Research Article Optimization of Multiband White-Light...

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

Advances in OptoElectronics 3

Table 2 Results 4-LED optimization

(a) Illuminant A 119877119886 = 93 119877min = 11987711 = 68 LER = 313 lmrad-WΔ(1199061015840V1015840) = 00038

Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887

lowastΔ119871lowast119877119894

1 058 055 minus062 023 952 018 043 003 004 953 065 001 minus010 minus076 964 087 200 014 004 875 047 089 016 005 906 084 059 097 038 857 040 minus015 046 minus006 948 017 minus034 minus004 minus008 999 041 minus055 minus070 minus008 9910 048 minus002 067 minus037 8611 245 561 201 058 6812 168 444 minus395 070 8113 031 054 020 017 9114 070 minus073 minus047 minus056 97Avg 073 mdash mdash mdash 90

(b) Illuminant D50 119877119886 = 95 119877min = 11987712 = 70 LER = 311 lmrad-WΔ(1199061015840V1015840) = 00010

Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 056 075 minus053 017 942 018 026 014 008 973 061 055 minus075 minus042 954 056 110 minus060 010 935 050 061 minus055 004 956 046 058 028 024 957 047 minus079 044 minus012 958 038 minus077 minus020 minus016 969 044 minus052 minus07 minus022 9610 013 minus023 014 minus012 9711 167 453 090 057 7912 393 701 minus878 017 7013 070 055 073 012 9214 070 minus018 minus087 minus030 95Avg 081 mdash mdash mdash 92

(c) Illuminant D65 119877119886 = 95 119877min = 11987712 = 63 LER = 298 lmrad-WΔ(1199061015840V1015840) = 00015

Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887



Table 3 Results for Illuminant A simulations

(a) S1 119877119886 = 84 119877min = 11987712 = 24 LER = 416 lmrad-W Δ(1199061015840V1015840) = 00134

Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 164 213 149 minus045 932 083 020 095 minus026 943 349 665 minus348 203 494 075 007 minus079 062 965 099 105 minus127 017 876 079 182 minus063 minus055 787 076 minus151 004 minus030 968 110 minus196 minus015 minus072 809 171 minus290 minus224 minus101 2610 209 142 minus325 088 4611 194 minus248 256 044 7312 518 119 minus127 minus264 2413 274 027 326 minus092 9314 342 442 minus311 148 64Avg 196 mdash mdash mdash 71

(b) S2 119877119886 = 94 119877min = 1198779 = 70 LER = 357 lmrad-W Δ(1199061015840V1015840) = 00054

Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 066 092 054 minus017 972 038 002 045 minus008 983 128 212 minus145 063 814 039 018 minus049 025 995 041 059 minus043 007 966 050 096 021 minus020 957 041 minus076 024 minus014 988 048 minus092 minus015 minus025 919 069 minus107 minus105 minus032 7010 065 019 minus101 028 8011 059 minus007 087 022 9412 210 538 minus497 minus093 7113 111 006 133 minus032 9714 141 141 minus144 045 85Avg 079 mdash mdash mdash 89

(c) S3 119877119886 = 96 119877min = 11987712 = 68 LER = 318 lmrad-W Δ(1199061015840V1015840) = 00034

Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 059 052 minus068 minus000 962 022 045 008 011 983 066 137 minus072 minus013 904 071 minus013 minus107 020 985 093 078 minus127 009 966 039 080 015 012 977 057 minus097 minus000 minus039 978 069 minus005 minus095 minus045 979 085 113 042 minus079 9710 022 minus019 minus034 010 9011 148 261 158 044 8912 290 815 minus740 minus036 6813 039 035 042 010 9914 081 012 minus101 minus008 92Avg 082 mdash mdash mdash 93


Table 4 Results for Illuminant D50 simulations


Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 213 327 156 minus035 902 163 minus024 190 minus025 963 304 592 minus324 185 584 113 minus087 minus161 058 905 123 130 minus147 015 876 093 150 047 minus029 857 114 minus252 036 minus024 908 118 minus235 minus043 minus058 829 155 minus189 minus265 minus041 3610 133 071 minus194 091 5711 145 minus203 191 065 7612 548 136 minus130 minus188 3013 382 103 440 minus087 8814 309 414 minus303 137 70Avg 208 mdash mdash mdash 74


Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 081 112 058 minus027 942 084 minus063 091 minus023 973 085 117 minus111 044 914 097 minus106 minus145 022 925 062 051 minus076 018 956 046 033 047 011 987 080 minus177 minus015 005 928 073 minus096 minus099 minus007 939 050 082 minus087 minus004 9410 024 minus100 minus009 001 9411 042 minus103 minus011 023 9112 241 508 minus568 009 7513 165 minus011 188 minus045 9314 097 091 minus110 035 92Avg 088 mdash mdash mdash 92


Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 055 068 048 minus009 942 051 minus061 044 minus026 973 057 083 minus054 045 954 036 089 014 005 975 036 030 040 005 986 032 059 013 minus006 967 029 minus035 022 022 978 081 minus149 073 006 889 133 minus356 minus185 007 6410 013 minus032 007 minus014 9911 010 minus015 015 minus000 9812 143 215 minus312 011 8913 092 minus043 100 minus040 9614 050 065 minus040 028 97Avg 058 mdash mdash mdash 93



Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 186 294 107 minus015 832 084 minus002 097 minus017 993 322 671 minus396 149 584 067 034 minus094 045 965 116 064 minus151 006 926 051 153 minus081 minus017 907 073 minus168 024 minus016 948 112 minus237 021 minus045 859 245 minus415 minus396 minus002 4210 209 182 minus335 083 6611 158 031 257 075 8612 851 167 minus165 minus156 3813 343 079 376 minus068 8314 322 450 minus346 111 71Avg 224 mdash mdash mdash 77


Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 100 117 083 minus025 962 017 001 017 minus009 963 146 291 minus177 067 814 053 109 009 039 975 022 029 minus010 015 976 026 069 minus045 minus004 937 011 003 minus006 minus012 998 019 007 007 minus022 979 022 minus017 minus037 minus010 8110 098 085 minus159 030 8011 111 137 154 059 9212 402 617 minus77 minus068 6913 155 003 167 minus041 9614 146 195 minus154 050 87Avg 095 mdash mdash mdash 90


Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887


1 026 013 minus031 007 932 052 minus071 044 minus022 923 028 minus038 033 020 954 067 minus134 minus047 minus039 955 037 001 minus043 minus019 946 029 074 minus030 minus020 927 063 minus089 minus035 047 958 087 minus085 minus095 065 919 217 050 minus296 162 7510 048 minus061 075 minus012 8411 159 minus345 minus110 minus088 8812 067 201 minus159 026 8813 034 minus066 004 minus015 9514 025 minus017 030 010 97Avg 067 mdash mdash mdash 91


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

119886119887(12)S4 = 1357 Δ119867119886119887lowast

(12)S4 =minus1296)

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


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


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

Table 6 Comparison of optimized peak wavelengths

Spectrum Real LEDs 460 nm 525 nm 590 nm 640 nmDescription ldquoBluerdquo ldquoGreenrdquo ldquoAmberrdquo ldquoRedrdquo

S1 A 25-nm 3-band 470 548 mdash 614S2 A 50-nm 3-band 471 548 mdash 621S3 A 25-nm 4-band 468 533 589 643S4 D50 25-nm 3-band 468 542 mdash 611S5 D50 50-nm 3-band 470 544 mdash 619S6 D50 25-nm 4-band 451 502 555 614S7 D65 25-nm 3-band 464 539 mdash 609S8 D65 50-nm 3-band 460 538 mdash 615S9 D65 25-nm 4-band 449 498 558 618

(120582119861= 460 nm) ldquoGreenrdquo (120582

119866= 525 nm) ldquoAmberrdquo (120582

119860=

590 nm) and ldquoRedrdquo (120582119877= 640 nm)

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


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


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)


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


[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

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



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




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887





Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887






Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887





Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887







119878119894 (120582) = 119868119894119890

minus(120582minus120582119894)221205752

120575 =Δ119894

2radic2 ln 2

(1)

where 119868119894120582119894 andΔ



119878V119895 =

119899

sum

1119878119894(120582) (2)



3 Results


50 and D

65







119886119887

lowast

andΔ119867119886119887


119886119887

lowast


119886119887

lowast





lowast

(12)D50 = 701Δ119867119886119887

lowast

(12)D50 = minus878 and Δ119862119886119887

lowast

(12)D65 = 955Δ119867119886119887

lowast

(12)D65 = minus1021)





1 S2 and S

3 where S

1represents




2and S3



3) However a


1) exhibits very



2and S




2and S3






50are


S5 and S

6 where S



6represents


50


4


119886119887(12)S4 = 1357 Δ119867119886119887lowast

(12)S4 =minus1296)


5and S



119886119887

lowast and Δ119867119886119887




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







65


8) and


119886values and


119886ge 87







65 particularly at


119894in

Table 5(a)



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)







119860=



6and S9

the 4-band D50

and D65


120582curve



3 has





3


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)



4 Conclusions


50 and D





and D65





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)




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887





Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887






Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887





Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887







119878119894 (120582) = 119868119894119890

minus(120582minus120582119894)221205752

120575 =Δ119894

2radic2 ln 2

(1)

where 119868119894120582119894 andΔ



119878V119895 =

119899

sum

1119878119894(120582) (2)



3 Results


50 and D

65







119886119887

lowast

andΔ119867119886119887


119886119887

lowast


119886119887

lowast





lowast

(12)D50 = 701Δ119867119886119887

lowast

(12)D50 = minus878 and Δ119862119886119887

lowast

(12)D65 = 955Δ119867119886119887

lowast

(12)D65 = minus1021)





1 S2 and S

3 where S

1represents




2and S3



3) However a


1) exhibits very



2and S




2and S3






50are


S5 and S

6 where S



6represents


50


4


119886119887(12)S4 = 1357 Δ119867119886119887lowast

(12)S4 =minus1296)


5and S



119886119887

lowast and Δ119867119886119887




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







65


8) and


119886values and


119886ge 87







65 particularly at


119894in

Table 5(a)



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)







119860=



6and S9

the 4-band D50

and D65


120582curve



3 has





3


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)



4 Conclusions


50 and D





and D65





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)




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887





Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887




Sample number Δ11986400Δ119862119886119887

lowastΔ119867119886119887







119878119894 (120582) = 119868119894119890

minus(120582minus120582119894)221205752

120575 =Δ119894

2radic2 ln 2

(1)

where 119868119894120582119894 andΔ



119878V119895 =

119899

sum

1119878119894(120582) (2)



3 Results


50 and D

65







119886119887

lowast

andΔ119867119886119887


119886119887

lowast


119886119887

lowast





lowast

(12)D50 = 701Δ119867119886119887

lowast

(12)D50 = minus878 and Δ119862119886119887

lowast

(12)D65 = 955Δ119867119886119887

lowast

(12)D65 = minus1021)





1 S2 and S

3 where S

1represents




2and S3



3) However a


1) exhibits very



2and S




2and S3






50are


S5 and S

6 where S



6represents


50


4


119886119887(12)S4 = 1357 Δ119867119886119887lowast

(12)S4 =minus1296)


5and S



119886119887

lowast and Δ119867119886119887




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







65


8) and


119886values and


119886ge 87







65 particularly at


119894in

Table 5(a)



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)







119860=



6and S9

the 4-band D50

and D65


120582curve



3 has





3


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)



4 Conclusions


50 and D





and D65





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)




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119878119894 (120582) = 119868119894119890

minus(120582minus120582119894)221205752

120575 =Δ119894

2radic2 ln 2

(1)

where 119868119894120582119894 andΔ



119878V119895 =

119899

sum

1119878119894(120582) (2)



3 Results


50 and D

65







119886119887

lowast

andΔ119867119886119887


119886119887

lowast


119886119887

lowast





lowast

(12)D50 = 701Δ119867119886119887

lowast

(12)D50 = minus878 and Δ119862119886119887

lowast

(12)D65 = 955Δ119867119886119887

lowast

(12)D65 = minus1021)





1 S2 and S

3 where S

1represents




2and S3



3) However a


1) exhibits very



2and S




2and S3






50are


S5 and S

6 where S



6represents


50


4


119886119887(12)S4 = 1357 Δ119867119886119887lowast

(12)S4 =minus1296)


5and S



119886119887

lowast and Δ119867119886119887




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







65


8) and


119886values and


119886ge 87







65 particularly at


119894in

Table 5(a)



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)







119860=



6and S9

the 4-band D50

and D65


120582curve



3 has





3


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)



4 Conclusions


50 and D





and D65





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)




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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







65


8) and


119886values and


119886ge 87







65 particularly at


119894in

Table 5(a)



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)







119860=



6and S9

the 4-band D50

and D65


120582curve



3 has





3


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)



4 Conclusions


50 and D





and D65





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)




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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)







119860=



6and S9

the 4-band D50

and D65


120582curve



3 has





3


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)



4 Conclusions


50 and D





and D65





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)




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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)



4 Conclusions


50 and D





and D65





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)




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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)




Acknowledgment


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Optimization of Multiband White-Light...

Documents

Transcript of Research Article Optimization of Multiband White-Light...