Vectorial Distributed Vibration Sensing Based on Two-Beam $\phi$-OTDR and Four-Core Fiber

A vectorial distributed vibration sensing approach based on two-beam
$\phi$
-OTDR and four-core fiber is investigated. The theoretical derivation shows that the vibration direction angle can be calculated from the arctangent of the ratio of the phase difference between two sets of orthogonal diagonal fiber core pairs in an untwisted homogeneous four-core fiber. The two-beam
$\phi$
-OTDR utilizes the interference of Rayleigh backscattered light from a pair of diagonal fiber cores and phase demodulation to obtain the distribution of the phase difference from the cores. Experiments confirm that this approach can measure vector vibrations in the range from 0° to 180° with an error of less than 1.24°. This approach requires no special fiber deployment or complex reconstruction algorithms, making it potentially useful in structural health monitoring and pipeline inspection applications.