超精密光学自由曲面面形误差评定算法的研究

项目名称： 超精密光学自由曲面面形误差评定算法的研究

项目编号： No.51205064

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 机械工程学科

项目作者： 张祥朝

作者单位： 复旦大学

项目金额： 25万元

中文摘要： 近年来，超精密光学元件的形状正在从简单的球面和平面转变为复杂的自由曲面。这些元件的面形质量对其光学性能有着决定性的影响。但目前ISO和国家标准中还没有关于复杂曲面面形评定的相关规定，而且精密测量仪器中缺乏此类功能模块，所以自由曲面的面形误差评定就成为当前精密工程领域亟需解决的课题。本项目基于光学功能应用，建立符合精密计量学规范的、具有自主知识产权的光学自由曲面面形误差评定算法体系。将研究曲面法向拟合、CAD模型匹配、子孔径拼接以及Banach参数空间的Zernike多项式拟合；明确法向Zernike多项式与Seidel光学像差之间的映射关联；分析算法的稳定性、健壮性、收敛精度、计算复杂度等数值性质；采用自适应Markov链Monte-Carlo法评估拟合匹配解的不确定度；并利用计量学中现有的简单形状的标准评定算法对所提出的算法进行对比验证。

中文关键词： 自由曲面；面形误差；评定算法；光学元件；不确定度

英文摘要： Recently, the shapes of ultra-precision optical components are becoming more and more complicated. Freeform surfaces have been widely applied in different fileds. The form qualities of these complex surfaces play an essentail role in their optical functionalities. However, the evaluating methods have not been standardised in ISO and Chinese national standards. Most of the precision measurement instruments do not have such capabalities. Consequently, development of the evaluating algorithms of the form errors of freeform surfaces has become an urgent task in the area of precision engineering. A system of evaluating algorithms will be establishd, which is required to have self-owned intellectual property rights, follow the metrologist standards and be consistent with the optical applications of freeform components. The orthogonal fitting of geometrical functions, matching of CAD models, stitching of sub-aperture images and fitting of Zernike polynomials in the Banach parameter space will be investigated. The mapping relationship between the Zernike polynomials of the orthogonal form errors and the Seidel aberrations will be identified. The numerical stability, robustness, convergence accuracy and computational complexity of the proposed algorithms will be investigated. The uncertainties of the fitted parameters wi

英文关键词： freeform surface；form error；evaluation algorithm；optical component；uncertainty