提出利用信赖域狗腿法解决通用非球面光学元件抛光后置求解的强非线性问题。基于低序体表示和齐次变换方法建立适用于任意非球面面形和任意轨迹抛光的正向运动学模型;基于信赖域狗腿法建立强非线性正向运动学模型的数值优化求解方法,获得相应的逆向运动学数值结果;对逆向运动学数值求解结果进行处理得到各轴控制量,用于抛光后置处理。对一初始面形均方根值为0.037λ的离轴非球面采用光栅线进行4轮抛光,采用螺旋线进行5轮抛光,加工元件的面形收敛到均方根值为0.012λ,总收敛效率达到67.57%,表明所提后置处理方法是正确的,能够用于非球面加工。

This paper proposes to use the trust region dogleg method to solve the high nonlinearity problem of post finishing of general aspheric optical components. Firstly, based on the low-order body representation and the homogeneous transformation method, a forward kinematic model suitable for any aspherical surface shape and arbitrary path is established. Then, a strong nonlinear forward kinematic model is established based on the trust region dogleg method. The numerical optimization method is used to obtain the corresponding inverse kinematics numerical results. Finally, the inverse kinematics numerical solution results are processed to obtain the control values of each axis for post processing. For an off-axis aspheric surface with an initial surface shape of root mean square 0.037λ, after four rounds of finishing with a raster line path planning and five rounds of finishing with a spiral path planning, the surface shape of the processed component converges to root mean square 0.012λ, and the total convergence efficiency reaches 67.57%, indicating that the proposed post-processing method is correct and can be used for aspheric processing.