Distributed fiber sparse-wideband vibration sensing by sub-Nyquist additive random sampling

The round trip time of the light pulse limits the maximum detectable vibration frequency response range of phase-sensitive optical time domain reflectometry ({\phi}-OTDR). Unlike the uniform laser pulse interval in conventional {\phi}-OTDR, we randomly modulate the pulse interval, so that an equivalent sub-Nyquist additive random sampling (sNARS) is realized for every sensing point of the long interrogation fiber. For an {\phi}-OTDR system with 10 km sensing length, the sNARS method is optimized by theoretical analysis and Monte Carlo simulation, and the experimental results verify that a wide-band spars signal can be identified and reconstructed. Such a method can broaden the vibration frequency response range of {\phi}-OTDR, which is of great significance in sparse-wideband-frequency vibration signal detection, such as rail track monitoring and metal defect detection.