Integrated Optomechanical Simulation and Surrogate Model Construction for Imaging Quality Prediction of Two-mirror Optical System

doi:10.12382/bgxb.2024.0278

Abstract

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

CLC Number:

TJ765.4

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-.

Figures/Tables 29

Fig.1 Overall framework

Fig.2 Pyramid diagram of standard Zernike polynomials

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

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

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

Fig.5 Fitting result of Zernike polynomial

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

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

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

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

Fig.10 Finite element mesh model of bolted joint

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

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

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

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

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

Fig.14 Specular deformation contours of primary and secondary mirrors

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

Fig.15 Solid model of ideal optical path

Fig.16 MTF curve of ideal optical path

Fig.17 Concentration curve of ideal optical path energy

Fig.18 Regression principle of SVR surrogate model

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

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

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

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

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

Fig.24 Comparison of predicted errors of different kernel functions

Fig.25 Average relative errors of different regression models

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