Direct detection Φ-OTDR based on UWFBG array using linear-phase-modulated double-pulse

We propose what we believe to be a novel direct detection phase-sensitive optical time-domain reflectometry (Φ-OTDR) based on ultra-weak fiber Bragg grating (UWFBG) array to achieve distributed vibration measurements with exceptional sensitivity and remarkable stability. Our system employs a pulse modulator to generate a double pulse and achieves linear phase modulation of one pulse by one cycle through a phase modulator. The phase change can be quantitatively demodulated using our proposed N-step phase-shifted demodulation algorithm. This method effectively mitigates the influence of phase noise of the laser and the pulse modulator, while also eliminating fluctuations in the half-voltage of the phase modulator. Compared with the existing phase modulation methods, our method avoids stringent requirements for the stability and precision of phase modulation. Moreover, we propose a phase-shifted approximation method, breaking the limitation of sensing length on the traditional differential approximation method and improving the accuracy significantly. The technique's effectiveness is experimentally demonstrated on a 1 km UWFBG array with a reflectivity of -40 dB to -45 dB and a spatial resolution of 10 m. Vibrations with different amplitudes are measured quantitatively with good linearity. The low-frequency self-noise is greatly suppressed and the overall self-noise is -54.3 dB rad