1. Introduction

Distributed Rayleigh-based acoustic sensors have achieved remarkable success, achieving extremely low noise floors over kilometers of fiber [1,2]. As a result, these sensors have become an increasingly important tool for a range of applications including intrusion detection, railway monitoring and seismic sensing [3–5]. One of the most widely adopted Rayleigh-based sensing architectures is phase-sensitive optical time domain reflectometry (Φ-OTDR) [6]. Φ-OTDR systems take advantage of Rayleigh scattering which occurs in the fiber as a result of small fluctuations in the fiber refractive index and density. These fluctuations are present in all commercial off-the-shelf fiber and so, Rayleigh-based sensors have the advantage that they do not require any modification of the fiber itself. This allows Rayleigh-based sensors to use existing fiber infrastructure, dramatically reducing the cost of deployment. For example, Rayleigh-based fiber sensors were recently used to measure seismic disturbances using existing undersea fiber links [7,8]. However, the vast majority of Rayleigh-based Φ-OTDR sensors are designed to work with single mode fiber and cannot take advantage of existing infrastructure based on multimode fiber. Multimode fiber deployment is also expected to increase as the telecom industry seeks to add bandwidth via spatial mode division multiplexing [9]. As a result, there has been growing interest in developing multimode-fiber-based Rayleigh sensors [10–14].

From a sensor design perspective, multimode fiber also offers some potential advantages compared with single mode fiber. First, multimode fiber has a much higher threshold for nonlinear effects, enabling the use of higher optical power which could lead to lower noise measurements. Secondly, multimode fiber can support hundreds to thousands of spatial modes. When all the spatial modes supported by a multimode fiber are used, the sensor can be completely immune to interference fading, which can degrade the performance of standard Φ-OTDR systems [15]. These advantages have the potential to yield multimode fiber sensors that outperform their single mode counterparts.

The main challenge in designing a Φ-OTDR system for use with multimode fiber is coping with the speckle pattern formed by interference between the modes of the fiber. The most common approach is to spatially filter the speckle pattern (e.g., by splicing the multimode fiber to a single mode fiber) and then use a standard Φ-OTDR system to record the backscattered light in one or two spatial modes [10–12]. However, these techniques discard much of the useful light and fail to take advantage of some of the unique features that multimode fibers offer. As an alternative, we recently proposed a multimode fiber Φ-OTDR sensor that used a high-speed camera to record the entire backscattered speckle field [13]. While this work showed that low-noise strain measurements in a multimode fiber are possible, the demonstration was extremely limited. The sensor was only capable of probing a single position in the fiber and physical delay lines were used to define the sensing location. In addition, the sensor range was limited to 20 m and it was unclear if mode mixing would have more pronounced effects in longer lengths of fiber.

In this work, we describe a fully distributed multimode fiber Φ-OTDR system that addresses each of these limitations. The sensor uses off-axis holography to record the entire backscattered field with a high-speed camera, while a pair of time-gated reference arms are used to interferometrically select light from two regions in the fiber. By electronically controlling the reference arm timing, the system is able to rapidly step between sensor locations, probing nearly 100 locations along a 2 km fiber. This approach enables a fully distributed sensor with a spatial resolution of 20 m, a noise floor of −61 dB re rad²/Hz (∼5 pε/√Hz), and a bandwidth of 400 Hz along a 2 km fiber. Alternatively, the same interrogation system can be electronically adjusted to probe any single sensor location with a bandwidth of 20 kHz and a noise floor as low as −92 dB re rad²/Hz (∼0.1 pε/√Hz).

2. Sensor design and experimental methods

The multimode Φ-OTDR sensor presented in this work relies on the same transduction mechanism as single-mode-fiber based coherent Φ-OTDR systems [2]. That is, the sensor measures the relative phase between light backscattered from two nearby regions of fiber. Changes in this relative phase are proportional to the strain experienced by the section of fiber between these two reflector regions. While this measurement principle is the same, a very different technique is required to isolate backscattered light from the two reflector regions in a multimode fiber. Our approach relies on recently developed high-speed cameras capable of recording the entire speckle field backscattered in a multimode fiber. State-of-the-art InGaAs cameras can operate at frame-rates in the 10-100 kHz range with exposure times as short as 1 µs [16]. While these frame-rates enable dynamic strain sensing at acoustic frequencies, they are still too slow to directly time-gate the Rayleigh backscattered light the way a high-speed photodetector is used in a single mode Φ-OTDR system. For example, a 1 µs exposure time would limit the spatial resolution to 100 m while a 100 kHz frame rate would result in a 1 km spacing between neighboring sensor locations. In order to overcome these limitations, we use time-gated reference pulses to interferometrically select backscattered light from a smaller region in the fiber than the camera exposure time would dictate. We also show that it is possible to partially compensate for the limited camera frame-rate by using spatial multiplexing. In particular, we use spatial frequency domain multiplexing to recover the speckle field from two regions of the fiber in each camera frame, doubling the sensor bandwidth.

Figure 1(a) shows a schematic of the experimental design. Continuous wave light (λ = 1549.27 nm) from a narrow linewidth (< 5 Hz) laser (OE Waves 4028) was amplified by an Er-doped fiber amplifier (EDFA) and split into two paths with a 90:10 coupler. In the interrogation arm, which received 90% of the light, an acousto-optic modulator (AOM₁) (Brimrose 500 MHz) was used to create 50 ns pulses at a repetition rate of 40 kHz (τ = 25µs). The pulses were amplified with EDFA₁ to a peak power of 10 W and a 200 GHz filter was used to suppress the amplified spontaneous emission (ASE). The amplified pulses were coupled through free space into a 2 km spool of graded-index multimode fiber (Corning OM2), which served as the fiber under test (FUT). The multimode fiber has a 50 µm core, a numerical aperture of 0.2, and supports about 100 modes at 1550 nm. The FUT was placed in an insulated container to isolate the fiber from environmental noise sources. The Rayleigh backscattered light was then directed onto a high speed InGaAs camera (Xenics Cheetah, 8 bit resolution, with a well depth of 6.5 ×10⁴ electrons) which recorded 66 × 52 pixel images with an exposure time of 1 µs at a frame rate of 40 kHz.

 

Fig. 1. (a) Experimental design of the distributed multimode fiber Φ-OTDR system. The inset at the right shows an example of the speckle pattern backscattered from the multimode fiber. The schematic at the top of the diagram shows how the reflector and sensor regions are distributed throughout the fiber. The reflector regions are color coded to match the timing diagram in (b). (b) Diagram showing the relative timing between the pair of LO pulses and the Rayleigh backscattered signal reaching the camera. The camera frame rate is synchronized so that each frame records the interference signal between a pair of LO pulses and RBS light from two distinct regions in the fiber.

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In the reference arm, AOM₂ was used to carve 50 ns pulses. The pulses were amplified by EDFA₂ and divided into two legs with a path length mismatch of 40 m. The reference pulses were directed to the camera, where they interfered with light backscattered from a pair of 5 m reflector regions in the multimode fiber. These reflecting regions were separated by 20 m in the FUT due to the 40 m path mismatch between the reference arms. Although the Rayleigh backscattered light is unpolarized, it is directed through a polarizing beam splitter (PBS) before being directed to the camera. While the PBS removes half of the backscattered light, it ensures good mixing efficiency with the light from the reference arms and rejects the specular reflection of the launch pulse from the fiber end facet.

In order to separate the interference signals formed using the two reference arm pulses, we used spatial frequency division multiplexing. This was accomplished by directing the reference pulses onto the camera at different angles in order to form orthogonal interference patterns with the Rayleigh backscattered light from the two reflector regions. We then used off-axis holography to separately demodulate the amplitude and phase of the Rayleigh backscattered light that temporally overlapped with each of the reference pulses [13]. The inset at the right of Fig. 1(a) shows an example of the demodulated speckle amplitude using one of the reference arm pulses.

By adjusting the relative timing between the interrogation pulse and the reference arm pulses, the sensor can probe the backscattered light from any position in the fiber. A diagram showing the relative timing between the LO pulses and the Rayleigh backscattering trace is shown in Fig. 1(b). In order to perform distributed measurements over the entire fiber, the LO pulses were generated with AOM₂ with a period of 25.4 µs, while the interrogation arm pulses were generated with AOM₁ every 25.0 µs. The repetition rate mismatch means that with each successive pulse the LO pulses are delayed an additional 400 ns with respect to the interrogation pulse. The changing delay between the interrogation and LO pulses allows the system to probe pairs of reflector regions separated by 40 m along the entire fiber in a round-robin format. Note that the camera exposure time was triggered to coincide with the arrival of the LO pulses. Using this technique, we probed 98 reflector regions separated by 20 m along a 2 km fiber every 1.25 ms (providing a sample rate of 800 Hz at each location), as shown in the top of Fig. 1(a).

The interference between the reference arms and the Rayleigh light provided a measurement of the time-varying amplitude $|{E({r,z,t} )} |$ and phase $\phi ({r,z,t} )$ of the Rayleigh backscattered speckle field from each reflector region. Here, r describes the position in the speckle pattern (i.e., the pixel on the camera), z describes the position of the reflector region along the length of the fiber, and t is the time of the measurement. To obtain the change in optical pathlength leading up to a given reflector region, we first calculated the average change in phase across each speckle pattern. In order to minimize the sensor noise and avoid the effect of interference fading, we used the amplitude at each pixel to compute a weighted average of the temporal phase derivative: $d{\phi _{ave}}({z,t} )= \mathop \sum \limits_r |{E({r,z,t} )} |\cdot d\phi ({r,z,t} )/\mathop \sum \limits_r |{E({r,z,t} )} |\; \; \; $where $d\phi ({r,z,t} )$ is the frame-to-frame phase change (i.e. $d\phi ({r,z,t} )= \phi (r,z,t) - \phi (r,z,t + \tau )$, where τ is the time between frames). The average time-varying phase of light backscattered from each reflector region in the fiber was then recovered by integrating $d{\phi _{ave}}({z,t} )$. The change in phase over a given sensor aperture (e.g., due to strain) was then obtained by calculating the relative phase between light from neighboring reflector regions.

To illustrate the spatial averaging process, we plotted dϕ(r,z,t) for all pixels at z = 1800 m into the fiber in Fig. 2(a). We also plotted the change in phase for 5 representative pixels in Fig. 2(b). In this measurement, the PZT was positioned 29 m into the fiber and driven at 40 Hz. While the phase recorded at each pixel was effectively random at the beginning of the measurement [see Fig. 2(c)], Figs. 2(a) and 2(b) confirm that the phase at each pixel exhibited the same response to strain introduced by the PZT. Thus, by averaging the phase derivative over all pixels, the sensor is able to extract the common response to a change in the optical pathlength leading up to a given reflector region. The processing time for the distributed sensor presented here is about 5 minutes for a 1.25 second recording. However, this data processing was not optimized and could be accelerated through parallelization.

 

Fig. 2. (a) Plot of dϕ(r,z,t) for all pixels at z = 1800 m into the FUT. A PZT positioned at 29 m was driven at 40 Hz for this measurement. (b) Plot of dϕ(r,z,t) for 5 pixels (r = 700, 1400, 1800, 2400, and 2500) showing that dϕ(r,z,t) is the same for all pixels. Also shown on the plot as a dashed line is the average of dϕ(r,z,t) across all pixels. The average value dϕ(r,z,t) of is integrated to yield the phase at each position along the fiber. (c) The integrated phase ϕ(r,z,t) for the 5 selected pixels. The average over all pixels is also shown as a dashed line. The initial phase for each of the pixels starts at a random value.

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As in most OTDR sensors, there exists a trade-off between the number of individual sensing points, the fiber length, and the sensor bandwidth. In addition to the normal constraint on the pulse repetition frequency imposed by the roundtrip time in the fiber, the maximum available camera frame rate introduced another limitation here. The maximum frame rate of the camera used in this work is 40 kHz and we were able to measure the phase from two reflector regions each frame. We could then divide the available frame-rate among as many sensors as desired, at the cost of reducing the bandwidth of each sensor. For example, we could measure a single sensor with a bandwidth of 20 kHz, 19 sensors with a bandwidth of 2 kHz, or 97 sensors with a bandwidth of 400 Hz. Higher spatial resolution is also possible by reducing the spacing between reflector regions, although more sensors would be required to cover the same total length of fiber, resulting in a reduced sensor bandwidth. For the sensor demonstrated here using 2 km of fiber, we use 97 sensors with a 20 m spatial resolution and a bandwidth of 400 Hz (set by the 800 Hz sample rate at each position). In the top inset of Fig. 1(a), we differentiate between two types of sensor apertures: those formed by a pair of reflector regions recorded on a single camera frame (“type 1”) and those formed using reflector regions recorded in sequential frames (“type 2”).

Finally, we expect that continuing advances in high-speed camera technology will directly improve the performance of this type of sensor. For example, increases in the camera frame rate would translate to either higher sensor bandwidth or an increased number of sensors at the same bandwidth.

3. Results

In order to evaluate the performance of the sensor, 9 m of fiber was wrapped on a piezo-electric cylinder (PZT) and positioned 1960 m into the FUT. The PZT was driven with a 40 Hz sinusoidal signal with an amplitude of 4.5 nε while we recorded data for 1.25 s. Figure 3(a) shows the measured phase at each sensor aperture along the FUT. The 40 Hz oscillation is clearly observed at the position of the PZT at the end of the fiber, while the phase remains relatively constant throughout the rest of the fiber. Figure 3(b) shows the power spectral density (PSD) of the measured sensor phase noise all along the fiber. The 40 Hz peak is detected at the PZT position. The inset in Fig. 3(b) shows a magnified view of the region around the PZT.

 

Fig. 3. (a) Measured relative phase all along the fiber. (b) Power spectral density of the sensor phase noise at all locations along the FUT. The inset in the plot shows a magnified view of the 40 Hz signal detected at the PZT location. (c) Power spectral density of the phase noise at the PZT position 1960 m into the FUT.

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Careful inspection of the high frequency region of the plot in Fig. 3(b) reveals that the phase noise alternates between a higher value and lower value all along the fiber. The lower noise positions correspond to the first type of sensor aperture shown in Fig. 1, while the higher noise locations correspond to the second sensor type. The first sensor type is formed by pairs of measurements using the same out-going pulse. As a result, this sensor type is relatively immune to laser phase noise and pulse-to-pulse variations in the phase accumulated in the EDFAs, since these effects will be common to the measurements of both reflector regions. However, the second sensor type is formed using measurements recorded with sequential pulses separated by 25 µs. In this case, the sensor is susceptible to laser phase noise, pulse-to-pulse variations in the phase accumulated in the EDFAs, as well as any changes in the optical pathlength through the launch and reference arm paths. These noise sources result in 12 dB higher noise for the second aperture type. To mitigate this effect, we could design the system to rely entirely on the first type of sensor aperture. This could be accomplished by moving the pair of LO pulses in 20 m steps between frames such that the second reflector region probed in the first frame would become the first reflector region probed in the second frame. However, this would also decrease the sensor bandwidth by a factor of 2.

Nevertheless, this measurement confirms that the system is capable of performing distributed measurements over the entire 2 km FUT. The PSD at the PZT position, 1960 m in the FUT, is shown in Fig. 3(c). The 40 Hz PZT signal is clearly observed with a total harmonic distortion of −32 dB indicating a high degree of linearity. We also found that the phase noise decreased with frequency, reaching a minimum value of −61 dB re rad²/Hz (or 4.9 pε/√Hz) between 376 and 400 Hz. At lower frequencies, the measured phase noise increased due to the impact of environmental noise. In particular, the system is sensitive to variations in the optical pathlength of the two reference arms which were not environmentally isolated during these experiments. This will be evident below, where we present the PSD recorded using a single sensor with 20 kHz of bandwidth. In that measurement, environmental noise was observed at frequencies up to ∼1 kHz and thus, the noise recorded in the distributed measurements shown in Fig. 3 includes environmental noise from higher frequencies that aliased into the available bandwidth. We therefore expect that environmentally isolating the fiber under test and the reference arm paths would minimize this effect and enable the system to exhibit a self-noise at or below −61 dB re rad²/Hz across the sensor bandwidth.

Cross-talk is another important metric in a distributed strain sensor. While cross-talk is typically very low in single-mode fiber Φ-OTDR systems, multimode fiber sensors could be more sensitive. For example, a strong modulation at one position in the fiber could introduce mode-coupling and thereby impact the measurement at each position down-stream. To evaluate this effect in our system, we recorded a measurement after moving the PZT to the front of the fiber. The PZT introduced a relatively strong modulation with an amplitude of 4.5 nε at 40 Hz. In Fig. 4(a) we plot the measured phase all along the fiber. The sinusoidal signal is clearly visible at the first sensor location; however, some indication of this modulation is visible at other locations in the fiber. Figure 4(b) shows the PSD of the measured signal all along the FUT. Again, the 40 Hz signal is strongest at the first sensor location, but is also detected at many other locations in the fiber. The relative strength of the 40 Hz signal at each position in the fiber is shown in Fig. 4(c), providing a measurement of the sensor cross-talk. We found that the 40 Hz signal is suppressed by at least 10 dB at each position in the fiber, while the average cross-talk level is about −20 dB. This degree of cross-talk is higher than in most single-mode Φ-OTDR systems, indicating that mode mixing may render multimode fiber Φ-OTDR sensors susceptible to nonlocal signals. Nevertheless, this level of cross-talk is acceptable for many applications.

 

Fig. 4. a) Time evolution of the measured phase all along the FUT. The PZT is positioned 29 m into the fiber (at the first sensor position) and driven with a 40 Hz signal. b) PSD of the phase noise in the FUT. c) The relative strength of the 40 Hz signal is shown at each position in the fiber. The maximum cross-talk level is −10 dB and the average level is −20 dB.

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Finally, we evaluated the performance of a single sensor position with the full available bandwidth of 20 kHz. In this case, a single 20 m sensor was positioned either 42 m or 1920 m into the FUT. The measured sensor phase noise at each position is shown in Fig. 5. As in the distributed measurements shown in Fig. 3, the environmental noise increases at lower frequencies. However, in this case, the measurement has sufficient bandwidth to observe a white noise floor beyond ∼1 kHz corresponding to the sensor self-noise. That is, the environmental noise power is lower than the sensor self-noise beyond ∼1 kHz. The average measured phase noise above 1 kHz was −92 dB re rad²/Hz (0.14 pε/√Hz) for the sensor 42 m into the FUT and −86 dB re rad²/Hz (0.27 pε/√Hz) for the sensor 1920 m in to the FUT. In Fig. 5, we also compared the measured noise with the predicted self-noise due to digitization and shot noise. The sum of these noise sources is also shown on the plot (labeled “combined noise”) indicating that the measured phase noise at the front of the fiber approaches the predicted self-noise limit above ∼1 kHz. The 6 dB increase observed in the sensor noise at the end of the fiber is higher than we would expect due to attenuation (∼0.29 dB/km) and may indicate the presence of mode coupling induced noise as light propagates down the fiber. Future work will investigate this effect more fully. Nevertheless, sub-pico-strain-level noise floors are possible at any position over the entire fiber length.

 

Fig. 5. Measured sensor phase noise 42 m and 1920 m into FUT. Also shown on the plot are the predicted digitization noise, shot noise, and combined noise.

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4. Summary

In summary, we have presented a distributed multimode fiber Φ-OTDR sensor. The sensor was formed using a pair of time-gated reference arms to optically select the light from two regions in the fiber. A 20 m sensing region was scanned down the fiber to form 97 sensing region along a 2 km multimode fiber. The Rayleigh backscattered light was collected on a high-speed camera and off-axis holography was used to recover the amplitude and phase of the speckle field from each reflector region. The distributed sensor had a bandwidth of 400 Hz, a 20 m spatial resolution, and a minimum noise floor of −61 dB re rad²/Hz over a 2 km range. In a single sensor configuration, the 20 m sensor had a bandwidth of 20 kHz and a noise floor of −86 dB re rad²/Hz (0.27 pε/√Hz). This work shows that emerging high-speed camera technology can be used to realize high performance, distributed multimode fiber Φ-OTDR sensors.