Robust laser self-mixing displacement demodulation via continuous wavelet–Hilbert transform for high-precision accelerometer calibration

The laser self-mixing grating interferometer based on Cr atom lithography gratings has been applied to the primary calibration of accelerometers due to its compact structure, low cost, high accuracy, and direct on-site traceability. However, the high line density of Cr gratings (4700 l/mm) introduces dense outliers in interferometric signals, complicating displacement demodulation via conventional derivative-based methods and causing frequent phase jumps. To address this challenge, we propose a hybrid algorithm integrating the continuous wavelet transform and the Hilbert transform, which enables robust displacement demodulation under high-noise conditions. Experimental validation on a commercial MEMS accelerometer demonstrated exceptional accuracy: 100 consecutive data segments were successfully demodulated with a displacement fitting goodness of <i>R</i>²=0.9964 (), and the derived sensitivity deviated by only 0.1% from the nominal value. This algorithm establishes a paradigm for the high-accuracy dynamic calibration of inertial sensors in field applications.