidi A Applications and Materials Science vol 209 no3 pp 461ndash464 2012
[6] R S Berns ldquoDesigning white-light LED lighting for the displayof art a feasibility studyrdquo Color Research and Application vol36 no 5 pp 324ndash334 2011
[7] S Soltic and A N Chalmers ldquoDifferential evolution for theoptimisation of multi-band white LED light sourcesrdquo LightingResearch amp Technology vol 44 no 2 pp 224ndash237 2012
10 Advances in OptoElectronics
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006
Figure 4 Optimized relative spectral power distributions (S4 S5 S6) for Illuminant D50
It was noteworthy in nearly all our results that the strongred (Sample 9) and strong blue (Sample 12) were badlyaffected by the truncation of the extrema of the synthesizedspectra
4 Conclusions
We have demonstrated that it is possible to simulate the CIEstandard illuminants A D
50 and D
65by mixing multiband
LED and Gaussian spectra The overall performance of theGaussian-based mixtures was better than the LED-basedcounterparts due to the freedom to select the most suitablepositions in the spectrum for the peak wavelengths in theGaussian mixtures
The simulation results show that 3-band Gaussian Illumi-nant A simulators could have CRI above 84 and LER double
that of Illuminant A Well designed 3-band Gaussian D50
and D65
simulators may have both CRI ge 85 and LER ge315 lmrad-W 4-band simulators improve color rendering bydistributing the bands in the visible spectrum
Our optimization techniques as described do not needto be constrained by the choice of test color samples colordifference formulae target spectrum or choice of standardobserver This is demonstrated in this paper where wehave shown how our previously published algorithm can bemodified to apply new color difference techniques to newobjectives in this case the achievement of specific sourceCCT targets
It should be noted that the spectra presented here areresults of simulations and further work is required toinvestigate the practical implementation of those spectra andto evaluate them in ldquoreal liferdquo situations
Advances in OptoElectronics 9
0
02
04
06
08
1
380 480 580 680 780
464 609539
0
02
04
06
08
1
380 480 580 680 780
460 538 615
0
02
04
06
08
1
380 480 580 680 780
449 498 618558
120582 (nm) 120582 (nm)
120582 (nm)
Figure 5 Optimized relative spectral power distributions (S7 S8 S9) for Illuminant D65
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors wish to acknowledge the support provided forthis work by the Technology Development Centre of theManukau Institute of Technology
References
[1] T Erdem S Nizamoglu X W Sun and H V Demir ldquoAphotometric investigation of ultra-efficient LEDs with highcolor rendering index and high luminous efficacy employingnanocrystal quantumdot luminophoresrdquoOptics Express vol 18no 1 pp 340ndash347 2010
[2] G He L Zheng and H Yan ldquoLED white lights with high CRIand high luminous efficacyrdquo in LED and Display Technologiesvol 7852 of Proceedings of SPIE 2010
[3] Y Ohno ldquoSpectral design considerations for white LED colorrenderingrdquoOptical Engineering vol 44 no 11 Article ID 1113022005
[4] A Zukauskas R Vaicekauskas F Ivanauskas R Gaska and MS Shur ldquoOptimization of white polychromatic semiconductorlampsrdquoApplied Physics Letters vol 80 no 2 pp 234ndash236 2002
[5] E Taylor P R Edwards and R W Martin ldquoColorimetry andefficiency of white LEDs spectral width dependencerdquo PhysicaStatus Solidi A Applications and Materials Science vol 209 no3 pp 461ndash464 2012
[6] R S Berns ldquoDesigning white-light LED lighting for the displayof art a feasibility studyrdquo Color Research and Application vol36 no 5 pp 324ndash334 2011
[7] S Soltic and A N Chalmers ldquoDifferential evolution for theoptimisation of multi-band white LED light sourcesrdquo LightingResearch amp Technology vol 44 no 2 pp 224ndash237 2012
10 Advances in OptoElectronics
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006
Figure 5 Optimized relative spectral power distributions (S7 S8 S9) for Illuminant D65
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors wish to acknowledge the support provided forthis work by the Technology Development Centre of theManukau Institute of Technology
References
[1] T Erdem S Nizamoglu X W Sun and H V Demir ldquoAphotometric investigation of ultra-efficient LEDs with highcolor rendering index and high luminous efficacy employingnanocrystal quantumdot luminophoresrdquoOptics Express vol 18no 1 pp 340ndash347 2010
[2] G He L Zheng and H Yan ldquoLED white lights with high CRIand high luminous efficacyrdquo in LED and Display Technologiesvol 7852 of Proceedings of SPIE 2010
[3] Y Ohno ldquoSpectral design considerations for white LED colorrenderingrdquoOptical Engineering vol 44 no 11 Article ID 1113022005
[4] A Zukauskas R Vaicekauskas F Ivanauskas R Gaska and MS Shur ldquoOptimization of white polychromatic semiconductorlampsrdquoApplied Physics Letters vol 80 no 2 pp 234ndash236 2002
[5] E Taylor P R Edwards and R W Martin ldquoColorimetry andefficiency of white LEDs spectral width dependencerdquo PhysicaStatus Solidi A Applications and Materials Science vol 209 no3 pp 461ndash464 2012
[6] R S Berns ldquoDesigning white-light LED lighting for the displayof art a feasibility studyrdquo Color Research and Application vol36 no 5 pp 324ndash334 2011
[7] S Soltic and A N Chalmers ldquoDifferential evolution for theoptimisation of multi-band white LED light sourcesrdquo LightingResearch amp Technology vol 44 no 2 pp 224ndash237 2012
10 Advances in OptoElectronics
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006
[8] A Chalmers and S Soltic ldquoTowards the optimum light sourcespectrumrdquo Advances in OptoElectronics vol 2010 Article ID596825 9 pages 2010
[9] Commission Internationale de lrsquoEclairage ldquoMethod of measur-ing and specifying color rendering properties of light sourcesrdquoTech Rep 133 CIE Vienna Austria 1995
[10] A Chalmers and S Soltic ldquoLight source optimization spectraldesign and simulation of four-bandwhite-light sourcesrdquoOpticalEngineering vol 51 no 4 Article ID 044003 2012
[11] D Sekulovski Private Communication Philips Lighting 2012[12] Commission Internationale de lrsquoEclairage ldquoImprovement to
industrial colour-difference evaluationrdquo CIE Publication 142CIE Vienna Austria 2001
[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997
[14] Commission Internationale de lrsquoEclairage ldquoColorimetryrdquo TechRep 15 CIE Vienna Austria 2004
[15] Lumileds Lighting ldquoLuxeon K2 Emitterrdquo Technical DatasheetDS51 Lumileds Lighting San Jose Calif USA 2006