A Noncontact 3-Degree-of-Freedom Displacement Sensor With Nanoscale Resolution

This study proposes a novel differential eddy current inductive displacement sensor (ECIS) that achieves synchronous three-axis (XYZ) displacement measurement, overcoming the limitations of traditional single-axis detection. The sensor incorporates a spiral excitation coil, an aluminum target, and differential receiving coils bonded to the target surface. A hybrid-domain optimization framework combining theoretical modeling and finite element analysis (FEA) was developed to address the challenges of multiphysics coupling in proximity to conductive targets. The coil geometry was systematically optimized through numerical calculations to maximize sensitivity while suppressing cross-axis interference. Experimental validation demonstrated a displacement range of ±1,500 μm in the x- and y-axes and ±130 μm in the z-axis, achieving quasistatic resolutions of 10 nm, 13 nm, and 0.45 nm, respectively. The cross-sensitivity between axes was maintained below ±0.5%. The sensor's thermal stability was enhanced through Zerodur® glass probe structures and differential topology, yielding a temperature drift coefficient of 162 ppm/°C. These results validate the proposed optimization methodology and highlight the sensor's potential for ultraprecision metrology.