A PGC demodulation algorithm based on harmonic mixing quadrature and differential cross-division for Φ-OTDR systems

Owing to its high accuracy, linearity, and broad dynamic range, the phase-generated carrier (PGC) demodulation algorithm is widely employed in distributed acoustic sensing (DAS) systems based on phase-sensitive optical time-domain reflectometry (Φ-OTDR). However, conventional PGC demodulation is susceptible to phase modulation depth (C) drift, carrier phase delay (CPD), and light intensity disturbance (LID), leading to linear and nonlinear distortions in the demodulated signal. To mitigate these effects, a PGC phase demodulation algorithm based on harmonic mixing quadrature and differential cross-division (PGC-HMQ-DCD) is proposed for Φ-OTDR systems. The algorithm utilizes phase orthogonality between signals generated by mixing the first and second harmonics with beat-frequency signals to eliminate CPD. Additionally, the differential cross-division method removes modulation depth drift and LID, thereby reducing the influence of all three factors on phase demodulation, without requiring phase unwrapping or feedback control. Simulations consistent with theoretical analysis indicate that the proposed algorithm outperforms other PGC demodulation methods. The experimental results further confirmed the effectiveness of the algorithm in the Φ-OTDR system, which achieved a signal-to-noise ratio (SNR) of 46.1 dB under a 2 km detection range, 10 m spatial resolution, and a background noise level of −68.2 dB rad²/Hz. These results demonstrate accurate recovery of vibration-induced phase variations in sensing fibers, confirming the practical applicability of the proposed method.