基于测量值计算像差的关键技术研究  

Study on Key Technology of Calculating Aberrations Based on Measured Data

作　　者：黄大刚[1] 王宝光[1] 辛运帏[2] 

机构地区：[1]天津大学精密测量技术与仪器国家重点实验室,天津300072 [2]南开大学信息技术科学学院,天津300071

出　　处：《传感技术学报》2007年第9期2019-2023,共5页Chinese Journal of Sensors and Actuators

基　　金：国家自然科学基金项目资助"多维坐标系统中复杂形体的虚拟定位技术研究"(59875066)

摘　　要：针对加工非球面注塑模具成本高、周期长的缺点,提出一种改进的试制方法,用光学间隔和玻璃元件曲率半径补偿非球面面形误差产生的像差,以减少修模次数.为按实际非球面测量值计算像差,提出一种计算非球面参数的方法,用曲面上的三维坐标测量值提取标准非球面方程的参数.首先在两个相互垂直的近似的中心剖面附近取值,并分别投影到这两个平面上;然后拟合曲线;再用这两条曲线在各自的平面内截取一组平行直线成一组线段,改变直线的斜率,使各线段中点共线,确定非球面的对称轴和顶点坐标;最后,平移、旋转坐标系后,将三维坐标降维,用多项式拟合成二维曲线,同时将标准形式方程中的无理项展为泰勒级数,对比二者的系数,得到标准非球面方程的参数.大量随机取值计算的统计结果表明,算法的误差达到测量误差的1/3.Aimed at the drawback of high cost and long time for making aspheric injection models, an improved trialproduction technology is raised. To diminish the times of mending models, aberrations caused by shape errors of aspheric surfaces are compensated by adjusting optical intervals and spherical radii of glass dements. To calculate aberrations according to the aspheric measurement values, a method of extracting aspheric parameters from 3D coordinates on aspheric surface is proposed. The coordinates are collected near two approximate central sections which are vertical to each other. These coordinates are projected on the two planes respectively, and then, utilized to fit into two curves. A group of parallel lines are intersected by the curves to obtain some line segments on its plane. The axis of symmetry and the top of the lines are determined by changing the slope of the lines until all mid-points are collinear. The coordinates are fitted into a 2D curve after the coordinate system is transforrmed, rotated and the dimensions are reduced. Meanwhile, the irrational item in the standard aspheric equation is expressed as Taylor series. The standard aspheric parameters can be obtained by comparing the corresponding coefficients. Statistical results from a great number of random data show that the errors of the algorithm are one third of measuring errors.

关 键 词：光学测量 像差补偿 非球面参数计算 曲线拟合 坐标变换 

分 类 号：TH74[机械工程—光学工程]