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  • Editor: Bernard Kippelen
  • Vol. 20, Iss. S2 — Mar. 12, 2012
  • pp: A245–A254
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Multispectral mixing scheme for LED clusters with extended operational temperature window

Ming-Chin Chien and Chung-Hao Tien  »View Author Affiliations


Optics Express, Vol. 20, Issue S2, pp. A245-A254 (2012)
http://dx.doi.org/10.1364/OE.20.00A245


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Abstract

LEDs have changed the concept of illumination not only in an expectation of the highest electroluminance efficiency but also in tremendous chances for smart lighting applications. With a cluster mixing, many studies were addressed to strategically manipulate the chromaticity point, system efficiency and color rendering performance according to different operational purposes. In this paper, we add an additional thermal function to extend the operational thermal window of a pentachromatic R/G/B/A/CW light engine over a chromaticity from 2800K to 8000K. The proposed model is experimentally validated to offer a full operable range in ambient temperature (Ta = 10° to 100°C) associated with high color quality scale (above 85 points) as well as high luminous efficiency (above 100 lm/watt).

© 2012 OSA

1. Introduction

Multispectral illumination with multichip LED clusters has the proven potential of revolutionizing the general lighting due to its unique characteristics to strategically modulate the spectral power distribution (SPD) to meet different operational purpose [1

1. G. He and L. Zheng, “Color temperature tunable white-light light-emitting diode clusters with high color rendering index,” Appl. Opt. 49(24), 4670–4676 (2010). [CrossRef] [PubMed]

, 2

2. G. He and L. Zheng, “White-light LED clusters with high color rendering,” Opt. Lett. 35(17), 2955–2957 (2010). [CrossRef] [PubMed]

]. A new technique, based on the use of general lens design rule to optimize the SPD of a LED cluster, was recently developed at NCTU [3

3. M. C. Chien and C. H. Tien, “Cluster LEDs mixing optimization by lens design techniques,” Opt. Express 19(S4Suppl 4), A804–A817 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S4-A804. [CrossRef] [PubMed]

]. This technique was demonstrated to provide the optimal operation with high color quality and efficiency over a wide range of chromaticity. Nevertheless, the assumption of constant thermal environment has prevented to a widespread diffusion of multichip LED clusters, thus precluding its transfer to practical use. In fact, the SPD of a LED more or less has the nonlinear dependence with the junction temperature and drive current, which in turn, results in the performance drift as well as the complexity in spectral modulation. In this study, based on the multispectral mixing scheme, we make an attempt to take the issues of thermal and drive current into consideration. Basically, a successful mixing scheme shall be able to provide two functions:

  • (a) Estimating the dependence of a LED white composite spectra on the junction temperature and drive current, respectively. Prior works analytically or empirically set either junction temperature or the drive current as the single parameter [1

    1. G. He and L. Zheng, “Color temperature tunable white-light light-emitting diode clusters with high color rendering index,” Appl. Opt. 49(24), 4670–4676 (2010). [CrossRef] [PubMed]

    7

    7. Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44(11), 111302 (2005). [CrossRef]

    ]. Although the single-color low power LED spectra in consideration of both temperature and current is available [8

    8. K. Man and I. Ashdown, “Accurate colorimetric feedback for RGB LED clusters,” Proc. SPIE 6337, 633702, 633702-8 (2006). [CrossRef]

    , 9

    9. F. Reifegerste and J. Lienig, “Modeling of the temperature and current dependence of LED spectra,” J. Light Vis. Environ. 32(3), 288–294 (2008). [CrossRef]

    ], there is still lack of the complete treatment for high power LED, whose model can be simply used to estimate the spectral behavior of phosphor-converted white light.
  • (b) Formulating the SPD to accommodate an optimization process. A multispectral mixing is a mathematically underdetermined optimization problem. We directly connect tristimulus values with drive current to reduce the degrees of freedom and then incorporate a proposed sampling methodology to find the optimum solution over a range of desired color temperatures [3

    3. M. C. Chien and C. H. Tien, “Cluster LEDs mixing optimization by lens design techniques,” Opt. Express 19(S4Suppl 4), A804–A817 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S4-A804. [CrossRef] [PubMed]

    ]. Afterward we complete the optimization process by removing the constraint in ambient temperature to further extend the operable range of the cluster.

The aim of this study is to implement a methodology, with consideration of temperature and drive current, to optimize the SPD of a LED white composite spectra with high color quality and possibly highest efficiency in a defined range of chromaticity. In this paper, we use color quality scale (CQS) as the merit figure of the light quality [10

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

]. Interested readers can refer to ref [11

11. A. Žukauskas, R. Vaicekauskas, and M. S. Shur, “Colour-rendition properties of solid-state lamps,” J. Phys. D Appl. Phys. 43(35), 354006 (2010). [CrossRef]

] for more discussion about color appearance and perceptual difference by various qualitative characteristics of lighting. In terms of system efficiency, we employ a factor: luminance efficiency (LE), where LE is defined as how much luminous flux (lm) normalized to the electrical input power (watt) expended to operate the LED [12

12. Y. Ohno, “Color rendering and luminous efficacy of white LED spectra,” Proc. SPIE 5530, 88–98 (2004). [CrossRef]

].

2. Measurement and modeling

2.1 Spectral measurement

In order to characterize the spectral property, we firstly launch the pulsed calibration measurement to obtain the database of forward voltage (Vf) subject to a set of two parameters: junction temperatures (Tj) and pulsed drive current (Id), respectively [13

13. Y. Xi and E. F. Schubert, “Junction-temperature measurement in GaN ultraviolet light-emitting diodes using diode forward voltage method,” J. Appl. Phys. 85, 2163–2165 (2004).

]. The sample LED is mounted inside an oven with every 10°C temperature increment. The junction temperature is assumed to be equivalent to oven temperature under the assumption that no additional thermal effect is induced by pulsed current with low duty cycle [14

14. Y. Gu and N. Narendran, “A non-contact method for determining junction temperature of phosphor-converted white LEDs,” Proc. SPIE 5187, 107–114 (2004). [CrossRef]

]. For each drive current, a calibration curve that profiles the relationship between the forward voltage Vf and junction temperatures Tj can be expressed by a linear estimation as shown in Eq. (1):
TjT2T1Vf(T2)Vf(T1)[VfVf(T1)]+T1
(1)
where T1 = 10 °C and T2 = 100 °C represent the extreme two cases as the thermal boundary. Afterward, a DC current (IDC) is applied through the sample LED mounted on a fixture (Arroyo Instruments, TEC 264-BB-DB9). The entire module is placed inside the cavity of an integrating sphere. The temperature of the fixture controlled by a thermoelectric cooler (Arroyo Instruments, TEC Source 5310) can be selected as the ambient temperature (Ta). With a set of ambient temperature (Ta) and DC current (IDC), as well as junction temperatures (Tj) and pulsed drive current (Id), the emitted SPD of each sample LED can be measured by the spectrometer (SR-UL1R, Topcon) attached to the integrating sphere. As the thermal states reach to the stable status, the junction temperature (Tj) can be determined by the interpolation mapping of the forward voltage according to the pulsed calibration measurement.

2.2 Spectral modeling

Generally, the SPD can be fitted by a single Gaussian function, which incorporates three parameters, the spectral power (P), peak wavelength (λ0) and spectral width (Δλ) with junction temperature [4

4. E. F. Schubert, Light Emitting Diodes, 2nd ed. (Cambridge University Press, 2006).

]. However, in most of cases, SPD is not perfectly symmetric, which would lead to numerical error by single Gaussian fitting. In order to overcome this issue, in this study, we proposed a double Gaussian function with two sets of parameters: (P,λ0,Δλ) and (P',λ0',Δλ'). All the parameters are functions of both junction temperature and drive current. The estimated M x N spectral matrix S˜ for a single-color LED can be modeled as Eq. (3):
S˜=G+G'
(3)
where G=(g1,,gM)T and G'=(g'1,,g'M)T are Gaussian spectral matrices. Here we temporarily omit G' due to the same treatment from Eqs. (4)(6). The matrix G has M spectral vectors g with N sampling wavelengths. For the nth point of mth row vector gm, gmn, its value can be accounted by Eq. (4):

gmn=pmexp{[λn(λ0)m]2/Δλm2}
(4)

For the phosphor-converted white LED S˜W(λ), the estimated spectrum is composed of two double Gaussian functions as given by Eq. (8):
S˜W(λ)={GB+GB',forλ<λBFGF+GF',forλ>λBF
(8)
where λBF denotes the boundary in the middle of blue (GB+GB') and fluorescence (GF+GF') component.

The spectral modeling of each component functions GB, GB', GF, and GF' follows the same mathematical manipulation as single-color case, shown in Eqs. (3)(7). A good agreement between the experimental measurement and spectral model can be obtained with R2 exceeding 0.98.

3. Optimization

3.1 Optimization process

The problem of color render is crucial when we are able to reproduce sources with different SPDs but equal correlated color temperature (CCT) (and even chromaticity). Such metameric will provide different CIE tristimulus values for a reflecting test sample if illuminated with one source or the other. In terms of LEDs cluster (K-type LED emitters, usually K > 3), metamerism appears as the SPD is synthesized for a target tristimulus value ε = [X Y Z]T. Before manipulating of SPD toward the target value, the current tristimulus value ε˜ can be described as Eq. (9):
ε˜=AS˜Tl
(9)
where rows of A are the sampled color matching functions with dimension N, the K x N spectral matrix S˜ now contains K-type modeled spectra [from Eq. (7) or Eq. (8)] extracted N discrete points, and l becomes the K x 1 all-ones vector. In this system, two implicit free variables junction temperature (Tj) and drive current (IDC) make the degrees of freedom to be 2K−3, results in the computational complexity to optimize the operational condition: the possibly highest objective function (included luminous efficiency and light quality) in a predefined chromaticity point ε. To solve this issue, we impose a constraint on a localized area (with small number of LEDs), where the ambient temperature Ta is assumed to be uniform among this area. Therefore the junction temperature Tj for each type LED can be determined by Eq. (2) once Ta and IDC are given. Such assumption, however, degenerates the degrees of freedom 2K−3 into K−3 + 1. On the other hand, we tend to directly relate the tristimulus value to drive current to further simplify the optimization process. We find a quadratic current basis iDC=[1(IDC)1(IDC)12(IDC)2(IDC)22(IDC)k(IDC)k2]T can precisely characterize ε˜ under a specific Ta . In sum, the Eq. (9) can be rewritten as Eq. (10) with lower degrees of freedom:
ε˜=CTiDC
(10)
where C is (2K + 1) x 3 coefficient matrix. Now we force current tristimulus to be equal to a target tristimulus ε˜=ε and randomly choose values for K−3 currents. An arbitrary current combination will readily be produced by extracting the positive solutions for remained currents. An initial current population, IDCp, of “combination changes” with various drive current could be generated. The corresponding initial Tj population, TjP, is obtained by introducing IDCp and Ta to Eq. (2). Similarly, the initial SPD population, S˜P, comes out via bringing the corresponded Tj and IDC from TjP and IDCp into Eq. (7) or (8) for single-color or phosphor-converted LEDs, respectively.

To evaluate the performance of the combinations in S˜P, based on the weighted sum method, we introduce Eq. (11) as a user-defined merit function (or called objective function) with two figures of merit: luminous efficiency (LE) and color quality scale (CQS), respectively:
f=w×CQS+(1w)×LE,subjecttow[0,1]
(11)
where w represents the weight factor for different operational purposes. As we insert each combination of S˜P into Eq. (11), a table of objective values becomes a function of SPD population S˜P, or equivalently, a function of IDCp. After defining the correspondence between the merit function and SPD, we bring the table into a globe searching engine, continuous genetic algorithm (CGA), to achieve an improved spectral synthesizing [15

15. R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms, 2nd ed. (John Wiley, 2004).

]. In the CGA, each row of the table composed of a value of merit function and the associated drive current combination is regarded as a chromosome. The chromosomes are ranked based on the value of merit function under a process of natural selection. The survivors are deemed fit enough to mate and to afford new offspring. By multiplying a certain mutation rate into the total number of drive currents, we are able to avoid the predicament of overly fast convergence or trapped at a local limitation. Finally, the described process is iterated for several generations until the convergence requirement is satisfied.

3.2 Merit analysis

Another aspect that must be taken into account in the frame work of realizing a smart lighting is the selection of weight factor w. Up to this point, a system with a user-defined merit function has been discussed. The weight factor, w, is then used to provide a freedom to determine the operational mode. When w = 0, the system is carried out in high efficiency mode, the objective function is entirely attributed to the efficiency consideration. The other extreme case (w = 1) would be high quality mode. In most of case, the user-defined intermediate value would be the kernel of the smart lighting operation. Also, Eq. (11) constitutes a two-dimensional optimal boundary (Pareto front, PF) between CQS and LE, respectively. Different weight values w would profile a series of locus of operating point. For the sake of computation efficiency, we adapt the proposed sampling methods to analyze the cluster performance among the CQS and LE and produce an appropriate value w if any section of PF fulfilled the required performance [3

3. M. C. Chien and C. H. Tien, “Cluster LEDs mixing optimization by lens design techniques,” Opt. Express 19(S4Suppl 4), A804–A817 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S4-A804. [CrossRef] [PubMed]

].

4. Design example

A direct experimental validation of the devised model is pursued. A pentachromatic mixing scheme is setup, where a high-power LEDs clusters is composed of four single-colors red/amber/green/blue (R/A/G/B) and a phosphor-converted cool-white (CW) LED. All the chips are commercially available (HELIO Optoelectronics Corp., HMHP-E1LW). Figure 2
Fig. 2 The power spectra of red (λR: 625nm, ΔλR: 20nm), green (λG: 523nm, ΔλG: 33nm), blue (λB: 465nm, ΔλB: 25nm), amber (λA: 587nm, ΔλA: 18nm) and cool-white LEDs at Ta of 10°C with IDC of 350mA. The upper right figure shows a real-field test designed for CT = 5000K and the lower right one shows the utilized LEDs attached on the temperature controllable fixture respectively.
shows the SPD of each channel under operational condition Ta = 10°C and IDC = 350mA, respectively. An adequate layout of LED pixel arrangement and first-order design delivers a uniform illumination upon the test Macbeth color checker [16

16. I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006). [CrossRef] [PubMed]

].

The first validation of the devised model is conducted by examining the temperature dependence of spectra under four color temperatures: CT = 3200K, 4600K, 6200K, and 7400K, respectively. The system is operated under a specific value of the ambient temperature, Ta = 50°C. The results are reported in Fig. 3
Fig. 3 The temperature dependence of spectra designed for CT = 3200K, 4600K, 6200K, and 7400K at Ta = 50°C. The chromaticity point shifts toward higher color temperature with the raise of Ta owing to the dramatic deterioration in LEs of the red and amber LEDs.
, where the illumination conditions fulfill the requirements of high luminance level (100 lm), negligible color deviation (Δxy < 0.01) and high quality (CQS > 85 points) with possibly highest luminous efficiency (LE). If we change the ambient temperature without compensation, the lighting performance would dramatically shift due to the thermal effects. Taking CT = 3200K for example, as ambient temperature increases from 10 °C to 100 °C, the chromaticity point would have an apparent change (Δxy > 0.5). On the other hand, in case of settled operational ambient temperature Ta = 50°C, the acceptable tolerance (Δxy < 0.01) of thermal dependence merely lie in a tiny window Ta = 42 °C ~56 °C. It is observed that the operational window changes with respect to different chromaticity points. The drift of chromaticity point subject to thermal dissipation becomes more severe at low CT, which is mainly attributed by amber and red color. The reason can be explained by Fig. 4
Fig. 4 The temperature dependence of LE for pentachromatic LEDs. When Ta is varied from 10 °C to 100 °C, LEs of amber and red AlInGaP LEDs decrease to 23% and 46% of that at 10 °C while LEs of InGaP LEDs are insensitive to temperature variation.
.

It is observed that the technique effectiveness is fully applied for the predefined requirements in smart lighting: high color quality scale (above 85), high luminous efficiency (above 100 lm/watt) over a wide range of color temperature (CT = 2800-8000K). The thermal compensation technique works with wide chromaticity locus and, in particular, it is proven to work with low color temperature noticeably influenced by thermal variation. Taking case I (CT = 3200K) for example, as the ambient temperature Ta changes from 10 °C to 100 °C, the power ratio of dominant red channel changes from 28% to 44%. The reason is due to when ambient temperature increases the luminous efficiency (LE) of dominant field (Red color) decreases. In order to keep the chromaticity point, we must extract more luminous flux from the red majority and thus more power ratio (Pin) is required accordingly. The consequence can be deduced in other operational conditions. As the lighting is operation at high color temperature (CT > 4600K), phosphor-converted white source is the dominant field (over 50%) due to its unique characteristics of high luminous efficiency and dully dependence upon the thermal effects. Therefore, in case of operation in high color temperature (CT), we suggest a scenario as following: (1) utilize phosphor-converted white source as a dominant field, accompanied by a small amount of other complementary single-color to keep light quality and fine chromaticity adjustment, (2) replace single red and amber emitters by two or more devices with less drive current, and thus reduce the thermal effect and enhance the entire cluster efficiency, (3) replace amber AlInGaP LED by phosphor-converted amber with higher flux density and better color stability [18

18. Philips Lumileds Lighting Campany, Netherlands, LUXEON Rebel PC Amber Datasheet DS62 (2010).

].

In sum, Fig. 5
Fig. 5 The LE contour of the pentachromatic LEDs cluster is performed under the predefined requirements (CQS > 85 points, lighting level = 100 lm and Δxy < 0.01). When the LE = 100 lm/W is selected as the minimum efficiency boundary, a full operation range for ambient temperature can be obtained for CT > 5200K.
shows the contour map of possibly highest luminous efficiency (LE) subject to predefined requirements (CQS > 85 points, high luminance level 100 lm and negligible color deviation Δxy < 0.01). With different operational ambient temperatures, it’s not likely to reach high efficiency at high ambient temperatures. The best performance (LE > 130 lm/W) lies in a narrow region about CT = 4000-6500K associated with self-evident low ambient temperature (Ta = 10 °C ~20 °C). If the LE = 100 lm/W is settled as the minimum requirement, a full operable range for Ta is workable only exists in high color temperature CT > 5200K.

4. Conclusion

A through methodology, which takes into account all aspects which can have influence on general lighting, has been firstly developed and experimentally validated. Firstly, a double Gaussian fitting is proposed to precisely describe the SPD of either phosphor-converted or single-color LEDs. Then we employ a user-define merit function to optimize the SPD of a LEDs cluster without loss of generality. In the optimization process, the degrees of freedom can be reduced from 2K−3 to K−2 under the localized uniform Ta. The optimal spectral synthesis can be completed by incorporating CGA and Tien’s method [3

3. M. C. Chien and C. H. Tien, “Cluster LEDs mixing optimization by lens design techniques,” Opt. Express 19(S4Suppl 4), A804–A817 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S4-A804. [CrossRef] [PubMed]

]. In order to validate the proposed scheme, we set up a pentachromatic R/G/B/A/CW cluster. At high ambient temperature Ta, the luminous efficiency would suffer from a severe deterioration at low color temperature. The main reason is due to the dominant fields, red and amber, are strongly dependent on thermal dissipation. In order to avoid such case, we suggest replacing single emitter by two or more ones, which are able to share the total luminous flux and reduce the thermal effect accordingly. This technique still leaves much space open and clearly more research must be carried out to explore its potential in full- the first, price and volume of the cluster being the realization of a commercial available solution. The preliminary demonstration presented here, however, indicate that proposed multispectral mixing scheme could create a major breakthrough in the field of general lighting and spectral technologies.

Acknowledgment

We appreciate the financial support provided by the National Science Council, Taiwan, under grants NSC 99-2221-E-009-067-MY3 and NSC 100-2622-E-009-003-CC2.

References and links

1.

G. He and L. Zheng, “Color temperature tunable white-light light-emitting diode clusters with high color rendering index,” Appl. Opt. 49(24), 4670–4676 (2010). [CrossRef] [PubMed]

2.

G. He and L. Zheng, “White-light LED clusters with high color rendering,” Opt. Lett. 35(17), 2955–2957 (2010). [CrossRef] [PubMed]

3.

M. C. Chien and C. H. Tien, “Cluster LEDs mixing optimization by lens design techniques,” Opt. Express 19(S4Suppl 4), A804–A817 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S4-A804. [CrossRef] [PubMed]

4.

E. F. Schubert, Light Emitting Diodes, 2nd ed. (Cambridge University Press, 2006).

5.

A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Modeling high-power light-emitting diode spectra and their variation with junction temperature,” J. Appl. Phys. 108(4), 043104 (2010). [CrossRef]

6.

S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light emitting diodes,” J. Appl. Phys. 97(5), 054506 (2005). [CrossRef]

7.

Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44(11), 111302 (2005). [CrossRef]

8.

K. Man and I. Ashdown, “Accurate colorimetric feedback for RGB LED clusters,” Proc. SPIE 6337, 633702, 633702-8 (2006). [CrossRef]

9.

F. Reifegerste and J. Lienig, “Modeling of the temperature and current dependence of LED spectra,” J. Light Vis. Environ. 32(3), 288–294 (2008). [CrossRef]

10.

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

11.

A. Žukauskas, R. Vaicekauskas, and M. S. Shur, “Colour-rendition properties of solid-state lamps,” J. Phys. D Appl. Phys. 43(35), 354006 (2010). [CrossRef]

12.

Y. Ohno, “Color rendering and luminous efficacy of white LED spectra,” Proc. SPIE 5530, 88–98 (2004). [CrossRef]

13.

Y. Xi and E. F. Schubert, “Junction-temperature measurement in GaN ultraviolet light-emitting diodes using diode forward voltage method,” J. Appl. Phys. 85, 2163–2165 (2004).

14.

Y. Gu and N. Narendran, “A non-contact method for determining junction temperature of phosphor-converted white LEDs,” Proc. SPIE 5187, 107–114 (2004). [CrossRef]

15.

R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms, 2nd ed. (John Wiley, 2004).

16.

I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006). [CrossRef] [PubMed]

17.

T. Mukai, M. Yamada, and S. Nakamura, “Characteristics of InGaN-based UV/blue/green/amber/red light-emitting diodes,” Jpn. J. Appl. Phys. 38(Part 1, No. 7A), 3976–3981 (1999). [CrossRef]

18.

Philips Lumileds Lighting Campany, Netherlands, LUXEON Rebel PC Amber Datasheet DS62 (2010).

OCIS Codes
(230.3670) Optical devices : Light-emitting diodes
(330.1690) Vision, color, and visual optics : Color
(330.1715) Vision, color, and visual optics : Color, rendering and metamerism

ToC Category:
Light-Emitting Diodes

History
Original Manuscript: December 2, 2011
Revised Manuscript: January 2, 2012
Manuscript Accepted: January 3, 2012
Published: January 31, 2012

Citation
Ming-Chin Chien and Chung-Hao Tien, "Multispectral mixing scheme for LED clusters with extended operational temperature window," Opt. Express 20, A245-A254 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-S2-A245


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References

  1. G. He and L. Zheng, “Color temperature tunable white-light light-emitting diode clusters with high color rendering index,” Appl. Opt.49(24), 4670–4676 (2010). [CrossRef] [PubMed]
  2. G. He and L. Zheng, “White-light LED clusters with high color rendering,” Opt. Lett.35(17), 2955–2957 (2010). [CrossRef] [PubMed]
  3. M. C. Chien and C. H. Tien, “Cluster LEDs mixing optimization by lens design techniques,” Opt. Express19(S4Suppl 4), A804–A817 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S4-A804 . [CrossRef] [PubMed]
  4. E. F. Schubert, Light Emitting Diodes, 2nd ed. (Cambridge University Press, 2006).
  5. A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Modeling high-power light-emitting diode spectra and their variation with junction temperature,” J. Appl. Phys.108(4), 043104 (2010). [CrossRef]
  6. S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light emitting diodes,” J. Appl. Phys.97(5), 054506 (2005). [CrossRef]
  7. Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng.44(11), 111302 (2005). [CrossRef]
  8. K. Man and I. Ashdown, “Accurate colorimetric feedback for RGB LED clusters,” Proc. SPIE6337, 633702, 633702-8 (2006). [CrossRef]
  9. F. Reifegerste and J. Lienig, “Modeling of the temperature and current dependence of LED spectra,” J. Light Vis. Environ.32(3), 288–294 (2008). [CrossRef]
  10. W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng.49(3), 033602 (2010). [CrossRef]
  11. A. Žukauskas, R. Vaicekauskas, and M. S. Shur, “Colour-rendition properties of solid-state lamps,” J. Phys. D Appl. Phys.43(35), 354006 (2010). [CrossRef]
  12. Y. Ohno, “Color rendering and luminous efficacy of white LED spectra,” Proc. SPIE5530, 88–98 (2004). [CrossRef]
  13. Y. Xi and E. F. Schubert, “Junction-temperature measurement in GaN ultraviolet light-emitting diodes using diode forward voltage method,” J. Appl. Phys.85, 2163–2165 (2004).
  14. Y. Gu and N. Narendran, “A non-contact method for determining junction temperature of phosphor-converted white LEDs,” Proc. SPIE5187, 107–114 (2004). [CrossRef]
  15. R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms, 2nd ed. (John Wiley, 2004).
  16. I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt.45(10), 2265–2272 (2006). [CrossRef] [PubMed]
  17. T. Mukai, M. Yamada, and S. Nakamura, “Characteristics of InGaN-based UV/blue/green/amber/red light-emitting diodes,” Jpn. J. Appl. Phys.38(Part 1, No. 7A), 3976–3981 (1999). [CrossRef]
  18. Philips Lumileds Lighting Campany, Netherlands, LUXEON Rebel PC Amber Datasheet DS62 (2010).

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