Fig. 1. Schematic of coherent detection φ-OTDR system

Fig. 2. Schematic of IQ demodulation

Fig. 3. Optical fiber RBS model

Fig. 4. Schematic of optical fiber RBS model under vibration

Fig. 5. Measured BPD noise signal distribution

Fig. 6. Simulation and measured signal spectrograms of optical fiber without vibration. (a) Simulation result; (b) measurement result

Fig. 7. Actual system demodulation results. (a) Amplitude variation curve; (b) 3D image of demodulated phase

Fig. 8. Comparison of demodulated waveform with applied vibration waveform

Fig. 9. Demodulated results of fiber under multiple vibration conditions

Fig. 10. Impact of sampling rate on demodulation effect (x-axis is logarithmic). (a) SNR of vibration detection at different sampling rates; (b) distortion at different sampling rates

Fig. 11. Comparison of demodulated and actual vibrations at different sampling rates and noise levels. (a) Sampling rate is 100 MHz,σ=0.080; (b) sampling rate is 1 GHz, σ=0.080; (c) sampling rate is 100 MHz, σ=0.010; (d) sampling rate is 1 GHz, σ=0.010

Fig. 12. Comparison of demodulated and actual vibrations at different ADC quantization bits and noise levels. (a) Number of ADC quantization bits is 8, σ=0.040; (b) number of ADC quantization bits is 16, σ=0.040; (c) number of ADC quantization bits is 8, σ=0.0050; (d) number of ADC quantization bits is 16, σ=0.0050

Fig. 13. Impact of pulse width on demodulation accuracy (x-axis is logarithmic). (a) SNR of vibration detection at different pulse widths; (b) distortion at different pulse widths

Fig. 14. Fitting results of the relationship between SNR of vibration detection, distortion, and pulse width under different noise levels. (a) Fitting results of SNR of vibration detection (x-axis is linear); (b) fitting results of distortion (x-axis is logarithmic)

Fig. 15. Comparison of demodulated and applied vibrations at different pulse widths and noise levels. (a) Pulse width is 20 ns, σ=0.040; (b) pulse width is 500 ns, σ=0.040; (c) pulse width is 20 ns, σ=0; (d) pulse width is 500 ns, σ=0

Fig. 16. Impact of magnification of EDFA on demodulation accuracy (x-axis is logarithmic). (a) SNR of vibration detection at different magnifications of EDFA; (b) distortion at different magnifications of EDFA

Fig. 17. Fitting results of the relationship between SNR of vibration detection, distortion, and magnification of EDFA under different noise levels (x-axis is logarithmic). (a) Fitting results of SNR of vibration detection; (b) fitting results of distortion

Fig. 18. Comparison of demodulated and actual vibrations at different magnifications of EDFA and noise levels. (a) Magnification of EDFA is 20, σ=0.080; (b) magnification of EDFA is 1000, σ=0.080; (c) magnification of EDFA is 20, σ=0.005; (d) magnification of EDFA is 1000, σ=0.005

Fig. 19. Impact of vibration position on demodulation accuracy (x-axis is linear). (a) SNR of vibration detection at different vibration positions; (b) distortion at different vibration positions

Fig. 20. Fitting results of the relationship between SNR of vibration detection, distortion, and vibration position under different noise (x-axis is linear). (a) Fitting results of SNR of vibration detection; (b) fitting results of distortion

Fig. 21. Comparison of demodulated and applied vibrations at different vibration positions and noise levels. (a) Vibration position is at 5.5 km, σ=0.040; (b) vibration position is at 0.5 km, σ=0.040; (c) vibration position is at 5.5 km, σ=0.005; (d) vibration position is at 0.5 km, σ=0.005