Measuring ultra-precision freeform surfaces using a robust form characterization method

Ultra-precision freeform surfaces are complex surfaces that possess non-rotational symmetry and are widely used in advanced optics applications. However, there is a lack of a surface characterization method that measures the form accuracy of the ultra-precision freeform surfaces with micrometre to sub-micrometre form accuracy. Due to the high precision requirement of the ultra-precision freeform surfaces, this inevitably involves the outliers in the measured data that would significantly affect the accuracy and the performance of the form characterization method. Although some research work has been found in the development of the form characterization method, most workers have not considered the influence of outliers. It is vital to incorporate robust estimation in the surface characterization method for catering for the influence of outliers. In this paper, a robust form characterization method (RFCM) is presented to characterize the form accuracy of the ultra-precision freeform surfaces. A series of computer simulation and experimental analyses were undertaken to verify the RFCM. The theoretical results agree well with the simulation and experimental results.