Free-Space Optical Heterodyne Interferometric Readout with SNR-Guided Adaptive Demodulation for Nanoscale Displacement Sensing

Accurate nanoscale displacement readout is essential for optical inertial sensors, precision positioning, and micro-vibration characterization. In this work, we develop a free-space optical heterodyne interferometric readout system for low-frequency nanoscale displacement sensing and establish an SNR-guided adaptive demodulation framework. Two complementary demodulation strategies are integrated: Bessel-function-based frequency-domain sideband extraction for small-amplitude low-SNR motion and IQ quadrature phase tracking for larger-amplitude displacement. The experimentally demonstrated framework maps the applicability regimes of the two methods and enables wavelength-referenced displacement readout over a range from sub-nanometer narrowband detection to 250 nm under the present experimental conditions. The implemented system achieves a repeated-measurement repeatability of 0.40 nm under a 10 Hz excitation condition, and spectral SNR analysis is consistent with time-domain statistical evaluation. Finally, the readout system is applied to a quartz pendulum inertial structure, demonstrating its potential for photonic displacement sensing and optical inertial sensor characterization.