基于弯曲像面的大视场超紧凑型镜头设计

毕诗文; 张星祥; 陈力; 刘俊豪; 范世杰; 付天骄

doi:10.37188/CO.2025-0076

基于弯曲像面的大视场超紧凑型镜头设计

doi: 10.37188/CO.2025-0076

cstr: 32171.14.CO.2025-0076

毕诗文^{1, 2,},
张星祥^1, ,,
陈力^{1, 2},
刘俊豪^{1, 2},
范世杰^{1, 2},
付天骄¹

1.
中国科学院长春光学精密机械与物理研究所, 吉林长春 130033
2.
中国科学院大学, 北京100049

基金项目: 长春光机所“旭光人才计划”（No. E4X011Y6U0）

详细信息

作者简介:
毕诗文（2001—），男，辽宁大连人，硕士研究生，2023年于辽宁大学物理学院获得理学学士学位，主要从事光学设计方面的研究。E-mail：bsw_ciomp@qq.com

张星祥（1977—），男，云南大理人，博士，二级研究员，2006年于中国科学院长春光学精密机械与物理研究所获得博士学位，主要从事空间宽幅成像技术、精密装调与拼接技术、在轨测试与处理方面的研究。E-mail：jan_zxx@163.com

中图分类号: TN202
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出版历程
- 网络出版日期: 2025-08-21

Design of an ultra-compact wide-angle lens incorporating a curved image surface

BI Shi-wen^{1, 2
,},
ZHANG Xing-xiang^{1
, ,},
CHEN Li^{1, 2},
LIU Jun-hao^{1, 2},
FAN Shi-jie^{1, 2},
FU Tian-jiao¹

1.
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China

Funds: Supported by “Dawnlight Talent Program” (No. E4X011Y6U0), Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences

More Information

Corresponding author: jan_zxx@163.com

摘要

摘要:
针对轻量化AR眼镜对搭载摄像头的大视场与高紧凑性的需求，本文提出了结合弯曲像面的设计方法。首先，由高斯光学理论对弯曲像面成像系统进行理论分析，推导各光学系统Petzval像面曲率特性，并通过双系统仿真对比，重点分析弯曲像面的性能优势。然后，采用分段多目标优化策略，设计了一款大视场紧凑性的光学系统。最后，对光学系统进行像质评价和公差分析。该光学系统由5片非球面塑料透镜和一片后置滤光片组成，系统焦距为3.1 mm，视场角可达80°，系统总长仅4.07 mm。设计结果表明：在223 lp/mm处，各视场的调制传递函数均优于0.32，全视场最大RMS光斑半径为2.41 μm，最大畸变为2.5%，相对照度均优于45%。研究成果可为曲面传感器的应用奠定基础，并为大视场紧凑型镜头的设计提供技术参考。
- 光学设计 /
- 紧凑型镜头 /
- 曲面CMOS /
- 大视场 /
- 主光线入射角
Abstract:
To address the demand for large field-of-view and high compactness in lightweight AR glasses equipped with cameras, this study proposes an optical design method incorporating a curved image plane. First, based on Gaussian optics theory, the curved image plane imaging system is theoretically analyzed. The Petzval surface curvature characteristics of various optical configurations are derived, and the performance advantages of the curved image plane are highlighted through comparative simulations of dual systems. Then, a wide-angle and compact optical system is designed using a segmented multi-objective optimization strategy. Finally, image quality evaluation and tolerance analysis are performed on the designed system. The compact optical system comprises five aspheric plastic lenses and a rear-mounted filter. It features a focal length of 3.1 mm, a field of view (FOV) up to 80°, and a total system length of only 4.07 mm. The design results show that at 223 lp/mm, the modulation transfer function (MTF) exceeds 0.32 across all fields. The maximum RMS spot radius is 2.41 μm, with a distortion of only 2.5%, and the relative illumination remains above 45% across the entire field. This work lays a foundation for the application of curved sensors and offers a technical reference for the design of wide-angle compact lenses.
- optical design /
- compact lens /
- curved CMOS /
- wide field-of-view /
- chief ray angle

HTML全文

图 1 弯曲像面上的弧长像高

Figure 1. Arc-length image height on curved image surface

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图 2 光学系统结构与调制传递函数示意图

Figure 2. Optical system configuration and modulation transfer function

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图 3 用像高和波长表示的畸变函数

Figure 3. Distortion function represented by image height and wavelength

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图 4 相对照度函数分布图

Figure 4. Relative illumination function distribution

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图 5 二维结构图

Figure 5. 2D Layout

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图 6 系统MTF曲线图

Figure 6. MTF of system

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图 7 系统点列图

Figure 7. Spot Diagram

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图 8 系统场曲与畸变图

Figure 8. Field Curvature and Distortion Diagram

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图 9 系统相对照度图

Figure 9. Relative Illumination Diagram

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图 10 300 mm物距下调焦前后光学性能参数对比

Figure 10. Comparative Analysis of Optical Performance Parameters at 300 mm Object Distance Before vs. After Focus Adjustment

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表 1 光学系统的Petzval像面曲率特性

Table 1. Petzval curvature characteristics of optical systems.

系统类型	透镜组合	屈光度特点	R_p	像面形状
显微系统	多正透镜	短焦距，高屈光度	正	凹向透镜
标准摄影	正负透镜组	正透镜主导	正	凹向透镜
鱼眼摄影	多负透镜	负透镜高屈光度	负	凸向透镜
开普勒望远	双正透镜	目镜短焦距主导	正	凹向透镜
伽利略望远	正负透镜组	负目镜高屈光度	负	凸向透镜

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表 2 设计指标

Table 2. Design Specifications

项目	参数
焦距/mm	3.0～3.3
F数	2.2
视场角/（°）	2ω=80
光学畸变/%	≤2.5
系统总长/mm	≤4.5
MTF/（lp/mm）	≥0.3@233（0-0.7Y）

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表 3 镜片参数

Table 3. Lens Parameters

序号	面型	曲率半径/mm	厚度/mm	材料	折射率	阿贝数
物面	标准面	无限	无限	—	—	—
光阑	偶次非球面	1.777	0.350	6015S-04	1.533	54.975
2	偶次非球面	9.877	0.110	—	—	—
3	偶次非球面	−1.763	0.250	OKP-4HT	1.631	23.415
4	偶次非球面	−3.625	0.100	—	—	—
5	偶次非球面	1.850	0.350	ARTON_FX4727	1.523	52.125
6	偶次非球面	5.162	0.500	—	—	—
7	偶次非球面	−5.604	0.350	PMMA	1.492	57.441
8	偶次非球面	−1.908	1.100	—	—	—
9	偶次非球面	135.235	0.350	OKP-4HT	1.631	23.415
10	偶次非球面	2.529	0.200	—	—	—
11	标准面	无限	0.200	H-K9L	1.517	64.212
12	标准面	无限	0.210	—	—	—
13	标准面	−20.000	0.000	—	—	—

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表 4 非球面系数

Table 4. Aspheric Coefficients

序号	k	A4	A6	A8	A10	A12
1	0.00000E+00	−7.02848E-02	−8.04067E-03	−1.76041E-01	−1.60913E-02	−4.84484E-02
2	2.08083E-01	−1.36408E-01	−3.30294E-02	−1.84115E-01	3.69911E-01	−3.12379E-01
3	0.00000E+00	2.79638E-01	−1.56058E-01	1.31685E-01	1.57258E-01	−2.49223E-01
4	1.29397E-02	2.02942E-01	−5.50542E-02	2.31616E-01	−3.01072E-01	6.48883E-02
5	0.00000E+00	−1.38136E-01	4.35390E-02	−6.98809E-02	1.06082E-01	−3.35713E-02
6	−1.30823E-02	1.28664E-02	−1.21648E-01	6.18287E-02	−2.44867E-02	3.36290E-02
7	−6.27958E-02	6.50400E-02	−4.97805E-03	−1.91219E-02	3.37033E-03	2.25369E-03
8	0.00000E+00	7.67427E-02	1.05464E-02	1.79650E-02	−8.40372E-03	4.07342E-04
9	2.53734E+01	−1.41854E-01	3.27186E-03	1.08393E-02	−1.66595E-03	−5.59933E-05
10	0.00000E+00	−1.13567E-01	2.48152E-02	−5.09814E-03	7.67813E-04	−6.13429E-05

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表 5 近景调焦性能参数变化率

Table 5. Near-field Focus Adjustment Performance Parameter Variation Rates

参数	物距		变化率
参数	无穷远	300 mm	变化率
MTF(@223 lp/mm)	0.32	0.29	−9.38%
RMS半径(μm)	2.41	2.64	+9.54%
场曲(mm)	0.025	0.026	+4.00%
畸变(%)	−2.5	−2.6	+4.00%
相对照度(%)	46	45.5	−1.09%

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表 6 公差分配

Table 6. Tolerance Allocation

公差类型	参数
曲率半径	±1.5 fringes
厚度	±0.0015 mm
偏心	±0.0015 mm
倾斜	±3'

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表 7 系统公差分析结果

Table 7. Tolerance Analysis Results

蒙特卡洛分析	MTF
90%	0.23129849
80%	0.24933111
50%	0.28139853
20%	0.31265427
10%	0.32439743

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