Distributed sparse signal sensing based on compressive sensing OFDR

The maximum detectable vibration frequency of an optical frequency domain reflectometry (OFDR) system is limited by the tunable rate of the laser source. Unlike uniform sampling with the time-resolved method, the sampling frequency is randomly modulated so that the vibration signal applied on the interrogation fiber is sampled by a multi-frequency sub-Nyquist sampling method and reconstructed by the compressive sensing technique. First, we give a full treatment to prove that the proposed method has the same performance as the conventional method. Second, in a further proof-of-concept experiment, the measurable frequency of a sparse signal is achieved up to 200 Hz with a sweeping rate of 40 nm/s. This method can recover the vibration signal with sampling rates less than that required by the Nyquist sampling theory, which is a significant step toward a high-performance OFDR system, especially for evaluating the intrinsic frequency of the object's structural condition.