In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence X-Ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results.

翻译：在光学纳米计量学中，数值模型被广泛用于参数重建。采用贝叶斯目标向量优化方法，我们将有限元数值模型拟合到掠入射X射线荧光数据集，以获取纳米结构线栅的几何参数。在重建过程中训练了基于高斯过程的随机机器学习代理模型，随后采用马尔可夫链蒙特卡洛采样器对这些代理模型进行采样，以确定重建模型参数的分布。所使用的有限元模型的数值离散化参数会影响前向模型的数值离散化误差。我们研究了有限元试探函数的多项式阶数对重建参数及模型参数分布的影响。研究表明，此类收敛性分析能够确定可实现高效精确重建结果的数值参数。