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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 3 — Apr. 4, 2013
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Wavelength dependence of colorimetric properties of lighting sources based on multi-color LEDs

Hongtao Li, Xianglong Mao, Yanjun Han, and Yi Luo  »View Author Affiliations


Optics Express, Vol. 21, Issue 3, pp. 3775-3783 (2013)
http://dx.doi.org/10.1364/OE.21.003775


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Abstract

Taking color quality scale (CQS) as color rendering assessment criterion, the parameters including each color LED’s peak wavelength λi and fractional radiant flux Ii are optimized using genetic algorithm to maximize the luminous efficacy of radiation (LER) of the spectral power distributions (SPDs) of multi-color white light source with 3 to 7 components while maintaining the deviation of its color and color-rendering capability from that of the reference light source within the specified scope. Then the wavelength dependence of these SPDs is analyzed. It is shown that to achieve a Qa greater than 95 (5-color LEDs) or even close to 100 (7-color LEDs), the spectral energy could be concentrated in the range of 410~675 nm, indicating that this wavelength range makes a major contribution to high color rendering properties. Spectra filtering experiments show that spectrum around 580nm is harmful to color rendering. To obtain a white light source composed of 3-color LEDs with CQS Qa ≥ 80 and correlated color temperature (CCT) within 2700-6500K, the energy ratios among 410-495nm, 495-595nm, and 595-675nm intervals, can be simplified as that of the reference source with the same CCT.

© 2013 OSA

1. Introduction

It is the aim of lighting technology to achieve a comfortable lighting environment with energy consumption as low as possible. In addition to the energy saving property which has been usually stressed when we talk about light sources, for general daylight illumination applications they should have high colorimetric performance, such as appropriate apparent color and good color-rendering capabilities [1

1. CIE, “Lighting of work places-Part 1: Indoor,” ISO 8995–1:2002(E)/CIE S 008/E:2001.

].

Solid state light source based on LEDs is on its way to large-scale applications in general lighting, and is believed to someday replace traditional lighting sources, such as incandescent lamps and fluorescent tubes. The current widely applied approach for commercial white light generation by LEDs is a combination of yellow phosphor with a blue LED. It has been successfully applied in outdoor lighting, such as street lighting, due to relative high efficiency compared with traditional lighting source. However, it is difficult to achieve high color rendering properties due to the lack of long-wavelength component in spectrum. As a result, it can’t be widely used in indoor daylight illumination applications, e.g. illumination in museums, homes, offices, and stores [2

2. E. F. Schubert, Light-emitting diodes (Cambridge University Press, 2003).

]. Therefore, the white light source by mixture of multi-color LEDs [2

2. E. F. Schubert, Light-emitting diodes (Cambridge University Press, 2003).

] has been widely studied. However, the relationship between colorimetric properties and the SPDs of multi-color white LED sources has not been systematically investigated.

In this paper, CQS is taken as the color rendering assessment criterion, and the SPD of white light source with multi-color LEDs is described as a function of the peak wavelength λi, full width at half maximum (FWHM) Δi and fractional radiant flux Ii of each color LED. These parameters are optimized using genetic algorithm to maximize LER of the SPD while keeping the deviation of its color and color-rendering capability from that of the reference light source within the specified scope. Then the wavelength dependence of these optimized SPDs is analyzed.

2. Physical model and mathematical procedure

White LED spectra studied here are composed of three or more narrow bands corresponding to the emission of multi-color LEDs. The emission line of the i-th color LED is approximated by Gaussian shapes with peak wavelength λi, full width at half maximum (FWHM) Δi and fractional radiant fluxes Ii. According to commercialized LED products, such as Phlips Lumileds Lighting Luxeon Rebel family, the values of c λi and Δi are
440nmλi680nm,i=1,2,,N
(1)
Δi={30nm,for520nmλi550nm20nm,forothers,i=1,2,,N
(2)
and
0Ii1,i=1,2,,N
(3)
respectively. The other constraint on Ii is that the sum of them is unit, that is
I1+I2++IN=1
(4)
With these parameters, SPD of solid state lighting source is then generated for visible wavelength range from 380 to 780 nm at 1 nm intervals

Then SPDs are optimized for the maximum luminous efficacy under given color and color rendering properties. The flowchart of establishing the optimization model is shown in Fig. 1
Fig. 1 The flowchart of establishing the optimization model.
. The objective function is the LER, defined as
LER=683lm/W×380780S(λ)V(λ)dλ380780S(λ)dλ
(5)
whereS(λ)is the SPD of light source andV(λ)is the spectra sensitivity function of human eye. The visible wavelength range from 380 to 780 nm with 1 nm intervals is used.

The CIE recommends black-body radiation or CIE daylight as reference source which is thought to have excellent colorimetric performance at a given CCT. The color and color rendering properties of white LED source is described by the deviation from that of the reference source. In this paper, we focus on establishing white LED sources that have the same color as a CIE reference source and proximate color rendering capability.

The constraint on the color of white LED source is specified by the deviation from that of the reference source, i.e. black-body radiation or CIE daylight for CCT below and above 5000K, respectively. The MacAdam ellipse [7

7. D. L. MacAdam, “Visual sensitivities to color differences in daylight,” J. Opt. Soc. Am. 32(5), 247–274 (1942). [CrossRef]

, 8

8. D. L. MacAdam, “Specification of small chromaticity differences,” J. Opt. Soc. Am. 33(1), 18–26 (1943). [CrossRef]

] centered at the chromaticity coordinates of the reference source is used to define this constraint, expressed as
DS=g11dx2+2g12dxdy+g22dy2M2
(6)
where dx and dy are the differences between the x and y coordinates of the white LED source and that of the reference source respectively, and g11, g12, g22 are coefficients of MacAdam ellipse centered at reference source coordinate (xr, yr), which can be obtained by interpolation of the original data of MacAdam’s 25 ellipses [7

7. D. L. MacAdam, “Visual sensitivities to color differences in daylight,” J. Opt. Soc. Am. 32(5), 247–274 (1942). [CrossRef]

, 8

8. D. L. MacAdam, “Specification of small chromaticity differences,” J. Opt. Soc. Am. 33(1), 18–26 (1943). [CrossRef]

]. M is the steps of MacAdam ellipse, and 7-step MacAdam ellipse is used here in accord with provisions of ANSI C78.377 [9

9. American National Standard, “Specifications for the Chromaticity of Solid state lighting Products (ANSI_NEMA_ANSLG C78.377–2008),” NEMA, 2008.

], while 4-step or other step MacAdam ellipse could also be used [10

10. Lighting Research Center, Rensselaer Polytechnic Institute, “Developing Color Tolerance Criteria for White LEDs,” http://www.lrc.rpi.edu/programs/solidstate/assist/pdf/ColorDiscriminationStudy.pdf.

]. In this paper, the solid state lighting source with CCT of #### K means that the chromaticity coordinates of this source stay within the 7-step MacAdam ellipse centered at coordinates of the reference source with CCT of #### K.

The constraint on color rendering properties of the solid state lighting source is specified by CQS [5

5. W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602 (2010). [CrossRef]

], recently introduced for rating color rendering properties of solid-state lamps, expressed as
Qa(SPD)Qc
(7)
where Qa is the general CQS [5

5. W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602 (2010). [CrossRef]

], and Qc is a given CQS value.

3. Results and discussion

3.1 Optimized SPDs for white LED source with different number of color LEDs

Firstly, the maximum Qa that white LED source can achieve for different CCTs using different number of color LEDs, is investigated. This is obtained by maximizing Qa(λi, Δi, Ii, i = 1,2,…,N) under constraints of Eq. (6) and Eqs. (1)(4). The results show that for CCT of 2700~6500K the maximum Qa of white LED source with 3, 4, 5, and 7 colors are in the range of 80~85, 90~95, 95~100, and approximate 100, respectively.

Given Qc as 80, 90, 95, 95 for 3, 4, 5 and 7 colors white LED source in Eq. (7) and CCT as 3500, 5000 and 6500K, the optimized white LED spectra are obtained, as shown in Fig. 2
Fig. 2 Optimized spectra of 3-, 4-, 5- and 7- colors white LED source with near maximum Qa for CCT of 3500K, 5000K, and 6500K.
. The LER of these SPDs are also shown in Fig. 2.

3.2 SPDs variation with different number of color LEDs

As the number of colors increases, the spectrum gradually extends to the short-wavelength and long-wavelength at the same time. As a result, the spectrum occupies a larger wavelength range, and meanwhile the power distribution becomes more uniform in the entire wavelength range. To achieve a Qa greater than 95 (5-color LEDs) or even close to 100 (7-color LEDs), the spectral energy can be concentrated in the range of 410-675 nm. This indicates that, if Qa is taken as the color rendering metric, spectrum in wavelength range of 410~675nm makes a major contribution to high color rendering properties while the role of spectrum in the short-wavelength (<410 nm) and the long-wavelength (> 675nm) range is less important. This is different from Walter’s observation that emission lower than 440nm or higher than 620nm is wasted [15

15. W. Walter, “Optimum lamp spectra,” J. Illuminating Engineering Society 7(1), 66–73 (1978).

], but is close to Einhorns’ observation that the useful radiation is located in the 430-660nm range [16

16. H. D. Einhorn and F. D. Einhorn, “Inherent efficiency and colour rendering of white light source,” Illum. Eng. 62(3), 154 (1967).

].

3.3 Harmful wavelength to color rendering properties of multi-color white LED source

3.4 Wavelength dependence of optimized SPDs for 3-color white LED source

As described in section 3.2, the more number of colors the white light source has, the higher color-rendering properties it achieves. However, the difficulty of color control and the cost increase along with number of colors. White light source with 3-color LEDs is a good trade off that it could get very acceptable color-rendering properties (CQS Qa > 80) as well as easy color adjustment. So, in this section a further analysis of the wavelength dependence of optimized SPDs of 3-color white LED source is carried out. As mentioned above, the maximum Qa of 3-color LEDs white spectra is in the range of 80~85. For CCT of 2700~6500K, the SPDs of white light source with 3-color LEDs are optimized for the maximum luminous efficacy with CQS Qa equal to or greater than 80, and the results are shown in Fig. 4
Fig. 4 SPDs of 3-color LEDs white source optimized for the maximum luminous efficacy under CCT of 2700K~6500K and CQS Qa equal to or greater than 80.
. Obviously, peak wavelengths of 3-color LEDs are in the red, green and blue region respectively, and they are labeled as R-, G- and B- LED respectively. Center wavelengths of R-, G- and B-LED under different CCT are shown in Table 3

Table 3. Center Wavelengths of R-, G- and B-LED Under Different CCT

table-icon
View This Table
| View All Tables
. As described in Section 2, a white LED source with CCT of #### K means not that it has the same chromaticity coordinates with the reference source, but that its chromaticity coordinates stay within the 7-step MacAdam ellipse centered at coordinates of the reference source with CCT of #### K. This makes the variation of SPDs of white LED source with CCT much complicated. But by and large, as can be seen from Fig. 4, In addition to the individual SPDs, as CCT increases from 2700 to 6500K, the center wavelength of R-, G- and B-LED all shift to shorter wavelength, the R-LED’s intensity continuously reduces and the Blue LED's intensity increases, while the G-LED’s intensity remains nearly constant.

In Fig. 5
Fig. 5 Compare of SPDs of 3-color LEDs white source optimized for the maximum luminous efficacy under CCT of 2700K~6500K and CQS Qa equal to or greater than 80 with SPDs of respective reference source.
, for CCT of 2700K~6500K, we compared SPDs of 3-color LEDs white source optimized for the maximum luminous efficacy with CQS Qa equal to or greater than 80 with that of reference source.

4. Conclusion

White LED spectra with 3 to 7 components are optimized for the maximum luminous efficacy under given CCT and given color rendering properties. The results indicate that, spectrum in 410-675nm wavelength range makes a major contribution to high color rendering properties, while the role of spectrum in the short-wavelength (<410 nm) and the long-wavelength (> 675nm) range is less important. Spectra filtering results shown that spectrum around 580nm is harmful to color rendering, and the color rendering properties can be effectively improved by removing spectrum in this region, especially when Qa is lower. For optimized SPDs of 3-color LEDs white source, it is found that the wavelength range could be divided into three intervals of 380-495nm, 495-595nm, and 595-675nm, respectively, and the energy ratio of these intervals is approximately the same as that of the reference source. It should be pointed out that the same analysis has been also carried out using CRI Ra as the color rendering assessment criterion, and the results also hold if CRI Ra is used.

Acknowledgment

This work was supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2011BAE01B07, and 2012BAE01B03), the National Basic Research Program of China (Grant Nos. 2011CB301902, and 2011CB301903), the High Technology Research and Development Program of China (Grant Nos. 2011AA03A112, 2011AA03A106, and 2011AA03A105), the National Natural Science Foundation of China (Grant Nos. 61176015, 60723002, 61176059, 60977022, and 51002085).

References and links

1.

CIE, “Lighting of work places-Part 1: Indoor,” ISO 8995–1:2002(E)/CIE S 008/E:2001.

2.

E. F. Schubert, Light-emitting diodes (Cambridge University Press, 2003).

3.

CIE, “Method of measuring and specifying colour rendering properties of light sources,” in CIE 13.3–1995(CIE, Vienna, Austria, 1995).

4.

CIE, “Colour rendering of white LED light sources,” in CIE 177:2007(CIE, 2007).

5.

W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602 (2010). [CrossRef]

6.

Y. Ohno and W. Davis, “Rationale of color quality scale,” (2010). http://www.digikey.com/us/en/techzone/lighting/resources/articles/rationale-of-color-quality-scale.html.

7.

D. L. MacAdam, “Visual sensitivities to color differences in daylight,” J. Opt. Soc. Am. 32(5), 247–274 (1942). [CrossRef]

8.

D. L. MacAdam, “Specification of small chromaticity differences,” J. Opt. Soc. Am. 33(1), 18–26 (1943). [CrossRef]

9.

American National Standard, “Specifications for the Chromaticity of Solid state lighting Products (ANSI_NEMA_ANSLG C78.377–2008),” NEMA, 2008.

10.

Lighting Research Center, Rensselaer Polytechnic Institute, “Developing Color Tolerance Criteria for White LEDs,” http://www.lrc.rpi.edu/programs/solidstate/assist/pdf/ColorDiscriminationStudy.pdf.

11.

G. Wyszecki and W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulae (Wiley, 2000).

12.

J. Holland, Adaptation in Natural and Artificial Systems (The University of Michigan Press, 1975).

13.

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, 3rd ed. (Springer-Verlag, 1996).

14.

Matlab Documentation, “Global Optimization Toolbox,” http://www.mathworks.cn/help/toolbox/gads/bsc7xh9-2.html.

15.

W. Walter, “Optimum lamp spectra,” J. Illuminating Engineering Society 7(1), 66–73 (1978).

16.

H. D. Einhorn and F. D. Einhorn, “Inherent efficiency and colour rendering of white light source,” Illum. Eng. 62(3), 154 (1967).

17.

W. A. Thornton, “Luminosity and color-rendering capability of white light,” J. Opt. Soc. Am. 61(9), 1155–1163 (1971). [CrossRef] [PubMed]

18.

H. H. Haft and W. A. Thornton, “High performance fluorescent lamps,” J. Illuminating Society 2(1), 29 (1972).

OCIS Codes
(230.3670) Optical devices : Light-emitting diodes
(230.6080) Optical devices : Sources
(330.1690) Vision, color, and visual optics : Color
(330.1715) Vision, color, and visual optics : Color, rendering and metamerism
(220.2945) Optical design and fabrication : Illumination design

ToC Category:
Vision, Color, and Visual Optics

History
Original Manuscript: August 31, 2012
Revised Manuscript: January 12, 2013
Manuscript Accepted: January 30, 2013
Published: February 7, 2013

Virtual Issues
Vol. 8, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Hongtao Li, Xianglong Mao, Yanjun Han, and Yi Luo, "Wavelength dependence of colorimetric properties of lighting sources based on multi-color LEDs," Opt. Express 21, 3775-3783 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-3-3775


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References

  1. CIE, “Lighting of work places-Part 1: Indoor,” ISO 8995–1:2002(E)/CIE S 008/E:2001.
  2. E. F. Schubert, Light-emitting diodes (Cambridge University Press, 2003).
  3. CIE, “Method of measuring and specifying colour rendering properties of light sources,” in CIE 13.3–1995(CIE, Vienna, Austria, 1995).
  4. CIE, “Colour rendering of white LED light sources,” in CIE 177:2007(CIE, 2007).
  5. W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng.49(3), 033602 (2010). [CrossRef]
  6. Y. Ohno and W. Davis, “Rationale of color quality scale,” (2010). http://www.digikey.com/us/en/techzone/lighting/resources/articles/rationale-of-color-quality-scale.html .
  7. D. L. MacAdam, “Visual sensitivities to color differences in daylight,” J. Opt. Soc. Am.32(5), 247–274 (1942). [CrossRef]
  8. D. L. MacAdam, “Specification of small chromaticity differences,” J. Opt. Soc. Am.33(1), 18–26 (1943). [CrossRef]
  9. American National Standard, “Specifications for the Chromaticity of Solid state lighting Products (ANSI_NEMA_ANSLG C78.377–2008),” NEMA, 2008.
  10. Lighting Research Center, Rensselaer Polytechnic Institute, “Developing Color Tolerance Criteria for White LEDs,” http://www.lrc.rpi.edu/programs/solidstate/assist/pdf/ColorDiscriminationStudy.pdf .
  11. G. Wyszecki and W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulae (Wiley, 2000).
  12. J. Holland, Adaptation in Natural and Artificial Systems (The University of Michigan Press, 1975).
  13. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, 3rd ed. (Springer-Verlag, 1996).
  14. Matlab Documentation, “Global Optimization Toolbox,” http://www.mathworks.cn/help/toolbox/gads/bsc7xh9-2.html .
  15. W. Walter, “Optimum lamp spectra,” J. Illuminating Engineering Society7(1), 66–73 (1978).
  16. H. D. Einhorn and F. D. Einhorn, “Inherent efficiency and colour rendering of white light source,” Illum. Eng.62(3), 154 (1967).
  17. W. A. Thornton, “Luminosity and color-rendering capability of white light,” J. Opt. Soc. Am.61(9), 1155–1163 (1971). [CrossRef] [PubMed]
  18. H. H. Haft and W. A. Thornton, “High performance fluorescent lamps,” J. Illuminating Society2(1), 29 (1972).

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