Electronic Interpolation Interface Based on Linear Subdivision Method for Sinusoidal Optical Encoders

Abstract

Sinusoidal optical encoders are widely utilized in precision positioning systems. With the development of precision positioning systems, higher resolution is required. Electronic interpolation is a promising technique to further improve the resolution of sinusoidal optical encoders. In this paper, we propose an electronic interpolation interface based on linear subdivision method with better practical accuracy. Firstly, a pseudo-linearized signal based on the difference between the absolute values of sine and cosine signals is generated. Then, a compensation signal with a ratiometric form is constructed, which has a better robustness to the non-ideal input signals. Finally, a nearly perfect linear output signal is obtained by combining these two signals. Thus, the displacement can be linearly determined without LUTs. It is shown that the theoretical nonlinear error of the proposed method is below 0.08° over a signal period of 360°, which corresponds to a theoretical interpolation error of 0.018 μm for sinusoidal optical encoders with a pitch of 80 μm. Moreover, theoretical analysis and simulation results indicate that the proposed method offers a better practical accuracy. In the experiment, the proposed electronic interpolation interface is developed in a field-programmable gate array (FPGA), and experiments are carried out to evaluate its performance. Both the theoretical and experiment results verify its effectiveness.