弹性薄膜液体透镜的优化设计及面形分析  

Optimization and Figure Analysis of Elastic Thin-Film Liquid Lens

作　　者：刘永明[1,2] 谢军[1] 李湘勤[1,2] 刘震宇[1] 

机构地区：[1]中国科学院长春光学精密机械与物理研究所应用光学国家重点实验室,吉林长春130033 [2]中国科学院大学,北京100049

出　　处：《中国激光》2013年第12期247-254,共8页Chinese Journal of Lasers

基　　金：国家自然科学基金(51275504)

摘　　要：为使弹性薄膜液体透镜的光学薄膜变形后面形满足光学系统对球面面形的设计要求,采用固体各向同性惩罚微结构拓扑优化模型和移动渐近算法优化算法,对液体透镜的弹性体支撑区域进行了拓扑优化,得到了满足收敛条件的拓扑构型。根据拓扑优化结果,对关键结构尺寸进行了形状优化。综合考虑加工制造等因素,设计了易于加工制造的光学透明弹性薄膜液体透镜。对光学薄膜进行了面形精度分析,计算了不同口径下的面形误差峰谷(PV)值和方均根(RMS)值。数值结果表明,光学薄膜变形面形在弦高为0.5mm,光学薄膜口径分别为100%、95%、90%时,优化结构面形误差PV值分别是初始结构面形误差PV值的5.7%、11.9%、2.5%,RMS值分别是初始结构RMS值的11.2%、21.9%、45.4%。用36项Zernike多项式对变形光学薄膜进行拟合,结果表明,优化结构的Zernike系数第4、第9、第16、第25项比初始结构明显降低。In order to meet the requirement of an optical system design on the spherical surface via the thin-film elastic deformation of liquid lens, a numerical optimization method is implemented on the elastomeric supporting region of liquid lens using the solid isotropic material with penalization type topology optimization model and moving asymptotes constrained optimization algorithm. The topological configuration meeting the convergence conditions is obtained. According to the topology optimization results, the shape optimization is further implemented for key structural dimensions. And a manufactureable elastic thin-film liquid lens is designed according to micromachining technology. Surface error of optical thin-film is analyzed based on the deformation of thin-film. The peak valley （PV） and root mean square （RMS） values about surface error are calculated on the different diameters. The numerical results show that the optical surface error PV values of the optimized structure are 5.7 %, 11.9 % and 2.5 % of the initial structure, respectively, and the RMS values are 11. 2%, 21. 9% and 45. 4% of the initial structure, respectively, at diameters of 100% ~ 95 % and 90 % of thin-film and the height of chord of 0.5 mm. The deformation of the optical thin film is fitted with 36 Zernike polynomials. Fitting results show that the 4th, 9th, 16th, 25th Zernike coefficients are also obviously reduced.

关 键 词：光学设计 液体透镜 拓扑优化 ZERNIKE多项式 面形精度 

分 类 号：O439[机械工程—光学工程]