基于V矩阵余弦相似度的高NA显微物镜公差分析

魏碧颖; 蒋大成; 胡驰; 周顺; 弓旭航; 蒋世磊

doi:10.37188/CO.2026-0075

基于V矩阵余弦相似度的高NA显微物镜公差分析

doi: 10.37188/CO.2026-0075

cstr: 32171.14.CO.2026-0075

魏碧颖^1,,
蒋大成^2,,
胡驰^1,,
周顺^1,,
弓旭航^1,,
蒋世磊^1, ,

1.
西安工业大学光电工程学院, 陕西西安 710021
2.
西安工业大学电子信息工程学院, 陕西西安 710021

基金项目: 陕西省教育厅科研计划（No. 21JY017）

详细信息

作者简介:
魏碧颖(2002—)，女，陕西西安人，硕士研究生，主要从事光学设计及光学装调技术研究方面的研究。E-mail：W2075104051@163.com

蒋大成(1991—)，男，河北辛集人，博士研究生，讲师，主要从事机器视觉及深度学习方面的研究。E-mail：djiang@xatu.edu.cn

胡　驰(1999—)，男，陕西西安人，博士研究生，主要从事微纳光学的研究。E-mail：1584233313@qq.com

周　顺(1979—)，男，江苏常州人，博士生导师，主要从事光电子薄膜及微纳光学方面的研究。E-mail：zsemail@126.com

弓旭航(1998—)，男，陕西咸阳人，硕士研究生，主要从事光学设计方面的研究。E-mail：2439088318@qq.com

蒋世磊(1963—)，男，河北石家庄人，教授，硕士生导师，2003年于电子科技大学获得硕士学位，主要从事光学精密仪器设计，光电检测与校正技术方面的研究工作。E-mail：2429765449@qq.com

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出版历程
- 网络出版日期: 2026-08-04

Tolerance analysis of high-na microscope objectives based on v-matrix cosine similarity

1.
School of Opto-Electronical Engineering, Xi’an Technological University, Xi’an, Shanxi 710021, China
2.
School of Electronic and Information Engineering, Xi’an Technological University, Xi’an, Shanxi 710021, China

Funds: Research Programs of the Shaanxi Provincial Department of Education (No. 21JY017)

More Information

Corresponding author: 2429765449@qq.com

摘要

摘要:
针对高数值孔径显微物镜公差分析中的补偿器耦合问题，本文提出一种基于V矩阵余弦相似度的补偿器选择方法，旨在降低补偿器间的负相关性，避免慧差、像散等无法同时收敛的问题。以数值孔径为0.9的无限远共轭显微物镜为研究对象，通过一阶有限差分法构建结构参量与像差参量之间的灵敏度矩阵，利用V矩阵余弦相似度与加权贪心策略，确定了6个有效补偿器。实验结果表明：系统波前像差RMS小于0.07 λ的累积概率从47%提高至97.7%，加工公差与装调公差从Q1等级降低至Q2等级，显著降低了光学系统的制造公差，有效地提高了系统良率。装调仿真实验进一步验证了该方法在高数值孔径显微物镜中的可行性与有效性。这一结果表明该方法可以选取合适的补偿器，有效地降低补偿器间的负相关性。
- 公差分析 /
- 显微物镜 /
- 余弦相似度 /
- 光学设计 /
- 计算机辅助装调
Abstract:
To address the issue of compensator coupling in the tolerance analysis of high-numerical-aperture microscope objectives, this paper proposes a compensator selection method based on the cosine similarity of the V-matrix, aiming to reduce negative correlations between compensators and avoid problems such as coma and astigmatism that cannot be simultaneously corrected. Taking an infinity-conjugate microscope objective with a numerical aperture of 0.9 as the subject of study, a sensitivity matrix between structural parameters and aberration parameters was constructed using the first-order finite difference method. By employing V-matrix cosine similarity and a weighted greedy strategy, six effective compensators were identified. Experimental results show that the cumulative probability of the system’s wavefront aberration RMS being less than 0.07 λ increased from 47% to 97.7%, while manufacturing and alignment tolerances were reduced from Q1 to Q2 grade, significantly lowering the manufacturing tolerances of the optical system and effectively improving system yield. Alignment simulation experiments further validated the feasibility and effectiveness of this method in high-numerical-aperture microscope objectives. These results demonstrate that this method can select appropriate compensators and effectively reduce the negative correlation among them.
- microscopic objective lens /
- tolerance analysis /
- cosine similarity /
- optical design /
- computer-aided alignment

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图 1 显微物镜系统图

Figure 1. Microscope objective lens system diagram

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图 2 Q1等级下的波前像差RMS累积概率分布图

Figure 2. Probability distribution of cumulative wavefront aberration under Q1 grade

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图 3 补偿器选择流程图

Figure 3. Compensator selection flowchart

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图 4 对角矩阵的奇异值

Figure 4. Eigenvalue of diagonal matrix

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图 5 基于V矩阵的结构参量相似度热力图

Figure 5. Structural parameter similarity heatmap based on V matrix

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图 6 补偿后Q2的波前像差RMS累积概率分布

Figure 6. Cumulative probability distribution of wavefront aberration in Q2 after compensation

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图 7 两种方法的良率对比图

Figure 7. Comparison of yield rates for the two methods

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图 8 失调系统的波前图

Figure 8. Wavefront map of a dysfunctional system

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图 9 装调后系统的波前图

Figure 9. Wavefront map of the system after adjustment

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图 10 装调前后的Zernike系数对比图

Figure 10. Comparison of Zernike coefficients before and after adjustment

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图 11 装调前后的高阶球差Zernike系数对比图

Figure 11. Comparison of Zernike coefficients for higher-order spherical aberration before and after adjustment

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图 12 装调前后的MTF对比图

Figure 12. Comparison chart of MTF before and after adjustment

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表 1 显微物镜技术指标

Table 1. Technical specifications for microscope objectives

Optical parameters /Unit	Value
Wavelength /$ \text{nm} $	785~850
Numerical aperture	0.9
Focal length /$ \text{mm} $	4.5
Object height /$ \text{mm} $	0.707
RMS wavefront aberration /λ	0.07

下载: 导出CSV

表 2 Q1等级加工与装调公差表

Table 2. Q1 grade machining and assembly tolerance table

Lens	Index	Radius	Thickness /mm	Irregularity	Tolerance of abbe/%	Surface tilt/(°)	Surface eccentricity/mm	ATH/mm	TIX/(°)	TIY/(°)	DEX/mm	DEY /mm
M1	0.0001	0.5	0.01	0.1	0.01	0.0028	0.001	0.01	0.0028	0.0028	0.001	0.001
M2	0.0001	0.5	0.01	0.1	0.01	0.0028	0.001	0.01	0.0028	0.0028	0.001	0.001
M3	0.0001	0.5	0.01	0.1	0.01	0.0028	0.001	0.01	0.0028	0.0028	0.001	0.001
M4	0.0001	0.5	0.01	0.1	0.01	0.0028	0.001	0.01	Installation and adjustment standard
M5	0.0001	0.5	0.01	0.1	0.01	0.0028	0.001	0.01	0.0028	0.0028	0.001	0.001
M6	0.0001	0.5	0.01	0.1	0.01	0.0028	0.001	—	0.0028	0.0028	0.001	0.001
M7	—							0.01	—

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表 3 Q2等级加工与装调公差表

Table 3. Q2 Grade machining and assembly tolerance table

Lens	Index	Radius	Thickness /mm	Irregularity	Tolerance of abbe/%	Surface tilt/(°)	Surface eccentricity /mm	ATH/mm	TIX/(°)	TIY/(°)	DEX/mm	DEY /mm
M1	0.0003	1	0.01	0.1	0.03	0.005	0.003	0.01	0.005	0.005	0.003	0.003
M2	0.0003	1	0.01	0.1	0.03	0.005	0.003	0.01	0.005	--	0.003	0.003
M3	0.0003	1	0.01	0.1	0.03	0.005	0.003	0.01	0.005	0.005	--	0.003
M4	0.0003	1	0.01	0.1	0.03	0.005	0.003	0.01	Installation and adjustment standard
M5	0.0003	1	0.01	0.1	0.03	0.005	0.003	0.01	--	0.005	0.003	0.003
M6	0.0003	1	0.01	0.1	0.03	0.005	0.003	—	0.005	0.005	--	--
M7	—							0.01	—

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表 4 失调系统的补偿量

Table 4. Compensation for the Imbalanced System

Compensator		Compensation value
Compensator of thickness/mm	Out-of-focus water surface	−0.0050
Compensator of decenter /mm	DEX3	−0.0022
	DEX6	0.0025
	DEY6	0.0031
Compensator of tilt /°	TIY2	0.0059
Compensator of tilt /°	TIX5	−0.0220

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