轴对称非球面设计参数测试技术

针对未知设计参数的旋转对称非球面,讨论了面型参数的拟合方法,对轴对称非球面设计参数测试技术进行了研究.利用接触式探针轮廓仪的测量数据,通过多项式拟合给出对称轴和顶点曲率初值,利用最小二乘法与约束变尺度迭代原理,对测量数据进行曲线拟合,获得非球面的设计参数值,拟合参数计算的面形数据与实测数据相比较,得到误差曲线及相应得面形误差PV值.拟合分析结果表明:该算法具有收敛速度快、稳定性好的特点,拟合参数很好地还原了加工曲面的设计参数,能够满足非球面镜的超精密加工精度要求,为非球面镜加工质量的评价以及后续补正加工提供了理论依据.

Testing Technology for Design Parameter of Axial Symmetry Aspheric Surface

Aiming at the unknown design parameter of rotary symmetry aspheric surface, discuss forming parameter fitting method, research on axial symmetry aspheric design parameter testing technology. Use contact probe filometer to measure data, acquire symmetry axis and end curvatures initial value by polynomial fitting, use least square method and restraint variable-dimension method to carry out curve fitting for measurement data, acquire aspheric surface design parameter, compare fitting parameter forming data with actual measurement data, and acquire PV value of error curve and related forming error. Fitting analysis results show that: the method has advantage of fast convergence speed and high stability, fitting parameter can restore design parameter of machining curve, meet ultra-precision machining requirements of aspheric mirror, and support aspheric mirror machining quality valuation and follow on compensation machining with theoretical basis.