Bayesian uncertainty evaluation of stitching interferometry for cylindrical surface

Abstract

Uncertainty evaluation is one of the most important concepts in metrological characterizations. This paper proposes a method for uncertainty evaluation of measurements of cylindrical surfaces by means of stitching interferometry. The proposed method is based on the Bayesian statistical analysis. The prior deviation for a tested surface is determined by both calculation of standard deviation through multiple measurements of a single sub-aperture and calibration of the optical system error. The probability distribution functions (PDF) of the prior and real misalignment error and measured data of the aperture are derived according to the stitching model. Simulated observations are approximated with the Gibbs Sampler using the Markov Chain Monte Carlo (MCMC) method. Our proposed method is a promising alternative to the ordinary least square technique (LST) with the maximum likelihood estimation (MLE) for obtaining the uncertainty of the misalignment and measurement error in the stitching results. Moreover, it can take the inevitable environment errors into account. The prediction of the uncertainty interval makes our method more attractive in industrial applications.