以PV值为优化目标的光学系统支撑结构

光机系统中支撑结构与光学元件的接触位置、接触面积、接触应力及支撑结构的柔度是光学系统成像质量的重要影响因素，为了降低因垂直方向支撑引起的几何像差，以像差指数PV值为优化目标，对单个透镜接触支撑结构进行了拓扑优化设计。首先建立接触拓扑优化模型，以采用Signorini接触条件建立的刚性支撑单向接触中的线弹性结构为例，验证了接触拓扑优化模型的正确性。用透镜变形函数来描述透镜的像差指数PV值，将其作为拓扑模型的优化目标。采用SIMP方法描述拓扑优化设计变量，采用扩展后的拉格朗日算子求解接触条件。采用MMA优化算法求解拓扑优化模型的最优解。通过拓扑优化设计变量的最优解，定义了满足几何畸变要求的支撑结构的最优拓扑结构。结果表明，该方法可使透镜PV值降低14%，面形RMS值降低13.8%。同时搭建实验平台，对透镜PV值和RMS值进行测试，得到的最佳接触支撑结构的支持试验结果表明，平面反射镜表面PV值分别降低了60.4%和42.9%，面形RMS值分别降低了74.3%和38.9%，优化后的接触支撑结构有效地提高了高精度单透镜支架的精度，具有很大的实际应用潜力。

Abstract

The contact position, contact area, contact stress and flexibility of single lens support structure in an optical system are important influencing factors of the system′s imaging quality. Topology optimization of the single-lens contact support structure is carried out using the aberration index PV value as the optimization objective to reduce geometric aberration aberration in the single mirror caused by gravitational force. We first establish the contact topology optimization model, then use a linear elastic structure in unilateral contact with a rigid support as-modeled by Signorini′s contact conditions as an example to verify the model. The aberration index PV value of the lens is described as a function of lens deformation; thus, the value serves as a functional objective of the topology optimization model. We use the SIMP method to describe the topology optimization design variables, and the augmented Lagrange multiplier method to solve the contact condition. The optimal solution of the topology optimization model can be solved via MMA optimization algorithm. The optimal topological configuration of supporting structures that satisfy geometric aberration requirements is defined by the optimal solution of the design variables. We found that the PV value of the lens can be reduced by 14% and the lens surface RMS value by 13.8% after applying the proposed method. We also tested the lens PV value and RMS value on an experimental platform supported by the optimal contact support structure. The surface of the plane mirror surface PV values decreased by 60.4% and 42.9%, and the RMS values by 74.3% and 38.9%. To this effect, the optimal contact support structure effectively improves the precision of the single lens support and demonstrates significant potential for practical application.

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李一芒, 周子云, 刘永明. 以PV值为优化目标的光学系统支撑结构[J]. 发光学报, 2019, 40(10): 1303. LI Yi-mang, ZHOU Zi-yun, LIU Yong-ming. Topology-optimization of Lens Contact Support Structures: PV Value as An Optimization Objective[J]. Chinese Journal of Luminescence, 2019, 40(10): 1303.

以PV值为优化目标的光学系统支撑结构

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