中文摘要：

在光学系统中应用非球面元件可以增加光学设计的灵活性,改善光学系统成像质量,提高光学性能,极大地减小光学系统的外形尺寸和质量。通过深入分析轴对称非球面精密磨削成型过程的加工特性,以及工艺过程中的刀具与工件弹性变形、刀具半径误差、轴向对刀误差等主要加工误差因素的成因,建立了刀具与工件变形量模型、刀具半径误差补偿理论模型及轴向对刀误差校正方法,并将其运用到非球面精密磨削成型与抛光加工过程中。由实验可知：通过误差补偿与校正,加工时间节省了60%以上,Φ51.5mm口径非球面抛光后的面形精度PV值为0.15μm（0.237λ）,RMS值达到0.023μm（0.036λ）,满足加工精度要求。实验验证了理论分析及误差补偿方法的正确性,实现了轴对称非球面光学零件的快速加工与检测。

英文摘要：

The optical design flexibilities and image qualities can be improved,and the size and weight of optical systems can be reduced by applications of aspheric components.In this paper,the tool and work piece deformation models were established and the compensation methods for the tool radius error and tool setting along the axial direction were proposed through the analyses of characteristics such as tool and work piece elastic deformations and processing errors in the milling and grinding process for axisymmetric aspheric surfaces with middle and small radius.The methods were applied in the milling and grinding processes and polishing process for aspheric surfaces.The experiments show that the processing time decreases by 60% with satisfactory precision.The surface accuracy of 0.15 μm（0.237λ） of PV value and 0.023 μm（0.036λ） of RMS value can be achieved for 51.5 mm diameter aspheric surfaces.The theoretical analyses and error compensation methods are validated through the experiments,and the results show that the rapid process of aspheric surfaces can be realized.