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Abstract
We introduce a coherent-MIMO Δϕ-OTDR based sensing technique that uses digital frequency division multiplexing of probing codes in order to mitigate the coherent fading issue in Δϕ-OTDR. Orthogonal frequency division multiplexing (OFDM) is used to probe the optical channel on several electrical subcarriers, and their responses are then combined according to specific reliability criterion to enhance the overall sensing sensitivity. This allows for a decrease of the noise floor in sensing measurements on standard single mode fiber (SSMF) and the mitigation of false alarms. Coherent MIMO-OFDM enables sensing over telecom fibers with a measured sensitivity level below $21\mathrm {p\varepsilon /\sqrt {Hz}}$ along 1.3km fiber over a mechanical bandwidth of 760Hz. Enhancements in the dynamic range for detection of mechanical excitation are presented with a gain over 18dB as compared to single-carrier probing.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Distributed optical fiber sensors (DOFS) are able to perform strain measurements on long distance as well as with very precise gauge length [1], therefore they are of interest in a growing number of fields, from the biomedical domain [2] to oil and gas industry [3] or smart-city applications [4]. In particular, differential phase-sensitive optical time-domain reflectometry ($\Delta \phi$-OTDR) is a powerful technique for detection, localization and identification of events of all scales, based on Rayleigh backscaterred light. $\Delta \phi$-OTDR can be performed on top of any kind of optical fiber, including deployed telecom cables. Generally, highly coherent laser sources are used to probe the sensor, together with coherent detection at the reception to retrieve the phase information.
Coherent phase-sensitive OTDR sensors are subject to three main impairments: polarization fading, coherent fading, and laser phase noise. The latter issue depends on the laser properties and specific methods were developed [5,6] that are not further addressed here. Polarization fading is due to polarization misalignment at the transmitter and receiver, and it is addressed mainly by polarization diversity methods [7,8], or can be solved by Coherent-MIMO sensing which consists in using polarization diversity both at the transmitter and at the receiver [9,10]. On the other hand, coherent fading is inherent to coherent $\phi$-OTDR and $\Delta \phi$-OTDR since the technique relies on the speckle pattern resulting from the interrogation of the fiber using a highly coherent source [11]. As a main drawback, the sensitivity randomly fluctuates along the fiber sensor and in time. This impairment is also referred to as Rayleigh fading, interference fading, signal fading, fading noise or speckle noise, as it exists in various fields of application. In the following, we keep the appellation "coherent fading". The impact of coherent fading can be limited either thanks to trace averaging [12] at a cost of reduced mechanical sensing bandwidth, or by the use of wavelength- and frequency-diversity methods. Wavelength-diversity methods rely on the independence that exists between the Rayleigh patterns of the same optical fiber that is interrogated at different wavelengths [13] with a $50$GHz wavelength spacing, thus requiring multiplexing and demultiplexing several optical carriers at the transmitter and receiver. Frequency-diversity methods require smaller spacing, around hundreds of MHz [14–16]. There are two main types of frequency-diversity interrogation: multiple pulses with different carriers sent to probe the fiber sensor [17]; single pulses with frequency chirping (linear frequency modulation, LFM) [18], from which the channel response of the fiber sensor is recovered by correlation at the receiver side. In $\phi$-OTDR, the introduction of a chirped pulse method can also allow to perform quantitative strain measurement [19] based on the amplitude of $\phi$-OTDR traces, thus avoiding some of the phase-related impairments. Recent works push forward the sensor optimization as they use a series of frequency-shifted interrogation pulses by combining frequency and polarization multiplexing in $\phi$-OTDR [20,21], thus injecting more individual pulses that would be allowed by the round-trip time of light in the fiber sensor and increasing the spectral occupancy without any impact on the probing duration. The associated optical setups may be complex which make them difficult to deploy for field tests outside the laboratories [22]. Instead, we choose here to tackle coherent fading by exploiting the Rayleigh phase pattern diversity. Our approach involves fully digital Orthogonal Frequency Division Multiplexing (OFDM) of probing codes to achieve carrier phase diversity, allowing for coherent fading mitigation while keeping a simple optical setup. First experimental results were displayed in [23].
The paper is organized as follows. In section 2., we remind the basic principles of coherent $\Delta \phi$-OTDR, the reasons for Rayleigh fading and its impact on sensing accuracy. Then, the novel carrier phase diversity channel estimation method used in this study is presented in section 3.. The method for mitigation of coherent fading is given in section 4.. Finally, section 5. provides an experimental validation of the study.
2. Coded coherent $\Delta \phi$-OTDR
2.1 Rayleigh backscattering and coherent fading
Distributed fiber sensing involves processing of the backscattered light from a probed optical fiber. The sensing signal is a summation of the contributions of the backscattered light from the probing signal $E_{in}$ all along the fiber sensor. Therefore, when $E_{in}$ consists of a rectangular pulse with an amplitude $E_0$ and a duration $T_S$, the complex optical field at the receiver side $E_{rx}$ can be expressed as:
Each $A_m e^{j\phi _m}$ term in 1 results from the sum of elementary contributions within the $m^{\mathrm {th}}$ segment:
where $N_{scat}$ is the number of elementary scatterers within segment $m$. Each scatterer is located at a distance $z_i$ from the fiber start, as displayed in Fig. 1, backscatters an amplitude $a(z_i)$ and rotates the phase of incident light by $\varphi (z_i)$. The model can be extended to a vector-format (for dual-polarization) using the Jones formalism, where the backscattered phase and amplitude are distributed over a $2\times 2$ Jones matrix $\mathbf {H}_m$ describing the evolution of the state of polarization (SOP) of the transmitted probe [10], as depicted in Fig. 1.
Fig. 1. Backscattering model: $M$ segments with $N_{scat}$ scatterers within each segment. $\mathbf {H}_m$ is the $2\times 2$ Jones matrix describing the SOP evolution up to segment $m$.
$\phi$-OTDR and $\Delta \phi$-OTDR techniques rely on the change of interference figure $E_{rx}$ when a vibration occurs. This effect allows to precisely retrieve the phase variation induced by the strain or vibration applied to the fiber. However, coherent fading happens when the summations in 2 interfere destructively, resulting in $A_m e^{j \phi _m} \rightarrow 0$ locally. Also, coherent fading occurrences are independent of the probing method used for interrogating the fiber sensor.
2.2 Coded interrogation
The choice of the probe signal for a fiber sensor depends on the system requirements such as the maximum length of the probed fiber, the spatial resolution and the desired mechanical bandwidth.
Single light pulses or pulse trains are the most common probe techniques and they allow to directly capture the backscattered response of the fiber sensor [25] ; spatial resolution is tuned by adjusting the pulse width $T_S$. We denote the spatial resolution as $L_S=cT_S/2n_g$. The covered mechanical bandwidth $B_{meca}$ is determined by the pulse repetition rate. However, there is a trade-off between signal to noise ratio in the longer distances and spatial resolution (when increasing the pulse temporal width) or non-linearity (when increasing the peak power). Frequency sweep [26] or multiple-frequency interrogation [20], linear frequency modulation [27], as well as coded interrogation [8,9,28] address this issue by spreading the probe power in time; a narrow temporal pulse is recovered by correlation at the receiver. Coded interrogation is especially interesting as it is digitally generated thus robust to frequency distortion effects [26], and with low Peak-to-Average Power Ratio (PAPR), thus very much suited for coexistence with telecommunication data, when applied over lit fibers. With a probing code of length $T_{code}$, the achieved mechanical bandwidth is $B_{meca}=1/2T_{code}$.
Coherent-MIMO [9,10] was proposed in that respect, with a multiple-input multiple-output (MIMO) approach through polarization multiplexing at the transmitter and polarization-diversity detection at the receiver side. It allows to retrieve not only the phase and amplitude along the fiber sensor but also the evolution of the backscattered state of polarization in the form of $2\times 2$ Jones matrices $\textbf {H}_{t,d}$ (where $t$ is the slow time index and $d$ distance index (fast time)). This probing technique was proven to fully solve the polarization fading issue [10]. The probing codes consist of two mutually orthogonal complementary pairs $\{G_{a1}, G_{b1}\}$ and $\{G_{a2}, G_{b2}\}$ derived from Golay codes, mapped to binary-phase-shift-keying (BPSK) symbols that jointly and continuously modulate two orthogonal polarization states of a narrow-linewidth laser source [9]. Figure 2 depicts the general scheme of Coherent-MIMO interrogation.
Fig. 2. Pol.: polarization, MZM: Mach Zehnder Modulator, LO: Local Oscillator, DSP: Digital Signal Processing. $T_S$: symbol duration, $T_{code}$: probing code duration.
Yet, any $\Delta \phi$-OTDR probing technique is still subject to coherent fading issues as described in subsection 2.1, whatever fine resolution, probing bandwidth are chosen. Hence, coherent fading mitigation without damage to the phase information is needed. The most interesting method yet is to use multiple uncorrelated channels to probe the line: the channels being either frequency channels [14] or different modes of an optical fiber [29], which in both cases will make the most of uncorrelated backscattered amplitudes and phases per channel. Therefore, we will adapt the Coherent-MIMO probing technique to solve the coherent fading issue.
3. Channel estimation scheme to mitigate coherent fading
An electrical bandwidth $B_{elec}$ around $100$MHz, fixed by the symbol rate $f_{Symb}$ and the pulse shaping, is usually used to sense a fiber. Over such a narrow bandwidth, the elementary scatterers have a flat amplitude spectrum response, and wavelength diversity cannot be achieved. However, to reach statistically independent intensity fading, the fiber should be probed with signals separated by $\Delta f \geq f_{Symb}$ [14,16,30] where $f_{Symb} = 1/T_S$. Therefore, we introduce an orthogonal frequency division multiplexing (OFDM) scheme to independently probe the line over several orthogonal subcarriers, verifying $\Delta f = f_{Symb}$ inside the electrical bandwidth $B_{elec}$.
The dual-polarization codes $\mathbf {E}_{in} = [\begin {smallmatrix} E_x \\ E_y \end {smallmatrix}]$ of length $N_{code}$ symbols for single-carrier Coherent-MIMO sensing are mapped onto $N_{sc}$ subcarriers. Figure 3 shows a simple example for one polarization axis and two subcarriers, $N_{sc}=2$. The subcarriers carry the same code $\{G_{a1}, G_{b1}\}$ for $N_{code}=8$. For sake of simplicity, we limit our study in this paper to the case where all $N_{sc}$ subcarriers enclose the same code as we introduce this digital frequency multiplexing technique for the first time in a $\Delta \phi$-OTDR scheme. The OFDM signal is created by serial-to-parallel, inverse fast Fourier transform (iFFT), and parallel-to-serial operations. No cyclic prefix is required as temporal spread induced by chromatic dispersion is too small compared to the symbol rate.
The OFDM code alphabet is limited here to $\{-1,0,1\}$, and the symbol rate of the OFDM flow combining $N_{sc}$ subcarriers is equal to $f_{symb, OFDM} = N_{sc}\times f_{symb}$, thus expanding the electrical bandwidth when the symbol rate is left unchanged. Note that this is a simplified case of OFDM interrogation where all probing subcarriers carry the same code. To better motivate the use of OFDM interrogation, other schemes could be proposed, where different codes could be loaded onto different subcarriers. This would still allow to probe a fiber sensor with orthogonal subcarriers, only with a more complex OFDM alphabet at the modulator side. In such various configurations, different codes with possibly different lengths may modulate the subcarriers. This would achieve other types of diversity, eg. in terms of mechanical bandwidth. In that particular configuration using the same code over the $N_{sc}$ subcarriers, the OFDM interrogation amounts to performing an interrogation of the fiber sensor with a $N_{sc}$-fold expanded version of the original code (done by inserting $N_{sc}-1$ zeros between symbols). Such a configuration maximizes the PAPR of the interrogation signal compared with other generic OFDM implementations, since the mean input power is kept constant and therefore it will end up being concentrated into the non-zero symbols. Yet, such PAPR is still negligible compared with pulsed interrogation as the power is still spread in time over multiple (OFDM) symbols, thus limiting any nonlinearity-related issues. Furthermore, the OFDM formalism is especially suitable for the linear combination of the backscattered signals at the receiver side through the demultiplexing of the carriers by means of an FFT operation.
Our purpose is to compare the sensing performances of the OFDM probing scheme with our single carrier reference case. For sake of fairness, the comparison is applied over the same bandwidth $B_{elec}$, which is achieved by mapping subcarriers with codes shorter by a factor of $N_{sc}$ compared with the single carrier case. In such a way, the code duration $T_{code}$ is left unchanged and so is the sensed mechanical bandwidth $B_{meca}$. Finally, the OFDM setup extension allows to perform $N_{sc}$ channel estimations at the sole cost of a spatial resolution reduction by a factor of $N_{sc}$ compared with the single-carrier coherent-MIMO case and with constant $B_{elec}$. The obtained estimations of Jones matrices are here again mathematically perfect [9], the overall spectral occupancy of the modulation is preserved and the mechanical bandwidth of the analysis also. The next step aims at combining the subcarrier estimations to minimize the Rayleigh fading effect.
4. Digital carrier phase diversity combining for coherent fading reduction
The subcarrier information is constructively combined in phase, independently at each fiber segment, by means of independent rotations at each subcarrier. This technique, known as "Rotated Vector Sum" was successfully used in [18] for combining phase estimates from independent optical channels, bringing a substantial SNR increase compared to a single channel sensing scheme.
4.1 Constructive combination
MIMO-OFDM interrogation yields Jones matrices responses for each time instant $t$, segment at distance $d$ and subcarrier index $n$: $\textbf {H}_{t,d,n}$. The backscattered SOP (b-SOP, evolution of the energy on the four terms of the Jones matrix) is common to all subcarriers at any time and distance, thus it is not involved in the combination of subcarrier information. However, the intensity of the backscattered field from some subcarriers within the sensing signal is potentially degraded in practice because of coherent fading, in which case the most accurate b-SOP is the one yielding the highest backscattered intensity among all subcarriers.
The independent phase and amplitude information is therefore enclosed in the sole Jones matrices determinants $\det ( \textbf {H}_{t,d,n})$ from which the local cumulated phase is extracted as $\phi _{t,d,n} = \frac {1}{2} \angle {\det ( \textbf {H}_{t,d,n})}$, and the reliability metric derived from the backscattered intensity as $R_{t,d,n} = |\det ( \textbf {H}_{t,d,n})|$ [31]. Consequently, we choose to constructively combine the subcarriers responses from their respective Jones matrix determinants $\det ( \textbf {H}_{t,d,n})$.
The rotated-vector-sum combination method is applied to the $D_{t,d,n} = \det ( \textbf {H}_{t,d,n})$ vectors, so as to maximize the combined modulus [18]. For a given segment index $d$, the time-average of phase $\overline {\phi }_{d,n}$ is derived for each subcarrier $n$ and subtracted from the phase of all $D_{t,d,n}$, such that the resulting combined determinants are:
The final differential phase between adjacent segments is obtained by subtracting the phases of adjacent $D_{t,d,combined}$, such that $\Delta \phi _{t,d,combined} = \frac {1}{2} (\angle {D_{t,d,combined}}-\angle {D_{t,d-1,combined}})$. The operation in 3 consists in removing the average cumulated phase values $\overline {\phi }_{d,n}$ and keeping the sole variations of the cumulated phase in time, per segment, since the relevant information is enclosed in the differential phases eventually. On the one hand, if the fiber segment is static (no mechanical perturbation), then the random variations of phase around the $\overline {\phi }_{d,n}$ are independent and they will fade after combination. On the other hand, if the fiber segment is mechanically excited, then all subcarriers are affected the same way such that their oscillations around the phase references $\overline {\phi }_{d,n}$ align, so magnifying the overall captured excitation. Moreover, we recently demonstrated in [31] that $|D_{t,d,n}|$ is not only the most accurate intensity estimator in MIMO sensing up to our knowledge but also a reliability criterion that informs about the ability to extract a fair phase estimation from any Jones matrix. Therefore, the combination in 3 is naturally weighted by the reliability metric $R_{t,d,n}$, hence a lower influence of the unreliable estimations on the final result.4.2 Individual carriers versus their combination: simulation
To detect mechanical events along the sensor, the differential phase standard deviation (denoted $\sigma _\varphi$, expressed in radians) is monitored along distance: theoretically zero-valued in absence of events, and non-zero positive in case of any detected disturbance. The $\sigma _\varphi$ from static measurements indicates the threshold value or sensitivity level below which an event cannot be detected. Also, the normalized reliability metric $R_{t,d,n}/\underset {t,d,n}{\max }(R_{t,d,n})$ gives a priori information on the soundness of the estimation [31]. Its minimum value in time per segment index $d$ gives an indication on the probability to get local unstable phases estimations giving rise to false alarms.
We simulate a 4-subcarrier OFDM interrogation of a static $1$km long single mode fiber (SMF), with laser noise $\Delta \nu = 75$Hz and additive gaussian white noise (AWGN) at the receiver (shot noise and thermal noise), we set $B_{meca}=760$Hz and $B_{elec}=50$MHz. The fiber is kept short such that the attenuation with distance does not participate to the fading effect, thus focusing the study on the sole coherent fading effect. Every separate subcarrier is monitored, alongside with the subcarrier combination. Figure 4 illustrates the enhancement brought by an OFDM interrogation.
Fig. 4. Simulation OFDM4, 1km SMF, $\Delta \nu = 75$Hz, AWGN at the receiver, individual subcarrier responses compared with combined response
Figure 4(a) gives the minimum reliability metric per segment versus distance, and shows that the reliability increases after subcarrier combination compared with individual subcarriers where it locally dives towards $0$. In other words, the worst case points are avoided. Figure 4(b) shows $\sigma _\varphi$ along distance, giving the noise floor above which a mechanical event can be detected. The combined measurement presents a noise floor below $0.01$rad all along the $1$km fiber, which is locally up to 7 times lower than the level given by a single subcarrier (subcarrier 3, around $850$m).
Notice that the combined $\sigma _\varphi$ in Fig. 4(b) reaches values that are even lower than the lowest $\sigma _\varphi$ per subcarrier at several locations ($300$m, $500$m, $880$m). This shows that in addition to avoiding the worst-case sensitivity situations, the OFDM combination scheme performs an averaging on the system noise and thus significantly enhances the overall sensitivity.
4.3 Impact of noises and OFDM contribution
The sensitivity gain brought by the OFDM approach is first quantified by simulation: the interrogations of a static, 1km-long SMF are simulated. Single-carrier, OFDM with 2 subcarriers and OFDM with 4 subcarriers interrogations are performed. The mechanical bandwidth is fixed to $B_{meca} = 760$Hz for all of the following measurements and simulations. We introduce two metrics to help fairly compare the sensing performance as a function of the number of subcarriers. $\mathrm {Intensity}_{dB}$ and SNR$_{\varepsilon,dB}$ are derived as follows:
A case with constant $B_{elec} = 50$MHz is considered, in which the spatial resolution decreases with the number of OFDM carriers according to $S_r = \{2.05\mathrm {m}, 4.10\mathrm {m}, 8.20\mathrm {m}\}$ for single-carrier, OFDM2 and OFDM4 respectively. The laser used for the following experimental measurements (section 5.) has an estimated linewidth of $\Delta \nu = 75$Hz over ms-range observation windows [33]. In the simulation, its phase noise is modeled as a Wiener process of variance $\sigma ^2 = 2\pi \Delta \nu T_S$ where $\Delta \nu$ is the Lorentzian laser linewidth and $T_S$ the duration of a symbol in the probing code. Fig. 5 displays the simulation results for intensity and strain sensitivity in presence of AWGN and laser phase noise. The observed probability density functions in Fig. 5 verify a tightening of the distributions as the number of subcarriers increases. Particularly, a decrease of the lower SNR values of the distribution is noticed thanks to OFDM, meaning that there are less low-energy and low-reliability fiber segments which are the most likely to trigger false alarms.
Fig. 5. SNR probability density distributions. 1km static simulation, laser phase noise $\Delta \nu = 75$Hz, AWGN at the receiver. $\mathrm {SNR}_{\varepsilon }=0$dB corresponds to $1\mathrm {n}\epsilon$ strain sensitivity.
That is, the use of phase diversity through OFDM with an adapted number of subcarriers decreases the low SNR$_{\varepsilon,dB}$ occurrences, thus improving the SNR$_{\varepsilon,dB}$ by almost $20$dB with 4 subcarriers (Fig. 5(b)).
Note that although a higher number of subcarriers can be used for channel interrogation, the sensitivity gain tends to decrease after a certain number of carriers, under the fixed constraints of equivalent electrical and mechanical bandwidths. Figure 6 shows the evolution of the SNR$_{\varepsilon,dB}$ probability density function when the number of subcarriers increases in the particular case of $B_{elec}=50$MHz on a 1km simulated distance. After interrogation on 4 subcarriers, an increase of carriers does not bring a significant sensitivity gain (lower mean sensitivity in Fig. 6(b) with 8 subcarriers); this is due to the use of a decreasing code order (smaller $N_{code}$) when increasing the number of subcarriers, which results in a lower achieved SNR [9].
Fig. 6. SNR$_{\varepsilon,dB}$ on 1km, for 1 to 16 subcarriers, simulation with 5000 points per interrogation method, $\Delta \nu = 75$Hz and AWGN noise at the receiver
5. Experimental measurements
The interrogating setup presented in Fig. 7 is based on our previous MIMO interrogation setup [33]: the probing codes are sent onto two orthogonal polarization axes through a dual-polarization $25$GHz I/Q Mach-Zehnder modulator to modulate the optical wavelength. Although Fig. 7 shows the general I/Q configuration, we restrict ourselves to a BPSK modulation per polarization in this work, as described previously in subsection 2.2.
OFDM sensing is introduced by inserting additional signal processing blocks before and after the optical setup, namely a MIMO-OFDM coding block at the probing codes generation stage performing iFFT (inverse fast Fourier transform) on parallel probing codes, and a MIMO-OFDM decoding block after coherent reception and analog-to-digital conversion to perform FFT on the OFDM coded subcarriers, before correlation and combination for fading mitigation. The core optical setup of the interrogator is thus left unchanged.
Fig. 7. OFDM-MIMO interrogation setup. MIMO: Multiple-Input/Multiple-Output, OFDM: Orthogonal Frequency Division Multiplexing, LO: Local Oscillator, ADC: Analog-to-Digital Converter, PZT: PiezoElectric Transducer
5.1 Static experiments
The experiments are first conducted in static mode, in laboratory conditions, in an acoustically insulated environment. The block described as "telecom cable under test" in Fig. 7 consists in a $1300$m long single mode fiber (SSMF) made of the junction of a $400$m SSMF spool with an other $900$m fiber spool. Similarly to the simulations in subsection 4.3, a configuration with $B_{elec} = 50$MHz is considered. The mechanical bandwidth is also kept at $B_{meca} = 760$Hz, and the frequencies below $60$Hz are filtered out to avoid capturing residual acoustic and electric noise from the lab.
The measurements are successively single-carrier, OFDM2 and OFDM4 2-second interrogations of the same fiber with $f_{Symb}=50$MHz, yielding spatial resolutions of $2.05$m, $4.10$m and $8.20$m respectively. The lengths of the probing code are $N_{code} = 32768$ symbols for single carrier interrogation, $N_{code} = N_{code,single}/N_{SC}$ for OFDM interrogations, such that $T_{code}=655\mu s$ yielding the $B_{meca} = 760$Hz mechanical bandwidth in all three cases.
The performance of these interrogations is displayed in Fig. 8. In Fig. 8(a), we show the obtained intensity distributions. Note that the mean value of each distribution depends on the normalization at the receiver after analog to digital conversion, hence a different mean value from one measurement to another. The main observation here is the shrinking of the distributions as the number of subcarriers increases. The distributions of SNR$_{\varepsilon,dB}$ values in Fig. 8(b) behave as predicted in Fig. 5(b) as the distribution shrinks when increasing the subcarriers number. The worst case SNR$_{\varepsilon,dB}$ improves by over $11$dB when comparing single-carrier interrogation to OFDM4, yielding a minimal SNR$_{\varepsilon,dB}=4.61$ which corresponds to a $\sigma _\varepsilon =0.59$n$\epsilon$ strain within $B_{meca} = 760$Hz and therefore $21$p$\varepsilon /\sqrt {Hz}$ strain density sensitivity floor.
Fig. 8. Static experimental trace, OFDM interrogation of 1.3km SSMF, constant $B_{elec}=50$MHz configuration
Thanks to subcarrier combination, the measured estimations of the fiber segments from Rayleigh-backscattered probing codes are more reliable, thus increasing the overall performance of intensity and phase estimations. Such a reduction of the noise floor (minimal SNR$_{\varepsilon,dB}$ values) is expected to decrease false alarm occurrences, together with an increase of the detection capabilities of the system in dynamic configurations.
5.2 Dynamic multicarrier sensing
A piezoelectric actuator is added to the fiber under test in the previously described laboratory configuration: $3.1$m of SSMF is wrapped around the actuator and connected between the $400$m an the $900$m fiber spools. The actuator is driven by a $440$Hz, $2$Vpp sine wave signal. Each measurement lasts for $2$ seconds similarly to the previous static interrogations.
Fig. 9 displays the experimental results for a constant $B_{elec}$ configuration: Fig. 9(a) predicts the reliability of the measurement along the fiber. The lower the minimal reliability values are, the higher the false alarm probability. Indeed, the low value at $1.14$km in Fig. 9(a) deserves some attention, as it translates into a false alarm in Fig. 9(b). Figure 9(b) shows the measured strain $\varepsilon$ in nm/m (or n$\epsilon$) along the fiber, used as the detection figure of mechanical events. The three compared measurements exhibit a significant peak around $420$m where the dynamic strain is applied, as expected. Also, the detection peak has a better dynamic range (defined as the ratio between false alarm level, namely highest peak in non-excited zones, and detection peak level) when the number of subcarriers increases, as the level of phase noise (false alarms) decreases thus gaining $3.67$n$\epsilon$ strain sensitivity in Fig. 9(b) between single carrier and OFDM4 cases thanks to OFDM coding and subcarrier combination. Figure 9(c) gives the optical phase measurement around the excitation detection in the frequency domain. Similarly to the detection stage, the identification gets better when the number of OFDM subcarriers increases, as the noise level on Fig. 9(c) shrinks by $15$dB between single-band interrogation and OFDM4. Therefore, taking both the noise level reduction and the peak level value in Fig. 9(c), the power spectral density dynamic is $18.4$dB higher in OFDM4 than in single-band interrogation, for a similar excitation level from the piezoelectric actuator.
Fig. 9. Interrogation of 1.3km SSMF excited by $440$Hz piezoelectric actuator at $420$m, 2 seconds measurement. Constant $B_{elec}=50$MHz
In accordance with previous static simulations and measurements (in subsection 4.3 and subsection 5.1 respectively), enhanced sensing performances are noticed with the use of OFDM interrogation and subcarrier aggregation compared to single-carrier interrogation. The detection performance improvement is mainly driven by the false alarms reduction, which is in line with the observed reliability metric increase of the measurements.
6. Conclusion
We introduced the principle of digital carrier phase diversity to coded-$\Delta \phi$-OTDR, aiming at the mitigation of coherent fading effects. The Orthogonal Frequency Division Multiplexing (OFDM) interrogation scheme was proposed and tested in specific cases where we multiplexed the same codes, together with a subcarrier combination method for coherent fading mitigation.
Combined with Coherent-MIMO sensing which already solves the polarization fading effect, the digital OFDM interrogation scheme allows to mitigate coherent fading issues, thus providing a sensing system which is immune to strong fading. Experimental measurements confirmed the great efficiency of this approach in terms of sensitivity and reliability of the measurements. We reported an improvement of the strain sensitivity over $11$ dB SNR$_{\varepsilon,dB}$ using 4 subcarriers as compared to single-carrier interrogation, reaching a sensitivity noise floor level below $21\mathrm {p\varepsilon /\sqrt {Hz}}$ strain density on $1.3$km single mode fiber. With dynamic measurements, we demonstrated a gain up to $18.4\mathrm {dB}$ dynamic range when comparing a 4-subcarriers measurement with single-carrier one in case of a $440$Hz piezoelectric sine wave excitation.
Finally, in this paper, we showed that a digital multiplexing technique can be used to harness phase diversity and mitigate coherent fading. We believe that the proposed OFDM approach, applied for the first time to the sensing domain up to our knowledge, is a powerful tool to enhance the performance of future DAS systems.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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