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Numerical Model of a Multiple-Input-Multiple-Output Distributed Acoustic Sensing System with Joint Phase and Birefringence Estimation

This paper introduces and experimentally validates a numerical model for a Multiple-Input-Multiple-Output Distributed Acoustic Sensing (MIMO-DAS) system that jointly estimates common optical phase and dynamic fiber birefringence using polarization-multiplexed coded sequences, thereby enabling improved event discrimination and sensitivity to both longitudinal and transverse fiber disturbances.

Original authors: Diane Prato, Mehran Mokhtari Sheramin, Renaud Gabet, Elie Awwad

Published 2026-08-07

📖 3 min read☕ Coffee break read

CC BY 4.0

Original authors: Diane Prato, Mehran Mokhtari Sheramin, Renaud Gabet, Elie Awwad

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world's internet as a giant, invisible nervous system made of glass threads. These threads, called optical fibers, carry our texts, videos, and calls across oceans and cities. But what if these same glass threads could also act as giant, super-sensitive ears and skin? This is the magic of "Distributed Acoustic Sensing" (DAS). Instead of planting thousands of tiny, expensive sensors along a road or a pipeline, engineers can turn the existing fiber optic cable itself into a massive sensor. They do this by shooting laser light down the fiber and listening to the faint echoes that bounce back.

Think of the fiber like a long, quiet hallway. When you shout, the sound bounces off the walls. In a fiber, the "shout" is a laser pulse, and the "echoes" come from tiny, natural imperfections inside the glass called Rayleigh scattering. Usually, scientists just listen to when the echo returns to figure out how far away something is. But there's a secret layer to this echo: the light also has a "twist" or orientation called polarization. Most old systems ignored this twist, focusing only on the timing. However, just like how a spinning top reacts differently to a push from the side versus a pull from behind, light's polarization reacts uniquely to different kinds of squeezes and stretches on the fiber. The big question researchers have been asking is: Can we listen to both the timing and the twist at the same time to tell exactly what kind of event is happening?

This paper introduces a clever new way to do exactly that. The authors, Diane Prato and her team, built a detailed computer model and tested it in a lab to create a "MIMO-DAS" system. MIMO stands for Multiple-Input-Multiple-Output, which is a fancy way of saying they send out two different streams of light at once, each with a different twist, and listen to how they both change. They used a special coding trick (called Golay sequences) to send these signals, which allows the sensing to happen right alongside regular internet data without causing a traffic jam.

The team discovered that by watching both the "common phase" (the timing of the echo) and the "birefringence" (how much the light's twist changes), they could act like a detective solving a crime scene. They found that if you pull on the fiber lengthwise (like stretching a rubber band), the timing of the echo changes, but the twist stays mostly the same. However, if you squeeze the fiber from the side (like pinching a hose), both the timing and the twist change in a specific way.

Through their simulations and lab experiments, they showed that this dual-ear approach can spot these differences clearly. They demonstrated that they could locate a disturbance with a precision of about 1.3 meters. In their tests, they successfully told the difference between a fiber being pulled lengthwise and one being squeezed sideways. While the paper notes that this method isn't perfect at measuring exactly how hard the squeeze is (because the math gets tricky depending on the angle of the squeeze), it is a powerful new tool for telling what kind of event is occurring. This means that in the future, networks could not only tell you that something happened on a pipeline or a railway track, but could also guess whether it was a train passing by (a longitudinal pull) or a rock falling on the cable (a transverse squeeze), all without adding a single extra sensor to the ground.

Technical Summary: Numerical Model of a MIMO-DAS with Joint Phase and Birefringence Estimation

Problem Statement
Distributed Optical Fiber Sensing (DAS) leverages existing telecommunications infrastructure for monitoring applications such as traffic surveillance, structural health monitoring, and earthquake detection. Conventional approaches typically focus on one of two metrics:

Differential-phase OTDR ( $\Delta\phi$ -OTDR): Estimates the common optical phase of backscattered light, which is highly sensitive to longitudinal strain but often neglects polarization aspects, making it unable to detect purely transverse or anisotropic perturbations.
Polarization-OTDR (P-OTDR): Exploits polarization properties to detect transverse deformations (bending, twisting, transverse stress). However, traditional P-OTDR often requires multiple input States of Polarization (SOPs), leading to longer measurement times that limit dynamic monitoring. Furthermore, it typically does not utilize the common phase, rendering it blind to axisymmetric perturbations.

The paper addresses the need for a multi-parametric dynamic sensing approach that can simultaneously estimate both the common optical phase and polarization-related quantities (specifically birefringence) to discriminate between different types of strain events (longitudinal vs. transverse/anisotropic) with high sensitivity and spatial resolution.

Methodology
The authors developed and experimentally validated a numerical model for a Multiple-Input-Multiple-Output Distributed Acoustic Sensing (MIMO-DAS) system. The methodology comprises three main components:

Fiber Propagation and Scattering Model:
- The fiber is modeled as a series of segments, each treated as a waveplate with linear birefringence.
- Static Conditions: Intrinsic birefringence is generated using a model where Stokes birefringence vector components follow independent Langevin processes, resulting in a Rayleigh distribution of birefringence magnitude and random orientation along the fiber.
- Dynamic Perturbations: The model incorporates the photoelastic effect and fiber elongation. It distinguishes between two event types:
  - Longitudinal Strain: Modeled as fiber elongation ( $\epsilon_z$ ) with Poisson contraction ( $\epsilon_x = \epsilon_y = -\nu\epsilon_z$ ). This alters the common phase via the photoelastic effect and length change but induces no additional birefringence (as $\epsilon_x = \epsilon_y$ ).
  - Transverse/Anisotropic Strain: Modeled with unequal transverse strains ( $\epsilon_x \neq \epsilon_y$ ), which induces additional birefringence. The model calculates the vector sum of intrinsic and event-induced birefringence in Stokes space, noting that the resulting magnitude is non-linear and dependent on the relative orientation of the fast axes.
MIMO-DAS System Architecture:
- The system uses Polarization Division Multiplexed (PDM) BPSK-mapped orthogonal Golay sequences to probe the fiber. This coding scheme reduces peak optical power, enabling coexistence with WDM data transmission while maintaining Signal-to-Noise Ratio (SNR).
- The system employs a dual-polarization coherent receiver to capture the backscattered signal.
- Signal Processing: The system estimates round-trip Jones matrices for each segment. From these matrices, it jointly extracts:
  - Common Phase ( $\phi$ ): Derived from the determinant of the Jones matrix.
  - Effective Birefringence ( $\Delta\beta_{eff}$ ): Derived from the eigenvalues of the product of consecutive Jones matrices, representing the accumulated retardance over a gauge length.
Validation Strategy:
- Numerical Simulation: The model was tested on a 3 km fiber with simulated longitudinal and transverse strain events.
- Experimental Validation: Lab experiments were conducted using two fiber spools (235 m and 1956 m) and a setup applying controlled longitudinal (via a piezoelectric stage) and transverse (via a fiber squeezer) strains.

Key Contributions

Joint Estimation Framework: The paper proposes a method to jointly estimate the common optical phase and effective linear birefringence magnitude from distributed Jones matrices in a dynamic MIMO-DAS system.
Event Discrimination: The study demonstrates that the system can discriminate between event types based on their distinct signatures:
- Longitudinal Strain: Affects the common phase significantly but leaves the birefringence magnitude largely unaffected.
- Transverse/Anisotropic Strain: Affects both the common phase and the birefringence magnitude.
Static Birefringence Characterization: The model successfully estimates the static distribution of effective birefringence, showing a Rayleigh distribution consistent with theoretical expectations for standard single-mode fibers.
Experimental Verification: The numerical model was validated against lab experiments, confirming the system's ability to detect, localize, and discriminate between longitudinal and transverse strains with a mean spatial resolution of approximately 1.3 meters.

Results

Static Conditions: The system estimated the effective birefringence magnitude along the fiber. The distribution of estimated values for a 1956 m fiber spool fit a Rayleigh distribution with a mean value of $\approx 0.57$ rad/m, consistent with theoretical predictions. The model also successfully distinguished between concatenated fiber spools with different mean birefringence values.
Dynamic Longitudinal Strain: Simulations and experiments showed that a sinusoidal longitudinal strain (800 Hz in simulation, 100 Hz in experiment) produced a clear signature in the differential phase estimation but was undetectable in the retardance (birefringence) traces.
Dynamic Transverse Strain: Anisotropic transverse strain (simulated and applied via a fiber squeezer) produced detectable signatures in both the differential phase and the retardance traces.
Spatial Resolution: Using a low-resolution factor (selecting the highest reflecting segments among groups of 5), the system achieved a mean spatial resolution of 1.28 m (approx. 1.3 m). The authors noted a trade-off between sensitivity and resolution, where higher resolution factors (e.g., 10) improved contrast but reduced spatial resolution.

Significance and Claims
The paper claims that by exploiting both phase and polarization estimates in a coded MIMO-DAS architecture, it is possible to improve event discrimination and sensitivity to transverse disturbances compared to state-of-the-art single-parameter systems. The authors emphasize that this approach allows for the detection of both isotropic (longitudinal) and anisotropic (transverse) disturbances.

However, the paper maintains a modest stance regarding the quantitative capabilities of the system. The authors explicitly state that the estimated effective birefringence does not vary linearly with the amplitude of the perturbation; its response depends non-linearly on the relative orientation between the intrinsic fiber birefringence and the event-induced birefringence. Consequently, while the system can discriminate the nature of the strain (longitudinal vs. transverse), it does not currently provide precise quantification of the strain magnitude without further knowledge of the orientation. The authors also note practical limitations, such as the low transfer of transverse strains from cable to fiber in real-world deployments, which may limit the detection of small transverse events. Future work is suggested to focus on understanding noise effects and conducting field trials.

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