Systematic error analysis and parameter design of a vision-based phase estimation method for ultra-precision positioning

Abstract

Ultra-precision position measurement is increasingly important in advanced manufacturing such as the semiconductor industry and fiber optics or photonics. A vision-based phase estimation method we proposed previously performs position measurement by imaging a 2D periodic pattern. In this paper, systematic errors of this method are analyzed and derived mathematically, which are classified into two types: spectrum leakage error caused by image truncation and window function modulation, and sub-pixel error resulting from discrete Fourier transform (DFT) intensity interpolation. Key design parameters are concluded including pattern period T, camera pixel size t and resolution N, as well as the type of window function used. Numerical simulations are conducted to investigate the relationship between the phase errors and design parameters. Then an error reduction method is proposed. Finally, the improved performance of parameter optimization is validated by a comparative experiment. Experimental results show the measurement errors of the prototype are within ∼2 nm in X or Y axis, and ∼1 µrad in axis, which reaches the sub-pixel accuracy better than 10−3pixel.