Distributed optical fiber sensing (DOFS) is a mature technology used for real-time monitoring of various physical parameters over long distances. Phase-sensitive optical time-domain reflectometry (ФOTDR), a DOFS technique based on Rayleigh scattering, is particularly useful for distributed acoustic sensing. A key limitation of ФOTDR is the trade-off between spatial resolution and detection bandwidth; high resolutions require high bandwidths, leading to increased system cost and complexity. While techniques like optical sampling and computational DOFs have been used to mitigate this, they still face challenges in terms of signal-to-noise ratio (SNR) and computational load. This paper introduces a new ФOTDR approach using optical frequency combs (OFCs) and dual-comb spectrometry. OFCs offer a means to improve SNR through signal coding, while dual-comb interference acts as an optical sampling technique, enabling time expansion of the received signal and thus reducing the required detection bandwidth. The use of electro-optic (EO) modulation allows for precise control of the spectral phase of the comb, further optimizing the system's performance.

The paper reviews existing DOFS techniques, highlighting the limitations of traditional ФOTDR in achieving high spatial resolutions with reasonable cost and complexity. It discusses previous attempts to improve SNR and reduce bandwidth requirements, including coherent detection ФOTDR, frequency-scanning ФOTDR, chirped-pulse ФOTDR, optical sampling techniques, and computational DOFs based on temporal ghost imaging. The authors point out the limitations of these existing methods, such as non-linear relationships between detected amplitude and strain/temperature variations, complex decoding algorithms, and limitations on the maximum achievable SNR due to nonlinear effects and limited pulse peak power.

The proposed method uses a dual-comb configuration for coherent ФOTDR sensing. A probe comb with a randomly coded spectral phase generates a train of noise-like waveforms in the time domain. This coding prevents the formation of high peak-power pulses, allowing for increased total energy launched into the fiber without inducing nonlinear effects. The backscattered signal is coherently detected using a second comb (local oscillator) with a slightly different line spacing. This dual-comb interference results in a multi-heterodyne process that downconverts the optical frequencies to the radio frequency (RF) domain, effectively expanding the time duration of the signal. The authors explain the process in both the frequency and time domains, highlighting how the time expansion factor is determined by the frequency difference between the two combs. The random spectral phase coding ensures that the relative phase of the combs cancels out, simplifying the decoding process. The mathematical formalism underpinning the signal processing and the cancellation of the phase code is provided in the supplementary materials. This allows for direct decoding of the amplitude and phase of the backscattered signal, providing high resolution measurements with a low detection bandwidth.

The experimental results demonstrate the time expansion capability of the proposed method. By adjusting the repetition rate offset between the two combs (δf), the authors achieve different time expansion levels. For instance, with a 40 Hz offset, the signal is expanded by a factor of 12,500, converting a 1.5 µs signal into an 18.7 ms signal. Reducing the offset to 20 Hz doubles the expansion time, as expected. The authors show that this time expansion directly translates to an improved signal-to-noise ratio (SNR), with a 3 dB average increase observed when using a smaller offset. This improvement in SNR is achieved without sacrificing the spatial resolution, which remains in the centimeter range. The authors demonstrate the capability of their approach to achieve cm-scale spatial resolution over 154 meters of fiber using a detection bandwidth in the MHz regime. The use of random phase-spectral coding allows the energy of the probe signal to be distributed along the entire period, increasing the total input power without increasing the peak power and avoiding non-linear effects.

The presented time-expanded ФOTDR approach significantly advances the capabilities of distributed fiber optic sensing. The key advantage is the ability to achieve high spatial resolution with dramatically reduced detection bandwidth requirements. This translates to lower system cost, reduced complexity, and potentially lower power consumption. The method's performance is enhanced by the use of random phase-spectral coding, which improves SNR without complex decoding algorithms. The ability to customize the time expansion factor allows for flexibility in balancing spatial resolution, acquisition time, and SNR. The results confirm the theoretical predictions and demonstrate the practicality of the approach for real-world applications. The superior SNR obtained allows for long-range sensing applications that were previously unreachable for high-resolution ФOTDR systems.

This paper presents a novel high-resolution ФOTDR scheme based on dual-comb spectrometry and random phase-spectral coding. The method successfully achieves centimeter-scale spatial resolutions over significant distances while significantly reducing the required detection bandwidth. This is achieved by the time expansion of the optical trace, allowing a trade-off between time resolution and SNR. The results demonstrate the potential of this approach for various applications, such as metrology, borehole monitoring, and aerospace, where high-resolution distributed sensing is crucial. Future work could focus on optimizing the phase coding strategy for further SNR enhancement and exploring new applications of this technology.

The current implementation is limited by the bandwidth of the available electro-optic modulators and the maximum length of fiber that can be effectively interrogated with the current system configuration. While the time expansion technique effectively improves SNR and reduces the required detection bandwidth, it also increases the acquisition time. The presented results demonstrate the functionality of the time expansion over a limited range and future studies should investigate the scalability to much larger distances. Also, environmental factors and variations in fiber properties could impact the accuracy and precision of measurements in real-world deployment scenarios. Further studies are needed to establish the stability of the system and the robustness to environmental variations in real applications.