Uncertainty Analysis of a Fiducial-aided Calibration and Positioning System for Precision Manufacturing of Optical Freeform Optics

Achieving high form accuracy of optical freeform surfaces in machining is extremely difficult due to their geometric complexity. A positioning or repositioning process is necessary for fabricating optical freeform surfaces during the machining and measuring processes. The concept of fiducial-aided calibration and positioning (FACP) has been developed to provide high-precision relative position data among different coordinate frames to minimize the repositioning errors. This paper attempts to establish an uncertainty analysis model to evaluate the uncertainty and reliability of the FACP method. Firstly, two kinds of the most-used configurations of the FACP systems available for carrying out experiments in both machining and measuring machines are designed with consideration of four main factors. Secondly, a linear transforming model is developed to connect different coordinate frames among the machine tool, on-machine measuring system and off-machine measurement instrument with
high precision. Hence, all the uncertainties associated with the FACP method are considered, and a modified chi-squared technique is used to identify the relationship between these uncertainties. Experimental work has been conducted on two machine tools with different on-machine probing systems. The results show that the transformation uncertainty is very small in the proposed linear transforming model, while the final accuracy of the FACP system is sensitive to the measurement results obtained from the on-machine measuring system.