Malus's law-enhanced Michelson interferometer with PSO-based calibration and data-driven error compensation for medical micro-displacement measurement.

Background: High-precision micro-displacement measurement is crucial for applications ranging from semiconductor manufacturing to biomedical diagnostics. However, conventional Michelson interferometry is fundamentally limited by the light source's coherence length and the inefficiency of manual fringe counting. Methods: This study introduces a modified Michelson interferometer that operates on Malus's law. The design converts the linear micro-displacement of a movable mirror into the rotation angle of a polarizer via mechanical coupling, which shifts the measurement principle from interference fringe observation to intensity modulation. This conversion establishes a quantitative relationship between displacement and light intensity, enabling automatic photoelectric detection. Additionally, an intelligent processing module was developed to support this hardware. This module includes a Particle Swarm Optimization (PSO) algorithm for the joint calibration of hardware parameters, an analytic inverse mapping for primary displacement computation, and a Gaussian Process Regression (GPR) model to compensate for residual instrument errors while providing per-measurement uncertainty bounds. Results: The proposed system successfully overcomes the coherence-length constraints of traditional interferometry. The integration of structural modifications, intelligent parameter calibration, and data-driven error compensation establishes a novel paradigm for measuring micro-displacement. Conclusion: The Malus's law-enhanced Michelson interferometer provides a robust and automated alternative to conventional systems. The technology demonstrates significant potential for biomedical micro-displacement monitoring, particularly for the non-contact acquisition of physiological signals in clinical settings.