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Abstract
We propose and demonstrate a method to perform quantitative phase-sensitive optical time domain reflectometry (Φ-OTDR) using multimode fiber. While most Φ-OTDR sensors use single-mode fiber, multimode fiber exhibits higher thresholds for non-linear effects, a larger capture fraction of Rayleigh backscattered light, and the potential to avoid signal fading by detecting many spatial modes in parallel. Previous multimode fiber based OTDR sensors discarded most of the backscattered light and thus failed to take advantage of these noise-reducing factors. Here, we show that by performing off-axis holography with a high-speed camera, we can record the entire Rayleigh backscattered field, maximizing the detected light level and making the sensor immune to fading. The sensor exhibits a high degree of linearity, a minimum phase noise of −80 dB [rel. rad2/Hz], and 20 kHz bandwidth.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past two decades, fiber optic sensors have become an increasingly popular tool for a wide range of sensing applications including perimeter security, structural health monitoring, geophysical experiments, and constructing distributed acoustic arrays [1–7]. Many of the most successful fiber sensors have taken advantage of Rayleigh backscattering using a technique called phase-sensitive optical time-domain reflectometry (Φ-OTDR) [1,2]. Rayleigh scattering is an elastic scattering process that occurs when light encounters fluctuations in the fiber’s refractive index [8]. The backscattered light is used to detect dynamic strain-induced changes in the fiber length and refractive index [9–11]. Since refractive index fluctuations naturally occur in all optical fiber, Rayleigh based sensors are able to use low-cost, commercially available optical fiber without the expensive modifications required, for example, in fiber Bragg grating based sensors.
Φ-OTDR systems can be divided into two categories: 1) amplitude-measuring systems [3,10,12–15] that are capable of detecting the presence of acoustic signals and 2) phase-measuring systems [11,16–22] that are capable of both detecting and quantifying acoustic signals. Amplitude-measuring Φ-OTDR detect acoustic signals by measuring changes in the amplitude or intensity of the backscattered light. However, no clear relationship exists between the measured amplitude fluctuations and the acoustic-induced strains. In contrast, phase-measuring Φ-OTDR systems use a variety of demodulation schemes to extract the magnitude of the acoustic-induced strain by measuring the phase, rather than simply the intensity, of the backscattered light. The demodulated phase is linearly proportional to the magnitude of the strain induced by the acoustic field [21]. These quantitative measurements of the strain extend the capabilities and industrial applications of OTDR fiber sensors.
Despite their success in some applications, existing Rayleigh based Φ-OTDR systems are limited by two significant disadvantages. First, Rayleigh scattering is an inherently weak process [8], leading to low backscattered light levels and corresponding high noise levels which limit sensitivity. While increasing the input laser power level could help, the onset of non-linear optical effects such as stimulated Brillouin scattering and four-wave mixing limits the amount of light that can be propagated by the fiber. These non-linear thresholds are particularly constraining since the vast majority of Rayleigh based sensors rely on single-mode fiber (SMF) [3,10,12–22]. Second, SMF based Rayleigh sensors are susceptible to signal fading when the backscattered Rayleigh light interferes destructively with itself [23].
Multimode fibers have the potential to address both of these limitations. While the Rayleigh scattering coefficient is a material property which is the same in single and multimode fiber, the capture efficiency in multimode fiber is nearly an order of magnitude higher [8]. In addition, multimode fibers have a much larger core, enabling the use of significantly higher input light levels before the onset of deleterious non-linear optical effects [24]. Secondly, a multimode fiber sensor capable of measuring the entire backscattered field avoids the effects of signal fading by discarding phase information from spatial modes with low intensity. While the advantages of multimode fiber such as higher input light levels and improved capture efficiency are well known, they have yet to be fully exploited in OTDR systems.
Recently there has been a renewed interest in multimode fiber for telecommunications [25], microscopy [26,27], and spectroscopy application [28]. However, multimode fiber presents several challenges in OTDR systems. First, typical multimode fibers support 100s to 1000s of spatial modes, which cannot be separately demodulated with the photodetector-based receivers used in single-mode fiber OTDR sensors. As a result, existing multimode fiber based Rayleigh sensors operate by spatially filtering the backscattered light, for example, by coupling to a single-mode fiber before detection [29,30]. While this solution simplifies the detection scheme, it also discards the vast majority of the backscattered light, mitigating the potential advantages of using a multimode fiber. In addition, coupling between spatial modes in the multimode fiber can degrade the sensor performance. Fortunately, mode coupling is typically a result of thermal drifts within the fiber that occur on timescales much slower than the acoustic frequencies of interest. As such, acoustic sensing represents an attractive application for multimode fiber sensors. Finally, modal dispersion in the multimode fiber can reduce the spatial resolution of a multimode fiber based OTDR sensor, particularly for sensors far away from the interrogation system. This limitation can be partially mitigated by using graded-index multimode fiber or limiting the total sensor length.
Here we demonstrate a multimode fiber phase-measuring Φ-OTDR system that uses a high-speed camera to detect the entire backscattered field, making the system immune to signal fading. Recent developments in camera technology enable frames rates that are fast enough to record acoustic frequencies. The sensor exhibits a phase noise as low as −80 dB [rel. rad2/Hz] and a bandwidth of 20 kHz. In addition, the Φ-OTDR sensor provides a linear response to axial strain with comparable sensitivity to a single-mode fiber, despite the presence of hundreds of spatial modes. The presented system overcomes many of the challenges that limit the performance of single-mode Φ-OTDR systems and represents an advance in fiber OTDR technology.
2. Sensor design and operation
Φ-OTDR acoustic sensors rely on measuring the acoustic-induced axial strain in optical fiber. Axial strain induces a change in both the refractive index and the length of the fiber, causing the phase of the propagating light to change. In a single-mode fiber, this phase change can be calculated as [7,31]:
where β is the propagation constant, L is the length of fiber under strain, ξ is the elasto-optic coefficient for the fiber, and ε(t) is the time varying strain. In a multimode fiber, the optical field can be expressed as a summation of many spatial modes:where z is the position along the fiber, An is the amplitude of the nth mode, ψn(x,y) is the spatial profile, ν is the optical frequency, βn is the propagation constant, ϕn is the initial phase, and dϕn(t) is the strain-induced change in phase of the nth mode. The change in phase can be expressed in the same form as Eq. (1): . Since the propagation constants, βn, have an approximately 1% variation across modes [32], the multimode fiber modes will experience very similar phase changes as a function of axial strain. As a result, we expect that the observed phase change measured for the total field summed over all modes will be nearly the same as the phase change experienced by a single spatial mode in a single-mode fiber. Very large strains in the fiber will lead to spatial mode mixing and degrade sensor performance. We examined this effect in section 3 below.Rayleigh scattering based detectors rely on measuring light that is scattered from naturally occurring refractive index variations in optical fiber. The power of the backscattered light from a position z along the fiber can be estimated from the following expression [8]:
where Pin is the input power, vg is the group velocity of the light, τ is the pulsewidth, αR is the Rayleigh scattering coefficient, S is the capture efficiency, and α is the total fiber attenuation. In this work, we used 2 km of graded index multimode fiber with a 50 μm diameter core and numerical aperture of 0.2 supporting ~870 spatial modes. Two km represents a realistic length for a fiber sensing system, although the approach described here could be applied to different fiber lengths. A summary of the various fiber parameters is given in Table 1. For graded-index fiber, the capture efficiency is estimated as [8]where NA is the numerical aperture and n is the refractive index of the core. Using the parameters given in Table 1, the multimode fiber used in this work has a capture efficiency of S = 4.53 × 10−3. For comparison, the capture efficiency for standard single-mode fiber (SMF-28) is S = 3.92 × 10−4. To verify that backscattered power behaves as predicted by Eq. (3), the Rayleigh backscattered power was measured with an amplified photodetector. Figure 1 shows that the measured backscattered power agrees with that predicted by Eq. (3).
Table 1. Graded-index multimode fiber sensor parameters
Fig. 1 Time-dependent trace of Rayleigh backscattered power from a graded-index multimode fiber measured with an amplified photodetector (shown in blue) and predicted by Eq. (3) (shown in orange).
Most single-mode Φ-OTDR systems rely on time-gating to identify light back-scattered from different parts of the fiber. This is achieved using a fast photodetector to continuously record the back-scattered light. However, even the fastest available high-speed cameras cannot reach the frame rates required to provide reasonable spatial resolution through time-gating. Therefore, we needed a different approach in order to spatially define the sensor. We achieved this by mixing the optical field of the Rayleigh backscatter with two local oscillators (LO) that were delayed to correspond to two different regions within the fiber. The difference in the phase measured with the two LOs, provided a localized measurement of the phase change (i.e. the axial strain) between the selected regions.
Figure 2 shows a schematic of the sensor. Overall, the sensor was comprised of a Mach-Zehnder interferometer with a sample arm containing the multimode fiber under test (FUT) and two reference arms. To leverage the availability of high-speed cameras operating in the visible spectrum, this proof-of-principle demonstration was completed using 532 nm light. Continuous wave light from a high-power fiber laser (IPG Photonics GLR-50) with λ = 532 nm was directed to an acousto-optic modulator (AOM), generating 20 ns pulses at 40 kHz. Using a half wave plate and polarizing beam splitter (PBS), we directed 80% (about 0.88 W peak power) of the light to the multimode fiber, while the rest of the light was split between the two reference arms.
Fig. 2 Schematic of the multimode Rayleigh acoustic sensor. Rayleigh scattering occurs at every point along the multimode fiber as shown in the upper right corner. The light from each delay line hits the camera at different angles as shown in the inset in the upper left corner so that the interference pattern from each delay corresponds to different spatial frequencies. AOM: acousto-optic modulator, HWP: half-wave plate, PBS: polarizing beam splitter, pol: polarizer, BS: beam splitter, FUT: fiber under test
The coupling efficiency into the fiber was measured to be about 72% and the fiber has a measured loss of 15 dB/km. Rayleigh scattering occurred at every point along the length of the multimode fiber, producing a backscattered speckle pattern from each position, as shown in the upper right corner of Fig. 2. The Rayleigh backscattered light was directed through a polarizing beam splitter, transmitting only the cross-polarized light and reducing the detected backscatter power by a factor of two. The cross-polarized backscattered light was directed to a high-speed camera (Vision Research Phantom v2512) where it was combined with light from the two reference lines. Light from the first reference arm (labelled “Delay 1”) was delayed in order to interfere with Rayleigh scattered light originating 5 m into the multimode fiber (labelled “Time-gated Region 1”), whereas light from the second reference arm (labelled “Delay 2”) was delayed to interfere with scattered light from 19 m into the multimode fiber (labelled “Time-gated Region 2”). By calculating the relative phase change between light scattered from these two regions, we are able to form a localized sensor at any position along the fiber. The sensor position is dictated by the delay lines and by adjusting the delay in the reference arms, the sensor region could be positioned at arbitrary locations within the fiber. The spatial resolution of each time-gated region was 2 m, determined by the 20 ns pulse width. For the 5 m and 19 m delays used here, modal dispersion is negligible, accounting for less than 0.3 ps or a 60 µm spread in the spatial resolution of the time-gated region. Delay 1 was implemented in free space, whereas the longer delay 2 was constructed with single-mode fiber to minimize divergence of the beam and space requirements.
Light from the two reference arms was directed to the camera at different angles (see inset in the upper left corner of Fig. 2) to produce interference fringes that were rotated by 90° with respect to one another. This enabled the scattered field from these two regions of the multimode fiber to be separately demodulated by mapping their interference signals to separate spatial frequencies.
To operate the sensor, the camera recorded 128 x 128 pixel images at 40 kHz for 250 ms. An example of a raw unprocessed image is shown in Fig. 3(a). We used off-axis holography [33] to recover the amplitude and phase of the scattered light from the two time-gated regions. A 2-dimensional fast Fourier transform (2D FFT) converted the measured interference pattern to the spatial frequency domain as shown in Fig. 3(b). The spatial frequencies corresponding to the interference between the Rayleigh backscattered light and the two reference arms were selected separately using two Hann windows as indicated by the red and green boxes in Fig. 3(b). An inverse 2D FFT on the selected windows recovered the amplitude and phase of the scattered light from the two regions as shown in Figs. 3(c)-3(f). This process was repeated for all of the recorded images, providing a time-dependent measurement of the phase at each pixel. The phase information is spatially-averaged over all pixels to get a measure of the time-varying phase. The spatial averaging is performed on the phase derivative as described in [34] and repeated for each of the time-gated regions. To avoid noise due to speckle fading when computing the spatial average, we did not use the phase associated with pixels that had amplitudes less than 20% of the maximum for a given frame. Previous work found that a 20% cutoff threshold was optimal for minimizing noise [34]. The recovered phase evolution provides a measurement of the strain that takes place anywhere along the fiber up to the corresponding time-gated region. Therefore, measurements with Delay 1 capture strain anywhere from 0 m to 5 m along the fiber and measurements with Delay 2 capture strain anywhere from 0 m to 19 m. The section of fiber between the two time-gated regions (labeled in Fig. 2) is the sensor region. The strain in the sensor region is obtained by subtracting the spatially-averaged time-varying phase of the 5 m time-gated region (Delay 1) from the phase measured with the 19 m time-gated region (Delay 2). Since the region between 0 m and 5 m is common to both the 5 m region and 19 m region, measurements of strain incident on the first 5 m of fiber are suppressed by the subtraction.
Fig. 3 a) Raw unprocessed image recorded on the camera with orthogonal interference fringes from each delay line. b) 2-dimensional FFT of the raw unprocessed image. A red box is shown around the spatial frequencies corresponding to delay 1 and a green box is around the frequencies for delay 2. The recovered amplitude and phase corresponding to delays 1 and 2 are shown in (c)-(f).
There are two important sources of noise, which limit the performance of the sensor: the laser phase and the shot noise. The laser phase noise was measured by constructing a separate interferometer with a free space path mismatch of 3 m corresponding to the average mismatch within the 20 ns pulsewidth. To estimate the shot noise, we first note that the powers of the reference arms are each about 2.5 mW, making them two orders of magnitude larger than the Rayleigh scattered light in the sample arm. Using such strong LOs helped to mitigate the camera read out noise. In this strong LO regime, the shot-noise-limited power spectral density of the instrument depends solely on the power of the backscattered Rayleigh light and can be expressed as [35]:
where, h is Plank’s constant, ν is the optical frequency, m is the mixing efficiency between the sample and local oscillators, fs is the sampling frequency, tC is the collection time, η is the quantum efficiency of the detector, and Ps is the optical power of the Rayleigh backscattered light. The derivation of Eq. (5) is given in the Appendix. The sum of the laser phase noise and the shot noise represents the minimum achievable phase noise for the Φ-OTDR system.3. Sensor characterization
We first confirmed that the multimode fiber-based sensor provides comparable strain sensitivity to a single-mode fiber. For this test, a separate Mach-Zehnder interferometer was constructed with a fiber-wrapped piezoelectric actuator tube (PZT) incorporated into the sample arm of the interferometer. We wrapped one meter of single-mode fiber and one meter of multimode fiber on the same PZT and measured the strain-induced phase change of light transmitted through each fiber. A sinusoidal signal with a root-mean-square (rms) amplitude of 100 mV was applied to the PZT and the recovered phase was recorded for a range of signal frequencies between 0.1 and 9 kHz. Light passing through the single-mode fiber experienced an average response of 5.74 ± 0.07 rad/V while light transmitted through the multimode fiber experienced an average response of 5.52 ± 0.13 rad/V. This measurement confirmed that light in a multimode fiber experiences effectively the same spatially-averaged phase change for a given axial strain as light in a single-mode fiber.
We then confirmed that the multimode fiber Φ-OTDR system was able to detect phase changes generated within the sensor region and suppress signals that originated outside of the sensor region (labeled in Fig. 2). To verify that the instrument behaves as expected, one meter sections of the multimode fiber were wrapped on two PZTs as shown in Fig. 2. Strain applied to the fiber by the PZT was used to simulate the strain induced by an acoustic signal incident on the fiber at that point. The first PZT was located 0.7 m into the multimode fiber (before the first time-gated region) and thus the phase subtraction process described above should remove any phase change introduced by this PZT. Figure 4(a) shows the measured signal from each delay and the signal from the sensor region when PZT1 was driven with a 12 kHz sinusoidal waveform with an amplitude of 10 mVrms. The background subtraction suppresses the signal outside the sensor region by about 10 dB. The second PZT was positioned 10 m into the multimode fiber and should therefore be detected only by the 19 m time-gated region (Delay 2). Figure 4(b) shows the measured signal using each delay and the signal in the sensor region when PZT2 was driven with the same amplitude and frequency as PZT1. As expected, the phase modulation due to the PZT was only observed for the 19 m delay. These results confirm that the Rayleigh sensor was sensitive to signals within the sensor region while signals outside that region were suppressed.
Fig. 4 (a) Signal measured with delay 1 and 2 with PZT1 driven. The subtracted signal suppresses the signal by 10 dB. (b) Signal measured with delay 1 and 2 with PZT2 driven.
To confirm that we are able to extract quantitative strain information from a multimode fiber despite the presence of many modes, we conducted a linearity test. A range of voltages between 3 mVrms and 30 mVrms were applied to PZT2, which corresponds to strains between 1.4 nε and 14 nε. The phase change was recorded at each voltage. Figure 5 shows that there is a linear relationship between the recovered phase and the applied signal magnitude. Measurements of large strains are limited by the slew rate of the interferometer. If the signal introduces a change in the phase of π or greater between two sequential measurements, this will introduce uncertainty in the phase unwrapping algorithm and corrupt the measurement. The slew rate limit has a 1/f dependence so that larger frequencies have a lower threshold [7]. As an example, given the 40 kHz sample rate of our sensor and the sensor sensitivity of 43.5 nε/rad, the maximum detectable strain for a 12 kHz signal is 73 nε. In addition, large strains can introduce spatial mode mixing and lead to a nonlinear sensor response. The R2 value of 0.9997 for the linear regression in Fig. 5 confirms a high level of linearity for strains between 1 and 14 nε at 12 kHz. This result demonstrates that multimode fiber responds linearly to the strain induced in the fiber, enabling quantitative acoustic measurements.
Fig. 5 Measured phase recorded with the multimode fiber Φ-OTDR system as a function of PZT drive voltage. The measurements were made with a 12 kHz sinusoidal signal and show a linear response.
Finally, the phase noise of the sensor was measured and is shown in Fig. 6. In this case, we turned both PZTs off and calculated the power spectral density of the measured phase from each delay and from the sensor region. Note that the sensor region noise is expected to be 3 dB above the individual delay line noise levels as a result of the phase subtraction. At low frequencies (below ~5 kHz) the sensor phase noise was limited by vibrations and acoustic noise in the lab, while at high frequencies we achieved a phase noise of about −80 dB [rel. rad2/Hz]. This phase noise corresponds to a minimum detectable strain of 4.4 pε/Hz1/2. Using the maximum detectable strain given by the slew rate, the overall dynamic range at 12 kHz is 84 dB.
Fig. 6 Phase noise of the multimode fiber Rayleigh acoustic sensor. The phase noise of each delay line is shown on the plot along with the sensor region phase noise. Also shown is the estimated shot noise and the measured laser phase noise, which combine to give the total expected sensor noise.
Also shown in Fig. 6 is the laser phase noise measured with the path mismatched free space interferometer described in section 2 and the shot noise calculated with Eq. (5). For the shot noise calculation the camera was used to measure the backscattered power from the sample arm and the mixing efficiency m was assumed to be unity. The shot noise and laser phase noise combine to yield the total expected sensor noise of −85 dB [rel. rad2/Hz], as shown on the plot. The measured phase noise approaches the expected sensor noise at high frequencies. The slightly higher measured noise could be due to an experimental mixing efficiency of less than 1 as well as the limited extinction ratio of the AOM (~30 dB).
As this analysis indicates, improving the sensor phase noise requires addressing both the laser phase noise and the shot noise. The laser phase noise could be improved either by using a laser with a longer coherence length or by using shorter pulses which would result in a reduced effective path mismatch. Reducing the shot noise level could be achieved by measuring the Rayleigh scattered light in both polarizations, since half the backscattered light was discarded in this initial demonstration. Due to the high threshold for nonlinear effects in multimode fiber, it is also possible to couple higher power into the fiber.
In the work presented here, the sensor was positioned in the first 20 m of the 2 km fiber. This position was chosen to limit the required length of the delay lines in the two reference arms. In principle, the sensor could be positioned much further into the fiber using longer reference arms, but better packaging of the reference arms would be required to avoid environmental noise. In addition, the noise floor of the sensor increases as the sensor is positioned further into the fiber due to attenuation. The effect of attenuation is particularly pronounced with 532 nm light, which was used in this initial demonstration, but the same approach could be extended to operate at 1550 nm where attenuation is lower. We would expect that the noise floor scaling with sensor position would then be similar to current single-mode OTDR systems.
4. Conclusion
In this work, we proposed and demonstrated a multimode fiber based Φ-OTDR system using Rayleigh backscatter to make quantitative acoustic measurements that are immune to signal fading. The system design is based on a Mach-Zehnder interferometer with two delayed reference arms to separately demodulate the back scattered field from a region 5 m and 19 m into the multimode fiber. Off-axis holography was used to retrieve the phase from each region. By computationally differencing the time-varying phase of light backscattered from these two regions, we showed that the sensor can measure phase changes (e.g. due to acoustic signals) in the region between these two positions. In the current design, the sensor location was fixed by the reference arm delays. However, in the future, the delays could be adjusted dynamically to re-position the sensor region and we are currently investigating techniques to enable a distributed multimode fiber based acoustic sensor.
The results reported here showed that the sensor exhibited a high level of performance without complications from mode coupling and without the need to calibrate the sensor. The sensor exhibited a linear response to signals originating within the defined sensor region, while suppressing signals outside of this region. In addition, the sensor achieved a minimum phase noise of −80 dB [rel. rad2/Hz]. For this proof-of-principle demonstration, 532 nm light was used in order to leverage existing camera technology. However, high-speed InGaAs cameras are approaching the necessary frame rates for acoustic measurements and could enable a similar approach at 1550 nm. The high nonlinear thresholds and large scattering capture efficiencies of multimode fiber make multimode OTDR systems an attractive area of research that could enable distributed sensors with even lower noise levels. This work provides the foundation for the future development of high performance multimode fiber Rayleigh sensors.
Appendix
Here we derive the expression for the shot noise limited phase noise power spectral density in the case of two strong local oscillators (LO) of equal power. The generated photocurrent I(t) on one pixel of the camera is:
where ILO and ϕLO are the photocurrent and phase of one of the LOs, Is and ϕs are the photocurrent and phase of the sample arm; ω is the frequency of light and m is the mixing efficiency between the sample arm and the LO. Therefore, the average signal power is:and the average noise power is [35]:where is the electron charge and is the collection bandwidth. Equation (8) assumes that the power of each LO is much greater than the sample arm power, such that the shot noise of the LOs dominate. Each sensor experiences the shot noise generated by the noise power of both the LOs. The shot noise limited variance in the phase is given by:where CNR is the carrier-to-noise ratio. The CNR is defined as the ratio of the average signal power to noise power:Equation (10) can be inserted into Eq. (9) to find the variance of the phase:where we have used the fact that the collection time and that , where η is the quantum efficiency of the detector.In this work we report the phase noise power spectral density, Sϕ,sn(f). Assuming, that the shot noise spectral density is independent of frequency, the variance of the phase noise in terms of the spectral density function is:
where the sample frequency fs accounts for integrating over all frequencies up to the Nyquist frequency of fs/2. Combining Eqs. (11) and (12) yields the shot-noise-limited power spectral density:Funding
U.S. Naval Research Laboratory (6.2 Base Program).
Acknowledgments
The authors thank Clay Kirkendall for many useful and stimulating discussions. Matthew J. Murray thanks the American Society for Engineering Education for support through a research fellowship.
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