Quantitative Analysis of the Measurement Uncertainty in Form Characterization of Freeform Surfaces Based on Monte Carlo Simulation

Freeform surfaces possessing no symmetry in rotation are widely used in many fields such as space optics for their superior optical properties. Due to their geometric complexities, the growth of application of these surfaces in precision industries is still hindered by a lack of definitive methodologies for traceable measurement of manufactured freeform surfaces. This paper presents a method for quantitative analysis of the measurement uncertainty in the form characterization of freeform surfaces. The study starts from developing a method for the form characterization of freeform surfaces, and the associated uncertainties are evaluated based on Monte Carlo simulation by quantitatively analyzing the uncertainty induced by the sampling strategy and the evaluation method. To integrate the effect of the workpiece form deviation, a profile simulation method is developed based on fractional Brownian motion, which can be used to generated random surface form error with given magnitude. Based on computer simulation, mathematical relationships between the magnitude of the critical errors and the resulting uncertainties are identified so that an estimation of uncertainty can be given for the measured surface parameters in a specific measurement. A case study is conducted to demonstrate the effectiveness of the proposed study which provides a better understanding of the associated uncertainty in the form characterization of freeform surfaces.