Spectral design methods for multi-channel LED light sources based on differential evolution

Fuzheng Zhang; Haisong Xu; Zhehong Wang

doi:10.1364/AO.55.007771

Applied Optics
Vol. 55,
Issue 28,
pp. 7771-7781
(2016)
•https://doi.org/10.1364/AO.55.007771

Spectral design methods for multi-channel LED light sources based on differential evolution

Fuzheng Zhang, Haisong Xu, and Zhehong Wang

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Fuzheng Zhang, Haisong Xu, and Zhehong Wang, "Spectral design methods for multi-channel LED light sources based on differential evolution," Appl. Opt. 55, 7771-7781 (2016)

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- Vision and Visual Optics
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About this Article
History
- Original Manuscript: June 24, 2016
- Revised Manuscript: August 13, 2016
- Manuscript Accepted: August 25, 2016
- Published: September 22, 2016
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 11, Iss. 11

Abstract

The methods were proposed to design the spectra of light sources with multi-channel LEDs based on a differential evolution (DE) algorithm. Specifically, to produce a desired illuminance level while matching a specific spectrum, a matching method combining the DE algorithm and photometry was verified by matching the Commission Internationale de l’Eclairage (CIE) standard illuminants A and D65 at the two desired illuminance levels (500 and 1000 lx) with a multi-channel LED array. Furthermore, considering that correlated color temperature (CCT), illuminance, and color rendering are of practical importance to general lighting, on the basis of photometry and colorimetry, the DE algorithm integrating a mechanism dealing with constraints was developed to optimize the CIE general color rendering index of light sources under a joint target of CCT and illuminance. Sixteen selected targets (eight CCTs from 2800 to 6500 K at 500 and 1000 lx, respectively) were realized with the LED array. The results indicate that the relative errors of CCT and illuminance are less than 0.7% and 1.5%, respectively, while achieving excellent or even perfect color rendering. These methods also enable a practical tool for smart and dynamic lighting.

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	Objective Function: $p$			Objective Function: RMSE
Target	GFC	$RMSE / (\times 10^{- 4})$	$p$	GFC	$RMSE / (\times 10^{- 4})$	$p$
A_500 lx	0.9960	1.8275	0.0619	0.9971	1.5536	0.0597
A_1000 lx	0.9968	3.2731	0.0603	0.9973	2.9711	0.0556
D65_500 lx	0.9936	2.6747	0.0809	0.9930	2.3730	0.0768
D65_1000 lx	0.9930	5.0735	0.0668	0.9950	4.6818	0.0803

	Objective Function: $p$							Objective Function: RMSE
Target	$Δ_{T c} / %$	$Δ_{u^{'}, v^{'}}$	$Δ_{E} / %$	$R_{a}$	$R_{9}$	$R_{f}$	$R_{g}$	$Δ_{T c} / %$	$Δ_{u^{'}, v^{'}}$	$Δ_{E} / %$	$R_{a}$	$R_{9}$	$R_{f}$	$R_{g}$
A_500 lx	9.38	0.0120	4.60	93	53	91	100	6.27	0.0078	4.40	93	53	92	98
A_1000 lx	8.47	0.0105	2.70	92	52	92	99	7.28	0.0093	4.00	93	58	92	99
D65_500 lx	2.14	0.0017	2.40	96	72	94	98	0.74	0.0059	3.00	94	58	92	96
D65_1000 lx	0.77	0.0060	0.50	93	57	93	96	5.60	0.0063	3.30	94	64	92	97

		Spectral Performance			Colorimetric Performance
Target		GFC	$RMSE / (\times 10^{- 4})$	$p$	$Δ_{T c} / %$	$Δ_{u^{'}, v^{'}}$	$Δ_{E} / %$	$Δ_{u^{'} 10, v^{'} 10}$	$M_{v}$	$R_{a}$	$R_{9}$	$R_{f}$	$R_{g}$
D65	500 lx	0.9894	3.3425	0.0955	4.23	0.0036	0.60	0.0040	0.48	98	93	97	101
D65	1000 lx	0.9903	6.3616	0.0895	3.18	0.0026	0.30	0.0032	0.47	99	97	97	101

	Mean	Best	Poorest	St. Dev
SA	0.1643	0.1069	0.2528	0.0344
GA	0.1063	0.0671	0.1605	0.0220
ES	0.0758	0.0643	0.1098	0.0110
PSO	0.0648	0.0576	0.0904	0.0096
Proposed	0.0603	0.0576	0.0658	0.0018

Target CCT/K		2800	3500	4000	4500	5000	5500	6000	6500
500 lx	$Δ_{T c} / %$	0.32	0.29	0.05	0.02	0.20	0.07	0.27	0.12
	$Δ_{u^{'}, v^{'}} / (\times 10^{- 4})$	6.49	4.71	5.48	5.04	4.80	2.01	12.48	12.68
	$Δ_{E} / %$	0.60	0.80	0.40	1.20	0.80	1.40	0.20	1.20
	$R_{a}$	96	97	98	98	98	99	99	99
	$R_{9}$	74	72	83	91	86	97	97	97
	$R_{f}$	93	94	96	97	96	96	97	95
	$R_{g}$	102	101	101	100	100	100	100	99
1000 lx	$Δ_{T c} / %$	0.68	0.23	0.15	0.16	0.10	0.35	0.08	0.26
	$Δ_{u^{'}, v^{'}} / (\times 10^{- 4})$	7.16	8.91	8.34	7.85	13.93	9.77	12.64	10.99
	$Δ_{E} / %$	1.10	0.90	0.80	0.70	0.80	0.50	0.50	0.70
	$R_{a}$	96	97	98	99	99	99	99	99
	$R_{9}$	73	80	90	93	96	93	99	93
	$R_{f}$	93	93	96	97	97	97	96	96
	$R_{g}$	102	101	100	100	100	100	99	100

	Mean	Best	Poorest	St. Dev
CHDE	84	96	57	9.71
ALGA	80	95	63	9.10
HMPSO	83	98	61	8.63
Proposed	98	99	96	0.96

	Mean	Best	Poorest	St. Dev
CHDE	84	96	57	9.71
ALGA	80	95	63	9.10
HMPSO	83	98	61	8.63
Proposed	98	99	96	0.96

Abstract

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Applied Optics