摘要
在离轴三反系统装调过程中,针对小范围失调情况下,失调量耦合导致的像差之间相互影响、失调量计算精度低、装调效率低等问题,构建了KAN-Transformer(Kolmogorov-Arnold network-Transformer)的离轴三反失调量预测模型。首先,以系统波前分解的多视场下第1至9项fringe Zernike系数作为模型输入,然后通过KAN-Transformer训练模型预测系统失调量数值,最后根据系统失调量数值调整迭代完成装调。基于KAN-Transformer离轴三反失调量预测模型,通过1000次失调量计算得出平均误差,实验结果表明,相对于基于反向传播(BP)、KAN、Transformer等神经网络模型,所提模型的平均误差分别提升了0.0095、0.0065、0.0048 mm,可以实现更高精度的失调量计算。KAN-Transformer神经网络模型可以有效避免陷入局部最优解并找到全局最优解,具有较好的鲁棒性,且能够更好地捕捉复杂光学系统中镜组失调量与系统波像差之间的非线性关系,实现失调量的非解析计算方式。所提方法提高了小范围失调下失调量计算精度,计算精度约提升了0.00618 mm。结果表明,KAN-Transformer模型训练的均方差误差和平均绝对误差均值相对于BP神经网络分别提高了44.6%、73.7%;相对于Transformer神经网络分别提高了25.3%、34.6%。
Objective During the assembly and adjustment process of an off-axis three-mirror optical system,a KAN-Transformer-based(Kolmogorov-Arnold network-Transformer-based)misalignment prediction model is developed to address issues such as the mutual coupling of aberrations due to misalignment,low calculation accuracy,and inefficiency in small-scale misalignments.The model uses 1 to 9 fringe Zernike coefficients derived from system wavefront decomposition across multiple fields of view as inputs.It employs the KAN-Transformer model to predict system misalignment values,which are then iteratively adjusted to complete the assembly process.Experimental results from 1000 misalignment calculations demonstrate that the KAN-Transformer model achieves an average error reduction of 0.0095,0.0065,and 0.0048 mm compared to back-propagation(BP),KAN,and Transformer models,respectively.This improved accuracy allows precise misalignment calculations,avoids local optima,and better captures the nonlinear relationships between mirror misalignments and system wavefront aberrations in complex optical systems.The method described enhances calculation accuracy under small-scale misalignments by approximately 0.00618 mm.Mean square error(MSE)and mean absolute error(MAE)for the KAN-Transformer model are improved by 44.6%and 73.7%,respectively,compared to BP networks,and by 25.3%and 34.6%,respectively,compared to Transformer networks.Methods The computer-aided assembly technique for large and complex optical systems utilizes simulations to calculate misalignment values for each optical component,guiding actual assembly and improving efficiency.This approach provides a more precise and efficient solution for assembling and debugging optical systems and is widely used in aerospace,military,and photolithography applications.The prediction model utilizes fringe Zernike coefficient data obtained from the wavefront decomposition of the optical system through an interferometer.It calculates the initial system misalignment using a trained prediction network and subsequently adjusts the optical system with precision to meet design specifications.To improve the accuracy of system misalignment predictions,a large dataset of misalignment values corresponding to the first to ninth fringe Zernike coefficients across five fields of view is proposed.The KAN module replaces the linear transformation layer in the Transformer architecture,resulting in the KAN-Transformer model,which facilitates faster and more accurate calculations of the system’s initial misalignment.Results and Discussions Firstly,a KAN-Transformer neural network model is developed(Fig.4)and jointly debugged using Zemax and Python.An API script is written to generate a dataset,yielding 10000 sets of imbalanced data for training.The network is trained on this dataset and subsequently used to simulate the installation and adjustment of an off-axis three-mirror optical system.The KAN-Transformer neural network achieves an average absolute error of 0.0012 mm in the case of small-scale misalignment(Fig.9).After incorporating the misalignment values into the off-axis three-mirror model,the wavefront aberrations are found to be 1.129λ,1.260λ,and 0.975λ(Fig.11).When these misalignment values are introduced into the neural network solution,the wavefront aberrations improve significantly to 0.066λ,0.078λ,and 0.035λ(Fig.12),meeting the system design requirements.Further analysis of 1000 different networks reveals that installation and adjustment prediction errors are significantly larger with the BP neural network,which has an average error of 0.0104 mm.The KAN neural network shows an average error of 0.0057 mm,while the Transformer neural network has an average error of 0.0074 mm.The KAN-Transformer neural network outperforms all others with the smallest average error of 0.0009 mm(Fig.13).To verify whether the model can effectively guide real-world installation and adjustment,1000 sets of simulated F(0°,0°),F(0°,2°),F(2°,2°)field-of-view PV error values and RMS error values of the off-axis three-mirror optical system are analyzed.The results indicate that compared to the central field of view,the PV error and RMS errors increase in the F(2°,2°)and F(0°,2°)fields of view.As the field-of-view angle increases,changes in the specular reflection direction cause greater deviations in the light propagation path,resulting in the gradual accumulation of wavefront errors and higher error values.However,these errors remain within acceptable limits,demonstrating that the KAN-Transformer misalignment prediction model provides sufficient accuracy to guide the actual installation and adjustment process(Fig.14).Conclusions The traditional sensitivity matrix method establishes the relationship between misalignment and aberration,solving it using mathematical models.In contrast,neural networks train on large datasets to understand the influence of misalignment on image quality,enabling non-analytical misalignment calculations.This approach avoids relying on exact representations of imaging forms and misalignment parameters,making it better suited for the increasingly complex tuning of optical systems.To achieve more accurate misalignment calculations after initial adjustments and reduce the number of iterations required,we propose an optical system misalignment prediction model based on KAN-Transformer.By integrating the KAN structure into the Transformer neural network,the model’s nonlinear representation capability is enhanced,improving accuracy for small-scale misalignment calculations and enabling non-analytical system misalignment determination.The MSE and MAE mean values of the KAN-Transformer model are 41.2%and 62.4%of those for the KAN neural network and 22.2%and 50.7%of those for the BP neural network,respectively,demonstrating superior prediction accuracy and generalization ability.For small-scale misalignments,the KAN-Transformer achieves a calculation accuracy of about 0.0008 mm,outperforming the Transformer model.Simulations and adjustments of off-axis three-mirror optical systems verify that the KAN-Transformer provides significantly higher accuracy,proving its ability to effectively guide actual assembly.
作者
盛雷
李丽娟
付西红
林雪竹
郭丽丽
Sheng Lei;Li Lijuan;Fu Xihong;Lin Xuezhu;Guo Lili(Key Laboratory of Photoelectric Measurement and Optical Information Transmission Technology of Ministry of Education,School of Optoelectronic Engineering,Changchun University of Science and Technology,Changchun 130022,Jilin,China;Zhongshan Institute of Changchun University of Science and Technology,Zhongshan 528437,Guangdong,China;Xi’an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences,Xi’an 710119,Shaanxi,China;University of Chinese Academy of Sciences,Beijing 100049,China)
出处
《光学学报》
北大核心
2025年第5期149-161,共13页
Acta Optica Sinica
基金
国家重点研发计划“引力波探测”重点专项(2021YFC222202100)
长春理工大学中山研究院引进创新科研团队项目(CXTD2023006)
西安光学精密机械研究所深化改革提升原始创新能力专项自主部署项目(S22-033)。
关键词
离轴三反系统
计算机辅助装调
神经网络
失调量计算
非线性误差
off-axis three-mirror optical system
computer-aided adjustment
neural network
imbalance calculation
nonlinear error
作者简介
通信作者:李丽娟,custjuan@163.com;通信作者:付西红,fuxh@opt.ac.cn。
