基于刚体位移的天线反射面拟合新算法  

Antenna Reflector Surface Fitting Algorithm Based on Rigid Body Displacement Principle

作　　者：马增祥[1,2,3] 杨德华[1,2] 王淑青[3,4] 程景全 

机构地区：[1]中国科学院国家天文台南京天文光学技术研究所,南京210042 [2]中国科学院天文光学技术重点实验室,南京210042 [3]中国科学院研究生院,北京100049 [4]中国科学院国家天文台,北京100012 [5]美国国立射电天文台,夏洛茨维尔VA22903-2475,美国

出　　处：《机械工程学报》2010年第18期29-35,共7页Journal of Mechanical Engineering

基　　金：国家自然科学基金(10973025);25米NRT射电望远镜资助项目

摘　　要：射电望远镜和雷达天线的反射面的加工误差和变形直接影响系统的工作性能。为准确计算反射面的实际误差,一般须对变形后的反射面进行最佳抛物面拟合。基于刚体空间运动原理,提出一种利用确定刚体位移的6自由度及抛物面的焦距共7个广义自由度来拟合空间抛物面的新方法。通过该方法可直接求得最佳抛物面的顶点空间位置、轴线方向及其焦距。回顾传统的由一般二次曲面推出特征值的抛物面拟合法和小变形下基于法向偏差的抛物面拟合方法,并通过计算实例与之进行比较。验证了方法的稳定性和精确性。同时还集成了一种简便的拟合误差求解方法。Manufacture errors and deformation of a radio telescope or radar antenna reflector have a direct effect on the system performance.To precisely figure out the actual surface error of a reflector,a best paraboloid fitting for the deformed reflector is necessary,Based on the space motion principle of a rigid body,a novel algorithm on paraboloid fitting is developed,which introduces 7 generalized degrees of freedom（DOF） defined as the 6 rigid body DOFs and the focal length of the paraboloid.The orientation and vertex position as well as the best focal length of the required best-fit paraboloid are explicitly computed by the least square procedure.Traditional fitting strategies based on quadric surface eigenvalues extraction and on normal deviation minimization with small deformation are reviewed and afterwards compared with the provided new method with examples.The application demonstrates the stability and accuracy of the proposed algorithm.Moreover,a simple error estimation method based on iteration concept is also included.

关 键 词：抛物面拟合 刚体位移 自由度 坐标变换 最小二乘法 误差 

分 类 号：TN957.2[电子电信—信号与信息处理]