自由曲面光学镜误差修正加工中输入控制量的算法

The Algorithm of Solving the Input Data in the Error Correction of Free-form Curved Lens

通过误差矩阵和模具的工作特性函数反求输入控制量是加工高精度的自由曲面光学镜所面临的难题。由于卷积方程往往是病态的 ,因此直接的傅里叶变换求解使结果发散。采用了最小平方函数和拉普拉斯算子范数来求得解的近似 ,然后进行自由曲面的误差修正。仿真结果证明效果较好。

It is a difficult problem to solve the inputted data when the matrix of error data and the working characteristics of the tool are known in precision machining. Because the convolution function is of ill-condition, so the result of direct Fourier transformation solution is divergent. In this paper, the least square and Laplace's method are used to calculate the approximate solution, to correct the error of the free-form curved lens.The result is proved perfect by computer simulation.