A Self-Adaptive Interpolation Method for Sinusoidal Sensors

Abstract

High-end equipment manufacturing industry has increasing requirements on high-resolution performances. To improve the measurement resolution obtainable from signals of sinusoidal sensors for digital measuring instruments and equipment, a self-adaptive interpolation method is proposed. A series of time periods of the sensor signal for equal spatial pitches are measured as measurement samples, and a spatial displacement interpolation method is performed using analysis on these time quantum. Using one-step-ahead forecast method, the time period of the sensor signal for the next spatial pitch is forecast based on correlation among the past measured time samples. A series of clock pulses with equal spatial equivalent are used as reference signals to interpolate sinusoidal signals from the sensors. In addition, an equivalent closed-loop control method is proposed to decrease the accumulated interpolation errors in real time. The experimental results prove that the maximum interpolation number achieves 400, and the actual measured interpolation errors are within $- 1.2^{\prime \prime }$ to $1.1^{\prime \prime }$ . The proposed interpolation method benefitting from the programming techniques provides an interesting possibility with the most cost-effective hardware to further improve the resolution performances.