1. Introduction

Traditionally, stimulated Brillouin scattering (SBS) based fiber optic sensors have been designed to measure static or slowly varying strain for applications such as structural health monitoring. These sensors operated by measuring and fitting the Brillouin gain spectrum to find the Brillouin frequency shift (BFS) which varies linearly with temperature and strain. This is typically achieved by introducing counter-propagating pump and probe beams to measure the Brillouin interaction at a known frequency offset. The BFS is obtained by repeatedly measuring the Brillouin interaction while tuning the pump or probe frequency. Despite its success, the need to record a large number of measurements while scanning the pump or probe frequencies limited the bandwidth of this approach, particularly in longer fibers [1]. However, interest in using the SBS process to perform high-speed dynamic strain measurements has increased steadily over the last decade and researchers have proposed a number of techniques to increase the speed of SBS based fiber sensors [1–11]. One of the most successful approaches is called slope assisted Brillouin optical time domain analysis (SA-BOTDA) [1,2,5–10]. In this technique, the pump and probe frequencies are fixed so that they interact at the maximum slope of the SBS gain or phase spectrum. The Brillouin frequency shift (BFS) is then measured as a change in the intensity or phase of the probe, providing single-shot measurements of the strain at the cost of reduced dynamic range. Methods have also been developed to extend the dynamic range of these techniques by changing the probe frequency to match the SBS spectrum at each point in the fiber [1,5,10,12] or by using multiple probes [5,9]. Frequency combs have also been employed to measure the entire SBS spectrum in a single shot but with an inherent trade-off between spatial and spectral resolutions [3,11].

An additional obstacle all distributed Brillouin sensors contend with is their sensitivity to non-local signals in which a change in strain in one part of the fiber can impact the strain measured at other positions. For example, pump-depletion can introduce this type of non-local signal since the gain at one position in the fiber will impact the transmitted pump power which subsequently affects the gain measured in the rest of the fiber [13–15]. This non-local mechanism has been addressed through a number of techniques ranging from simply the limiting the probe power [13] to modulating the probe frequency to reduce the effect on the pump [14,16], to continuously replenishing the pump [17–19], or developing alternative measurement techniques with reduced gain dependence [5,8,15]. This host of work has led to the development of distributed Brillouin sensors with unprecedented bandwidth and sensitivity.

In this work, we show that operating at such high frequency exposes these sensors to an additional source of non-local signals resulting from dynamic strain induced Doppler shifts. As light passes through a section of fiber exposed to a time-varying strain, it experiences a time-varying change in the optical path length, analogous to the classic Doppler shift in which a moving body creates a variable optical path length. This Doppler frequency shift breaks the implicit assumption that the frequency difference between the pump and probe beams is known. Brillouin sensors are extremely frequency sensitive and a change in the frequency of the pump or probe has the same impact on the SBS interaction as a change in the BFS. As a result, a localized dynamic strain that changes the frequency of the transmitted probe (or pump) light will create an apparent signal throughout the fiber. This effect is independent of the measurand (e.g. Brillouin gain, loss, or phase) or measurement technique (e.g. Brillouin optical time domain analysis [BOTDA], Brillouin optical correlation domain analysis [BOCDA], dynamic Brillouin gratings, or spontaneous Brillouin scattering [20]), is equally detrimental at all strain levels, and becomes increasingly significant at higher frequencies. Moreover, this effect is not unique to Brillouin based fiber sensors, although its impact will vary depending on the sensing mechanism. For example, a recent work investigated this effect in the context of Rayleigh scattering based optical frequency domain reflectometry (OFDR) systems [21].

Below, we describe the origin of this frequency shift and the mechanism through which it produces a non-local signal in a typical fiber Brillouin sensor. We present an analytic model to describe the relative strength of this non-local signal as a function of the frequency and spatial extent of a strain event. Experimentally, we constructed a slope-assisted BOTDA system to validate this model, confirming that these non-local signals are readily observed. Finally, we present a method to suppress this type of non-local signal in our measurement and experimentally demonstrate high-speed (1 MHz sensing bandwidth in 40 m of fiber), low-noise (2.6 nε/Hz^1/2) measurements with significantly reduced sensitivity to non-local signals.

2. Theory

Brillouin-based strain sensors operate by monitoring strain-induced changes in the BFS [20] . This is typically accomplished by measuring the SBS interaction between a counter-propagating pump and probe with a known frequency separation. Under this assumption, changes in the gain and/or phase of the SBS interaction can be attributed to the local BFS and thus to the local strain. However, a change in the frequency of the pump or the probe will also impact the SBS interaction and this change is generally indistinguishable from a change in the BFS. In this section, we describe how time-varying strain in the fiber under test can introduce a frequency shift, resulting in the appearance of non-local signals throughout the fiber.

A change in the strain over a section of fiber will change the length and the refractive index of the fiber, altering the phase accumulated by light passing through the strained section of fiber. This phase change, Δφ, due to a strain, $\mathrm{\xi }$, over a length, ${L_\varepsilon }$, can be expressed as [22]:

As an example to illustrate how this frequency shift introduces a non-local signal in a typical SBS measurement, we consider a standard BOTDA setup such as the one shown schematically in Fig. 1(a). In this case, a pulsed pump is launched into one end of the fiber under test (FUT) with frequency ${f_{pump}}$ while CW probe light having frequency ${f_{probe}}$ is injected at the opposite end of the fiber. For the purposes of illustration, we can assume the entire fiber is in the same initial state with a BFS equal to ${f_{SBS}}$. We can then define a variable, ${\Delta }f$, to describe the offset between the BFS and the frequency difference between the pump and probe as ${\Delta }f \equiv \; {f_{pump}} - {f_{probe}} - {f_{SBS}}$. This variable describes the offset between the probe and the peak of the Brillouin gain spectrum. The BOTDA sensor extracts ${\Delta }f$ at each position in the fiber by measuring the gain and/or phase of the transmitted probe as a function of time. As long as the frequency offset between the pump and probe is known, the sensor can then recover the local BFS (${f_{SBS}}$) from the measured ${\Delta }f$ at each position in the fiber.

 

Fig. 1. (a) Schematic depiction of a typical Brillouin fiber sensor in the presence of dynamic strain. To the left of the dynamically strained section, the probe has been Doppler shifted by $\Delta {f_{NL}}$ resulting in a non-local change in the measured SBS gain and phase. Similarly, to the right of the strained region, the pump is shifted by $\Delta {f_{NL}}$ also creating a non-local signal. In the strained segment the SBS spectrum is displaced by $\Delta {f_{SBS}}\; $creating a localized change in gain and phase. (b) The normalized magnitude of the non-local Doppler shift vs. frequency for various lengths of fiber under dynamic strain. These are compared to the frequency change due to a local strain using a standard value of 50 kHz/με. This non-local signal presents significant limitations on many practical measurements of interest.

Download Full Size | PDF

However, this assumption breaks down in the presence of a dynamic strain. If we assume a region near the middle of the fiber experiences a time-varying strain, we can divide the fiber into three sections, as shown in Fig. 1(a). In the strained region of fiber, the BFS will change providing the desired local measurement: ${\Delta }f = {\Delta }{f_{SBS}}$. However, the regions to the left and right of the strained section are also sensitive to this strain. At any point to the left of the strained section, the frequency of the transmitted probe light is shifted by ${\Delta }{f_{NL}}$, changing its offset from the peak of the Brillouin spectrum and resulting in a non-local measurement where ${\Delta }f ={-} {\Delta }{f_{NL}}$. At any point to the right of the strained section, the pump frequency is shifted by ${\Delta }{f_{NL}}$ creating the opposite effect on the measurement: ${\Delta }f ={+} {\Delta }{f_{NL}}.$ As a result, a localized dynamic strain event has the potential to produce an apparent signal at all points in the fiber. Moreover, since this non-local signal affects ${\Delta }f$ directly it is independent of both the SBS sensing technique (BOTDA, SA-BOTDA, BOCDA, etc.,) and the measurand (gain, loss, or phase). This effect would also impact spontaneous Brillouin scattering based sensors (e.g. Brillouin optical time domain reflectometry [BOTDR]). However, since these systems operate without a counter-propagating probe beam, the non-local signal would be restricted to positions after a dynamic strain event where the pump frequency is shifted.

The relative strength of this non-local signal depends on the frequency of the dynamic strain event and the length of fiber under strain. To illustrate this dependency, we calculated the non-local frequency shift per unit strain for a sinusoidal strain as a function of the frequency of the strain and the length of fiber under strain, as shown in Fig. 1(b). The local BFS per unit strain of ${\Delta }{f_{SBS}}/ \varepsilon \approx 50\; \textrm{kHz}/\mathrm{\mu \varepsilon }$ is shown as a black dotted line for comparison. This plot shows that the non-local frequency shift becomes significant and can even exceed the signal due to the local BFS at quite practical frequencies and fiber lengths. As an example, a dynamic strain of ∼1 kHz over 10 m of fiber will produce a non-local signal with nearly the same amplitude as the local signal. If the same 1 kHz signal is limited to 1 m of fiber, the non-local signal will be suppressed by a factor of 10, but even this level of cross-talk is unacceptable for many applications. It is therefore critical to consider this source of non-local signals in Brillouin sensors designed to detect high frequency dynamic signals.

While the comparison in Fig. 1(b) focused on sinusoidal strain, this effect can be generalized for an arbitrary, time-varying strain profile as

3. Experiment

To experimentally confirm that a time-varying strain can introduce this type of non-local signal, we chose a standard phase measuring SA-BOTDA architecture (Fig. 2(a)). We followed the technique proposed in [25] which combined a pulsed pump with a CW probe that was phase modulated at a frequency ${f_{RF}}$. After phase modulation, the probe includes three frequency components: the original carrier frequency along with two side-bands separated from the carrier by ${f_{RF}}$ and with a 180° phase difference between them. The probe frequencies were tuned so that only one of the sidebands interacts strongly with the pump. Figure 2(b) shows the optical frequency scheme overlaid with the SBS spectrum. The carrier acts as a local oscillator allowing us to measure the phase of the interacting probe while the non-interacting sideband is used as an amplitude reference. After interacting with the pump in the fiber under test, the transmitted probe light is measured on a photodetector. The detected photocurrent at the phase modulation frequency, ${f_{RF}}$, is [26]:

 

Fig. 2. (a) Schematic of the system used in this work (EOM: electro-optic modulator, PD: photodiode, BPF: tunable band-pass filter, EDFA: erbium doped fiber amplifier, ${\Phi }$-Mod: phase modulator, PZT: 10 m piezo-electric transducer driven fiber strain stage, FUT: fiber under test). (b) The optical frequency scheme used in this section. (c) Spectrogram of the strain power spectral density vs. position. This demonstrates the lack of a localized signal at the PZT₁ drive frequency, 2.4 kHz, and the modest localization at the PZT₂ drive frequency, 300 Hz. The 4 kHz calibration tone is also shown denoting uniform transduction along the length of the fiber. (d-e) Slices of the strain PSD at the two PZT drive frequencies vs. position. Plotted in yellow are the calculated local and non-local signals. (f) The relative phase of the measured strain tones vs. position showing the sign change as the non-local signal changes from a Doppler shift in the pump to one in the probe.

Download Full Size | PDF

where the first term results from interference between the lower sideband and the carrier and the second term results from interference between the upper side-band and the carrier. After IQ demodulation, the measured phase, ${\theta _{meas}}$, is given by:

The strain can then be recovered from the measured phase as:

The experimental setup used to perform this measurement is shown in Fig. 2(a). A low noise seed laser was split into pump and probe arms. The probe was modulated by a Mach-Zehnder intensity modulator at ${f_{SBS}} + {f_{RF}}$ using a microwave signal generator. Additionally, the signal generator was frequency modulated at 4 kHz with a deviation of 100 kHz. This frequency modulation was used to calibrate the frequency-to-phase transduction of the SBS process ($d{\Delta }f/d{\theta _{meas}}$). A tunable bandpass filter then removed the upper sideband produced by the intensity modulator. Finally, the probe was directed to an electro-optic phase modulator that was driven with a modulation amplitude of ${\sim} \pi /5$ radians at 160 MHz. On the pump arm, an intensity modulator produced 40 ns pulses at a repetition rate of 2 MHz. The polarization was controlled to maximize the overlap between the pump and probe throughout the fiber. The FUT included two piezo-electric transducer (PZT) driven fiber stretching stages with 10 m of fiber on each. The fiber on the PZT stages was minimally pre-strained so that ${f_{SBS}}$ was within ±5 MHz throughout the FUT. A separate interferometer was used to calibrate the strain introduced by the PZT stages. The amplified probe was detected and digitized at 1 GS/s and the phase was recovered computationally via IQ demodulation using a low-pass filter with a FWHM of 36 ns, commensurate with our 40 ns pump pulse in order to maintain our spatial resolution. Note that for the purposes of this demonstration, no attempt was made to address polarization fading or the limited dynamic range.

As shown in Fig. 1(b), the relative strength of the non-local signal depends on the frequency of the strain. To highlight this dependence, we chose two representative strain frequencies, driving one of the PZTs with a 2.4 kHz modulation and the other PZT with a 300 Hz modulation. Figure 2(c) shows a spectrogram of the measured strain power spectral density (PSD) vs. position in the fiber. The shaded regions indicate the extent of the two strain stages. Although the strain was applied locally, the signals at 300 Hz and 2.4 kHz are observed throughout the fiber. Moreover, while the 300 Hz signal is strongest at the appropriate PZT₂ position, the 2.4 kHz signal actually appears to be weaker at the PZT₁ position. We also found that the frequency modulated (FM) calibration tone at 4 kHz is visible with nearly constant amplitude throughout the FUT. This confirms that the frequency-to-phase transduction was relatively constant throughout the fiber indicating that the probe was near the center of the Brillouin gain spectrum throughout the fiber. Figures 2(d)–2(e) show cross-sectional slices of the spectrogram vs. position at 2.4 kHz and 300 Hz along with the expected local and non-local signals predicted from Eq. (4) (processed with the same low-pass filter used in the IQ demodulation process). In the case of a 300 Hz signal, the local signal is 10 dB stronger than the non-local signal, in excellent agreement with the predicted values. The non-uniformity across the PZT₂ region is likely due to a non-uniform strain applied across the 10 m of fiber on the strain stage. In the case of a 2.4 kHz strain, the non-local signal is expected to dominate and the measured signal agrees with the predicted non-local signal everywhere except in the PZT₁ region. In the strained region itself, the non-local frequency shift is accumulating as the pump and probe propagate. While the magnitude of the non-local signal should be constant whether the Doppler shift is applied to the pump or the probe (i.e. to the left or right of the strained region), its impact on ${\Delta }f$ is opposite in sign for the two processes. In the center of the strained region, the frequency shift resulting from the Doppler shift in the pump and probe are equal and opposite, resulting in a minima in the measured strain. We can also observe this effect by considering the phase of the strain on either side of the PZT, as shown in Fig. 2(f). As expected, the measured phase undergoes a $\pi $ phase change from one side of the PZT to the other. This measurement confirms the model outlined in Section 2 and indicates that even in the regime where the non-local signal is weaker than the local, it can still introduce deleterious cross-talk.

Next, we introduce a technique to suppress this type of non-local signal by simultaneously probing both the Brillouin gain and absorption spectra. SBS measurements using both the amplification and attenuation effects have been previously employed [18,19,27] to enable baseband detection or suppress non-local signals due to pump depletion. Here, we show that incorporating both interactions allows us to differentiate between the local and non-local signals. The proposed frequency scheme is illustrated in Figs. 3(a)–3(c) which shows the overlap between a gain probe and a loss probe with the Brillouin gain and absorption spectra, respectively. In the first panel (Fig. 3(a)), the probe is frequency shifted due to a non-local dynamic strain event. In this scheme both the gain probe and loss probe will shift in the same direction.

 

Fig. 3. (a-c) Dual probe optical frequency scheme used to suppress the non-local Doppler shift. Doppler shifts in the pump or probe create opposite changes in the offset of the gain and loss probes from the SBS absorption and gain spectra. In contrast, shifts in the SBS frequency have the same effect on the offset of the gain and loss probes from the absorption and gain spectra. (d) The optical frequency scheme used in this section. (e) Spectrogram of the strain power spectral density vs. position. The non-local Doppler shift is suppressed allowing signal localization. (f-g) Slices of the strain PSD at the two PZT drive frequencies vs. position showing clear localization of the signal. The measured values agree well with the calculated local and non-local signals.

Download Full Size | PDF

Crucially, these frequency shifts result in opposite changes in the Brillouin phase, as indicated by the probe positions on the purple SBS phase curve drawn in Fig. 3(a). In contrast, if the BFS itself is changed due to a local strain, as shown in Fig. 3(b), the gain and loss probes will experience the same phase shift. Finally, if the pump is shifted as shown in Fig. 3(c), the gain and loss probes again experience opposite Brillouin phase shifts. Thus, a detection scheme that sums the SBS phase accumulated by the gain and loss sidebands will remain sensitive to a local BFS, while the SBS phases induced by a non-local frequency shift of either the pump or probe will have opposite sign and tend to cancel each other out. As a more quantitative analysis, we can express the frequency offsets between the gain and absorption probes and the Brillouin gain and absorption spectra as:

Fortunately, a slight modification to the phase measuring SA-BOTDA system presented previously can accomplish this. Specifically, we introduced an additional set of three probe lines, as shown in Fig. 3(d), shifted so that one of these probes is centered on the Brillouin absorption spectra. Experimentally, this was achieved by opening the tunable bandpass filter shown in Fig. 2(a) to transmit both the upper and lower sidebands produced by the intensity modulator. The gain and absorption probes were then directed to the phase modulator which added a pair of sidebands to each probe. After interaction with the pump in the FUT, the combined probe consisting of three absorption-side lines and three gain-side lines was detected, producing four interference signals at ${f_{RF}}$ in the electrical domain:

In order to confirm this prediction, we performed strain measurements using this updated experimental setup with probes aligned to both the Brillouin gain and absorption spectra. The gain for these measurements was set to ∼12% reducing the expected sensitivity to non-local signals by ∼18 dB. A spectrogram of the measured strain PSD vs. position is shown in Fig. 3(e), recorded while the PZT stages were driven at 2.4 kHz and 300 Hz, respectively. The strain localization is dramatically improved compared with the measurement reported in Fig. 2(e). Cross-sectional plots at the two PZT frequencies are shown in Figs. 3(f)–3(g) along with the calculated local and non-local signals from Eqs. (4) and (10) (without using the approximation). In Fig. 3(f), the strain at 2.4 kHz shows clear localization, in sharp contrast to the measurement shown in Fig. 2(d). In Fig. 3(g), the non-local signal at 300 Hz is no longer observed, having been suppressed below the noise level of this measurement. In both cases, the measured result agrees well with the predictions.

 

Fig. 4. (a) Measured phase PSD vs position for 2.4 kHz and 1.1 kHz PZT drive frequencies for various levels of gain. As the gain increases the suppression of the non-local Doppler shift diminishes. (b) Measured and calculated values of phase per unit με for either local or non-local signals shown for three drive frequencies (2.4 kHz, 1.1 kHz, 300 Hz).

Download Full Size | PDF

To further illustrate the ability of this technique to suppress non-local signals, we recorded a series of strain measurements as a function of pump power in order to vary the gain and absorption. Based on Eq. (10), we expect the non-local signals to be more pronounced at higher pump power (as ${G_{SBS}}$ increases). Figures 4(a)–4(b) show cross-sectional plots of the measured phase PSD at two different PZT drive frequencies (1100 and 2400 Hz respectively) vs. position for var${G_{SBS}})$ious levels of gain (${G_{SBS}}$). As expected, the non-local signal increases with probe amplification/attenuation, even exceeding the local signal at sufficiently high gain in the case of a 2.4 kHz signal. This effect is summarized in Fig. 4(c) which shows the calculated (lines) and measured (symbols) local and non-local response in units of mrad/με. This transduction coefficient describes the measured phase (${\theta _{meas}}$ in Eq. (10)) per unit strain. The calculations used a value of 55 MHz for ${{\Gamma }_{SBS}}$, calculated from the FM calibration tone, and standard material values to derive a gain coefficient of ${g_B} =$ $0.54\; \; {\textrm{W}^{ - 1}}{\textrm{m}^{ - 1}}$. The local SBS transduction is independent of gain until ${G_{SBS}}$ approaches ∼1, at which point the small gain approximation breaks down. In contrast, the non-local signal transduction coefficient increases linearly with ${G_{SBS}}$. The measured data agrees well with the predicted values over the entire range of gain and strain frequency. The slight deviation between the measured local signal and the calculated values at high gain and high frequency is due to the competition between the local and non-local signal transduction mechanisms.

In addition to suppressing non-local signals due to a time-varying strain, this architecture is fully compatible with low-noise, high bandwidth distributed strain sensing. The sensor bandwidth is only limited by the round trip time in the fiber. In this study, the fiber length was 40 m and the pulse repetition frequency was set at 2 MHz, providing a sensor bandwidth of 1 MHz. The strain noise is shown in Fig. 5, indicating a minimum detectable strain of 2.6 nε/Hz^1/2 (2.6 με rms per measurement acquired at a 1 MHz sampling rate without averaging). Although the dynamic range is limited to ∼1200 µε in the current implementation (i.e.$\; {{\Gamma }_{SBS}} \cdot d\varepsilon /d{\Delta }f$), this could be increased by tuning the probe frequency to track the BFS at different positions in the fiber following the technique presented in [4]. In addition, introducing the frequency modulation shown in Fig. 2(a) provides a form of in-situ calibration, which could be used as a feedback to track the BFS as a function of position in the FUT. Finally, since this technique suppresses the effect of a frequency change to the pump or probe, it also reduces the dependence on laser frequency noise, which could help enable low noise strain sensing over long distances. In fact, the noise measured here (2.6 nε/Hz^1/2) compares very favorably with other low noise dynamic Brillouin measurements with important caveats related to the short fiber (40 m) and a relatively long pulse (4 m) used here. For instance Bergman et al., reported 10 nε/Hz^1/2 in ∼5 m of PM fiber with a 20 cm resolution and a 1 MHz sampling rate using a phase coded dynamic Brillouin grating configuration [28]. Peled et al., reported ∼220 nε/Hz^1/2 (∼5 με rms sampled at ∼10 kHz with 10 averages) in 100 m of fiber with 1 m resolution [1]. Yang et al., reported ∼235 nε/Hz^1/2 (5.26 με rms sampled at 250 kHz with 250 averages) in 400 m of single mode fiber with 2.5 m resolution in an enhanced dynamic range measurement [29].

 

Fig. 5. The measured strain noise using the dual probe technique described above. The average strain noise is 2.6 $\textrm{n}\mathrm{\varepsilon }/\textrm{H}{\textrm{z}^{1/2}}$. The higher noise at low frequencies is environmental and the 4 kHz calibration signal is indicated.

Download Full Size | PDF

4. Conclusions

We presented a new mechanism that can produce non-local signals in Brillouin fiber sensors in the presence of dynamic strain. We then presented a model describing how a time-varying strain induced Doppler shift introduces a non-local signal in a typical Brillouin fiber sensor and analyzed the operating regimes where this type of non-local signal becomes significant. We then experimentally confirmed the predicted non-local signal strength using a phase-measuring SA-BOTDA system. Finally, we introduced an approach to mitigate this type of non-local signal by simultaneously probing both the Brillouin gain and absorption spectra and investigated the limitations of this approach. Using this new architecture, we experimentally demonstrated low-noise dynamic strain sensing with significantly reduced sensitivity to non-local signals. The sensor achieved a minimum detectable strain of 2.6 $n\varepsilon /H{z^{1/2}}$ and a bandwidth of 1 MHz.