Design of a free-form surface microlens array optical system with high efficiency and uniformity

Zhenmin Zhu; Peiqi Yao; Weihua Zheng

doi:10.1364/AO.398971

Applied Optics
Vol. 59,
Issue 23,
pp. 6939-6944
(2020)
•https://doi.org/10.1364/AO.398971

Design of a free-form surface microlens array optical system with high efficiency and uniformity

Zhenmin Zhu, Peiqi Yao, and Weihua Zheng

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Zhenmin Zhu, Peiqi Yao, and Weihua Zheng, "Design of a free-form surface microlens array optical system with high efficiency and uniformity," Appl. Opt. 59, 6939-6944 (2020)

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Abstract

The microlens array has been widely applied in LED lighting source due to its special optical properties, but most of the research lacks the analysis and optimization of the complete mathematical models. Hence, the new design method of a free-form surface microlens array optical system is proposed in this paper. Based on the characteristics of TIR and the law of refraction, a complete mathematical model of the free-form microlens is established. By numerically solving a set of differential equations, the profile of the free-form surface microlens is obtained. Then we rotate the profile to get the free-form surface microlens. Finally, the proposed microlens array is simulated and analyzed in near-field and far-field situations, respectively. We also discuss the influence of microlens array characteristics on illumination performance. The result shows the uniformity and efficiency have been improved, both of which can reach more than 90%.

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Equations (13)

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Size of System (mm)	Size of Microlens Array	Efficiency	Uniformity
$L = 500$ , $R 1 = 0.5$	$10 \times 10$	90.75%	88.83%
	$11 \times 11$	90.53%	89.66%
	$13 \times 13$	90.10%	90.67%
	$15 \times 15$	89.65%	90.95%
$L = 500$ , $R 1 = 1$	$10 \times 10$	84.06%	87.04%
	$11 \times 11$	84.53%	85.78%
	$13 \times 13$	84.38%	86.65%
	$15 \times 15$	84.00%	86.87%
$L = 300$ , $R 1 = 0.5$	$10 \times 10$	91.46%	87.20%
	$11 \times 11$	91.35%	87.85%
	$13 \times 13$	91.09%	87.94%
	$15 \times 15$	90.78%	88.45%
$L = 300$ , $R 1 = 1$	$10 \times 10$	84.82%	85.94%
	$11 \times 11$	86.42%	85.97%
	$13 \times 13$	84.71%	86.03%
	$15 \times 15$	84.20%	84.93%

Size of System (mm)	Size of Microlens Array	Efficiency	Uniformity
$L = 2000$ , $R_{1} = 0.5$ , $R_{2} = 1000$	$10 \times 10$	89.743	89.97
	$11 \times 11$	89.743	91.83
	$13 \times 13$	89.745	92.25
	$14 \times 14$	89.741	92.56
$L = 2000$ , $R_{1} = 1,$ $R_{2} = 1000$	$10 \times 10$	85.424	89.17
	$11 \times 11$	86.141	90.35
	$13 \times 13$	86.652	91.19
	$14 \times 14$	86.654	92.01
$L = 3000$ , $R_{1} = 0.5$ , $R_{2} = 1500$	$10 \times 10$	89.735	90.00
	$11 \times 11$	89.736	92.13
	$13 \times 13$	89.739	92.37
	$14 \times 14$	89.736	92.38
$L = 3000$ , $R_{1} = 1,$ $R_{2} = 1500$	$10 \times 10$	85.452	88.78
	$11 \times 11$	86.206	91.15
	$13 \times 13$	86.779	91.28
	$14 \times 14$	86.803	92.38

Size of System (mm)	Size of Microlens Array	Efficiency	Uniformity
$L = 500$ , $R 1 = 0.5$	$10 \times 10$	90.75%	88.83%
	$11 \times 11$	90.53%	89.66%
	$13 \times 13$	90.10%	90.67%
	$15 \times 15$	89.65%	90.95%
$L = 500$ , $R 1 = 1$	$10 \times 10$	84.06%	87.04%
	$11 \times 11$	84.53%	85.78%
	$13 \times 13$	84.38%	86.65%
	$15 \times 15$	84.00%	86.87%
$L = 300$ , $R 1 = 0.5$	$10 \times 10$	91.46%	87.20%
	$11 \times 11$	91.35%	87.85%
	$13 \times 13$	91.09%	87.94%
	$15 \times 15$	90.78%	88.45%
$L = 300$ , $R 1 = 1$	$10 \times 10$	84.82%	85.94%
	$11 \times 11$	86.42%	85.97%
	$13 \times 13$	84.71%	86.03%
	$15 \times 15$	84.20%	84.93%

Size of System (mm)	Size of Microlens Array	Efficiency	Uniformity
$L = 2000$ , $R_{1} = 0.5$ , $R_{2} = 1000$	$10 \times 10$	89.743	89.97
	$11 \times 11$	89.743	91.83
	$13 \times 13$	89.745	92.25
	$14 \times 14$	89.741	92.56
$L = 2000$ , $R_{1} = 1,$ $R_{2} = 1000$	$10 \times 10$	85.424	89.17
	$11 \times 11$	86.141	90.35
	$13 \times 13$	86.652	91.19
	$14 \times 14$	86.654	92.01
$L = 3000$ , $R_{1} = 0.5$ , $R_{2} = 1500$	$10 \times 10$	89.735	90.00
	$11 \times 11$	89.736	92.13
	$13 \times 13$	89.739	92.37
	$14 \times 14$	89.736	92.38
$L = 3000$ , $R_{1} = 1,$ $R_{2} = 1500$	$10 \times 10$	85.452	88.78
	$11 \times 11$	86.206	91.15
	$13 \times 13$	86.779	91.28
	$14 \times 14$	86.803	92.38

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Applied Optics