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

Abstract

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, ΔX, ΔY and ΔZ. 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, ΔY and ΔZ, and ΔX, 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.

Impact of the Imperfect Polarizing-Beam Splitter and Quarter-Wave Plate and Non-Ideal Laser Beam on the Accuracy of Nano-Displacement Laser Encoder

“…When the scale grating on the stage moves as a displacement of Δx along the x-axis and Δz along the z-axis, these displacements causes phase difference on positive and negative first order diffracted beams, respectively, due to the Doppler effect as follows [21]- [22]:…”

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Compliance and control characteristics of an additive manufactured-flexure stage

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