两反式光学系统光机集成仿真与成像质量预测代理模型构建

doi:10.12382/bgxb.2024.0278

摘要/Abstract

摘要：

两反式光学系统广泛应用于空间遥感、探测制导等领域,装配是影响光学系统成像质量的关键环节,当前各种装配误差与光学系统成像质量之间的关联关系缺少系统研究,无法为光学系统实时装调提供支撑。提出两反光学系统装配与成像的联合仿真方法。采用有限元仿真方法获得镜面面形误差,利用Zernike多项式对其进行精确拟合,通过光学产品设计与分析软件对包含Zernike多项式的镜面变形误差和装配位姿偏差进行光路成像仿真,以能量集中度作为成像质量定量评价指标,获得不同装配误差条件下的光学系统成像质量数据。建立包含局部和全局混合核函数的支持向量回归(Support Vector Regression,SVR)代理模型,对装配误差和成像质量之间的关联关系进行精确拟合。研究结果表明:与单一核函数/无核函数的SVR模型相比,所建立的混合核函数SVR代理模型具有最小的成像质量预测误差(平均预测误差仅有6.51%);所提装配与成像联合仿真方法和混合核函数SVR代理模型,能够为不同装配误差条件下的光学系统实时装调提供辅助支撑。

关键词: 光学系统, 装配误差, 能量集中度, 支持向量回归代理模型, 混合核函数

Abstract:

The two-mirror optical system is widely used in the fields and space remote sensing,detection,guidance and so on.Assembly is a key step that impacts the imaging quality of optical system.Currently,there is a lack of systematic research on the correlation between various assembly errors and imaging quality of optical system,which hinders real-time adjustment of optical system.In this study,a joint simulation method is proposed for the assembly and imaging of two-mirror optical system.This method involves using finite element simulation to obtain mirror surface figure errors,followed by precise fitting using Zernike polynomials.Subsequently,optical design and analysis software is employed to conduct the light path imaging simulations for the mirror surface figure errors fitted by Zernike polynomials and the assembly position deviations.The energy concentration degree serves as a quantitative evaluation index for assessing the imaging quality of optical system under different assembling error conditions.Furthermore,a support vector regression (SVR) surrogate model that incorporates both local and global mixed kernel functions is established to accurately capture the correlation between assembly errors and imaging quality.Research results indicate that the mixed kernel function SVR surrogate model proposed in the paper exhibits the smallest imaging quality prediction error with an average prediction error of only 6.51% compared to single kernel function or no kernel function SVR models.The proposed joint simulation method for assembly and imaging,along with the mixed kernel function SVR surrogate model,provides auxiliary support for real-time adjustment of optical systems under varying assembly error conditions.

Key words: optical system, assembly error, energy concentration, support vector regression surrogate model, mixed kernel function

中图分类号:

TJ765.4

薛奋琪, 巩浩, 刘检华, 朱荣全, 谢惟楚, 雷静婷. 两反式光学系统光机集成仿真与成像质量预测代理模型构建[J]. 兵工学报, 2025, 46(3): 240278-.

XUE Fenqi, GONG Hao, LIU Jianhua, ZHU Rongquan, XIE Weichu, LEI Jingting. Integrated Optomechanical Simulation and Surrogate Model Construction for Imaging Quality Prediction of Two-mirror Optical System[J]. Acta Armamentarii, 2025, 46(3): 240278-.

图/表 29

图1 总体框架

Fig.1 Overall framework

图2 标准Zernike多项式金字塔图

Fig.2 Pyramid diagram of standard Zernike polynomials

表1 标准Zernike多项式前16项及其含义

Table 1 The first 16 terms of standard Zernike polynomials and their meanings

项	n	m	多项式表达式	像差
Z₁	0	0	1	偏移
Z₂	1	1	ρ·cosθ	倾斜-x轴
Z₃	1	1	ρ·sinθ	倾斜-y轴
Z₄	2	2	ρ²·cos(2θ)	1阶像散-x轴
Z₅	2	0	2ρ²-1	离焦
Z₆	2	2	ρ²·sin(2θ)	1阶像散-y轴
Z₇	3	3	ρ³·cos(3θ)	1阶三叶草像差-x轴
Z₈	3	1	(3ρ³-2ρ)·cosθ	1阶彗差-x轴
Z₉	3	1	(3ρ³-2ρ)·sinθ	1阶彗差-y轴
Z₁₀	3	3	ρ³·sin(3θ)	1阶三叶草像差-y轴
Z₁₁	4	4	ρ⁴·cos(4θ)	1阶四叶草像差-x轴
Z₁₂	4	2	(4ρ⁴-3ρ²)·cos(2θ)	2阶像散-x轴
Z₁₃	4	0	6ρ⁴-6ρ²+1	1阶球差
Z₁₄	4	2	(4ρ⁴-3ρ²)·sin(2θ)	2阶像散-y轴
Z₁₅	4	4	ρ⁴·sin(4θ)	1阶四叶草像差-y轴
Z₁₆	5	5	ρ⁵·cos(5θ)	1阶五叶草像差-x轴

图3 前16项标准Zernike多项式代表的二维波面形状

Fig.3 The shapes of two-dimensional wave represented by the first 16 iterms of standard Zernike polynomials

图4 前16项标准Zernike多项式代表的三维波面形状

Fig.4 The shapes of three-dimensional wave represented by the first 16 iterms of standard Zernike polynomials

图5 Zernike多项式拟合结果

Fig.5 Fitting result of Zernike polynomial

图6 两反光学系统装配及成像联合仿真流程

Fig.6 Assembly and imaging co-simulation process of two-mirror optical system

图7 两反光学系统结构及组成

Fig.7 Structure and composition of two-mirror optical system

图8 沿轴向剖面和横向剖面的外螺纹轮廓

Fig.8 Schematic diagram of the external External thread profile along the axial and transverse profiles

图9 内外螺纹网格建模过程

Fig.9 Schematic diagram of modeling process for the internally and externally threaded meshed

图10 螺栓连接结构有限元网格模型

Fig.10 Finite element mesh model of bolted joint

图11 两反光学系统有限元网格模型

Fig.11 Finite element mesh model of two-mirror optical system

图12 结构钢材料真实应力-应变曲线

Fig.12 True stress-strain curve of stainless steel material

表2 有限元模型材料属性

Table 2 Material properties of finite element model

材料	密度/(kg·m^-3)	弹性模量/GPa	泊松比
2A12	2850	74.2	0.36
6061T6	2700	69	0.33
结构钢	7750	193	0.31

表3 6种不同的螺栓头网格划分方式

Table 3 Six different ways to mesh bolt head

编号	网格类型	节点数量	网格数量	最小单元尺寸/mm
Mesh1	六面体网格	61850	57600	约0.14
Mesh2	四面体网格	5747	24911	0.30
Mesh3	四面体网格	4639	20188	0.40
Mesh4	四面体网格	3699	15552	0.50
Mesh5	四面体网格	3491	15023	0.60
Mesh6	四面体网格	3178	13135	0.65

图13 不同网格尺寸及形状下的扭拉关系曲线

Fig.13 Torque-tension relationship curves for different mesh sizes and shapes

图14 主次镜镜面变形云图

Fig.14 Specular deformation contours of primary and secondary mirrors

表4 主次镜设计参数

Table 4 Design parameters of primary and secondary mirrors

镜头	曲率半径/mm	半直径/mm	圆锥系数	4阶项	6阶项	8阶项	10阶项
主镜	-107.771	43	-1	-	-	-	-
次镜	-57.815	13.2	0	4.644× 10^-6	-3.428× 10^-9	3.799× 10^-12	-3.355× 10^-15

图15 理想光路实体模型

Fig.15 Solid model of ideal optical path

图16 理想光路MTF

Fig.16 MTF curve of ideal optical path

图17 理想光路能量集中度

Fig.17 Concentration curve of ideal optical path energy

图18 SVR代理模型回归原理

Fig.18 Regression principle of SVR surrogate model

图19 z轴不同旋转角度下的光学系统成像结果

Fig.19 Imaging results of optical system at different rotation angles along z-axis

图20 不同螺栓预紧力作用下主镜面形拟合的Zernike多项式系数

Fig.20 Zernike polynomials coefficients of primary mirror shape fitting under different bolt preloads

图21 装配误差影响下的点阵图

Fig.21 Dot matrix plot under the influence of assembly errors

图22 测试集预测值和真实值

Fig.22 Scatter plot of the predicted and true values in the test set

图23 重复试验下测试集平均相对误差

Fig.23 Mean relative error of data in the test set under repeated experiments

图24 不同核函数预测误差对比

Fig.24 Comparison of predicted errors of different kernel functions

图25 不同回归模型的平均相对误差

Fig.25 Average relative errors of different regression models

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