针对光学元件高精度确定性加工，提出并实现了基于自适应步长算法实现离子束抛光轨迹段划分及进给速度求解。首先，对常规的等步长算法实现抛光轨迹段划分所存在的诸多问题进行了重点分析。其次，针对这些问题，提出了等效驻留时间轮廓计算方法及自适应步长算法，有效地避免了等步长法所存在的问题。然后，采用新算法对600 mm平面反射元件进行了实例计算，经加工后，元件98%口径内的面形精度峰谷(PV)值由110.22 nm(λ/5.7，λ=632.8 nm)收敛至4.81 nm(λ/131.6)。最后，基于自研的离子束抛光设备，实现了光学元件在100 mm口径内面形PV值小λ/70的超高面形精度。

For high-precision deterministic processing, equal profile of dwell-time and adaptive step size algorithms are presented in this paper to solve processing path feed-rate. Firstly, we analyze the issues that exist in the conventional and other step algorithm. And then, for these issues, the adaptive step size algorithm is introduced. Finally, a Ф600 mm plane reflector element is taken to be an instance. The result shows that after four combinations of processing, the surface accuracy of peak-valley (PV) value and the root mean square (RMS) value was reduced to 4.81 nm (λ/131.6)and 0.495nm(λ/1278.4) from 110.22 nm (λ/5.7) and 13.998 nm (λ/45.2) ( λ=632.8 nm) respectively in the 98% caliber of the element. By using the new algorithm in our ion beam figuring machine, we obtained a reflector optical element whose PV value is less than λ/70 in Ф100 mm caliber.