Design and construction of a single unit multi-function optical encoder for a six-degree-of-freedom motion error measurement in an ultraprecision linear stage

This paper presents the method of a six-degree-of-freedom (DOF) posture measurement in a linear stage by employing a single unit of an optical encoder. The proposed optical encoder was constructed to simultaneously measure the posture along the traveling axis; angular errors, pitch, yaw and roll; and translational errors, Δ X , Δ Y and Δ Z . It consists of a diffractive optical element, a corner cube, four separate two-dimensional position-sensitive detectors, four photodiodes and auxiliary optics components. The circularly polarizing interferometric technique was integrated to measure the displacement of the stage along the traveling axis in a robust manner and the resolution was estimated to be less than 0.4 nm. Two types of stages were employed for the measurement implementation, the piezoelectric transducer-driven and the ballscrew-driven, and they were feedback-controlled for the traveling axis, respectively. With a single travel of the stage, it provided a six-DOF motion error with a high resolution, less than 0.03 arcsec, 20 nm and 0.4 nm for angular errors, Δ Y and Δ Z , and Δ X , respectively, at the same time. As a result, it was seen that motion errors of the stage have relevance to the driving mechanism and the whole construction of the stage.