Optimal spectra of white LED integrated with quantum dots for mesopic vision

Linlin Zan; Duyang Lin; Ping Zhong; Guoxing He

doi:10.1364/OE.24.007643

1. Introduction

Today’s white light-emitting diodes (WLEDs) are commonly specified by photopic vision. Some spectral optimizations for WLEDs have been obtained by nonlinear program for maximizing luminous efficacy (of radiation) of photopic vision (LER_p) under constraints of designated color rendering properties [1–4]. However, the human eyes have different visual responses at different ambient light conditions, where mesopic lighting condition falls between 0.005 cd/m² and 5 cd/m² [5–7]. The outdoor lighting such as road lighting generally falls into the mesopic vision region [8–10]. It was found that the high scotopic/photopic (S/P) ratio of the source is predicted to yield better perceived brightness along with better visual acuity [11, 12]. Recently, it was reported that WLED integrated with quantum dots (QDs) can realized the S/P ratios higher than 2.50 [13, 14]. For optimal spectra of WLED under mesopic vision, a few studies, as far as we know, have been reported in the literature [15, 16]. In 2013, the InGaN-based white LEDs integrated with QDs have been computationally investigated, which found S/P ratios > 3.80 and color rendering indices [17] (CRIs) > 70 for three-hump LEDs and S/P ratios > 3.90 and CRIs > 70 for four-hump LEDs under a CCT of 45000 K by maximizing S/P ratio [15]. In 2014, it was reported that the spectral parameters of QD-WLEDs with both CRI ≥ 85 and CQS [18] ≥ 85 possessing the highest mesopic luminance for all four road lighting standards together with the scotopic and photopic vision regimes [16]. However, the mesopic luminous efficacy of light sources depends on not only the S/P ratio but also the photopic luminous efficacy. So the maximizing S/P ratio cannot be chosen as the optimal objective function for mesopic vision. In this work, the spectral optimization model of QD-WLED for mesopic vision, including down-conversion energy loss, was developed under the constraint of designated color rendering properties. Unity quantum efficiency was adopted to consider the ideal case in this model. The optimal spectra of QD-WLEDs for mesopic vision, photometric and colorimetric performances at CCTs of 2700 K to 45000 K, as well as the limited mesopic luminous efficacy of optimal QD-WLEDs for four road lighting standards of the USA and the UK were presented. Finally, the highest LE_ms of optimal QD-WLEDs with 50% of the radiant efficiency of blue chip and 70% of the overall efficiency of the film consisting of multiple QDs for four road lighting standards were estimated.

2. Spectral optimization model of QD-WLED for mesopic vision

The QD-WLED consists of a blue (430-500 nm) chip, green (500-550 nm), yellow (550-590 nm) and red (590-680 nm) QDs. The relative spectral power distribution (SPD) of a QD-WLED, S_QD-W(λ), is given by [2],

S_{QD-W} (λ) = \sum_{i = 1}^{4} q_{i} S_{i} (λ, λ_{0 i}, Δ λ_{i})

where the subscripts i = 1, 2, 3 and 4 refer to a blue chip, green, yellow and red QDs, respectively. S_i, q_i, λ_0i and ∆λ_i refer to the relative SPD, proportion of the relative SPD, peak wavelength (WL), full width at half maximum (FWHM), respectively, for each color component. We employ Ohon’s model [19] of SPD for each color component. Because of three mixed constraints, 4 × 3-dimensional space will be reduced to 9-dimensional space for a particular CCT [20].

Unity quantum efficiency is adopted to consider the ideal case in this model. Thus, the absorbed proportion (q_ab) of the blue light by the QDs layer can be calculated as follows [1]:

q_{a b} = \sum_{i = 2}^{4} q_{i} \int_{λ} S_{i} (λ, λ_{0}_{i}, Δ λ_{i}) λ d λ / \int_{λ} S_{1} (λ, λ_{1}, Δ λ_{1}) λ d λ

The limited photopic luminous efficacy (LLE_p) including down-conversion energy loss can be calculated by

{LLE}_{p} 686 \int_{λ} V (λ) S_{QD-W} (λ) d λ / \int_{λ} (q_{1} - q_{ab}) S_{1} (λ, λ_{01}, Δ λ_{1}) d λ

The mesopic luminous efficiency model related to the photopic and scotopic states functions can be expressed as follows [7]:

M (x) V_{m} (λ, x) = xV (λ) + (1 - x) V' (λ)

where V_m(λ, x) is the spectral luminous efficacy function at mesopic lighting conditions, x is the adaptation coefficient which depends on the visual adaptation of the eye, V(λ) and V’(λ) are the spectral luminous efficacy functions in the photopic and scotopic states, respectively, and M(x) is the normalization factor to keep the maximum of V_m(λ, x) at 1. The spectral power distribution of light source S(λ) is given, and the mesopic luminous efficacy of radiation, LER_m(x), can be calculated as follows,

{LER}_{m} (x) = \frac{x + 683 (S / P) (1 - x) / 1699}{x + 683 (1 - x) / 1699} {LER}_{p}

where

S / P = \frac{\int_{380}^{780} 1699 V' (λ) S (λ) d λ}{\int_{380}^{780} 683 V (λ) S (λ) d λ}

,

{LER}_{p} = \frac{\int_{380}^{780} 683 V (λ) S (λ) d λ}{\int_{380}^{780} S (λ) d λ}

. Other mesopic quantities can be calculated using Eq. (5), so the mesopic luminance (L_m) can be calculated by

L_{m} (x) = \frac{x + 683 (S / P) (1 - x) / 1699}{x + 683 (1 - x) / 1699} L_{p}

From Eq. (6), the maximizing L_m is equivalent to the maximizing S/P ratio for a given L_p. The limited mesopic luminous efficacy, LLE_m(x) can be calculated by

{LLE}_{m} (x) = \frac{x + (1 - x) (S / P) (683 / 1699)}{x + (1 - x) (683 / 1699)} {LLE}_{p}

From Eq. (7), the mesopic luminous efficacy of light sources depends on not only the S/P ratio but also the photopic luminous efficacy. So the maximizing S/P ratio cannot be chosen as the optimal objective function for mesopic vision.

In order to optimize spectra of a QD-WLED for mesopic vision, we introduce an objective function for the QD-WLED:

\begin{array}{l} F = {\bar{LLE}}_{m} = \sum_{x = 0}^{1} {LLE}_{m} (x, λ_{0 b}, λ_{0 g}, λ_{0y}, λ_{0r}, Δ λ_{b}, Δ λ_{g}, Δ λ_{y}, Δ λ_{r}) / 11 \\ (under conditions of CRI \geq I and CQS \geq J) \end{array}

where x = 0, 0.1, ……, and 1.0. Notice that the chromaticity difference from the Planckian or daylight locus on the CIE 1960 uv chromaticity diagram (Duv) is smaller than 0.0054 for a various of CCTs [17]. Hence the optimization problem reduces to finding maximum of the objective functions (F).

For the QD-WLED, FWHM ranges are selected as 20-30 nm for the blue chip [21–23], and 30-50 nm for green, yellow and red QDs. In optimization, a fast Pareto genetic algorithm [24] is chosen because it is able to scan a vast set of solutions, does not depend on a starting solution, is useful for complex problems, and most importantly can be easily modified to estimate the Pareto optimal set.

3. Results and discussions

3.1. Spectral optimization for mesopic vision under CRI ≥ 70 and CQS ≥ 60

3.1.1. Optimal spectra of QD-WLED for mesopic vision

The optimal peak WL, and relative radiant flux (Φ_e%) of each color component, as well as their performance of QD-WLEDs with CRI ≥ 70 and CQS ≥ 60 at CCTs of 2700 K to 45000 K (Duv ≤ 0.0054) have been obtained by nonlinear program for maximizing F. The simulation results are shown in Table 1. The simulation results show that q_y = 0 and the optimal FWHM of each color is 30 nm, and that the optimal peak WLs for blue chip, green and red QDs decreases as CCT increases for QD-WLEDs with CRI ≥ 70 and CQS ≥ 60. The optimal SPDs of QD-WLEDs with CRI ≥ 70 and CQS ≥ 60 at CCTs of 2700 K to 45000 K (Duv ≤ 0.0054) for mesopic vision are shown in Fig. 1.

Table 1. Optimal peak WL and Φ_e (%) of each color, and their performance of QD-WLEDs with CRI ≥ 70 and CQS ≥ 60 at CCTs of 2700 K to 45000 K, where the optimal ∆λ of each color is 30 nm.

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Fig. 1 Optimal SPDs of QD-WLEDs with CRI ≥ 70 and CQS ≥ 60 at CCTs of 2700 K to 45000 K (Duv ≤ 0.0054) for mesopic vision

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In order to explain the optimal FWHM, we explored the relationship between the maximum ${\bar{LLE}}_{m}$ and FWHM of each color. The relationships of the highest ${\bar{LLE}}_{m}$ of QD-WLEDs with CRI ≥ 70 and CQS ≥ 60 at CCT = 4500 K and the FWHM of each color component were shown in Table 2. For the other CCT, also has a similar relationship. So the optimal FWHM of each color was 30 nm.

Table 2. Relationships of the highest ${\bar{L L E}}_{m}$ of QD-WLEDs with CRI ≥ 70 and CQS ≥ 60 at CCT = 4500 K and the FWHM of each color component.

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3.1.2. S/P ratio versus CCT

The relationships of S/P ratio versus CCT are shown in Fig. 1 for maximizing, ${\bar{LLE}}_{m}$ maximizing S/P ratio, and [15]’s results. The results show that the S/P ratio for maximizing ${\bar{LLE}}_{m}$ increases as CCT increases, but the S/P ratio is smaller than the maximum of S/P ratio at each CCT. So the maximizing S/P ratio cannot be chosen as the optimal objective function for mesopic vision. In addition, [15]’s results are also derived from maximizing S/P ratio. However, Fig. 2 indicates that the S/P ratio reported by [15] is smaller than the maximum of S/P ratio at each CCT. So [15]’s results are not optimal for maximizing S/P ratio under the same parameter conditions.

Fig. 2 Relationships of S/P ratio versus CCT for maximizing ${\bar{L L E}}_{m}$ , maximizing S/P ratio, and [15]’s results.

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3.1.3. LLE_p versus CCT and LER_p versus CCT

The relationships of LLE_p versus CCT, and LER_p versus CCT are shown in Figs. 3 and 4, respectively, for maximizing, ${\bar{L L E}}_{m}$ maximizing S/P ratio, and [15]’s results, The results show that both LLE_p and LER_p decrease as CCT increases for maximizing ${\bar{L L E}}_{m}$ . However, both LLE_p and LER_p quickly increase as CCT increases from 2700 to 6000 K for maximizing S/P ratio, and they start to decrease very slowly as CCT increases after 6000 K. Both LLE_p and LER_p for maximizing ${\bar{L L E}}_{m}$ are much higher than that for maximizing S/P ratio at each CCT. Although the S/P ratio for maximizing S/P ratio is larger than that for maximizing ${\bar{L L E}}_{m}$ at each CCT, both LLE_p and LER_p for maximizing S/P ratio are much smaller than that for maximizing ${\bar{LLE}}_{m}$ . This is because the optimal peak WLs of red increases rapidly as CCT decreases for max S/P model, and are much larger than that for maximizing LLE_p in the range of 2700 K - 6000 K. So, the LLE_ps for maximizing S/P ratio are much lower than that for maximizing, ${\bar{L L E}}_{m}$ and the LLE_ps for maximizing S/P ratio decreases rapidly as CCT decreases. So the optimization of mesopic luminous efficacy could not be achieved by the maximizing S/P ratio. In addition, [15]’s results are also derived from maximizing S/P ratio. However, Fig. 4 indicates that the relationship of LER_p versus CCT reported by [15] differs very much from that for maximizing S/P ratio under the same parameter conditions. So, [15]'s results are invalidated.

Fig. 3 LLE_p versus CCT for maximizing, ${\bar{L L E}}_{m}$ maximizing S/P ratio, and [15]’s results.

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Fig. 4 LER_p versus CCT for maximizing, ${\bar{L L E}}_{m}$ maximizing S/P ratio, and [15]’s results.

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3.1.4. Maximum ${\bar{L L E}}_{m}$ versus CCT

The relationship of the maximum ${\bar{L L E}}_{m}$ versus CCT has been obtained by applying the optimization model on the QD-WLED. The simulation results are shown in Fig. 5, which shows that the maximum ${\bar{L L E}}_{m}$ value quickly increases to 471.6 lm/W from 2700 to 10000 K, and it starts to decrease very slowly to 468.8 lm/W after 10000 K. For maximizing S/P ratio, the relationship of ${\bar{L L E}}_{m}$ versus CCT is shown in Fig. 5, which shows that the ${\bar{L L E}}_{m}$ values for maximizing S/P ratio are much smaller than that for maximizing ${\bar{L L E}}_{m}$ at each CCT. So Fig. 5 further shows that the optimization of luminous efficacy for mesopic vision cannot be achieved by the maximizing S/P ratio. In addition, ${\bar{L L E}}_{m}$ values obtained by [15]’s results are also shown in Fig. 5, which shows that their ${\bar{L L E}}_{m}$ values are smaller than that for maximizing ${\bar{L L E}}_{m}$ at each CCT. So, [15]’s results are not optimal for the mesopic vision.

Fig. 5 ${\bar{L L E}}_{m}$ versus CCT for maximizing, ${\bar{L L E}}_{m}$ maximizing S/P ratio, and [15]’s results.

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3.2. Spectral optimization for mesopic vision under CRI ≥ 85 and CQS ≥ 85

The optimal peak WL, and relative radiant flux (Φ_e%) of each color component as well as their performance of QD-WLEDs with CRI ≥ 85 and CQS ≥ 85 at CCTs of 2700 K to 45000 K (Duv ≤ 0.0054) have been obtained by nonlinear program for maximizing F. The simulation results are shown in Table 3. The simulation results show that the optimal FWHM of each color is 30 nm, that the optimal peak WLs decrease as CCT increases for blue chip, green and red QDs, and that the optimal peak WL increases as CCT increases for yellow QD for QD-WLEDs with CRI ≥ 85 and CQS ≥ 85. The S/P ratio for maximizing ${\bar{L L E}}_{m}$ increases as CCT increases. The maximum ${\bar{L L E}}_{m}$ quickly increases to 452.6 lm/W from 2700 to 15000 K, and it starts to decrease to 451.1 lm/W very slowly after 15000 K. The optimal SPDs of QD-WLEDs with CRI ≥ 85 and CQS ≥ 85 at CCTs of 2700 K to 45000 K (Duv ≤ 0.0054) for mesopic vision are shown in Fig. 6.

Table 3. Optimal peak WL and Φ_e (%) of each color, and their performance of QD-WLEDs with CRI ≥ 85 and CQS ≥ 85 at CCTs of 2700 K to 45000 K, where the optimal ∆λ of each color is 30 nm.

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Fig. 6 Optimal SPDs of QD-WLEDs with CRI ≥ 85 and CQS ≥ 85 at CCTs of 2700 K to 45000 K (Duv ≤ 0.0054) for mesopic vision

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In order to explain the optimal FWHM, we explored the relationship between the maximum ${\bar{L L E}}_{m}$ and FWHM of each color. The relationships of the highest ${\bar{L L E}}_{m}$ of QD-WLEDs with CRI ≥ 85 and CQS ≥ 85 at CCT = 4500 K and the FWHM of each color component were shown in Table 4. For the other CCT, also has a similar relation. So the optimal FWHM of each color was 30 nm.

Table 4. Relationships of the highest ${\bar{L L E}}_{m}$ of QD-WLEDs with CRI ≥ 85 and CQS ≥ 85 at CCT = 4500 K and the FWHM of each color component.

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3.3. Applications in road lighting

To examine the efficiency of optimal QD-WLEDs in the mesopic region, we selected four photopic luminance levels [16] so that the road lighting standards in the USA [8] and the UK [9, 10] are satisfied. MES 1 refers to a luminance level of 0.50 cd/m² for the freeway (0.40-0.60 cd/m²), collector (0.40-0.80 cd/m²), and local road lighting (0.30-0.60 cd/m²) conditions according to the USA, and the link road standards for the UK (0.50-0.75 cd/m²). MES 2 refers to a luminance level of 0.80 cd/m² for the US standards of express way (0.60-1.00 cd/m²), major road lighting (0.60-1.20 cd/m²) and the secondary distributor lighting standard of the UK (0.75-1.50 cd/m²). MES 3 refers to a luminance level of 1.25 cd/m² for strategic route (1.00-1.50 cd/m²), major distributor (1.00-1.50 cd/m²), and secondary distributor (0.75-1.50 cd/m²) in the UK. MES 4 refers to a luminance level of 1.75 cd/m² for motorway lighting standards (1.50-2.00 cd/m²) in the UK.

The LLE_ms of optimal QD-WLEDs with CRI ≥ 70 and CQS ≥ 60 as well as CRI ≥ 85 and CQS ≥ 85 for four road lighting standards under CCTs of 2700 K to 45000 K are shown in Table 5. The results show that the LLE_m reached the highest of 375.1 lm/W at CCT = 5000 K for MES 1, 359.7 lm/W at CCT = 3500 K for MES 2, 350.2 lm/W at CCT = 3000 K for MES 3, and 344.9 lm/W at CCT = 2700 K for MES 4 for CRI ≥ 70 and CQS ≥ 60, and that the LLE_m reached the highest of 362.0 lm/W at CCT = 5000 K for MES 1, 345.6 lm/W at CCT = 4000 K for MES 2, 336.7 lm/W at CCT = 3500 K for MES 3, and 331.4 lm/W at CCT = 3500 K for MES 4 for CRI ≥ 85 and CQS ≥ 85.

Table 5. LLE_ms of optimal QD-WLEDs for four road lighting standards under CCTs of 2700 K to 45000 K

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The spectral parameters, photopic luminance (L_p), mesopic luminance (L_m), and CCT of the QD-WLED spectra with CRI ≥ 85 and CQS ≥ 85 exhibiting the highest L_m for the simulated four mesopic road lighting standards were reported by [16]. To compare with [16]’s results, the L_m values of optimal QD-WLEDs with the highest LLE_m and the highest L_m reported by [16] for MES 1 (L_p = 0.577 cd/m²), MES 2 (L_p = 0.932 cd/m²), MES 3 (L_p = 1.340 cd/m²), MES 4 (L_p = 1.886 cd/m²) at all CCTs are shown in Table 6. The results show that the L_m values of optimal QD-WLEDs with the highest LLE_m are higher than the highest L_m reported by [16]. So it is further demonstrated that the spectral optimization model by using ${\bar{LLE}}_{m}$ as the objective function can achieve better performance of QD-WLEDs for mesopic vision.

Table 6. L_m values of optimal QD-WLEDs with the highest LLE_m and the highest L_m reported by [16] for four road lighting standards.

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For the real blue chips and semiconductor nanophosphors of colloidal QD, we chose that the radiant efficiency (η_eb) of blue chip is 50%, and the overall efficiency (η_{QDs’ film}) of the film consisting of multiple QDs. The photopic luminous efficacy (LE_P) can be estimated by

L E_{p} = \frac{683 η_{e b} \int_{λ} V (λ) S_{Q D - W} (λ) d λ}{\int_{λ} (q_{b} + q_{a b}) S (λ, λ_{b}, Δ λ_{b}) d λ}

where

q_{ab} = \frac{q_{g} \int_{λ} S (λ, λ_{0 g}, Δ λ_{g}) λ d λ + q_{y} \int_{λ} S (λ, λ_{0 y}, Δ λ_{y}) λ d λ + q_{r} \int_{λ} S (λ, λ_{0 r}, Δ λ_{r}) λ d λ}{η_{QDs'film} \int_{λ} S (λ, λ_{0 b}, Δ λ_{b}) λ d λ}

.

The mesopic luminous efficacy (LE_m) can be calculated by Eq. (7).

The highest LE_ms of optimal QD-WLEDs with η_e,b = 50%, η_{QDs’ film} = 70% are shown in Table 7. The results show that QD-WLEDs with η_e,b = 50%, η_{QDs’ film} = 70% could achieve better performance of QD-WLEDs for four road lighting standards.

Table 7. Highest LE_m of optimal QD-WLEDs with η_e,b = 50%, η_{QD’ film} = 70% for four road lighting standards.

View Table | View all tables in this article

4. Conclusions

An spectral optimization model for mesopic luminous efficacy of QD-WLED consisting of a blue chip, green, yellow and red QDs, including down-conversion energy loss, has been developed under constraint of designated color rendering properties. The optimized peak wavelength and FWHM of each color component, as well as photometric and colorimetric performances of the QD-WLEDs with CRI ≥ 70 and CQS ≥ 60 as well as CRI ≥ 85 and CQS ≥ 85 for maximizing ${\bar{LLE}}_{m}$ at CCTs of 2700 K to 45000 K were presented. The results show that the optimal QD-WLEDs could achieve better performance for four road lighting standards. All in all, it was suggested that QD-WLEDs make strong candidates for replacing conventional light sources in the future as they enhance the vision quality in the road lighting in addition to energy saving. Therefore, they offer the potential to enable safer efficient lighting on the roads.

Acknowledgments

The work was supported by National Natural Science Foundation of China (51575099) and Natural Science Foundation of Shanghai (15ZR1401700).

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CCT (K)	λ_0b (nm)	λ_0g (nm)	λ_0r (nm)	Φ_{e, b} (%)	Φ_{e, g} (%)	Φ_{e, r} (%)	CRI	CQS	S/P	${\bar{L L E}}_{m}$ (lm/W)
2700	492.8	543.8	605.6	24.45	19.02	56.53	70	60	1.54	399.1
3000	488.8	542.0	604.5	27.09	20.64	52.27	70	63	1.70	413.6
3500	483.9	539.2	602.9	30.63	22.46	46.91	70	67	1.92	430.7
4000	480.4	536.7	601.6	33.47	23.55	42.98	70	68	2.10	441.9
4500	477.9	534.8	600.5	35.90	24.23	39.88	70	69	2.25	449.5
5000	476.9	533.1	599.8	37.63	25.16	37.21	70	68	2.40	460.2
5700	475.3	532.2	598.8	40.75	24.93	34.33	70	69	2.57	465.5
6500	473.6	531.0	598.0	43.16	24.90	31.94	70	69	2.73	468.5
8000	471.7	529.8	597.3	46.59	24.63	28.78	70	70	2.97	470.9
10000	470.3	528.9	596.8	49.58	24.20	26.22	70	70	3.18	471.6
15000	468.8	528.2	596.6	53.41	23.45	23.15	70	70	3.47	471.0
20000	468.2	527.9	596.5	55.17	23.04	21.79	70	71	3.61	470.3
25000	467.9	527.7	596.6	56.16	22.80	21.04	70	71	3.69	469.8
30000	467.7	527.7	596.6	56.79	22.64	20.58	70	71	3.75	469.4
35000	467.5	527.6	596.6	57.22	22.53	20.25	70	71	3.78	469.2
40000	467.4	527.6	596.6	57.53	22.44	20.03	70	71	3.81	469.0
45000	467.4	527.6	596.6	57.76	22.38	19.85	70	71	3.83	468.8

Blue		Yellow		Red
∆λ_b (nm)	${\bar{L L E}}_{m}$ (lm/W)	∆λ_g (nm)	${\bar{L L E}}_{m}$ (lm/W)	∆λ_r (nm)	${\bar{L L E}}_{m}$ (lm/W)
30	449.48	30	449.48	30	449.48
29	449.21	32	449.24	32	448.22
28	448.94	34	449.01	34	446.91
27	448.66	36	448.79	36	445.56
26	448.39	38	448.60	38	444.16
25	448.12	40	448.42	40	442.73
24	447.85	42	448.25	42	441.26
23	447.58	44	448.09	44	439.76
22	447.31	46	447.94	46	438.23
21	447.05	48	447.80	48	436.67
20	446.80	50	447.65	50	435.09

CCT (K)	λ_0b (nm)	λ_0g (nm)	λ_0y (nm)	λ_0r (nm)	Φ_{e, b} (%)	Φ_{e, g} (%)	Φ_{e, y} (%)	Φ_e,r (%)	CRI	CQS	S/P	${\bar{L L E}}_{m}$ (lm/W)
2700	475.1	535.3	567.6	611.6	15.23	22.68	8.40	53.69	85	85	1.37	359.1
3000	473.2	533.9	568.2	610.9	17.47	24.88	7.84	49.81	85	85	1.52	375.8
3500	470.4	532.2	569.1	610.4	19.55	28.25	7.81	44.39	87	85	1.69	396.9
4000	469.3	531.2	569.7	609.7	23.69	28.98	7.48	39.85	87	85	1.89	412.0
4500	468.3	530.5	569.9	609.2	27.25	29.22	7.21	36.32	87	85	2.06	422.2
5000	469.1	530.9	569.5	608.9	30.21	29.86	6.35	33.58	87	85	2.21	435.0
5700	468.0	530.3	570.2	608.3	33.69	29.69	6.23	30.39	87	85	2.38	441.7
6500	467.0	529.7	570.8	607.9	36.74	29.44	6.06	27.76	87	85	2.54	446.2
8000	465.6	528.8	571.7	607.5	40.82	28.95	5.76	24.47	87	85	2.77	450.3
10000	464.5	528.1	572.4	607.2	44.16	28.43	5.47	21.93	87	85	2.98	452.1
15000	463.1	527.1	573.3	606.9	48.26	27.65	5.07	19.02	87	85	3.26	452.6
20000	462.6	526.6	573.6	606.9	50.08	27.27	4.86	17.78	87	85	3.39	452.2
25000	462.2	526.4	573.9	606.9	51.11	27.05	4.74	17.11	87	85	3.47	451.9
30000	462.1	526.3	573.9	606.9	51.79	26.87	4.63	16.71	87	85	3.52	451.6
35000	461.9	526.1	574.1	606.9	52.18	26.80	4.60	16.42	87	85	3.56	451.4
40000	461.8	526.0	574.1	606.9	52.49	26.73	4.55	16.23	87	85	3.58	451.2
45000	461.7	525.9	574.1	606.9	52.73	26.67	4.52	16.08	87	85	3.60	451.1

Blue		Green		Yellow		Red
∆λ_b (nm)	${\bar{L L E}}_{m}$ (lm/W)	∆λ_g (nm)	${\bar{L L E}}_{m}$ (lm/W)	∆λ_y (nm)	${\bar{L L E}}_{m}$ (lm/W)	∆λ_r (nm)	${\bar{L L E}}_{m}$ (lm/W)
30	422.16	30	422.16	30	422.16	30	422.16
29	422.09	32	421.88	32	422.14	32	421.14
28	422.02	34	421.74	34	422.11	34	420.10
27	421.94	36	421.55	36	422.08	36	419.04
26	421.86	38	421.37	38	422.05	38	417.96
25	421.77	40	421.20	40	422.01	40	416.87
24	421.68	42	421.05	42	421.97	42	415.76
23	421.59	44	420.90	44	421.91	44	414.63
22	421.49	46	420.77	46	421.85	46	413.42
21	421.38	48	420.64	48	421.79	48	412.16
20	421.28	50	420.52	50	421.72	50	410.84

	LLE_m (lm/W)
	CRI ≥ 70 and CQS ≥ 60				CRI ≥ 85 and CQS ≥ 85
CCT (K)	MES 1	MES 2	MES 3	MES 4	MES 1	MES 2	MES 3	MES 4
2700	363.0	355.7	349.3	344.9	335.6	330.8	326.6	323.7
3000	367.6	358.3	350.2	344.6	343.1	336.5	330.8	326.8
3500	371.7	359.7	349.3	342.1	353.3	344.4	336.7	331.4
4000	372.8	358.8	346.7	338.2	356.8	345.6	335.9	329.2
4500	372.3	356.6	343.1	333.6	357.8	344.7	333.4	325.5
5000	375.1	357.9	342.9	332.5	362.0	347.2	334.4	325.4
5700	372.7	353.8	337.5	326.2	360.7	344.3	330.0	320.1
6500	369.4	349.2	331.8	319.7	358.4	340.5	325.1	314.4
8000	363.5	341.6	322.8	309.6	353.7	334.0	317.1	305.2
10000	357.6	334.4	314.4	300.4	348.6	327.6	309.4	296.7
15000	349.2	324.4	303.0	288.1	341.0	318.3	298.7	285.0
20000	345.1	319.6	297.6	282.3	337.1	313.7	293.5	279.4
25000	342.7	316.8	294.5	278.9	334.9	311.1	290.5	276.2
30000	341.2	315.1	292.6	276.9	333.4	309.4	288.7	274.2
35000	340.1	313.9	291.2	275.4	332.4	308.2	287.3	272.7
40000	339.3	313.0	290.2	274.4	331.7	307.4	286.4	271.7
45000	338.8	312.3	289.5	273.5	331.1	306.7	285.6	270.9

Optimal spectra of white LED integrated with quantum dots for mesopic vision

Abstract

1. Introduction

2. Spectral optimization model of QD-WLED for mesopic vision

3. Results and discussions

3.1. Spectral optimization for mesopic vision under CRI ≥ 70 and CQS ≥ 60

3.1.1. Optimal spectra of QD-WLED for mesopic vision

3.1.2. S/P ratio versus CCT

3.1.3. LLE_p versus CCT and LER_p versus CCT

3.1.4. Maximum ${\bar{L L E}}_{m}$ versus CCT

3.2. Spectral optimization for mesopic vision under CRI ≥ 85 and CQS ≥ 85

3.3. Applications in road lighting

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (6)

Tables (7)

Equations (9)

Optics Express

		[16]’s results		optimal QD-WLEDs
	L_p (cd/m²)	CCT (K)	L_m (cd/m²)	CCT (K)	L_m (cd/m²)
MES 1	0.577	3417	0.625	5000	0.676
MES 2	0.932	3243	0.980	4000	1.021
MES 3	1.340	3243	1.393	3500	1.416
MES 4	1.886	3164	1.930	3500	1.963

		Mes 1	Mes 2	Mes 3	Mes 4
QD-WLED (CRI ≥ 70 and CQS ≥ 60)	CCT (K)	5000	3500	3000	2700
QD-WLED (CRI ≥ 70 and CQS ≥ 60)	highest LE_m (lm/W)	145.9	136.9	131.9	129.0
QD-WLED (CRI ≥ 85 and CQS ≥ 85)	CCT (K)	5000	4000	3500	3500
QD-WLED (CRI ≥ 85 and CQS ≥ 85)	highest LE_m (lm/W)	137.5	128.8	123.2	121.4

Abstract

1. Introduction

2. Spectral optimization model of QD-WLED for mesopic vision

3. Results and discussions

3.1. Spectral optimization for mesopic vision under CRI ≥ 70 and CQS ≥ 60

3.1.1. Optimal spectra of QD-WLED for mesopic vision

3.1.2. S/P ratio versus CCT

3.1.3. LLEp versus CCT and LERp versus CCT

3.1.4. Maximum LLE¯m versus CCT

3.2. Spectral optimization for mesopic vision under CRI ≥ 85 and CQS ≥ 85

3.3. Applications in road lighting

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (6)

Tables (7)

Equations (9)

Optics Express

3.1.3. LLE_p versus CCT and LER_p versus CCT

3.1.4. Maximum ${\bar{L L E}}_{m}$ versus CCT