离子束加工中驻留时间的求解模型及方法

驻留时间求解问题是离子束加工中的关键问题．通常，离子束加工过程可以描述为一个包含驻留时间的二维卷积方程，理论上通过反卷积即可以求解出驻留时间．然而，反卷积问题是一个病态问题，所以驻留时间一般较难很好地求解出．为了解决这个问题，介绍了一个离散的线性模型——CEH模型，分析了该模型的优点．提出应用截断奇异值分解法（TSVD）来求解CEH模型；深入分析了该方法的优点，并利用“L-曲线”分析了驻留误差和加工量之间的关系以及用“L-曲线”对CEH模型中去除点和驻留点的不同取法进行了评价．仿真结果表明，CEH模型和TSVD方法对于求解光学镜面离子束加工中的驻留时间很有效．

Model and Method to Determine Dwell Time in Ion Beam Figuring

To determine the dwell time is an important problem in ion beam figuring. Usually, the ion beam figuring process can be described by a two-dimensional convolution equation including dwell time and thus it can be solved theoretically by deconvolution. However, deconvolution is an ill-posed problem. Therefore the dwell time is difficult to be well solved. In order to solve the problem, a discrete linear model named CEH model was introduced and its advantages were discussed. And the truncated singular value decomposition (TSVD) method was proposed to solve the dwell time in CEH model. Furthermore, L-curve was introduced to analyze the relationship between the residual rms error and the material removal amount, and to evaluate the different picking methods of removal and dwell grid points in CEH model. Simulation results show that CEH model and TSVD method are suitable to determine the dwell time in optics fabrication using ion beam figuring.