Michelson Interferometric PZT Nanodisplacement Measurement Based on Adaptive Mode Decomposition and Sinusoidal Phase Regression

In nanometric displacement measurement, laser interferometry exhibits high sensitivity to sub-period displacements. However, the interferometric signals are often incomplete in period and limited in amplitude, making them susceptible to high-frequency noise and drift. Therefore, an improved nanoscale displacement measurement method is proposed, combining band-limited dynamic-noise-assisted CEEMDAN with sinusoidal-regression demodulation. By constraining the noise band and adaptively tuning the noise amplitude during injection, the low-frequency trend component is effectively purified. Based on the prior parameters such as laser wavelength and displacement rate to constrain the fitting solution space, the linear least squares fitting method is used to process the trend signal to achieve high-precision phase recovery and quantitative displacement measurement. Experiments show that the method remains stable under electromagnetic interference and impulse noise conditions, improving the signal-to-noise ratio by about 2.6 dB. The measurement error is 1-3 nm within the 20-300 nm range, and the stability is improved by approximately 62%, while also satisfying real-time feasibility. Overall, the method achieves nm-level accuracy with enhanced robustness to industrial noise and real-time computational efficiency.