Magnetic Induction-Based Planar Displacement Sensing With Sub-Micrometer Resolution

Abstract

Displacement sensing at the sub-micrometer scale is crucial for applications such as precision manufacturing, micropositioning, and scanning probe microscopy. In this article, a novel method is proposed that uses magnetic induction for measuring sub-micrometer displacements in three degrees of freedom. This approach uses simple coils and a synchronous demodulation circuit for measurement. An excitation coil generates an alternating magnetic field and four sensing coils measure its instantaneous intensity. Fit functions are proposed to estimate the position from each sensing coil’s output; these functions can calculate displacement over a large range with small errors. The sensor’s output characteristics are found to be highly dependent upon the shape of the coils. An analytical approach is presented to predict the output characteristics for various shapes of the sensing and excitation coils, and is used to test the sensitivity for various shape combinations. The developed sensor is characterized and a ( ${\pm } \sigma $ ) resolution of 600 nm is achieved over a bandwidth of 100 Hz and a range of $200~\mu $ m. Further, this displacement signal is fed back to a piezo stage to eliminate positioning errors that arise due to hysteresis. A 70% (rms) reduction in tracking error is achieved in closed-loop operation, relative to the open-loop. Synchronous detection reduces power supply noise levels by 24 dB, improving the signal-to-noise ratio. The method is immune to electromagnetic interference (EMI), stray magnetic fields, and environmental ingress, making it a suitable option for use in high-noise industrial applications.