  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.
