Time-expanded phase-sensitive optical time-domain reflectometry

Distributed optical fibre sensing (DOFS) enables monitoring of temperature, strain, pressure and birefringence over long distances with a single fibre, offering cost-effective, real-time multipoint measurements. Phase-sensitive optical time-domain reflectometry (ФOTDR), based on Rayleigh scattering, underpins distributed acoustic sensing by detecting backscattered light from highly coherent pulses to infer local variations along the fibre. While amplification can extend ranges beyond 100 km, a key limitation is the non-linear relation between detected amplitude and strain/temperature, addressed by variants such as coherent detection, frequency-scanning, and chirped-pulse ФOTDR. Spatial resolution scales inversely with pulse width (≈1 m per 10 ns), so centimetre-scale resolution normally demands hundreds of MHz to GHz detection bandwidth, increasing cost and complexity. Optical sampling can lower bandwidth demands; computational DOFS with temporal ghost imaging can reduce sampling rate; and coded pulse sequences can increase SNR by raising average launched energy without increasing peak power, though often requiring heavy decoding. This work proposes a coherent ФOTDR scheme using frequency combs and dual-comb detection with random spectral phase coding to reduce peak power, increase SNR, and achieve large time expansion of traces, enabling high spatial resolution with MHz-range detection bandwidth and straightforward decoding.

The paper reviews multiple approaches to improve ФOTDR: coherent detection of the backscattered signal by mixing with a reference; frequency-scanning and chirped-pulse ФOTDR to address non-linear amplitude-to-perturbation relations; optical sampling to reduce required detection bandwidth; computational DOFS leveraging temporal ghost imaging to lower sampling rates; and coding techniques (e.g., launching coded pulse sequences within the fibre round-trip time) to raise SNR by increasing average energy while maintaining peak power, albeit with higher computational decoding costs. It also references dual-comb schemes used in other contexts and prior quasi-distributed sensing with multiplexed Bragg gratings, highlighting limitations of cavity-laser-based combs for true distributed sensing compared to flexible electro-optic combs.

The proposed coherent ФOTDR employs electro-optic (EO) frequency combs for both probe and local oscillator (LO). The probe comb carries a random spectral phase (uniform in [−π, π]) across its lines to suppress formation of high peak-power pulses, producing a train of noise-like waveforms with period 1/f (f is comb spacing). This spreads energy over the entire period, enabling higher total launched energy without triggering fibre nonlinearities or component saturation; peak-power reduction scales approximately linearly with the number of lines N. The fibre under test (FUT) encodes its impulse response onto the backscattered field e_bs(t) = e_1(t) * b_r(t). Coherent detection is realized via dual-comb (DFC) interference: the LO is a second comb with identical spectral phase and slightly different line spacing f + δf (δf ≪ f). After photodetection and low-pass filtering to select beat notes of neighbouring lines, the RF spectrum forms a comb at q·δf (integer q), compressing the optical bandwidth BW by CF = f/δf. Because the probe and LO spectral phases are matched, relative phase cancels, yielding a flat RF spectrum whose complex amplitudes carry the backscattered field’s amplitude and phase, enabling straightforward recovery without heavy digital decoding. In the time domain, dual-comb interference yields a sequence of cross-correlations (interferograms) due to the repetition-rate offset: the LO walks through the probe period Tr = 1/f with an effective step set by δf. Each interferogram acquisition time is Tac = 1/δf, providing a temporal expansion factor CF = Tac/Tr = f/δf. The FUT length must satisfy L ≤ c·Tr/(2n), i.e., the probe period must exceed the round-trip time. EO-comb generators permit electronic reconfiguration of f, δf, bandwidth and spectral coding to tailor resolution, range, and expansion.

• The approach enables centimetre-scale spatial resolution with MHz-range detection bandwidths, as stated in the abstract (cm-scale over 1 km claimed potential), by time-expanding traces via dual-comb detection.
• Experimental demonstration: probe and LO combs with 2.5 GHz optical bandwidth (≈4 cm nominal spatial resolution) and comb spacing f = 500 kHz, yielding 5,000 lines (thus 5,000 independent spatial points). Maximum measurable distance for this configuration is ≈205 m (n = 1.45).
• Repetition-rate offset δf tunable to tens of Hz to control time expansion. For δf = 40 Hz, expected CF = f/δf = 12,500. For a 154 m sensing length, the trace expands from ≈1.5 μs to ≈18.7 ms, matching observations. For δf = 20 Hz, duration doubles as expected.
• Multiple consecutive traces show good repeatability under identical settings.
• SNR comparison shows an average 3 dB increase for the smaller offset (20 Hz) due to reduced acquisition bandwidth, consistent with theory.
• The random spectral phase coding spreads energy across the signal period, allowing increased launched energy without high peak power and improving SNR; the decoding is intrinsic to the dual-comb heterodyne process.

The work addresses the core limitation of conventional ФOTDR—requirement for high detection bandwidth to achieve cm-scale resolution—by leveraging dual-comb spectral downconversion and time expansion (factor CF = f/δf). This reduces detection bandwidth from GHz to MHz while preserving fine spatial resolution. Random spectral phase coding mitigates peak power, enabling higher average energy and thus higher SNR without invoking fibre nonlinearities. The experimentally observed 3 dB SNR gain when halving δf demonstrates the tunable trade-off between acquisition bandwidth and sensitivity. The method inherently performs decoding during heterodyne detection, simplifying processing compared with conventional coded-pulse OTDR approaches. The EO-comb platform allows electronic reconfiguration to match application requirements, outperforming cavity-laser dual-comb schemes in flexibility and suitability for true distributed sensing where reflectivity per section is extremely low. A key trade-off is that greater time expansion (smaller δf) reduces the maximum measurable acoustic bandwidth, which must be balanced against SNR and acquisition time, and the measurable range is constrained by the probe period relative to fibre round-trip time.

The paper introduces a dual-comb, time-expanded coherent ФOTDR that combines EO frequency combs with random spectral phase coding to achieve cm-scale spatial resolution using only MHz-range detection bandwidth. The approach delivers intrinsic decoding, tunable time expansion, and improved SNR by distributing energy over the probe period, while maintaining flexibility through electronic reconfiguration of comb parameters. Experimental results validate large temporal expansion (e.g., CF ≈ 12,500 at δf = 40 Hz), increased SNR with reduced δf, and repeatable distributed measurements. The technique opens avenues for applications in metrology, borehole monitoring, and aerospace, and provides a framework to tailor resolution–range–bandwidth trade-offs via comb spacing and repetition-rate offset.

• Trade-off between time expansion and dynamic measurement capability: decreasing δf increases SNR and acquisition time but reduces the maximum measurable acoustic bandwidth.
• The measurable range is limited by the probe period (requirement period > 2Ln/c), linking comb spacing f to maximum fibre length; for example, f = 500 kHz implies a ≈205 m maximum distance (n = 1.45).
• Demonstrated experiment used a 2.5 GHz optical bandwidth over ≈154–205 m; while cm-scale over 1 km is claimed as potential, such extended-range performance is not experimentally shown in the provided excerpt.
• Requires mutually coherent combs with matched spectral phase, and precise control of δf and filtering to isolate the desired RF beat notes.