Abstract

The authors build on previous experience in the optimization of white-light sources based on combinations of narrow-band spectra. They extend those concepts by using delta-function spectra to study the prospects of future optimal laser-based sources. The optimization process is based on a trade-off between the color rendering properties and the luminous efficacy of the radiation. Optimal solutions for four, five and six delta-function spectra with correlated color temperatures in the 3000 to 5500 K range are presented and analyzed. White-light sources with these properties would likely find wide acceptance in numerous lighting applications.

© 2013 OSA

1. Introduction

The primary purpose of this work is to aid in the development of eco-friendly lighting systems. Worldwide, efforts have been aimed at producing white light sources based on light-emitting diodes (LEDs) either by combining the output of multiple narrow-band LEDs [1,2], or using blue light to irradiate a yellow-emitting phosphor [3,4]. Subsequently, it has been established that tetrachromatic combinations of blue, green, yellow and red LEDs can provide light sources characterized by good to excellent color rendering performance and high luminous efficacy of radiation (LER) [57]. Both color rendering and LER depend on the emitted spectrum of the light source and are often contra-variant. A source that contains only light at 555 nm would have an excellent LER of 683 lumens per radiant watt (lm/rad-W), and very poor rendering of the majority of colored objects. Typically, the color rendering properties of light sources are evaluated using the CIE color rendering index CRI [8], currently the only internationally endorsed metric for color rendering evaluation. To improve color rendering, more wavelengths must be included in the source, consequently lowering its LER value and increasing the complexity of the design. Regardless, by fine-tuning the spectral intensity (I), peak emission wavelength (λp) and full-width-at-half-maximum (FWHM) of the individual LEDs in a mixture, a balance can be found between the above two properties of the composite spectrum [911].

To aid in finding the best composite mixtures the authors proposed an optimization approach [12] based on differential evolution (DE). The DE approach was successful in optimizing LED-based illuminants [12] as well as artificial source spectra based on different mathematical functions (Gaussian-, rectangular- and triangular-shaped spectral bands) which free the design from constraints intrinsic to currently available light sources [11].

A study on the maximum achievable luminous efficacy for solid -state lighting, including spectra with linewidths as low as 1nm, showed that there is no LER penalty for narrow spectra [13]. In particular, a LER value of 408 lm/W at a CRI of 90 was achieved by positioning central wavelengths of 1-nm linewidths at 614 nm, 583 nm, 530 nm and 463 nm. Furthermore, recently published visual experiments showed that the color rendering of mixtures of four lasers was practically indistinguishable from that of other (widely known) light sources [14]. Laser mixtures were shown to be able to deliver satisfactory color rendering, 83CRI91, over a range of correlated color temperatures, 2840KCCT5670K, using lasers with linewidths of <0.2 nm (yellow, green, blue) and <2 nm (red). However, no mention is made of the LERs for those mixtures. The paper [14] instead highlights the high conversion efficiencies achievable in lasers at high current densities. Hence, there is the prospect of synthesizing efficient white-light illuminants having spectral outputs confined to several narrow discrete bands within the visible range as well as to select the wavelengths that produce the “best” visual effect.

Taking account of the range of factors discussed above, we now consider it to be worth investigating whether fine tuning the spectral intensities and peak emission wavelengths of the individual delta functions in a mixture could improve on our earlier mixed-LED spectra [12,15] and on the results published in [14]. In the work reported here, the resolution of wavelengths is changed from 5 nm to 1 nm allowing the DE algorithm to optimize delta-function-like monochromatic illuminants. The chief purpose of this investigation is therefore to define optimum numbers and optimum wavelengths of such discrete bands within the visible range. In doing so, the authors hope to encourage the development of laser sources with the most appropriate spectra for the design of highly efficient white-light sources.

We next explain the importance of LER and color rendering in the design of optimal sources, as well as the optimization algorithm we have developed, following which we outline our experimental work in the design of optimized laser white-light sources.

2. Background

2.1 Color rendering

The fundamental idea behind the CIE color rendering index (CIE CRI) is a comparison of the surface colors of eight color samples of moderate to medium saturation illuminated in turn by a test source and a reference illuminant of the same correlated color temperature (CCT). Each test color sample is assigned an individual index, Ri, and the official index CRI is defined as the average of the eight Ri values. The maximum value for CIE CRI is 100, which is achieved if all eight test color samples are unchanged under the test source and reference illuminant.

It has been shown that a light source can have a good CIE CRI but still give very poor rendering of saturated colors [2]. Hence, more research groups are adopting multi-index [11,14] and multimetric [14,16] approaches for assessing white light sources. In our optimization process, we use a multi-index approach [11,12,15] and include the additional six CIE test color samples [8] representing saturated red, yellow, green and blue, and two samples representing light human complexion and leaf-green colors respectively. The average of the Ri for the first eight test colors is referred to as Ra. The additional six indices result in an index we referred to as Rb, and Rc is used to denote the average of all 14 indices. Furthermore, we found it useful to include in the optimization algorithm the Ri index for the test color yielding the worst color-rendering performance (i.e.Rmin=min{Ri},i=1,2,...,14).

Using the additional six saturated color samples allows for more detailed evaluation of light sources, but it does not eliminate the drawbacks of the current metric for color rendering assessment, namely the fact that the metric is based on an outdated color space and color adaptation formula. It is not our intention to make any judgments concerning the relative merits of the CIE CRI or any other alternative systems [16,17], and we carry out optimizations using the current standard (i.e. the CRI system). However, we also endorse a multimetric approach (as a way of enhancing the assessment of color rendering) and further characterize the color rendering capabilities of the resultant spectra in an alternative metric, i.e. Color Quality Scale (CQS) [18]. This has the added advantage of permitting a comparison of our results with those published in [14] where both CRI and CQS indices were used.

The CQS metric compares 15 saturated test color samples when illuminated with the test source and its matching reference illuminant, which is defined in the same way as for the CRI calculations. The CQS employs a more recent color space (CIE 1976) and chromatic adaptation transform (CMCCAT2000). It combines the color differences with a root mean square lowering the impact of extreme color differences, which are possible for mixtures with significant gaps in the SPD, on the result of the overall color rendering assessment.

Again, we found it useful for more thorough color-rendering investigation of an illuminant to both report the value of the general CQS index (Qa) and to identify the test color yielding the worst color-rendering performance in CQS (i.e.Qmin=min{Qi},i=1,2,...,15).

2.2 Luminous efficacy

The overall efficacy of the light source (ηlum) is a product of two components: (1) the energy conversion efficiency (η), a dimensionless efficiency describing an electrical-to-radiant energy conversion (W/W) and (2) the luminous efficacy of radiation (ηrad) or LER (lm/rad-W) which compares the amounts of luminous flux and radiant flux emitted by the source. Since this research is concerned purely with optimizing the spectra of delta-function mixtures, and not with the physical processes for producing those spectra, the focus of the present investigation is the luminous efficacy of radiation:

ηrad=ηrad(max)λV(λ)S(λ)dλλS(λ)dλ.
According to Eq. (1) LER depends on the spectral power distribution of the light source S(λ) and the eye sensitivity function for photopic vision V(λ). It is noteworthy that the spectral power distribution of the ‘red’ component in a mixture plays an important role in achieving a maximal LER [13] since a narrower Sred minimizes the reduction in LER by limiting the radiated power at wavelengths where V(λ) decreases rapidly. The narrowness of other individual Si in spectral regions where V(λ) is broad (e.g. Sgreen) or low (e.g. Sblue) is less critical for maximizing the LER value.

2.3 Optimization process

The mixtures of delta-functions describing theoretical laser spectra were optimized using the DE approach as described in earlier work [12]. The DE approach utilizes a population-based evolutionary algorithm where a population of possible solutions is evaluated using a fitness function (f), and only those solutions having better performance are further optimized and others are removed from the optimization. This selection process is repeated over a number of ‘generations’.

Each solution consists of n individual delta-function spectra, {S1, S2, ..., Sn}, where each is characterized by two quantities: its relative intensity (Ii1) and wavelength (λpi[380780]nm), i.e. Si={Ii,λpi}. The algorithm searches for an optimal solution (i.e. spectrum) by finding the optimal Ii and λpi values. Hence, the best solution is a vector Sopt={I1,...,In,λp1,...,λpn}.

The success of the DE technique is predicated on a proper selection of the fitness function f, relevant to the purpose of the optimization. Here the intent is to simultaneously enhance both the efficacy and color rendering performance of the spectrum, and experimentation was carried out to explore different fitness functions based on the CRI and LER. It was finally decided to adopt the formulation given in Eq. (2):

f=aRa+bRb+cRc+dRmin+eηrad
where the user-selected weighting factors a, b, c, d, and e (which can theoretically be any real numbers) control the influence of Ra, Rb, Rc, Rmin and ηrad respectively on the optimization of the mixture.

The optimization process can be guided to prefer one of the characteristics over others. When a = 1 and b = c = d = e = 0 the process will select spectra with higher Ra values and rejects others, resulting in a spectrum optimized for Ra. On the other hand, using the same value for all weighting factors (e.g. a = b = c = d = e = 1) promotes a CRI/LER tradeoff which can result in a spectrum with a high LER at the expense of the color rendering properties.

The choice was made to focus on the optimization of 4-, 5- and 6-band spectra and to explore the benefits, if any, of using N > 4 bands in the performance of the overall mixture.

3. Experimental results

The results of the CRI optimization of mixtures of delta-function spectra are tabulated with the values of the color-rendering indices (Ra, Rb, Rc, R9, Rmin, Qa, Qmin), the luminous efficacy of the radiation (ηrad) and the correlated color temperature (Tc) rounded to the nearest integer. Note that ηrad is in units of lumens per radiant watt and Tc .in kelvins. The values of the R9 index allow for comparison with the laser white mixtures published in [14] as well as to explore how the mixture renders the red sample color.

Spectra with Ra ≥ 90 are here regarded as optimized. The optimized spectra are sorted by their performance indicators Ra and ηrad, and the results are shown in Tables 1, 2, and 3. Columns ir and iq show the index of the test color sample with lowest color rendering Rmin and Qmin respectively. In all experiments, the peak value of each of constituent band in the mixture was constrained to be ≤1. Some spectra with Ra < 90 are presented and discussed in Table 4 and Section 3.4. Those spectra are considered suboptimal due to their lower CRI and/or LER values. However they still possess properties that should prove attractive in certain classes of usage, and they are included here for general information.

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Table 1. Optimization of mixtures of 4 delta-function spectraa

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Table 2. Optimization of mixtures of 5 delta-function spectraa

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Table 3. Optimization of mixtures of 6 delta-function spectraa

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Table 4. Mixtures of ‘suboptimal’ tetrachromatic mixturesa

We plot the corresponding spectra over the wavelengths from 380 nm to 780 nm and provide the wavelengths of the individual delta-functions. In total, nine optimal and 3 suboptimal spectra are presented and analyzed.

3.1 Tetrachromatic illuminants

The results of the optimization of four delta-functions are summarized in Table 1. All of the three spectra in Table 1 have the same CIE CRI value of 90, a moderate to high LER (≥357 lm/rad-W) and can be described as warm white. Sopt3 scored satisfactorily in both CRI and CQS metrics and its color rendering is comparable with the warm white source reported in [14]. With the correlated color temperature of 3480 K this mixture would most likely find wide acceptance in numerous general lighting situations. We note that the worst rendering is for CIE Sample 12 (strong blue) and CQS Sample 5 (moderately saturated medium aquamarine).

By contrast, the other two spectra (Sopt1, Sopt2) scored poorly in the CQS metric. On the positive side, these mixtures have a rather high LER (≥410 lm/rad-W), higher than Sopt3 and the 408 lm/rad-W reported in [13]. The Sopt1 mixture would be useful in general purpose lighting. However, the case of Sopt2 is questionable since Tc = 2719 K is slightly below the accepted average for the GLS filament lamp (~2850 K) and may appear too reddish.

The corresponding spectra are shown in Fig. 1. The three reported spectra give average values of the peak wavelengths of 455 with a spread of 23 nm (for blue), 525 nm with a spread of 18 nm (for green), 576 nm with a spread of 21 nm (for yellow) and 622 nm with a spread of 10 nm (for red). The variations in ‘red’ wavelengths are the smallest, followed by those of green, yellow and blue. This highlights the fact that our optimization algorithm is able to capture the importance of the red component on the LER of the mixed white source [13]. It is interesting to observe the size of the individual peaks in the mixture. The Sopt1 and Sopt2 spectra have three prominent peaks at the wavelengths of ‘green’, ‘yellow’ and ‘red’ components and a rather small ‘blue’ peak. The blue component is much higher in the Sopt3 spectrum; increasing the correlated color temperature of the mixture but reducing the LER. The spectrum occupied by the four bands decreases (Sopt1: ∆λp = 174 nm, Sopt2: ∆λp = 170 nm, Sopt3: ∆λp = 158 nm) and the bands collectively shift to higher wavelengths. These shifts to higher wavelengths result in a decreasing LER, a behavior that has also been described in [13].

 

Fig. 1 Relative spectral power distributions versus wavelengths (nm) for the three optimized spectra of tetrachromatic illuminants with Ra = 90 and ηrad ≥ 357 lumens per radiant watt. Numbers above each delta function show the individual peak wavelengths in nm.

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3.2 Pentachromatic illuminants

The results of the optimized “5 band” illuminants named Sopt4, Sopt5 and Sopt6 are given in Table 2. The spectra have a high color-rendering (Ra ≥ 90), a high LER (≥364 lm/rad W) and correlated color temperature ~3000 to 4000 K. All of the three spectra have no problem rendering the CIE red sample (R9 ≥ 90). Spectra Sopt5 and Sopt6 scored satisfactorily in CQS, while Sopt4 yielded a poorer CQS result. Overall, the introduction of the 5th delta-function did not have a significant effect on the characteristics of the illuminants. However, using the ‘additional’ band resulted in spectra providing a set of higher correlated color temperatures.

The wavelengths and intensities of the delta-functions in the pentrachromatic spectra are shown in Fig. 2. In each case, the 5th constituent tends to approach or merge with another prominent constituent to form an ‘overlap’ region. This is particularly visible in the Sopt5 spectrum where the difference between the second (λp2 = 502 nm) and third (λp3 = 510 nm) peak wavelengths is only 8 nm. These two constituents form a wider green component which improves the color-rendering. In the Sopt4 and Sopt6 spectra the additional delta-function merged with the red component extending the red region to lower wavelengths (Sopt4) and higher wavelengths (Sopt6). The additional band at the long-wavelength position (λp5 = 651 nm) caused the expected decrease of LER (to 364 lm/rad-W), together with improvements in Qa and Qmin.

 

Fig. 2 Relative spectral power distributions versus wavelengths (nm) for the three optimized spectra of pentachromatic illuminants with Ra > 90, ηrad ≥ 364 lumens per radiant watt. Numbers above each delta function show the individual peak wavelengths in nm.

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3.3 Hexachromatic illuminants

We further explored mixtures of delta-functions by introducing one more constituent. This complicates the design of a white-light source both during the optimization and in the practical implementation of the light source. However, we deemed it worthwhile to explore the hexachromatic mixtures which are capable of providing excellent color rendering, and so might be important for special lighting applications.

The results of the optimized hexachromatic mixtures are tabulated in Table 3 and the corresponding spectral power distributions are shown in Fig. 3. The Sopt7 and Sopt8 spectra have an excellent color rendering both in CRI (Ra ≥ 94) and CQS (Qa = 92) and a moderate LER (≥317 lm/rad W). The Sopt7 case is unique in that it is the only optimum spectrum we have produced where one of the wavelengths is at 780 nm; and the LER would clearly be improved if this constituent were to be eliminated (with little or no effect on color rendering performance). Sopt8 provides the best combination yet achieved of superb CRI and good LER performance at a high CCT. On the other hand, Sopt9 has the highest LER of all the three spectra and the poorest CQS color-rendering. It is interesting to observe the overlap region in the red region of the Sopt9 mixture (∆λpred = 53 nm) where three red constituents positioned at 615 nm, 628 nm and 668 nm provide a wider red coverage. The prominent red constituent has the maximum intensity (I615 = 1) and the intensities of other two constituents are seen to decrease as their wavelengths increase (I628 = 0.362, I668 = 0.082) lowering their influence on the overall LER.

 

Fig. 3 Relative spectral power distributions versus wavelengths (nm) for the three optimized spectra of hexachromatic illuminants with Ra ≥ 90, ηrad ≥ 317 lumens per radiant watt. Numbers above each delta function show the individual peak wavelengths in nm.

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3.4 Suboptimal mixtures

Here, three mixtures (S1, S2, S3) with correlated color temperatures of ~3500, 4000 and 5500 K are presented (Table 4 and Fig. 4). We label them suboptimal due to our criterion that optimal spectra must have Ra ≥ 90. While the mixtures have a lower Ra, their LER values could be considered high, hence these mixtures were optimized for higher LERs and correlated color temperatures. S1 is an example of a warm white with a very high LER (450 lm/rad W). The Ra of 83 is still satisfactory for many general lighting applications, although the Qmin of 1 could be of concern. The S2 and S3 spectra have both a poorer rendering in the CRI metric and lower LER, but somewhat improved rendering of CQS samples. S1 has prominent peaks in the ‘green’, ‘yellow’ and ‘red’ regions with a ‘blue’ of 0.05 at 453 nm. The blue of S3 is at 478 nm with an intensity of 0.475, while its ‘red’ constituent is at 677 nm with an intensity of 0.05.

 

Fig. 4 Relative spectral power distributions versus wavelengths (nm) for the three suboptimal spectra of tetrachromatic illuminants with Ra ≥ 71, ηrad ≥ 364 lumens per radiant watt. Numbers above each delta function show the individual peak wavelengths in nm.

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It must be noted that the tetrachromatic mixtures tend to have better overall performance at lower correlated color temperatures, and at the moment we believe that this is linked to the optimization process rather than any intrinsic characteristic of delta-function mixtures. It is noteworthy that a similar behavior is reported for the mixtures of ultra-efficient LEDs [9] and hence further investigations will be required to determine the relationships between CCT, LER and color-rendering of illuminants based on multiple narrow spectra in general.

4. Conclusions

We have shown that white-light spectra based on 4, 5 or 6 delta-functions can be optimized both for high color-rendering and luminous efficacy with CCTs in the 3000 to 5500 K range, and would most likely find wide acceptance in numerous lighting applications. Although others have previously shown that laser mixtures can provide effective white-light illumination, we believe that this is the first in-depth investigation of the optimization of such mixtures in terms of both LER and color rendering. We also show, with the aid of two color rendering scales, that it is possible to achieve high color rendering performance by appropriate choices of spectral wavelengths, even when there are extensive gaps in the spectrum.

The introduction of 5th and 6th delta functions did not significantly improve the overall characteristics of the resultant illuminants as compared with tetrachromatic mixtures. However, our hexachromatic mixtures did have significantly better overall color-rendering than the 4- and 5-band mixtures, while sacrificing some LER and adding to set-up complexity. The additional delta-function(s) tend to ‘join’ other prominent peaks forming ‘overlap’ regions similar to those in multi-band LED mixtures [6,12] and other spectra with wider bandwidths [11].

Our experiments show that reporting R9 as a measure of color-rendering performance of a white-light source could be misleading because the color rendering of other color test samples could be much poorer. Hence, we advocate for better transparency in communicating color rendering properties of white-light sources by reporting the values of the worst color-rendering indices (Rmin and Qmin).

To end on a practical note it is clear that, for a laser mixture to be a useful white light source, the laser outputs must be thoroughly mixed to avoid effects such as speckle and colored shadows. The mixture will need to be diffused to assist the mixing process and to remove speckle. At this point, it was considered important to establish the feasibility of optimizing laser mixtures, but it is recognized that these aspects will have to be taken into account in the design and implementation of a practical white-light source.

Acknowledgments

The authors wish to acknowledge the support of this work by the EET School of the Manukau Institute of Technology.

References and links

1. Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J. 38(1), 1–6 (2007). [CrossRef]  

2. Y. Ohno, “Simulation analysis of white LED spectra and color rendering,” in Proceedings of CIE Expert Symposium on LED Light Sources, Tokyo, 2004.

3. R. Stevenson, “The LED’s dark secret,” IEEE Spectr. •••, 23–27 (2009).

4. A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today 54(12), 42–47 (2001). [CrossRef]  

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

6. A. Žakauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett. 80(2), 234–236 (2002). [CrossRef]  

7. G. He, L. Zheng, and H. Yan, “LED white lights with high CRI and high luminous efficacy,” Proc. SPIE 7852, 78520A (2010). [CrossRef]  

8. Commission Internationale de l’Eclairage, “Method of measuring and specifying colour rendering properties of light sources,” CIE Publication 13.3, CIE, Vienna (1995).

9. T. Erdem, S. Nizamoglu, X. W. Sun, and H. V. Demir, “A photometric investigation of ultra-efficient LEDs with high color rendering index and high luminous efficacy employing nanocrystal quantum dot luminophores,” Opt. Express 18(1), 340–347 (2010). [CrossRef]   [PubMed]  

10. T. Erdem, S. Nizamoglu, and H. V. Demir, “Computational study of power conversion and luminous efficiency performance for semiconductor quantum dot nanophosphors on light-emitting diodes,” Opt. Express 20(3), 3275–3295 (2012). [CrossRef]   [PubMed]  

11. A. Chalmers and S. Soltic, “Light source optimization: spectral design and simulation of four-band white-light sources,” Opt. Eng. 51(4), 044003 (2012). [CrossRef]  

12. S. Soltic and A. N. Chalmers, “Differential evolution for the optimisation of multi-band white LED light sources,” Lighting Res. Tech. 0, 1–14 (2011).

13. M. E. Coltrin, J. Y. Tsao, and Y. Ohno, “Limits on the maximum attainable efficiency for solid-state lighting,” Proc. SPIE 6841, 684102, 684102-12 (2007). [CrossRef]  

14. A. Neumann, J. J. Wierer Jr, W. Davis, Y. Ohno, S. R. J. Brueck, and J. Y. Tsao, “Four-color laser white illuminant demonstrating high color-rendering quality,” Opt. Express 19(S4Suppl 4), A982–A990 (2011). [CrossRef]   [PubMed]  

15. A. Chalmers and S. Soltic, “Towards the optimum light source spectrum,” Adv. Optoelectron. 2010, 596825 (2010). [CrossRef]  

16. X. Guo and K. W. Houser, “A review of colour rendering indices and their application to commercial light sources,” Lighting Res. Tech. 36(3), 183–199 (2004). [CrossRef]  

17. Y.-H. Chao, H.-S. Chen, P. Sun, M. R. Luo, J. Liao, and A. Lin, “New experimental data for evaluating colour rendering indexes,” AIC 2012 Interim Meeting, In Color we live: Color and Environment, Taipei 2012, pp. 238–241.

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

References

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  1. Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J.38(1), 1–6 (2007).
    [CrossRef]
  2. Y. Ohno, “Simulation analysis of white LED spectra and color rendering,” in Proceedings of CIE Expert Symposium on LED Light Sources, Tokyo, 2004.
  3. R. Stevenson, “The LED’s dark secret,” IEEE Spectr.•••, 23–27 (2009).
  4. A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today54(12), 42–47 (2001).
    [CrossRef]
  5. Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng.44(11), 111302 (2005).
    [CrossRef]
  6. A. Žakauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett.80(2), 234–236 (2002).
    [CrossRef]
  7. G. He, L. Zheng, and H. Yan, “LED white lights with high CRI and high luminous efficacy,” Proc. SPIE7852, 78520A (2010).
    [CrossRef]
  8. Commission Internationale de l’Eclairage, “Method of measuring and specifying colour rendering properties of light sources,” CIE Publication 13.3, CIE, Vienna (1995).
  9. T. Erdem, S. Nizamoglu, X. W. Sun, and H. V. Demir, “A photometric investigation of ultra-efficient LEDs with high color rendering index and high luminous efficacy employing nanocrystal quantum dot luminophores,” Opt. Express18(1), 340–347 (2010).
    [CrossRef] [PubMed]
  10. T. Erdem, S. Nizamoglu, and H. V. Demir, “Computational study of power conversion and luminous efficiency performance for semiconductor quantum dot nanophosphors on light-emitting diodes,” Opt. Express20(3), 3275–3295 (2012).
    [CrossRef] [PubMed]
  11. A. Chalmers and S. Soltic, “Light source optimization: spectral design and simulation of four-band white-light sources,” Opt. Eng.51(4), 044003 (2012).
    [CrossRef]
  12. S. Soltic and A. N. Chalmers, “Differential evolution for the optimisation of multi-band white LED light sources,” Lighting Res. Tech.0, 1–14 (2011).
  13. M. E. Coltrin, J. Y. Tsao, and Y. Ohno, “Limits on the maximum attainable efficiency for solid-state lighting,” Proc. SPIE6841, 684102, 684102-12 (2007).
    [CrossRef]
  14. A. Neumann, J. J. Wierer, W. Davis, Y. Ohno, S. R. J. Brueck, and J. Y. Tsao, “Four-color laser white illuminant demonstrating high color-rendering quality,” Opt. Express19(S4Suppl 4), A982–A990 (2011).
    [CrossRef] [PubMed]
  15. A. Chalmers and S. Soltic, “Towards the optimum light source spectrum,” Adv. Optoelectron.2010, 596825 (2010).
    [CrossRef]
  16. X. Guo and K. W. Houser, “A review of colour rendering indices and their application to commercial light sources,” Lighting Res. Tech.36(3), 183–199 (2004).
    [CrossRef]
  17. Y.-H. Chao, H.-S. Chen, P. Sun, M. R. Luo, J. Liao, and A. Lin, “New experimental data for evaluating colour rendering indexes,” AIC 2012 Interim Meeting, In Color we live: Color and Environment, Taipei 2012, pp. 238–241.
  18. W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng.49(3), 033602 (2010).
    [CrossRef]

2012

2011

S. Soltic and A. N. Chalmers, “Differential evolution for the optimisation of multi-band white LED light sources,” Lighting Res. Tech.0, 1–14 (2011).

A. Neumann, J. J. Wierer, W. Davis, Y. Ohno, S. R. J. Brueck, and J. Y. Tsao, “Four-color laser white illuminant demonstrating high color-rendering quality,” Opt. Express19(S4Suppl 4), A982–A990 (2011).
[CrossRef] [PubMed]

2010

A. Chalmers and S. Soltic, “Towards the optimum light source spectrum,” Adv. Optoelectron.2010, 596825 (2010).
[CrossRef]

G. He, L. Zheng, and H. Yan, “LED white lights with high CRI and high luminous efficacy,” Proc. SPIE7852, 78520A (2010).
[CrossRef]

T. Erdem, S. Nizamoglu, X. W. Sun, and H. V. Demir, “A photometric investigation of ultra-efficient LEDs with high color rendering index and high luminous efficacy employing nanocrystal quantum dot luminophores,” Opt. Express18(1), 340–347 (2010).
[CrossRef] [PubMed]

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

2009

R. Stevenson, “The LED’s dark secret,” IEEE Spectr.•••, 23–27 (2009).

2007

M. E. Coltrin, J. Y. Tsao, and Y. Ohno, “Limits on the maximum attainable efficiency for solid-state lighting,” Proc. SPIE6841, 684102, 684102-12 (2007).
[CrossRef]

Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J.38(1), 1–6 (2007).
[CrossRef]

2005

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

2004

X. Guo and K. W. Houser, “A review of colour rendering indices and their application to commercial light sources,” Lighting Res. Tech.36(3), 183–199 (2004).
[CrossRef]

2002

A. Žakauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett.80(2), 234–236 (2002).
[CrossRef]

2001

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today54(12), 42–47 (2001).
[CrossRef]

Bergh, A.

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today54(12), 42–47 (2001).
[CrossRef]

Brueck, S. R. J.

Chalmers, A.

A. Chalmers and S. Soltic, “Light source optimization: spectral design and simulation of four-band white-light sources,” Opt. Eng.51(4), 044003 (2012).
[CrossRef]

A. Chalmers and S. Soltic, “Towards the optimum light source spectrum,” Adv. Optoelectron.2010, 596825 (2010).
[CrossRef]

Chalmers, A. N.

S. Soltic and A. N. Chalmers, “Differential evolution for the optimisation of multi-band white LED light sources,” Lighting Res. Tech.0, 1–14 (2011).

Coltrin, M. E.

M. E. Coltrin, J. Y. Tsao, and Y. Ohno, “Limits on the maximum attainable efficiency for solid-state lighting,” Proc. SPIE6841, 684102, 684102-12 (2007).
[CrossRef]

Craford, G.

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today54(12), 42–47 (2001).
[CrossRef]

Davis, W.

Demir, H. V.

Duggal, A.

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today54(12), 42–47 (2001).
[CrossRef]

Erdem, T.

Gaska, R.

A. Žakauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett.80(2), 234–236 (2002).
[CrossRef]

Guangdi, S.

Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J.38(1), 1–6 (2007).
[CrossRef]

Guo, X.

X. Guo and K. W. Houser, “A review of colour rendering indices and their application to commercial light sources,” Lighting Res. Tech.36(3), 183–199 (2004).
[CrossRef]

Haitz, R.

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today54(12), 42–47 (2001).
[CrossRef]

He, G.

G. He, L. Zheng, and H. Yan, “LED white lights with high CRI and high luminous efficacy,” Proc. SPIE7852, 78520A (2010).
[CrossRef]

Houser, K. W.

X. Guo and K. W. Houser, “A review of colour rendering indices and their application to commercial light sources,” Lighting Res. Tech.36(3), 183–199 (2004).
[CrossRef]

Ivanauskas, F.

A. Žakauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett.80(2), 234–236 (2002).
[CrossRef]

Lei, Z.

Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J.38(1), 1–6 (2007).
[CrossRef]

Ming, L. Q.

Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J.38(1), 1–6 (2007).
[CrossRef]

Neumann, A.

Nizamoglu, S.

Ohno, Y.

A. Neumann, J. J. Wierer, W. Davis, Y. Ohno, S. R. J. Brueck, and J. Y. Tsao, “Four-color laser white illuminant demonstrating high color-rendering quality,” Opt. Express19(S4Suppl 4), A982–A990 (2011).
[CrossRef] [PubMed]

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

M. E. Coltrin, J. Y. Tsao, and Y. Ohno, “Limits on the maximum attainable efficiency for solid-state lighting,” Proc. SPIE6841, 684102, 684102-12 (2007).
[CrossRef]

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

Y. Ohno, “Simulation analysis of white LED spectra and color rendering,” in Proceedings of CIE Expert Symposium on LED Light Sources, Tokyo, 2004.

Shur, M. S.

A. Žakauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett.80(2), 234–236 (2002).
[CrossRef]

Soltic, S.

A. Chalmers and S. Soltic, “Light source optimization: spectral design and simulation of four-band white-light sources,” Opt. Eng.51(4), 044003 (2012).
[CrossRef]

S. Soltic and A. N. Chalmers, “Differential evolution for the optimisation of multi-band white LED light sources,” Lighting Res. Tech.0, 1–14 (2011).

A. Chalmers and S. Soltic, “Towards the optimum light source spectrum,” Adv. Optoelectron.2010, 596825 (2010).
[CrossRef]

Stevenson, R.

R. Stevenson, “The LED’s dark secret,” IEEE Spectr.•••, 23–27 (2009).

Sun, X. W.

Ting, L.

Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J.38(1), 1–6 (2007).
[CrossRef]

Tsao, J. Y.

A. Neumann, J. J. Wierer, W. Davis, Y. Ohno, S. R. J. Brueck, and J. Y. Tsao, “Four-color laser white illuminant demonstrating high color-rendering quality,” Opt. Express19(S4Suppl 4), A982–A990 (2011).
[CrossRef] [PubMed]

M. E. Coltrin, J. Y. Tsao, and Y. Ohno, “Limits on the maximum attainable efficiency for solid-state lighting,” Proc. SPIE6841, 684102, 684102-12 (2007).
[CrossRef]

Vaicekauskas, R.

A. Žakauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett.80(2), 234–236 (2002).
[CrossRef]

Wierer, J. J.

Xia, G.

Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J.38(1), 1–6 (2007).
[CrossRef]

Xiaoling, G.

Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J.38(1), 1–6 (2007).
[CrossRef]

Yan, H.

G. He, L. Zheng, and H. Yan, “LED white lights with high CRI and high luminous efficacy,” Proc. SPIE7852, 78520A (2010).
[CrossRef]

Žakauskas, A.

A. Žakauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett.80(2), 234–236 (2002).
[CrossRef]

Zheng, L.

G. He, L. Zheng, and H. Yan, “LED white lights with high CRI and high luminous efficacy,” Proc. SPIE7852, 78520A (2010).
[CrossRef]

Adv. Optoelectron.

A. Chalmers and S. Soltic, “Towards the optimum light source spectrum,” Adv. Optoelectron.2010, 596825 (2010).
[CrossRef]

Appl. Phys. Lett.

A. Žakauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett.80(2), 234–236 (2002).
[CrossRef]

IEEE Spectr.

R. Stevenson, “The LED’s dark secret,” IEEE Spectr.•••, 23–27 (2009).

Lighting Res. Tech.

X. Guo and K. W. Houser, “A review of colour rendering indices and their application to commercial light sources,” Lighting Res. Tech.36(3), 183–199 (2004).
[CrossRef]

S. Soltic and A. N. Chalmers, “Differential evolution for the optimisation of multi-band white LED light sources,” Lighting Res. Tech.0, 1–14 (2011).

Microelectron. J.

Z. Lei, G. Xia, L. Ting, G. Xiaoling, L. Q. Ming, and S. Guangdi, “Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs,” Microelectron. J.38(1), 1–6 (2007).
[CrossRef]

Opt. Eng.

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

A. Chalmers and S. Soltic, “Light source optimization: spectral design and simulation of four-band white-light sources,” Opt. Eng.51(4), 044003 (2012).
[CrossRef]

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

Opt. Express

Phys. Today

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today54(12), 42–47 (2001).
[CrossRef]

Proc. SPIE

G. He, L. Zheng, and H. Yan, “LED white lights with high CRI and high luminous efficacy,” Proc. SPIE7852, 78520A (2010).
[CrossRef]

M. E. Coltrin, J. Y. Tsao, and Y. Ohno, “Limits on the maximum attainable efficiency for solid-state lighting,” Proc. SPIE6841, 684102, 684102-12 (2007).
[CrossRef]

Other

Y.-H. Chao, H.-S. Chen, P. Sun, M. R. Luo, J. Liao, and A. Lin, “New experimental data for evaluating colour rendering indexes,” AIC 2012 Interim Meeting, In Color we live: Color and Environment, Taipei 2012, pp. 238–241.

Commission Internationale de l’Eclairage, “Method of measuring and specifying colour rendering properties of light sources,” CIE Publication 13.3, CIE, Vienna (1995).

Y. Ohno, “Simulation analysis of white LED spectra and color rendering,” in Proceedings of CIE Expert Symposium on LED Light Sources, Tokyo, 2004.

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Figures (4)

Fig. 1
Fig. 1

Relative spectral power distributions versus wavelengths (nm) for the three optimized spectra of tetrachromatic illuminants with Ra = 90 and ηrad ≥ 357 lumens per radiant watt. Numbers above each delta function show the individual peak wavelengths in nm.

Fig. 2
Fig. 2

Relative spectral power distributions versus wavelengths (nm) for the three optimized spectra of pentachromatic illuminants with Ra > 90, ηrad ≥ 364 lumens per radiant watt. Numbers above each delta function show the individual peak wavelengths in nm.

Fig. 3
Fig. 3

Relative spectral power distributions versus wavelengths (nm) for the three optimized spectra of hexachromatic illuminants with Ra ≥ 90, ηrad ≥ 317 lumens per radiant watt. Numbers above each delta function show the individual peak wavelengths in nm.

Fig. 4
Fig. 4

Relative spectral power distributions versus wavelengths (nm) for the three suboptimal spectra of tetrachromatic illuminants with Ra ≥ 71, ηrad ≥ 364 lumens per radiant watt. Numbers above each delta function show the individual peak wavelengths in nm.

Tables (4)

Tables Icon

Table 1 Optimization of mixtures of 4 delta-function spectraa

Tables Icon

Table 2 Optimization of mixtures of 5 delta-function spectraa

Tables Icon

Table 3 Optimization of mixtures of 6 delta-function spectraa

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Table 4 Mixtures of ‘suboptimal’ tetrachromatic mixturesa

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

η rad = η rad(max) λ V(λ)S(λ)dλ λ S(λ)dλ .
f=a R a +b R b +c R c +d R min +e η rad

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