Ratiometric-Linearization-Based High-Precision Electronic Interpolator for Sinusoidal Optical Encoders

Abstract

Electronic interpolation is the key technology for further improving the measurement resolution of optical encoders. In this paper, an electronic interpolator based on the ratiometric linearization conversion method is presented. The proposed method converts the sinusoidal encoder signals into a nearly perfectly linear output signal through mathematical manipulation that only involves basic operations of addition, subtraction, multiplication, and division. Thus, the displacement can be precisely determined using a simple linear equation. Furthermore, quadrature interpolation pulses are also generated from the linear output signal by using the amplitude subdivision method. Since the linearization procedure is based on the ratiometric operation, interpolation accuracy is independent of amplitude fluctuation of the encoder signals. Theoretical analysis shows that the nonlinear error of the proposed interpolator is below ±0.0034 rad over a signal period of 2π rad, which corresponds to an interpolation error of ±0.0108 μm for a linear optical encoder with a pitch of 20 μ m. In the experiment, the proposed strategy is successfully implemented within a field programmable gate array, and applied to a 20 μm-pitch optical encoder. Experiments are performed to demonstrate the effectiveness of the proposed method.