Frequency Stability Requirements in Quasi-Integer-Ratio Time-Expanded Phase-Sensitive OTDR

Time-expanded phase sensitive (TE-ϕ)OTDR is a recently reported technique for distributed fiber sensing that relies on the use of an electro-optic dual frequency comb (DFC) scheme. A distinctive feature of this approach is its ability to provide high spatial resolution (on the centimeter scale) with detection bandwidths orders of magnitude lower than those of conventional ϕOTDR systems. The stringent trade-off between resolution, range and sensing bandwidth that exists in TE-ϕOTDR has demonstrated to be substantially relaxed by implementing two frequency combs with quasi-integer-ratio repetition rates. However, employing very dissimilar line separations (with a ratio between them >100) is challenging due to the need of keeping the coherence over long sequences of interferograms, which eventually limits the attainable range. In this paper, we formulate the requirements for the frequency stability of the reference clock used in a quasi-integer-ratio DFC scheme. This analysis allows us to stablish the limits on the number of comb lines (i.e., on the number of available independent sensing points) for a particular reference clock. By using a rubidium atomic clock (with a relative frequency stability of ∼10
⁻¹³
), we demonstrate up to 10
⁵
sensing points along 2 km of fiber with tens of Hz sensing bandwidth.