Modeling and analysis of uncertainty in on-machine form characterization of diamond-machined optical micro-structured surfaces

Ultra-precision diamond machining is widely used in the manufacture of optical micro-structured surfaces with sub-micron form accuracy. As optical performance is highly-dependent on surface form accuracy, it is critically important to use reliable form characterization methods for surface quality control. To ascertain the characteristics of real machined surfaces, a reliable on-machine spiral scanning approach with high fidelity is presented in this paper. However, since many uncertainty contributors that lead to significant variations in the characterization results are unavoidable, an error analysis model is developed to identify the associated uncertainties to facilitate the reliable quantification of the demanding specifications of the manufactured surfaces. To accomplish this, both the diamond machining process and the on-machine spiral scanning procedure are investigated. Through the proposed model, via the Monte Carlo method, the estimation of form error parameters of a compound eye lens array is conducted in correlation with form deviations, scanning centering errors, measurement drift and noise, etc. Application experiments, using an on-machine scanning tunneling microscope, verify the proposed model and also confirm its potential superiority over the conventional off-machine raster scanning method for surface characterization and quality control.