Approach to accuracy improvement and uncertainty determination of radius of curvature measurement on standard spheres

In high accuracy radius of curvature (ROC) measurement, significant discrepancy may exist in results on the same optical surface obtained by different techniques. Metrological standard sphere is a potential solution to this problem. Mathematical models are built up to characterize the relationship between the ROC of standard spheres and the roundness error as well as the aperture angle. Equations for calculating the uncertainty of ROC are derived and tested on several ROC measuring methods. The reason for the inconsistency between results of different techniques is analyzed and solutions are proposed. A method is developed which can remarkably reduce the uncertainty of ROC. Experiments are carried out on a set of high quality spheres whose diameters are from 11 mm to 93 mm and roundness below 0.1 μm, measured by instruments with relative accuracy of 10−5-10−6, which are a length measuring machine, a profilometer and a homemade differential confocal system. Relative uncertainties of ROC are calculated and analyzed against several factors. Experimental results show good consistency with theoretical analysis. Approaches to trace the ROC to the metrological length standard area discussed.