Wavefront Aberration Fitting for Economic Tolerance Application

Hao Jiang; Yuan Hu; Jiaqi Huo; Zhiliang Zhao; Yuegang Fu

doi:10.3788/AOS222002

Acta Optica Sinica, Volume. 43, Issue 13, 1320003(2023)

Wavefront Aberration Fitting for Economic Tolerance Application

Hao Jiang¹, Yuan Hu^1、*, Jiaqi Huo¹, Zhiliang Zhao², and Yuegang Fu¹

¹Key Laboratory of Opto-Electronic Measurement and Optical Information Transmission Technology of Ministry of Education, School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun 130022, Jilin, China

²Chengdu Tyggo Photo-Electricity Co., Ltd., Chengdu 610041, Sichuan, China

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Figures & Tables(13)

Fig. 1. Schematic of wavefront aberration

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Fig. 2. Schematic of ray tracing of two adjacent surfaces

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Fig. 3. Layout of doublet lens

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Fig. 4. Fitting results of tolerance $Δ t_{3}$ and wavefront aberration by different methods. (a) Sequential derivation method; (b) formula transfer term method; (c) Youngworth method

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Fig. 5. Fitting results of tolerance $Δ θ_{3}$ and wavefront aberration by different methods. (a) Formula transfer term method; (b) Youngworth method

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Fig. 6. Fitting results of tolerance $Δ t_{1}$ , $Δ t_{2}$ and wavefront aberration. (a) (b) Formula transfer term method; (c) (d) Youngworth method

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Fig. 7. Fitting results of tolerance $Δ t_{1}$ , $Δ N_{2}$ and wavefront aberration. (a) (b) Formula transfer term method; (c) (d) Youngworth method

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Fig. 8. Relationship between wavefront aberration and relative cost

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Table 1. Parameters of doublet lens
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Table 1. Parameters of doublet lens
Curvature radius $r$ /mm Thickness $t$ /mm Material Semi-diameter /mm
70.534 4.50 H-QK1 6
56.886 4.50 H-ZLAF92 6
283.154 75.4 — 6
Infinity — — —

Table 2. First-order sensitivity coefficient $\partial W / \partial p_{i}$ of wavefront aberration of the doublet lens
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Table 2. First-order sensitivity coefficient $\partial W / \partial p_{i}$ of wavefront aberration of the doublet lens
Surface Curvature Decenter Tilt Thickness Refractive index
1 1.4722 1.6000×10^-5 0.0011 9.5011×10^-5 -0.0087
2 1.6060 -6.0781×10^-5 -0.0035 3.9299×10^-4 0.0421
3 -2.7965 -8.0878×10^-6 -0.0023 4.9030×10^-4 —

Table 3. Second-order sensitivity coefficient $\partial^{2} W / \partial p_{i}^{2}$ of wavefront aberration of the doublet lens
View table
Table 3. Second-order sensitivity coefficient $\partial^{2} W / \partial p_{i}^{2}$ of wavefront aberration of the doublet lens
Surface Curvature Decenter Tilt Thickness Refractive index
1 -265.1139 2.0255×10^-4 2.5870 2.0028×10^-5 1.9704
2 -152.4075 -0.0012 7.9242 1.3450×10^-5 -0.9853
3 -808.7249 4.4243×10^-5 -0.6192 -6.4956×10^-5 —

Table 4. Cross-sensitivity coefficient $\partial^{2} W / (\partial p_{i} \partial p_{j})$ of wavefront aberration of the doublet lens

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Table 4. Cross-sensitivity coefficient $\partial^{2} W / (\partial p_{i} \partial p_{j})$ of wavefront aberration of the doublet lens

Parameter	$c_{1}$	$c_{2}$	$c_{3}$	$t_{1}$	$t_{2}$	$t_{3}$	$N_{1}$	$N_{2}$
$c_{1}$	—	-264.56040	441.0748	0	0	0	14.3980	-14.3980
$c_{2}$	-264.5604	—	529.2140	0	-0.07120	0	0	-14.3951
$c_{3}$	441.0748	529.21400	—	0.0720	0.14400	0.0720	-14.3997	14.3997
$t_{1}$	0	0	0.0720	—	0	0	0.0118	-0.0118
$t_{2}$	0	-0.07120	0.1440	0	—	0	0	0
$t_{3}$	0	0	0.0720	0	0	—	0	0
$N_{1}$	14.3980	0	-14.3997	0.0118	0	0	—	2.3502
$N_{2}$	-14.3980	-14.39510	14.3997	-0.0118	0	0	2.3502	—

Table 5. Set of optimal tolerance for machining wavefront aberration of $- 0.5 λ$
View table
Table 5. Set of optimal tolerance for machining wavefront aberration of $- 0.5 λ$
Surface Curvature radius $r$ /d_fringe Thickness $t$ /mm Decenter $e$ /mm Tilt $θ$ /（°） Refractive index
1 -2 -0.080 -0.10 -0.050 0.0005
2 2 -0.050 -0.09 -0.050 -0.0004
3 2 -0.048 0.10 0.048 —
Image — — — — —

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Hao Jiang, Yuan Hu, Jiaqi Huo, Zhiliang Zhao, Yuegang Fu. Wavefront Aberration Fitting for Economic Tolerance Application[J]. Acta Optica Sinica, 2023, 43(13): 1320003

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Paper Information

Category: Optics in Computing

Received: Nov. 16, 2022

Accepted: Mar. 2, 2023

Published Online: Jul. 12, 2023

The Author Email: Hu Yuan (huy@cust.edu.cn)

DOI:10.3788/AOS222002

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Parameters of doublet lens

Table 1. Parameters of doublet lens

Table 2. First-order sensitivity coefficient ∂W/∂pi of wavefront aberration of the doublet lens

Table 2. First-order sensitivity coefficient ∂W/∂pi of wavefront aberration of the doublet lens

Table 3. Second-order sensitivity coefficient ∂2W/∂pi2 of wavefront aberration of the doublet lens

Table 3. Second-order sensitivity coefficient ∂2W/∂pi2 of wavefront aberration of the doublet lens

Table 4. Cross-sensitivity coefficient ∂2W/∂pi∂pj of wavefront aberration of the doublet lens

Table 4. Cross-sensitivity coefficient ∂2W/∂pi∂pj of wavefront aberration of the doublet lens

Table 5. Set of optimal tolerance for machining wavefront aberration of -0.5λ

Table 5. Set of optimal tolerance for machining wavefront aberration of -0.5λ

Table 2. First-order sensitivity coefficient $\partial W / \partial p_{i}$ of wavefront aberration of the doublet lens

Table 2. First-order sensitivity coefficient $\partial W / \partial p_{i}$ of wavefront aberration of the doublet lens

Table 3. Second-order sensitivity coefficient $\partial^{2} W / \partial p_{i}^{2}$ of wavefront aberration of the doublet lens

Table 3. Second-order sensitivity coefficient $\partial^{2} W / \partial p_{i}^{2}$ of wavefront aberration of the doublet lens

Table 4. Cross-sensitivity coefficient $\partial^{2} W / (\partial p_{i} \partial p_{j})$ of wavefront aberration of the doublet lens

Table 4. Cross-sensitivity coefficient $\partial^{2} W / (\partial p_{i} \partial p_{j})$ of wavefront aberration of the doublet lens

Table 5. Set of optimal tolerance for machining wavefront aberration of $- 0.5 λ$

Table 5. Set of optimal tolerance for machining wavefront aberration of $- 0.5 λ$