A vision-based method for planar position measurement.

In this paper, a vision-based method is proposed for three-degree-of-freedom (3-DOF) planar position () measurement. This method uses a single camera to capture the image of a 2D periodic pattern and then uses the 2D discrete Fourier transform (2D DFT) method to estimate the phase of its fundamental frequency component for position measurement. To improve position measurement accuracy, the phase estimation error of 2D DFT is analyzed and a phase estimation method is proposed. Different simulations are done to verify the feasibility of this method and study the factors that influence the accuracy and precision of phase estimation. To demonstrate the performance of the proposed method for position measurement, a prototype encoder consisting of a black-and-white industrial camera with VGA resolution (480  ×  640 pixels) and an iPhone 4s has been developed. Experimental results show the peak-to-peak resolutions to be 3.5 nm in X axis, 8 nm in Y axis and 4 in axis. The corresponding RMS resolutions are 0.52 nm, 1.06 nm, and 0.60 respectively. [ABSTRACT FROM AUTHOR]