基于面形斜率的高斯径向基自由曲面优化设计及公差分析

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

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。

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.