Estimation of measurement uncertainty caused by surface gradient for a white light interferometer

Although the scanning white light interferometer can provide measurement results with subnanometer resolution, the measurement accuracy is far from perfect. The surface roughness and surface gradient have significant influence on the measurement uncertainty since the corresponding height differences within a single CCD pixel cannot be resolved. This paper presents an uncertainty estimation method for estimating the measurement uncertainty due to the surface gradient of the workpiece. The method is developed based on the mathematical expression of an uncertainty estimation model which is derived and verified through a series of experiments. The results show that there is a notable similarity between the predicted uncertainty from the uncertainty estimation model and the experimental measurement uncertainty, which demonstrates the effectiveness of the method. With the establishment of the proposed uncertainty estimation method, the uncertainty associated with the measurement result can be determined conveniently.