研究了三轴离子束系统抛光大口径高陡度离轴非球面过程中镜面曲率变化对离子束抛光去除函数的影响。提出了利用修正矩阵修正各驻留点处的去除函数信息, 进而实现对高陡度离轴非球面高精度抛光的方法。该方法通过对离轴非球面进行坐标转换来降低陡度变化对去除函数的影响; 基于Sigmund溅射理论分析离子束抛光非球面材料的去除率, 建立离子束抛光非球面去除函数模型, 计算了材料去除率在非球面各驻留点处的变化。最后, 根据投影原理计算在各驻留点处去除函数的半宽, 得到以驻留点矩阵为基础的去除函数修正矩阵, 从而掌握每一个驻留点处的去除函数信息, 然后根据计算机控制光学表面成形(CCOS)原理解得加工驻留时间分布。选取口径为900 mm×680 mm, 离轴量为350 mm 的离轴体育场型非球面镜进行了抛光实验, 实验显示抛光后非球面镜面形精度的RMS值由32.041 nm达到11.566 nm, 收敛率达 2.77, 对实际加工具有指导意义。

The effect of curvature change of a mirror surface on the removal function of ion beam figuring was explored. A new higher precision figuring method for a highly steep off-axis asphere was proposed by using a correction matrix to calculate the removal function in different dwell points. The coordinate transformation for the off-axis asphere was used to decrease the effect of steep change on the removal function, the material removal rate of ion beam figuring asphere was analyzed based on Sigmund sputtering theory and a mathematics model of the removal function of the ion beam figuring asphere was established to calculate the variation of the material removal rate in different well points. The FWHMs (full wave and half maximum) of removal functions on different dwell points were calculated based on projection theory. Then the correction matrix for removal function was obtained based on the dwell point matrix, by which the information of removal function on every dwell points was calculated. Furthermore, the dwell time could be computed by Computer Controlled Optical Surfacing(CCOS) theory. At last, the experiments were performed by combing with a simulation. A silicon off-axis sphere mirror with a size of 900 mm×680 mm and an off-axis magnitude of 350 mm was figured. Obtained the RMS value of profile accuracy for the off-axis asphere mirror changes from 32.041 nm to 11.566 nm and the rate of convergence is up to 2.77. The experimental result demonstrates that the correction matrix for removal function of ion beam figuring satisfies the requirement of optical fabrication.