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Optimization of solid-state lighting spectra is performed to achieve beneficial and tunable circadian effects. First, the minimum spectral circadian action factor (CAF) of 2700 K white light-emitting diodes (LEDs) is studied for applications where biologically active illumination is undesirable. It is found that white-LEDs based on (i) RGB chips, (ii) blue & red chips plus green phosphor, and (iii) blue chip plus green & red phosphors are the corresponding minimum-CAF solutions at color-rendering index (CRI) requirements of 80, 90, and 95, respectively. Second, maximum CAF tunability of LED clusters is studied for dynamic daylighting applications. A dichromatic phosphor-converted blue-centered LED, a dichromatic phosphor-converted green-centered LED, and a monochromatic red LED are grouped to obtain white spectra between 2700 K and 6500 K. A maximum CAF tunability of 3.25 times is achieved with CRI above 90 and luminous efficacy of radiation of 313 - 373 lm/W. We show that our approaches have advantages over previously reported solutions on system simplicity, minimum achievable CAF value, CAF tunability range, and light source efficacy.
© 2016 Optical Society of America
1. Introduction
Today, solid-state lighting (SSL) based on light-emitting diodes (LEDs) is replacing traditional lighting technologies in a rapid rate, due to SSL’s high energy efficiency, long lifetime, spectral flexibility, environmental friendliness, fast response, and small size [1–4]. Beyond vision functions, light could also affect human circadian rhythms [5–10], with an effect even more powerful than any drug [10]. An intuitive example is that the natural daylight, with its periodic change of spectrum and intensity, serves as a pace-maker for human’s “internal clock” to synchronize and re-calibrate to a 24-hour rhythm. SSL’s flexibility in spectral design makes it an excellent technology for smart, beneficial, and tunable lighting applications [2, 11]. Interest in the use of lighting for possible health benefits has grown rapidly, including utilizing artificial lighting to mimic the circadian effect of natural daylight [11], improve sleep quality [10, 12], physiology, alertness and cognitive performance [13], release seasonal affective disorder (SAD) [14], depression [15], jetlag, and possible health issues associated with shift work [9].
Parallel to the rapid development of LED technology, the biological impact of light is also studied extensively. Starting from the turn of the millennium, the non-image-forming intrinsically photosensitive retinal ganglion cells (ipRGCs) was discovered in retina [16]. The ipRGCs report light stimuli to the suprachiasmatic nucleus (SCN) to slow down the melatonin secretion in human blood, and therefore affecting the circadian phase. Melatonin promotes sleepiness, slows down body functions and lowers activity levels [13]. The spectral sensitivity of melatonin suppression was measured [17, 18], and the action spectrum of light’s circadian effect was proposed [19–22] based on these experimental data. While the photopic eye-sensitivity has a peak at 555 nm [23], the circadian action spectrum reaches its peak at blue wavelength. Despite some limitations [9, 11, 24], we choose the Gall model [19, 22, 25, 26] for circadian-effect calculations in this work.
The circadian action factor (CAF) ac, which is defined as the ratio of the circadian efficacy to luminous efficacy, is obtained as follows [19, 20, 22]:
where P (λ) is spectral power distribution (SPD) of a light source, and K is a normalization constant which makes ac = 1 for the SPD of the CIE standard daylight illuminant D65. Equation (1) can be written aswhere x and y values are the CIE chromaticity coordinates. From Eq. (2), one finds that the value of ac is determined by two factors: (i) the value of , which is determined by the color coordinate of a white light spectrum and monotonically decreases along the planckian locus from high to low correlated color temperatures (CCTs); and (ii) the value of , which is determined by the specific SPD. Due to the similarity of C (λ) and normalizedin spectral distribution (see Fig. 1), the circadian effect of white light has a clear trend to increase with increasing color temperature. Therefore, the spectral design for minimum circadian action should focus on low CCTs while the design for maximum circadian action should focus on high CCTs.
Fig. 1 Comparison of photopic eye-sensitivity function V (λ) [23], circadian spectral efficiency function C (λ) [19], and CIE standard color matching function [3].
Optimization of artificial white light spectra has been an important research topic. Numerous studies have been focused on lighting’s energy efficiency and color rendition parameters, such as luminous efficacy of radiation (LER), luminous efficacy (LE), color rendering index (CRI), and CCT [27–30]. With the advance of photobiology research and LED technology, it is now possible to optimize white light spectra in a new dimension – circadian effect – for possible health benefits. This effort has already been started: Kozakov et al. [25] proposed modified spectra of fluorescent and HID lamps for suitable melatonin-suppression effects; Oh et al. [11] demonstrated a tunable circadian effect based on four-package white LEDs; and Žukauskas et al. [26] studied the CAF tunability range of white spectra based on a cluster of four direct-emitting LEDs. These previous works are important. However, to our knowledge, the minimum achievable CAF of white LED spectra has not been systematically investigated; and based on our study (this work), four channels may not be necessary to achieve a wide CAF tunability.
In this work, first, we systematically investigate the minimum achievable CAF value of a white LED spectrum for “evening lighting”, by comparing popular white-LED approaches at a fixed color temperature of 2700 K. Second, we propose a new approach to maximize CAF tunability of LED clusters, for dynamic daylighting, based on only three tunable channels. We adopt partially phosphor-converted, dichromatic blue-centered and green-centered LEDs for additional spectral design flexibility. We show that our approach could achieve higher performance and lower system complexity compared to previous solutions.
2. Minimum circadian action factor of 2700 K white LED spectra for “evening lighting”
First, we report on the spectral optimization of 2700 K white LEDs for “evening lighting” applications where biologically active illumination is undesirable. For example, a reduced circadian action for bedroom lighting and shower lighting could minimize the disruption of human circadian rhythm and facilitate a good night sleep. Given a certain level of illuminance that is required for meeting vision tasks, a lower-CAF design of lighting spectrum leads to a lower “biological illuminance” accompanies such vision function. The color temperature of 2700 K is chosen due to the consideration that CAF has a trend to decrease with decreasing CCT (as shown by Eq. (2)). 2700 K is a typical color temperature of an incandescent bulb, is very popular for bedroom lighting, and in many cases is the lowest color temperature option in SSL product portfolios [31]. “Candle light” and “fire light” spectra have much lower CCTs such as 2000 K [32, 33], therefore can provide even smaller CAF values; however, such a low color temperature is currently not widely adopted for residential general illumination. Therefore, the following spectral optimization of white LEDs focus on the color temperature of 2700 K. A similar calculation can be applied to any other color temperatures.
Spectra of direct-emitting InGaN (blue & green) and AlInGaP (red) LED chips and phosphors are used as color components of a white LED spectrum. Popular approaches to generate white light include the spectral combinations of (i) direct-emitting blue, green, and red chips [27] (denoted as RGB LED), (ii) direct-emitting blue and red chips plus green (or yellow) phosphor [29, 30] (denoted as RGpB LED), and (iii) blue chip plus green and red phosphors [34] (denoted as RpGpB LED). The spectrum of a direct-emitting LED chip is typically modeled by a Gaussian function on the wavelength scale, with a full-width at half maximum (FWHM) of 30 nm [26, 27, 35]; phosphor in applications of SSL has a large diversity with single or multiple emission bands. In this work, we restrict the phosphor selection to those only having a single emission band with predictable width, and employ the model of Gaussian functions on the photon energy scale [34, 35]. The SPD of phosphor Pphosphor (λ) is then modeled as
where λ0 is the corresponding wavelength of peak energy on the photon energy scale, h is the planckian constant, c is the speed of light, and W is the FWHM measured in photon energy scale. Žukauskas et al. [34] demonstrated that such a spectral distribution, with W = 0.27 eV, can be used to accurately describe a variety of single-band Eu2+ phosphors (4f 65d 1 - 4f 7 transitions) with peak wavelength spanning from 450 to 650 nm. The hosts of such Eu2+ phosphors include Chalcogenides, Silicates, Aluminates, Nitridosilicates, SiONs, and SiAlONs [34]. This phosphor model is adopted in this work.We start with the optimization based on the RGpB LED solution. The requirement of properly reproducing color of illuminated objects places restrictions on the design of light source spectra and therefore the achievable range of CAF. Despite some limitations [36] and development of new evaluation methods [37], we choose the general CRI, or Ra [38] to evaluate light sources’ color rendering ability because it is currently widely accepted in lighting industry.
Due to the fact that there is a trade-off between achievable low CAF and high CRI, attention is paid to bi-objective Pareto optimal solutions [39, 40]; that is, solutions that cannot be improved in either of the objectives without degrading the other objective [40]. In this case, [CAF, CRI]T is an objective function vector, and [λ1, λ2, λ3, I1, I2, I3]T is a design vector, where λn and In (n = 1, 2, or 3) are the wavelength and intensity contribution from each color component, and the foot notes 1, 2, and 3 represent blue chip, green phosphor, and red chip, respectively. One of the most widely used methods to obtain Pareto optimal solutions is to convert the bi-objective (vector) optimization problem into a series of single-objective (scalar) problems [40], frequently by using the weight-sum method [40, 41]. Here, we create a series of single-objective functions to be minimized:
where Fσ is an aggregated, weighted sum of the two objectives (− CRI and CAF to be minimized), k is a positive scale factor, and σ is a variable weight factor, between 0 and 1, that controls the trade-off between lower CAF and higher CRI values. When a series of solutions at various σ values are found by minimizing the single-objective equations, a set of corresponding data points (CRI, CAF) in the two-dimensional objective space are obtained, which forms the Pareto frontier [40]. In this study, the Pareto frontier defines the minimum achievable CAFs at various CRI values.To obtain the minimum value of Fσ at each σ value, we apply the additive-color-mixing constraints [29] for the 2700 K white target to reduce the 6-dimensional design parameter space of {λ1, λ2, λ3, I1, I2, I3} into a 3-dimentional independent parameter space {λ1, λ2, λ3}. For each wavelength combination, the equations to obtain [I1, I2, I3]T from [λ1, λ2, λ3]T can be found in our previous work [29]. The SPD of the white spectra can then be obtained, based on which the CAF can be calculated from Eq. (1), the CRI can be calculated according to the CIE 1995 publication [38], and Fσ can be obtained from Eq. (4). The problem of finding the minimum value of Fσ can then be solved by any method of nonlinear programming [42] with three variables λ1, λ2, and λ3. Here, we make use of the Interior Point Algorithm [43–45] because it allows constrained optimization. Such spectral optimization problems have also been solved by other methods such as the Downhill Simplex Method (Nelder-Mead) [42]. In this work, we obtain the same optimization results by using both methods.
Take the optimization of 2700 K white spectra as an example, we search the regions of 400 nm ≤ λ1 ≤ 500 nm, 500 nm ≤ λ2 ≤ 650 nm, and 600 nm ≤ λ3 ≤ 750 nm using the procedures described above, and choose k = 276 and σ varies from 0 to 0.8, with an interval of 0.01, to achieve well-distributed data points as the minimum CAFs in the desired CRI range of 60 to 100. The result is shown as the red cycles in Fig. 2(a), with the corresponding data points for σ = 0 and σ = 0.8 marked.
Fig. 2 (a) CAF vs. CRI for 2700 K white sources based on the RGpB solution, and (b) the representative spectra with various CAFs.
To further confirm the minimum CAFs obtained, and show a distribution of CAF vs. CRI from various combinations of component wavelengths, we perform another search by enumerating the color-mixing combinations based on choosing wavelengths of the three color components at every 5 nm, within the same wavelength range of 400 nm ≤ λ1 ≤ 500 nm, 500 nm ≤ λ2 ≤ 650 nm, and 600 nm ≤ λ3 ≤ 750 nm (therefore totally 20181 combinations), the result is plotted as the blue dots (only those with CRI > 60 are shown) in Fig. 2(a). It is clearly shown that the Pareto frontier based on our bi-objective nonlinear optimization perfectly marks the boundary of minimum achievable CAFs at various CRI values.
Compared to the 2700 K black-body emission spectrum, which has a CAF of 0.364, it is found that white LEDs could have either higher or lower circadian actions based on its spectral design. At CRI of 80, for example, the CAF of 2700 K RGpB white LED sources could vary from 73% to 133% of the CAF value of the incandescent spectrum with the same color temperature. Despite the claims that the strong blue spectral component of white LEDs, originates from the InGaN pump chip, causes negative melatonin-suppression effect (so-called “blue hazard”) in residential lighting and display lighting of mobile devices [10, 46], our result indicates that a white-LED spectrum could actually impose less melatonin-suppression effect compared to that of an incandescent lamp. As an example, the spectra of commercial Luminus CXM-14-27-80 and CXM-14-27-90 white LEDs are measured, and their CAF and CRI values are also plotted in Fig. 2(a). These two LEDs both show lower spectral CAF compared to that of an incandescent bulb, therefore are more suitable for “evening lighting”. Figure 2(b) shows the corresponding spectra of the 2700 K black-body emission (at visible wavelengths), the Luminus LEDs, and the minimum possible CAF solution at CRI of 80.
Next, we compare the minimum achievable CAFs among three popular white-LED approaches: RGpB, RpGpB, and RGB LED packages. Similar optimization routines are performed, and the results are shown below.
Figure 3(a) shows the minimum CAFs (Pareto frontiers) at various CRI values (only minimum CAFs less than that of the 2700 K planckian radiator are shown in the figure). One finds that among the three approaches, the minimum CAF at CRI of 80, 90, and 95 are achieved by the RGB, RGpB, and RpGpB solutions, respectively, with the corresponding CAF values of 0.25, 0.29, and 0.32, respectively. Therefore, the best white-light-generation solution for minimum CAF depends on the color-rendition requirement. Figure 3(b) shows the corresponding LERs of the data points in Fig. 3(a). Note that LER is the ratio of luminous flux to optical power of a light source, it is different from LE that the former is solely determined by the SPD of a light source, while the latter also takes into account the energy conversion efficiency from electrical to optical power [29]. It is found that the RGB solution and the RGpB solution leads to much higher LERs (> 360 lm/W) compared to those based on the RpGpB solution. The RGB white LED solution, however, suffers from the very low optical-to-electrical conversion efficiency of green LED chips (referred to as the “green gap” [4, 47]), therefore it could still have a relatively low overall LE despite of its high LER. Figures 3(c), 3(d), and 3(e) show the lowest-CAF spectra at CRI of 80, 90, and 95, respectively.
Fig. 3 (a) Minimum CAF vs. CRI (Pareto frontiers) for 2700 K sources based on RGB, RGpB, and RpGpB white-LED solutions, (b) the corresponding LERs, and the corresponding spectra for lowest CAFs at CRI of (c) 80, (d) 90, and (e) 95.
3. Maximum tunability of circadian action factor for dynamic daylighting between color temperatures of 2700 K and 6500 K
It is desirable to dynamically tune the circadian action of indoor lighting to convey a sense of day / night rhythm, especially in situations where natural daylight is insufficient. For example, a high circadian-action lighting in the morning could help to ease awakening, increase body alertness, potentially improve work efficiency, and potentially phase advance the circadian timing system; while a low circadian-action lighting in the evening could help to not suppress melatonin secretion and improve sleep quality [10, 13].
The maximum tunability of CAF between color temperatures of 2700 K and 6500 K is investigated. Equation (2) indicates that an important part of the CAF tunability originates from the shift of color coordinate from the warm to the cool white end on the planckian locus. The principle of additive color mixing indicates that for any target color coordinate within the triangle formed by the coordinates of the three color channels, only a single spectrum solution could be obtained [27]. There exists no freedom to vary the mixed spectrum (and thus CAF) by adjusting flux contributions from each channel. However, additional flexibility in spectral design can be created by adopting dichromatic color channels, which can be easily realized by using partially phosphor-converted blue-centered and green-centered LEDs, in addition to a monochromatic red LED channel. To achieve maximum CAF tunability, we design the three color channels in a manner that the minimum CAF is achieved at 2700 K, with flux contributions from only the green-centered LED and the red LED; while the maximum CAF is achieved at 6500 K, with flux contributions only from the blue-centered LED and the same red LED. The problem now is converted into two sets of CAF optimizations based on trichromatic color mixing (the RGpB approach) that is discussed in the previous section, with the constraint that the same red LED being used in these two sets of color mixing. In other words, this approach allows one to use up to five chip / phosphor spectral components while maintaining the number of channels to three, which is a big advantage for the reduction of complexity and cost on the control system.
Take the optimization of the blue-centered LED (channel) as an example: we introduce an objective function Gσ to be maximized at 6500 K, a certain red LED wavelength, and a fixed CRI of 90:
where the foot notes BC-1 and BC-2 represent the blue InGaN chip and the phosphor components of the blue-centered LED, respectively. The constraint of color-mixing for 6500 K white target reduces the 5-dimensional design parameter space into a 2-dimensional space. Using the optimization method that is discussed earlier in this work, the maximum value of the constrained nonlinear function Eq. (5) can be found. A similar approach can be used to obtain the minimum CAF at 2700 K, a certain red LED wavelength, and a fixed CRI of 90, based on a green-centered LED and the same red LED.The maximum circadian tunability, ac, max (6500 K) / ac, min (2700 K), is then calculated as a function of the wavelength of the common red LED. Figure 4(a) shows that the circadian tunability reaches its maximum of 3.25 times at red LED wavelength of 623 nm, with ac, min (2700 K) = 0.294 and ac, max (6500 K) = 0.957. The spectra of the corresponding dichromatic blue-centered LED (peaks: 465 nm and 549 nm), the green-centered LED (peaks: 455 nm and 556 nm), and the monochromatic red LED (peak: 623 nm) are shown in Fig. 4(b). The CAF of the blue-centered, green-centered, and red channels are 1.152, 0.414, and 0, respectively. Note that the requirement of red LED being the same for the two optimizations only introduces very little compromise on the minimum and maximum achievable CAFs (0.3% increase of the minimum CAF at 2700 K and 1.0% decrease of maximum CAF at 6500 K), but allows the total number of channels reduced to three.
Fig. 4 (a) CAF tunability between 2700 K and 6500 K, as a function of the common red LED wavelength. (b) The optimized spectra of three LEDs for maximum CAF tunability.
The optimized LED cluster can be tuned, by varying the flux contribution from each channel, to cover a CCT range from 2700 K to 6500 K on the planckian locus. The color coordinates of the three LED channels as well as the white color points of 2700 K, 3000 K, 4000 K, 4870 K, and 6500 K are shown in Fig. 5(a). The corresponding white spectra at various color temperatures are shown in Fig. 5(b).
Fig. 5 (a) Color coordinates of three LEDs as well as white color points on the planckian locus. (b) Spectra of the tunable LED cluster at 2700 K, 3000 K, 4000 K, 4870 K, and 6500 K.
The CAF and LER values as a function of CCT for the three-channel tunable LED cluster are plotted in Fig. 6. With increasing CCT, the contribution from the blue-centered LED increases, therefore, the circadian effect of white light spectra increases while the spectral efficacy decreases. With a high CRI of 90, such a light source could be used for high-quality indoor lighting applications where the CAF can be tuned by a factor of 3.25, ranging from 0.294 (about 81% of the CAF of the 2700 K incandescent spectrum) to 0.957 (about 96% of the CAF of the CIE standard daylight illuminant D65). As a comparison, Ref [26]. shows that based on four channels of direct-emitting LED chips, a CAF tunability of 3.11 times, ranging from 0.351 to 1.038, can be achieved at color fidelity index [36] of 90. Therefore, besides the advantage of reducing the number of tunable channels from four to three, our approach could have advantages on minimum achievable CAF value, CAF tunability range, and light source efficacy (direct-emitting green and yellow LED chips have very low electrical-to-optical conversion efficacy, or “green gap” [4, 29, 47, 48]).
4. Conclusion
In this work, we demonstrate that for 2700 K indoor “evening lighting”, white LED solutions based on (i) RGB chips, (ii) blue & red chips plus green phosphor, and (iii) blue chip plus green & red phosphors are the corresponding desirable solutions for minimum circadian action, at CRI requirements of 80, 90, and 95, respectively. We also demonstrate that three-channel LED clusters based on a dichromatic phosphor-converted blue-centered LED, a dichromatic phosphor-converted green-centered LED, and a monochromatic red LED can achieve a CAF tunability of 3.25 times, with CRI above 90 and LER of 313 – 373 lm/W within the CCT tunable range of 2700 K to 6500 K. Besides the reduction of system complexity, this approach could have advantages on minimum achievable CAF value, CAF tunability range, and light source efficacy compared to previously reported solutions.
Acknowledgments
This work was supported by the College of Architecture and Urban Planning, Tongji University and the Shanghai Summit Program.
References and Links
1. S. Nakamura and G. Fasol, The Blue Laser Diode: GaN Based Light Emitters and Lasers (Springer, 1997).
2. E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005). [CrossRef] [PubMed]
3. E. F. Schubert, Light-Emitting Diodes, 2nd ed. (Cambridge University, 2006).
4. P. Pust, P. J. Schmidt, and W. Schnick, “A revolution in lighting,” Nat. Mater. 14(5), 454–458 (2015). [CrossRef] [PubMed]
5. L. Wetterberg, Light and Biological Rhythms in Man (Pergamon Press, 1993).
6. J. Aschoff, Biological Rhythms (Handbook of Behavioral Neurobiology No. 4) (Plenum, 1981).
7. R. Wurtman, M. J. Baum, and J. T. Potts, The Medical and Biological Effects of Light (The New York Academy of Sciences, 1985).
8. L. Bellia, F. Bisegna, and G. Spada, “Lighting in indoor environments: visual and non-visual effects of light sources with different spectral power distributions,” Build. Environ. 46(10), 1984–1992 (2011). [CrossRef]
9. R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014). [CrossRef] [PubMed]
10. C. A. Czeisler, “Perspective: casting light on sleep deficiency,” Nature 497(7450), S13 (2013). [CrossRef] [PubMed]
11. J. H. Oh, S. J. Yang, and Y. R. Do, “Healthy, natural, efficient and tunable lighting: four-package white LEDs for optimizing the circadian effect, color quality and vision performance,” Light Sci. Appl. 3(2), e141 (2014). [CrossRef]
12. T. Partonen, “Effects of morning light treatment on subjective sleepiness and mood in winter depression,” J. Affect. Disord. 30(2), 99–108 (1994). [CrossRef] [PubMed]
13. Licht.de publications, Impact of Light on Human Beings (licht.de, 2014).
14. R. W. Lam, Beyond Seasonal Affective Disorder: Light Treatment for SAD and non-SAD Disorders (American Psychiatric Press, 1996).
15. C. I. Eastman, M. A. Young, L. F. Fogg, L. Liu, and P. M. Meaden, “Bright light treatment of winter depression: a placebo-controlled trial,” Arch. Gen. Psychiatry 55(10), 883–889 (1998). [CrossRef] [PubMed]
16. D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295(5557), 1070–1073 (2002). [CrossRef] [PubMed]
17. G. C. Brainard, J. P. Hanifin, J. M. Greeson, B. Byrne, G. Glickman, E. Gerner, and M. D. Rollag, “Action spectrum for melatonin regulation in humans: evidence for a novel circadian photoreceptor,” J. Neurosci. 21(16), 6405–6412 (2001). [PubMed]
18. K. Thapan, J. Arendt, and D. J. Skene, “An action spectrum for melatonin suppression: evidence for a novel non-rod, non-cone photoreceptor system in humans,” J. Physiol. 535(1), 261–267 (2001). [CrossRef] [PubMed]
19. D. Gall, “Circadiane Lichtgrößen und deren messtechnische ermittlung,” Licht 54, 1292–1297 (2002).
20. D. Gall and K. Beiske, “Definition and measurement of circadian radiometric quantities,” in Proceedings of the 2004 CIE Symposium on Light and Health: Non-visual Effects (Commission Internationale de l’E´ clairage, 2004), pp. 129–132.
21. M. S. Rea, M. G. Figueiro, and J. D. Bullough, “Circadian photobiology: an emerging framework for lighting practice and research,” Light. Res. Technol. 34(3), 177–190 (2002). [CrossRef]
22. Deutsches Institut fur Normung (DIN), Optical Radiation Physics and Illuminating Engineering – Part 100: Non-visual Effects of Ocular Light on Human Beings – Quantities, Symbols and Action Spectra, DIN V 5031–100:2009–06 (2009).
23. International Commission on Illumination (CIE), Commission internationale de l'Eclairage proceedings, 1924 (Cambridge University, 1926).
24. M. S. Rea, M. G. Figueiro, J. D. Bullough, and A. Bierman, “A model of phototransduction by the human circadian system,” Brain Res. Brain Res. Rev. 50(2), 213–228 (2005). [CrossRef] [PubMed]
25. R. Kozakov, H. Schopp, St. Franke, C. Stoll, and D. Kunz, “Modification of light sources for appropriate biological action,” J. Phys. D Appl. Phys. 43(23), 234007 (2010). [CrossRef]
26. A. Žukauskas and R. Vaicekauskas, “Tunability of the circadian action of tetrachromatic solid-state light sources,” Appl. Phys. Lett. 106(4), 041107 (2015). [CrossRef]
27. A. Žukauskas, 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]
28. A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, and M. S. Shur, “Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering,” Appl. Phys. Lett. 93(5), 051115 (2008). [CrossRef]
29. Q. Dai, L. Hao, Y. Lin, and Z. Cui, “Spectral optimization simulation of white light based on the photopic eye-sensitivity curve,” J. Appl. Phys. 119(5), 053103 (2016). [CrossRef]
30. G. He and H. Yan, “Optimal spectra of the phosphor-coated white LEDs with excellent color rendering property and high luminous efficacy of radiation,” Opt. Express 19(3), 2519–2529 (2011). [CrossRef] [PubMed]
31. For example, Osram product catalog, “OSLON SSL 150 White,” http://www.osram-os.com/osram_os/en/products/product-catalog/leds-for-general-lighting/oslon-ssl-150-white/index.jsp.
32. A. Žukauskas, R. Vaicekauskas, and P. Vitta, “Optimization of solid-state lamps for photobiologically friendly mesopic lighting,” Appl. Opt. 51(35), 8423–8432 (2012). [CrossRef] [PubMed]
33. A. Zabiliūtė, R. Vaicekauskas, P. Vitta, and A. Žukauskas, “Phosphor-converted LEDs with low circadian action for outdoor lighting,” Opt. Lett. 39(3), 563–566 (2014). [CrossRef] [PubMed]
34. A. Žukauskas, R. Vaicekauskas, P. Vitta, A. Zabiliūtė, A. Petrulis, and M. Shur, “Color rendition engineering of phosphor-converted light-emitting diodes,” Opt. Express 21(22), 26642–26656 (2013). [CrossRef] [PubMed]
35. G. He and J. Tang, “Spectral optimization of color temperature tunable white LEDs with excellent color rendering and luminous efficacy,” Opt. Lett. 39(19), 5570–5573 (2014). [CrossRef] [PubMed]
36. W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602 (2010). [CrossRef]
37. Illuminating Engineering Society, IES TM-30–15 Method for Evaluating Light Source Color Rendition (2015).
38. International Commission on Illumination, Method of Measuring and Specifying Colour Rendering Properties of Light Sources, CIE Publication No. 13.3 (1995).
39. W. Stadler, “A survey of multicriteria optimization, or the vector maximum problem,” J. Optim. Theory Appl. 29(1), 1–52 (1979). [CrossRef]
40. I. Y. Kim and O. L. de Weck, “Adaptive weighted-sum method for bi-objective optimization: Pareto front generation,” Struct. Multidiscipl. Optim. 29(2), 149–158 (2005). [CrossRef]
41. L. A. Zadeh, “Optimality and non-scalar-valued performance criteria,” IEEE Trans. Automat. Contr. 8(1), 59–60 (1963). [CrossRef]
42. R. Kozakov, S. Franke, and H. Schopp, “Approach to an effective biological spectrum of a light source,” Leukos 4, 255–263 (2008).
43. R. H. Byrd, J. C. Gilbert, and J. Nocedal, “A trust region method based on interior point techniques for nonlinear programming,” Math. Program. 89(1), 149–185 (2000). [CrossRef]
44. R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban, “An interior algorithm for nonlinear optimization that combines line search and trust region steps,” Math. Program. 107(3), 391–408 (2006). [CrossRef]
45. MathWorks documentation, “Find minimum of constrained nonlinear multivariable function,” (MathWorks, 2016) http://www.mathworks.com/help/optim/ug/fmincon.html?s_tid=gn_loc_drop.
46. K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011). [CrossRef] [PubMed]
47. U. S. Department of Energy SSL program, Solid-State Lighting R&D Plan (May 2015), prepared by Bardsley Consulting, SB Consulting, SSLS, InC., LED lighting Advisors, and Navigant Consulting, Inc. (2015), pp. 51–53, http://energy.gov/sites/prod/files/2015/06/f22/ssl_rd-plan_may2015_0.pdf.
48. A. Liu, A. Khanna, P. S. Dutta, and M. Shur, “Red-blue-green solid state light sources using a narrow line-width green phosphor,” Opt. Express 23(7), A309–A315 (2015). [CrossRef] [PubMed]
