Numerical models are used widely for parameter reconstructions in the field of optical nano metrology. To obtain geometrical parameters of a nano structured line grating, we fit a finite element numerical model to an experimental data set by using the Bayesian target vector optimization method. Gaussian process surrogate models are trained during the reconstruction. Afterwards, we employ a Markov chain Monte Carlo sampler on the surrogate models to determine the full model parameter distribution for the reconstructed model parameters. The choice of numerical discretization parameters, like the polynomial order of the finite element ansatz functions, impacts the numerical discretization error of the forward model. In this study we investigate the impact of numerical discretization parameters of the forward problem on the reconstructed parameters as well as on the model parameter distributions. We show that such a convergence study allows to determine numerical parameters which allow for efficient and accurate reconstruction results.

翻译：数值模型被广泛应用于光学纳米计量领域的参数重构。为获取纳米结构线栅的几何参数，我们采用贝叶斯目标向量优化方法，将有限元数值模型拟合于实验数据集。在重构过程中训练高斯过程代理模型，随后利用马尔可夫链蒙特卡洛采样器对代理模型进行采样，以确定重构模型参数的完整模型参数分布。数值离散参数（如有限元试探函数的多项式阶次）的选择会影响前向模型的数值离散误差。本研究探究前向问题的数值离散参数对重构参数及模型参数分布的影响，证明此类收敛性分析能够确定实现高效精确重构结果所需的数值参数。