A Positioning System Design Based on Tunnel Magnetoresistance Sensors for Rapid Zoom Optical Lens

In response to the accurate positioning issue for high-speed moving lens groups in rapid zoom optical lenses with voice coil motors (VCMs), we demonstrate a positioning system design based on tunnel magnetoresistance sensors. The equivalent magnetic charge method and finite element method (FEM) simulations were utilized to compute the magnetic field distribution of the magnetic grating encoder. Based on analytical computation, the optimal air gap δ_S between the sensor and magnetic grating is determined to be δ_S = 0.15 mm, which balances magnetic flux density amplitude and total harmonic distortion. In addition, a simplified fitting model is proposed to reduce computational complexity. We quantify the magnetic interference of VCM through three-dimensional flux leakage mapping by FEM analysis, deriving an optimal sensor position O_S, with a 24 mm y-offset and 20 mm z-offset relative to the VCM's origin O_V. The position error caused by interference remains below 5 μm with maximum deviations at trajectory endpoints of the moving group. The original signal output is processed and corrected, and eventually, the measured displacement exhibits a linear relationship with actual displacement. Our study provides a comprehensive framework for the design and optimization of magnetic positioning systems in optical applications with electromagnetic motors.