Quadrature Signal Extraction by Current Modulation in Self-Mixing Interferometry for Displacement Sensing

Abstract

This article proposes a method for generating quadrature self-mixing interference (SMI) signals using the current modulation for real-time displacement sensing. By applying a square-wave current to a semiconductor laser, periodically phase-modulated SMI signals are produced at a certain distance. Subsequently, a pair of quadrature SMI signals is obtained by separately sampling at the high and low levels of the square-wave signal, followed by an interpolation process. Finally, the target’s motion displacement is reconstructed by quadrature phase unwrapping algorithm. The method demonstrates excellent robustness, achieving reconstruction accuracy better than 20 nm under 7-dB Gaussian noise in simulation. Experiments for both sinusoidal vibrations and nonharmonic moving targets are conducted, with a displacement reconstruction error of 22.3 nm. This method does not require any additional optical components to produce phase modulation, significantly reducing system complexity and cost. Furthermore, this article analyzes the algorithm’s applicability under different distances, current modulation coefficients, and modulation voltages, providing a reference for the application of current modulation methods in SMI displacement measurements.