Roll error measurement system for linear moving stages using four capacitance sensors

In this paper, a measurement system for roll error (angular error of a linear moving stage) is described. The proposed system consists of four capacitance sensors located at four vertices of a tetragon in a fixture. Unnecessary measured data due to global surface roughness on the measuring target is eliminated using a differential method. First, a mathematical model for the proposed system is developed using the error synthesis modeling technique. The zero adjustment difference is a critical parameter for precise measurement. Therefore, an additional measurement procedure is developed to estimate the zero adjustment difference. The x- and y-directional offset errors, which are deviation from the designed position of hole for holding a capacitance sensor, introduce an error in the estimation of roll error. Therefore, a virtual experiment is performed with different values of x- and y-directional offset error to analyze their effect. Then, the roll error is measured using the proposed measurement system. A comparison of the measured data from the proposed method (four capacitance sensors) and the conventional method (two capacitance sensors and a straight-edge) is performed. Finally, the proposed method is verified using a hypothesis test.