High-speed correlation-based 2-D in-plane motion sensing with single-nanometer precision

Abstract

This article presents the design and implementation of a laser speckle-based sensor for real-time measurement of translational in-plane displacements with single-nanometer precision. The system combines a high-speed camera, a laser diode, and an field-programmable gate array (FPGA) for real-time data acquisition and processing. A comprehensive comparison of subpixel in-plane motion estimation algorithms is conducted, identifying the paraboloid curve-fitting approach as an effective compromise between estimation accuracy and FPGA implementation complexity. The optimized paraboloid fitting enables high-resolution motion estimation in both translational degrees of freedom, requiring only 220 ns computation time. Experimental validation on three different optically rough samples demonstrates that the sensor achieves a precision of at least 5 nm across at measurement rates of several kilohertz. Additional measurements at motion frequencies up to 300 Hz show reliable resolution of motion amplitudes down to 10 nm. These results demonstrate the suitability of the in-plane sensor for integration into high-precision tracking applications.