Frequency Response Enhanced Quantitative Vibration Detection Using Fading-Free Coherent $\varphi$-OTDR With Randomized Sampling

A frequency response enhanced quantitative vibration detection scheme for interference fading suppressed coherent phase-sensitive optical time domain reflectometry ( $\varphi$ -OTDR) is proposed and demonstrated. By utilizing randomized sampling, the proposed scheme not only breaks the inherent limitation between the sensing range and the maximum detectable frequency in conventional $\varphi$ -OTDR systems, but also allows for quantitative measurement of the vibration amplitude by tracking the peak intensity of the discrete Fourier transformation spectrum of the phase signals. The operation principle and the measurement accuracy are mathematically analyzed through the frequency spectrum estimator unbiasedness and the estimation standard deviation, which provides a comprehensive guidance for parameter configuration in practical applications. For proof of concept, quantitative detection of vibration signals up to 384 kHz is realized over a 5.4 km fiber, while the conventional solutions only reach 18.5 kHz as restricted by the Nyquist sampling theorem. The proposed sensing scheme paves the way to enable ultra-high frequency quantitative vibration detection using $\varphi$ -OTDR.