Design method for conformal systems based on plane-symmetric aberration theory
doi: 10.37188/CO.EN-2025-0044
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摘要:
针对共形光学系统设计中理论指导不足、过度依赖试错优化的问题，本文提出一种基于平面对称系统像差理论的设计方法。通过建立全局面型参数与局域面型参数的转换关系，将现有像差理论拓展至共形系统，实现了各表面像差贡献的解析计算。基于该理论框架，构建了两步式设计策略：首先，通过分析整流罩外表面的像差贡献分布规律，选取像差贡献最小的万向节点位置作为系统初始结构；其次，在拱形校正器优化过程中，逐步引入与像差相关的自由曲面参数，并构建像差系数评价函数。为验证方法的有效性，对同一设计指标组合不同万向节点位置与优化方法，完成14组共形系统的对比设计。结果表明：采用本文方法设计的系统在42 lp/mm空间频率处全视场调制传递函数（MTF）优于0.4，成像质量接近衍射极限，性能达到传统设计方法的2.4倍。该方法为高性能共形光学系统设计提供了系统的理论指导。
Abstract:The design of conformal optical systems often suffers from insufficient theoretical guidance, resulting in repeated trial-and-error optimization. To address this, we introduce a design method based on aberration theory for plane-symmetric systems. By converting global surface parameters into local surface parameters, the aberration theory is generalized to conformal systems, enabling analytical calculation of each surface’s aberration contribution. Using this formulation, we propose a two-step design strategy. First, the optimal gimbal position is determined by minimizing the aberration contribution of the dome’s outer surface. Second, during arch-corrector optimization, freeform parameters associated with dominant aberrations are progressively introduced, and an aberration-coefficient-based merit function is employed. To validate the effectiveness of the proposed method, comparative designs of 14 conformal systems were completed for identical specifications across different gimbal positions and optimization approaches. Results demonstrate that the system designed using our method achieves a full-field modulation transfer function (MTF) exceeding 0.4 at a spatial frequency of 42 lp/mm, with imaging quality approaching the diffraction limit—representing a 2.4× improvement over conventional design methods. This approach provides systematic theoretical guidance for the design of high-performance conformal optical systems.
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Key words:
- conformal optics /
- aberration theory /
- freeform optics
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Figure 1. Global coordinate system (XYZ) and local coordinate system (X’Y’Z’). (a) Overall view. (b) Enlarged view.
Figure 4. Local surface parameters of the dome’s outer surface. (a) Freeform parameter
$ {F}_{02} $ . (b) Freeform parameter$ {F}_{21} $ .
Figure 6. Variation of aberration surface contribution with gimbal position. (a)
$ {W}_{02002} $ . (b)$ {W}_{03001} $ .
Figure 7. Conformal system layout obtained by two optimization methods at different gimbal positions.
Figure 8. Average RMS spot diameter of the conformal systems obtained by two optimization methods at different
$ {L}_{GP} $ .
Figure 9. MTF of the conformal systems obtained by two optimization methods at different
$ {L}_{GP} $ when look angle is 40°.Table 1. Aberration terms in plane-symmetric systems
Group Vector form Name First group $ {W}_{00000} $ Constant piston Second group $ {W}_{01001}\left(\boldsymbol{i}\cdot \boldsymbol{\rho }\right) $ Field displacement $ {W}_{10010}\left(\boldsymbol{i}\cdot \boldsymbol{H}\right) $ Linear piston $ {W}_{02000}\left(\boldsymbol{\rho }\cdot \boldsymbol{\rho }\right) $ Defocus $ {W}_{11100}\left(\boldsymbol{H}\cdot \boldsymbol{\rho }\right) $ Magnification $ {W}_{20000}\left(\boldsymbol{H}\cdot \boldsymbol{H}\right) $ Quadratic piston Third group $ {W}_{02002}{\left(\boldsymbol{i}\cdot \boldsymbol{\rho }\right)}^{2} $ Constant astigmatism $ {W}_{11011}\left(\boldsymbol{i}\cdot \boldsymbol{H}\right)\left(\boldsymbol{i}\cdot \boldsymbol{\rho }\right) $ Anamorphism $ {W}_{20020}{\left(\boldsymbol{i}\cdot \boldsymbol{H}\right)}^{2} $ Quadratic piston $ {W}_{03001}\left(\boldsymbol{i}\cdot \boldsymbol{\rho }\right)\left(\boldsymbol{\rho }\cdot \boldsymbol{\rho }\right) $ Constant coma $ {W}_{12101}\left(\boldsymbol{i}\cdot \boldsymbol{\rho }\right)\left(\boldsymbol{H}\cdot \boldsymbol{\rho }\right) $ Linear astigmatism $ {W}_{12010}\left(\boldsymbol{i}\cdot \boldsymbol{H}\right)\left(\boldsymbol{\rho }\cdot \boldsymbol{\rho }\right) $ Field tilt $ {W}_{21001}\left(\boldsymbol{i}\cdot \boldsymbol{\rho }\right)\left(\boldsymbol{H}\cdot \boldsymbol{H}\right) $ Quadratic distortion I $ {W}_{21110}\left(\boldsymbol{i}\cdot \boldsymbol{H}\right)\left(\boldsymbol{H}\cdot \boldsymbol{\rho }\right) $ Quadratic distortion II $ {W}_{30010}\left(\boldsymbol{i}\cdot \boldsymbol{H}\right)\left(\boldsymbol{H}\cdot \boldsymbol{H}\right) $ Cubic piston $ {W}_{04000}{\left(\boldsymbol{\rho }\cdot \boldsymbol{\rho }\right)}^{2} $ Spherical aberration $ {W}_{13100}\left(\boldsymbol{H}\cdot \boldsymbol{\rho }\right)\left(\boldsymbol{\rho }\cdot \boldsymbol{\rho }\right) $ Linear coma $ {W}_{22200}{\left(\boldsymbol{H}\cdot \boldsymbol{\rho }\right)}^{2} $ Quadratic astigmatism $ {W}_{22000}\left(\boldsymbol{H}\cdot \boldsymbol{H}\right)\left(\boldsymbol{\rho }\cdot \boldsymbol{\rho }\right) $ Field curvature $ {W}_{31100}\left(\boldsymbol{H}\cdot \boldsymbol{H}\right)\left(\boldsymbol{H}\cdot \boldsymbol{\rho }\right) $ Cubic distortion $ {W}_{40000}{\left(\boldsymbol{H}\cdot \boldsymbol{H}\right)}^{2} $ Quartic piston 
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Table 2. Specifications of the system.
Parameter Specification Material of dome ZnS Fineness ratio (L/D) 1 Diameter of dome (D) 180 mm Shape of dome Ellipsoid Thickness of dome 4 mm Wavelength 3.7–4.8 μm Field of regard (FOR) ±40° Field of view (FOV) 2°×2° Entrance pupil diameter 45 mm F-number 2 Pixel size 1.2 μm
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