Tolerance desensitization method based on principal component analysis and nodal aberration theory

Objective Optical systems with low tolerance sensitivity have good machinability and high manufacturing yield, reducing processing and adjustment costs. To achieve this, it is necessary to evaluate and optimize the system's tolerance sensitivity in its design, so it is necessary to study related desensitization methods. Traditional desensitization methods include using global optimization algorithms, establishing multiple structures or a combination of both to conduct extensive searches in the solution space, which requires a large amount of computational resources and has low optimization efficiency. Besides, the method by controlling the system structure and ray tracing parameters (such as surface curvature, ray deflection angle, etc.) or optimizing specific aberration distributions to obtain tolerance-insensitive structures lacks the analysis of introduced aberrations, and there is still a certain blindness in the setting of evaluation functions, which also affects the optimization efficiency. Therefore, in order to achieve higher optimization efficiency, this paper proposes a tolerance desensitization method based on the analysis and control of introduced aberrations, and provides corresponding operation counts. Methods Zernike polynomials are used to quantify aberrations. Based on this, linear algebra theory and Monte Carlo analysis are used to find the aberration change rule of the system after introducing perturbations. The main introduced aberrations are then determined through the aberration field and eigenvalue distribution after dimension reduction (Fig.7, Fig.11). Asymmetric perturbations and axial perturbations that may occur during the system manufacturing process are modeled. The introduced aberrations caused by the perturbations are described based on the node aberration theory, and the key surfaces are determined through statistical analysis (Fig.8, Fig.12). According to the correspondence between Zernike terms and wave aberrations, the aberration space is transformed, and a corresponding evaluation function is proposed. Based on the previous analysis, the weights and application surfaces of each term of the evaluation function are determined, and then it is included in the optimization process to suppress the generation of new aberrations. The analysis and optimization ideas of this method are shown (Fig.3). Results and Discussions This method has been applied to the design of the F#11 optical system (Structure 1) and the NA0.5 optical system (Structure 2). After optimization, the expected machining performance has been significantly improved. Taking the MTF performance at the specified spatial frequency on the axis with a 98% confidence level as an example, the performance of the two systems after optimization has increased by about 68% (Fig.9) and 20% (Fig.13) respectively. Compared with the optimization using the TOLR operation number in Zemax software, the optimization time of Structure 1 has been reduced from 7 hours to 36 minutes, and tolerance desensitization has been successfully achieved in the optimization of Structure 2. Conclusions A method for reducing tolerance sensitivity based on the analysis and suppression of introduced aberrations is proposed. The obtained Zernike coefficient matrix is processed by the method of principal component analysis, and the dimensionality reduction of the aberration space is realized according to the obtained eigenvalues and their corresponding eigenvectors. After analyzing the dimensionally reduced aberration space, the main introduced aberration items after perturbation are clarified. The types of aberrations caused by asymmetric perturbations and axial perturbations in the optical system are analyzed, and the quantitative expression of the introduced aberration items is obtained based on the node aberration theory. According to the correspondence between Zernike terms and primary aberrations, the expression of the evaluation function M is derived. The evaluation function is applied to two design examples, and the optimization results show that this method has higher optimization efficiency compared to existing methods, and it has a tolerance desensitization effect on optical systems with different complexities and different introduced aberration characteristics. © 2024 Chinese Society of Astronautics. All rights reserved.