采用非均匀有理B样条曲面延展光学元件面形误差

在离子束抛光工艺中,为了提高驻留时间求解算法在工件边缘处的求解精度,通常需要对原始面形误差数据进行边缘虚拟延展。要求原始面形误差数据与虚拟延展面光滑拼接,并在延展区域具有可控的不确定性。非均匀有理B样条(NURBS)曲面常用在机械制造领域对复杂形状物体进行三维建模。引入非均匀有理B样条曲面并结合泽尼克(Zernike)多项式拟合对一典型的圆形光学元件面形误差自由曲面数据进行延展。通过对典型面形误差曲面延展前后的等效功率谱密度曲线分析可以看出,延展后在面形误差频率大于0.05mm-1时其面形误差改善量均大于70%;将该典型延展面应用于特定驻留时间求解算法中,使得预测加工精度的均方根值由1.18nm改善至0.19nm。这表明,采用非均匀有理B样条曲面延展光学元件面形误差能够获得光滑拼接的虚拟延展曲面,并能大大改善离子束抛光工艺中驻留时间算法的求解精度。

Surface Error of Optical Components Extended with Non-Uniform Rational B-Spline Surface

In the technique of ion beam figuring, it often needs to extend the original surface error data to improve the dwell time solving precision on the edge. The virtual extended surface should be smoothly stitched with the original surface error data and should have controllable uncertain ability. Non-uniform rational B-spline (NURBS) surface is usually used in the mechanism fabrication field to model three-dimensional (3D) objects. Using the non-uniform rational B-spline surface and combining with the Zernike polynomial fitting method, a typical tested original free-form surface error data set is extended. The power spectral density curves of typical original surface error and the extended surface error show that the surface error is improved by more than 70% when the error spatial frequency is greater than 0.05 mm-1. This extended surface is also used in the dwell time algorithm, and the forecasted machining precision is improved from 1.18 nm to 0.19 nm in root mean square (RMS) value. The results show that smooth virtual extended surface can be got and the computing precision of the dwell time algorithm can be improved by using non-uniform rational B-spline surface to extend the surface error of the optical components.