Imaging Quality Prediction and Measurement for Optical Microlens Array

Jinfeng Wei; Hailong Wang; Suet To; Sujuan Wang

doi:10.3788/AOS221605

Acta Optica Sinica, Volume. 43, Issue 4, 0411001(2023)

Imaging Quality Prediction and Measurement for Optical Microlens Array

Jinfeng Wei^1、aff, Hailong Wang^1、aff, Suet To^2、aff, and Sujuan Wang^1、*

¹State Key Laboratory of Precision Electronic Manufacturing Technology and Equipment, Guangdong University of Technology, Guangzhou 510006, Guangdong, China

²State Key Laboratory in Ultra-Precision Machining Technology, The Hong Kong Polytechnic University, Hongkong999077, China

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Abstract Get PDF(in Chinese)

Figures & Tables(16)

Fig. 1. Distribution mode transformation algorithm for microlens array

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Fig. 2. Direct imaging of microlens array based on pixel rearrangement method

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Fig. 3. Schematic diagram of basic geometric parameters of annular microlens array

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Fig. 4. Simulation results of ideal microlens array. (a) Original light field image; (b) final image; (c) sagittal PSF curve

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Fig. 5. Microlens array. (a) Aluminum 6061 alloy mold prepared by slow tool servo turning; (b) microlens array prepared by UV curing fabrication

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Fig. 6. Measurement results of lens units at different positions on PMMA lens. (a) Lens unit 0-0; (b) lens unit 1-1; (c) lens unit 2-1; (d) lens unit 2-6

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Fig. 7. Simulation results of microlens array imaging with error. (a) Original light field image; (b) final image; (c) sagittal PSF curve

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Fig. 8. Measurement platform

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Fig. 9. Focal spot array

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Fig. 10. Experimental results of microlens array light field imaging. (a) Original light field image (annular distribution); (b) original light field image (rectangular distribution); (c) final image; (d) sagittal PSF curves

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Table 1. Basic geometric parameters of microlens array
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Table 1. Basic geometric parameters of microlens array
Parameter Value
Pitch size L /mm 0.78
Number of array layers 3
Curvature radius of lens unit R_q /mm 15
Lens depth h /µm 5
Height of flat substrate T /mm 0.5

Table 2. Slow servo turning parameters and diamond tool parameters of microlens array

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Table 2. Slow servo turning parameters and diamond tool parameters of microlens array

Processing parameter	Value
Spindle speed n /（r·min^-1）	30
Feed rate F /（mm·min^-1）	0.4
Number of discrete points per revolution of equal angle $n_{θ}$	500
Equal arc length trajectory discrete arc length Δl /µm	15
Tool corner nose radius R_T /mm	0.53
Tool relief angle γ /（°）	10
Vibration amplitude A_x /nm	8
Vibration amplitude A_y /nm	6
Vibration amplitude A_z /nm	5
Vibration frequency f_x /Hz	61.2
Vibration frequency f_y /Hz	35
Vibration frequency f_z /Hz	90.2

Table 3. Measured curvature radius, pupil aperture, and lens height of each lens unit

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Table 3. Measured curvature radius, pupil aperture, and lens height of each lens unit

Lens unit label	Curvature radius /mm	Diameter of pupil aperture /mm	Lens height /μm
0-0	15.792	0.74	4.45
1-1	16.253	0.73	4.16
1-2	15.933	0.74	4.45
1-3	15.804	0.73	4.29
1-4	15.736	0.73	4.26
1-5	15.696	0.74	4.48
1-6	15.746	0.74	4.39
2-1	16.664	0.75	4.38
2-2	15.939	0.75	4.53
2-3	16.207	0.75	4.53
2-4	15.819	0.75	4.52
2-5	15.897	0.76	4.80
2-6	15.901	0.75	4.53
2-7	15.953	0.76	4.66
2-8	15.747	0.75	4.50
2-9	15.927	0.75	4.62
2-10	15.938	0.75	4.61
2-11	15.875	0.75	4.75
2-12	15.825	0.75	4.52

Table 4. Fitted profile coefficient of lens unit 0-0
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Table 4. Fitted profile coefficient of lens unit 0-0
Fitting coefficient Value
A₀ -2.27×10⁶
A₁ 1.07×10⁴
A₂ 7265
A₃ -7.984
A 3.7449×10^-5
ω₀ -121.4
µ₀ 0

Table 5. Focal length measurement results

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Table 5. Focal length measurement results

Lens unit label	Measured value /mm	Simulation value /mm	Error /μm
0-0	31.2	32.281	-1.081
1-1	31.1	33.223	-2.123
1-2	31.4	32.569	-1.169
1-3	31.3	32.305	-1.005
1-4	33.1	32.166	0.934
1-5	31.0	32.084	-1.084
1-6	31.0	32.187	-1.187
2-1	31.2	34.063	-2.863
2-2	31.0	32.581	-1.581
2-3	31.4	33.129	-1.729
2-4	31.1	32.336	-1.236
2-5	31.2	32.495	-1.295
2-6	31.7	32.504	-0.804
2-7	32.2	32.61	-0.410
2-8	31.2	32.189	-0.989
2-9	31.0	32.557	-1.557
2-10	31.8	32.579	-0.779
2-11	31.0	32.450	-1.450
2-12	31.2	32.348	-1.148

Table 6. Focal spot measurement results

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Table 6. Focal spot measurement results

Lens unit label	Focal spot area /µm²	Radial deviation /µm	Angular deviation /（°）
1-1	1139	0	0
1-2	1121	-6.2	0.06
1-3	1157	-9.0	-0.10
1-4	1179	-6.8	-0.12
1-5	1149	-9.0	-0.16
1-6	1168	-8.4	-0.12
2-1	1205	-19.0	0
2-2	1141	-18.3	0.01
2-3	1166	-25.4	-0.01
2-4	1133	-19.0	-0.02
2-5	1208	-21.9	0.04
2-6	1162	-14.5	-0.01
2-7	1214	-20.7	-0.06
2-8	1162	-16.8	-0.15
2-9	1205	-22.5	-0.01
2-10	1142	-20.6	0.06
2-11	1184	-21.3	0.09
2-12	1143	-14.5	-0.01

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Jinfeng Wei, Hailong Wang, Suet To, Sujuan Wang. Imaging Quality Prediction and Measurement for Optical Microlens Array[J]. Acta Optica Sinica, 2023, 43(4): 0411001

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