New approach to accuracy enhancement and traceability realization of radius of curvature measurement

High accuracy radius of curvature (ROC) measurement of optical surfaces is usually realized by techniques such as autocollimation, interferometry and profilometry, with theoretical accuracy as high as 10^-6. In practical application, significant discrepancy may exist in results obtained by different methods owing to figure error of measured surfaces. In this paper, mathematical models are built up to characterize the relationship between the ROC and the figure error as well as the aperture angle. Based on the models, equations for calculating the ROC accuracy are derived and tested on several ROC measuring methods. Experiments are carried out on a set of high quality spheres whose diameters are from 11mm to 93mm and roundness is from 0.03μm to 0.07μm, measured by instruments with top level accuracy, which are a length measuring machine, a profilometer and a homemade differential confocal system. Uncertainties are calculated and analyzed against several factors. The reason for the discrepancy between different methods is explained. An approach is also proposed which could reduce the uncertainty of ROC by 1~2 scales, making it possible to trace the results of ROC measuring instruments to the primary standard of length via diameter and roundness measurement method.