Self-Calibration Method for the Four Buckets Phase Demodulation Algorithm in Triangular Wave Hybrid Modulation

The four buckets phase demodulation method is a widely used sinusoidal modulation and demodulation technique in interferometry. Strict calibration is essential to minimize nonlinear errors in subsequent measurements. The core of the algorithm calibration lies in determining the initial phase value of the modulation signal that matches the modulation depth while overcoming the influence of system phase delay. Currently, there are few systematic calibration methods specifically designed for optical fiber interferometry. This paper proposes a self-calibration method based on triangular wave mixing for four buckets phase demodulation in fiber optic interferometric probes, which efficiently achieves self-calibration of the phase demodulation while the measured object remains stationary. Simulations and experimental validations were conducted, demonstrating that the optimal initial phase value of 0.62 rad during phase demodulation can be accurately identified under static conditions. The calibrated phase value was then applied to the displacement measurement, where the target displacement was effectively detected, resulting in a root mean square (RMS) error of 3.0337 nm and an average error of 2.4479 nm.