Optimization and tolerance analysis of freeform surface using Gaussian RBF-Slope model

Xing ZHAO; Liu-chang XIAO; Zan ZHANG; Ling-jie WANG; Xiao-dong ZHANG

doi:10.3788/OPE.20192712.2499

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Optimization and tolerance analysis of freeform surface using Gaussian RBF-Slope model

Modern Applied Optics | 更新时间：2020-07-09

- Optimization and tolerance analysis of freeform surface using Gaussian RBF-Slope model
- Optics and Precision Engineering Vol. 27, Issue 12, Pages: 2499-2508(2019)
- 作者机构：
  
  1.南开大学现代光学研究所，天津 300350
  2.天津市光电传感器与传感网络技术重点实验室，天津 300350
  3.中国科学院长春光学精密机械与物理研究所光学系统先进制造技术中国科学院重点实验室，吉林长春 130033
  4.天津大学精密测试技术及仪器国家重点实验室天津微纳制造工程技术中心，天津 300072
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20192712.2499
  CLC： O439; TN873
- Received：24 June 2019，
  
  Accepted：21 August 2019，
  
  Published：25 December 2019
- 稿件说明：
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Xing ZHAO, Liu-chang XIAO, Zan ZHANG, et al. Optimization and tolerance analysis of freeform surface using Gaussian RBF-Slope model[J]. Optics and precision engineering, 2019, 27(12): 2499-2508.
DOI：

Xing ZHAO, Liu-chang XIAO, Zan ZHANG, et al. Optimization and tolerance analysis of freeform surface using Gaussian RBF-Slope model[J]. Optics and precision engineering, 2019, 27(12): 2499-2508. DOI： 10.3788/OPE.20192712.2499.

摘要

基于面形斜率的高斯径向基自由曲面模型在面形表征和系统设计中具有优势，但基函数数目较多，导致优化效率低、公差分析困难等问题。本文对基于面形斜率的高斯径向基模型优化设计和公差分析方法开展研究，利用模型的面形表征局域特性，将全局优化和局部优化相结合，提出了一种新的优化设计方法。利用数学统计的方法，确定了基函数系数和自由曲面面形矢高之间的线性关系，直接设定系数公差范围初值，通过大样本统计后确定自由曲面的合理面形公差。将该优化设计和公差分析方法应用到基于面形斜率的高斯径向基自由曲面型头戴显示系统，设计结果表明：头戴显示系统全视场内在23 lp/mm处大于0.3，系统最大畸变为3.45%，达到了系统设计指标，并基于公差分析结果进行实验系统集成，成功实现了图像显示。本文所提出的优化设计方法和公差分析方法为基于面形斜率的高斯径向基自由曲面模型和其他局域型自由曲面模型的应用提供了重要的借鉴意义。

Abstract

A model with radial basis functions based on surface slope (RBF-BS) has advantages in terms of its characterizations and optimal system design. However

using this model can lead to some problems such as low optimization efficiency and difficulties in conducting tolerance analysis owing to the use of too many basis functions in RBF-BS. Thus

a method of achieving the optimal design and performing tolerance analysis with this model was proposed. This study combined global and local optimizations to develop a new optimization design method based on the local characteristics of the RBF-BS model. The linear relationship between the coefficient of basis function and freeform surface sag was determined by the method of mathematical statistics

and the initial range of tolerance of coefficients was directly determined. The reasonable tolerance value of freeform surface sag was acquired by large-sample statistics. When the proposed method of achieving the optimized design and performing tolerance analysis was applied to a head-mounted display system with a freeform surface using the RBF-BS model

the results indicate that the average modulation transfer function in the entire field view exceeds 0.3

and the largest distortion is 3.45%

which are consistent with the system design target. Based on the results of tolerance analysis

the experimental system integration successfully achieves the display of picture. The proposed method of achieving the optimized design and performing tolerance analysis provides valuable information about RBF-BS and other local freeform surface models.

关键词

Keywords

references

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Related Institution

School of Optoelectronics, Beijing Institute of Technology

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Key Laboratory of Optical Information Science and Technology of the Ministry of Education, Institute of Modern Optics, Nankai University

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