## Abstract

Distributed acoustic sensing (DAS) via fiber-optic reflectometry techniques is finding more and more applications in recent years. In many of these applications, the position of detected acoustic or seismic sources is defined with a single longitudinal coordinate which specifies the distance between the detection point in the fiber to the DAS interrogator. In this paper we describe a DAS system which is intended to operate in a fluid (air or water) and to detect and localize moving objects, with three spatial coordinates, using the acoustic waves they generate or reflect and their Doppler shifts. The new method uses optical frequency domain reflectometry (OFDR) and lumped Rayleigh reflectors (LRR's) to ensure sufficiently high sensitivity for operation in fluid media. The new method was used to track a narrowband (CW) signal source.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Distributed Acoustic Sensing (DAS) via fiber-optic reflectometry techniques is gaining increasing attention in recent years [1–5]. These applications include intrusion detection, monitoring transportation, leakage identification, vertical seismic profiling and more. In many of these applications the fiber is embedded in, or firmly attached to a solid medium (such as the ground). The position of detected acoustic or seismic sources is commonly defined with a single longitudinal coordinate which specifies the distance between the detection points in the fiber to the DAS interrogator. In this paper we describe a new DAS method which allows operation in a fluid (air or water) and detection and localization of moving objects, with three spatial coordinates, using the acoustic waves they generate or reflect and their Doppler shifts. Hence, the DAS-fiber functions as an acoustic antenna and the system as the receiving unit of a Doppler sonar. The method can be used in air for identification and tracking of moving or flying objects (e.g. drones), or in water for detection and study of marine life (dolphins etc.) or underwater vehicles. It can potentially function as the receiver of an active sonar or a bistatic sonar or as a stand-alone unit for detection and tracking of targets which emanate acoustic signals. The current study provides a proof of concept of the proposed technique. This is done by locating and tracking a moving target which emanates a single acoustical tone in air. The operation of DAS in air is challenging due to the large acoustic impedance mismatch between the optical cable and the air. To meet this challenge and to increase the sensitivity of the system we used 100 meter fiber spools as sensors and Lumped Rayleigh Reflectors (LRR's) [6]. LRR's are sections of the sensing fiber which are inserted into acoustic insulation boxes to allow constructive addition of their complex backscatter phasors. The operation of LRR's was previously demonstrated with a coherent phase-OTDR system. In this work Dynamic-OFDR, which offers a more favorable trade-off between sensitivity and spatial resolution [7], was used to interrogate the LRR's for the first time. The resulting increased SNR and the relatively high scan rate (20 kHz) enabled the detection of a moving acoustic source, analysis of its Doppler spectra and extraction of velocity and location information.

## 2. Theory

#### 2.1 Lumped Rayleigh reflectors

LRR's are sections of the sensing fiber which are enclosed in acoustically insulating boxes. The insulating boxes ensure that the mutual phases between the backscattered light of fiber segments, which reside in the same box, remain constant, at least over some observation time, thus keeping the phase variations of the backscattered signals from these segments constant in space and varying only in time. Two consecutive LRR's enable measurement of dynamic phase variations which occur in the fiber section between them. The theory of LRR's is described in details in [6] and is briefly reviewed here for clarity.

A DAS interrogator produces a matrix, $R\left(k,q\right)$, which describes the complex backscatter profile of the sensing fiber as a function of time. Here $k$ denotes time-index and $q$ represents position. Consider two extended fiber segments, $U$ and $V$, with lengths ${L}_{U}$ and ${L}_{V}$, which were placed in two acoustically insulating boxes. Another fiber segment that is located between the boxes is exposed to the environment and acts as a sensing element. $U$ and $V$ are taken longer than the spatial sampling resolution, $\Delta z$, so that the boxes contain ${N}_{U}={L}_{U}/\Delta z$ and ${N}_{V}={L}_{V}/\Delta z$ spatial samples whose complex reflections can be represented by two vectors ${\overrightarrow{r}}_{U}\left(k\right)$ and ${\overrightarrow{r}}_{V}\left(k\right)$ respectively. The two sequences of vectors correspond to two blocks of raw data in the measured matrix $R\left(k,q\right)$.

Thanks to the acoustic insulation it can be assumed that the magnitudes of the components of ${\overrightarrow{r}}_{U}$ and ${\overrightarrow{r}}_{V}$ remain stationary (at least over some predefined acquisition time). The acoustic insulation also guarantees that the mutual phase between two segments which reside in the same box remains constant. As the sensing segments are excited the phases of all components of ${\overrightarrow{r}}_{U}$ and ${\overrightarrow{r}}_{V}$ are modified with the same (common) additive phase terms. The difference between the common phase terms is the desired signal. Under these assumptions, the complex amplitudes of the reflections from the LRR's $U$ and $V$are defined by:

#### 2.2 Extracting the radial velocity of a source from the phase signal

A sound source which moves in the vicinity of a sensing segment induces in the segment optical phase variations which are proportional to the pressure of the acoustic signal. Short Time Fourier Transform (STFT) of the phase signal, ${\phi}_{\text{signal}}\left(k\right)$, results in a spectrogram of the measured phase, $\Phi \left(i,j\right)$ where $i$ is frequency index and $j$ is the new time index. The actual frequency and time are obtained via $f\left(i\right)=i\Delta f$ and $t\left(j\right)=j\Delta t$ respectively, where $\Delta f$ and $\Delta t$ are the corresponding grid intervals.

Due to Doppler shift, the signal emitted from a moving single-tone source would appear in the spectrogram as a peak whose center varies with time. If the peak is sufficiently strong with respect to the ambient noise and other spectral components, the instantaneous frequency of the tone, as perceived by the sensor, can be readily obtained from:

#### 2.3 Tracking

Once the magnitude of the radial velocity, ${v}_{l}^{r}$, is found, it can be used by a variety of methods to provide position information. Depending on the measured source properties, number of sensors and other system specifications, different localization algorithms are available [8–10]. In this study we demonstrate source localization in two dimensions, where the source and the sensors reside in the same plane, defined by the unit normal vector $\widehat{n}$.

We denote the velocity vector of the source as $\overrightarrow{v}$ and its radial and transverse components with respect to sensor $l$, as ${\overrightarrow{v}}_{l}^{r}\equiv {v}_{l}^{r}{\widehat{v}}_{l}^{r}$ and ${\overrightarrow{v}}_{l}^{t}\equiv {v}_{l}^{t}{\widehat{v}}_{l}^{t}$ respectively. Here ${\widehat{v}}_{l}^{r,t}$ denotes a unit radial/transverse velocity vector (Fig. 1(b)). The source velocity can be expressed as a vector sum:

where ${v}_{l}^{r}$is the value calculated in Eq. (4) for sensor $l$ and ${v}_{l}^{t}$ is an apriori unknown scalar. The unit vectors ${\widehat{v}}_{l}^{r,t}$ can be expressed as:## 3. Experimental setup

The optical setup (Fig. 1) comprised an OFDR interrogator, similar to the one described in details in [11]. It consisted of an ultra-coherent 1550.12nm tunable laser source whose instantaneous frequency was swept in a sinusoidal manner. The laser output was split between a reference arm and a sensing arm. The Rayleigh backscattered light from the sensing arm was combined with the reference and the result was detected with a balanced photoreceiver (400MHz). Agilent oscilloscope was used to acquire the optical data at a sampling frequency of 1Gsamples/s.

The sensing arm (see Fig. 1(a)) comprised three LRR's which were 100m optical fiber spools placed inside acoustically insulated boxes [6]. Between the LRR's there were two additional 100m optical fiber spools that acted as the sensors.

To test the localization performance of the proposed method a remote-control toy car was used. A cell phone which was placed on the car roof was used to generate a tone. It generated a 9kHz tone while the car was moving with a velocity of ~1.5m/s in front of the sensors. The laser scan frequency was set to 20kHz.

The interrogator acquired a 131072 X 2048 complex backscatter profile matrix of the fiber, $R\left(k,q\right)$. The matrix was divided into sections according to the locations of the spool sensors. ${R}_{U}\left(k\right)$, ${R}_{V}\left(k\right)$ and ${\phi}_{\text{signal}}^{l}\left(k\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left\{\text{\hspace{0.17em}}l=1,2\right\}$ were calculated for each sensor according to Eq. (1) and Eq. (2). From ${\phi}_{\text{signal}}^{l}\left(k\right)$, the spectrograms ${\Phi}^{l}\left(i,j\right)$ were calculated using an FFT with window size of 8192 and overlap of 8000 samples, resulting in $\Delta t=9.6\text{ms}$. To implement the determination of the instantaneous frequency according to Eq. (3) the search for the peak location was performed sequentially for increasing values of $j$. In each iteration the peak search was performed in a window centered around the instantaneous frequency in the previous iteration. Then, a median filter with window size of 23 was applied to the frequency signal. This procedure, which is based on the assumption that the target velocity cannot change abruptly, resulted in a smoother instantaneous frequency signals.

## 4. Results

The trajectory of the target in the experiment was independently recorded by a video camera. The motion’s profile was as follows: rest (~0-1sec); acceleration (~1-1.8sec); constant velocity (~1.8-5.5sec); deceleration (~5.5-5.8sec); rest (5.8-6.2sec). Figure 2 presents experimental results. A representative spectrogram of the signal recorded by one of the sensors during the motion of the target, is presented in Fig. 2(a). The Doppler shift is clearly visible and agrees well with the expected shift given the motion profile of the target. Figure 2(b) shows the frequency shift extracted from the two sensors in the experiment: ${\tilde{f}}_{\text{signal},1}-{f}_{\text{signal}}$ (blue) and ${\tilde{f}}_{\text{signal},2}-{f}_{\text{signal}}$ (red), where ${\tilde{f}}_{\text{signal},l}$ refers to the frequency measured by sensor $l$.

Figure 3 shows the trajectory of the target as estimated from the DAS system as well as the trajectory obtained from examination of the video. The good agreement is evident.

## 5. Discussion and conclusions

In this paper, Doppler spectral shift was used for the first time by a DAS system to detect and localize a tone source. The LLR method was used to increase the sensitivity of the system, in order to overcome the acoustic impedance mismatch between the fiber and air. Some aspects of the proposed method are worthy of further discussion.

First, since the main goal of this paper was to prove the concept of DAS-based Doppler tracking, the maximum performance of the system in more conventional terms such as range, spatial resolution or sensitivity, was not tested. Hence, the current experimental sensing-fiber length (500m) is by no means indication to the maximum length. This value is expected to be in the range of ten's of kilometers as in previous demonstrations of dynamic OFDR. This, in turn, will allow implementation of ten's of sensing spools and LRR's. The spatial resolution with which the Rayleigh profile of the fiber was measured was ~5m. This meter-scale resolution was needed for preventing overlap of the 'sensing' and the LRR regions in the backscatter profile. It should be noted that as the proposed system operates like a phased array antenna the relevant spatial resolution is actually its beam diameter (namely, transverse dimensions of its main lobe). Characterization of this parameter, however, was outside the scope of this work.

Second, the implementation of the method described above assumed prior knowledge of the emitter frequency and its initial position. Such assumption is not uncommon in papers about Doppler tracking [12]. While these details may not be available in many cases, the results are important as a proof of concept. In more realistic scenarios the method can be modified to estimate the missing data via the use of more sensing sections and incorporation of additional information regarding the deployment configuration.

Third, in this experiment the tracked object was emitting a narrowband CW signal (namely, a tone). Such capability is useful for active Doppler sonars or in cases were the target has an intrinsic CW source or was intentionally fitted with one. However, it will be even more beneficial to allow tracking of sources of signals which are not necessarily single frequency tones. According to our preliminary measurements this task presents further challenges: the spreading of the spectrum over a wider range of frequencies requires advanced tracking algorithms [8] and additional improvement in the system's sensitivity. This can be achieved with the use of better acoustic to optic transduction scheme. In the current study the sensing elements were conventional fiber spools and no attempts were made to increase their response to acoustic signals. It is expected that the use of appropriately designed acoustic transducers such as mandrels, compliant cylinders etc. will significantly improve the sensitivity, accuracy and range of the system [13–15].

The new method has some inherent limitations. In a distributed fiber-optic reflectometric system the maximum update rate is limited by the roundtrip time in the fiber according to ${f}_{\text{UR}}<c/2L$ where $L$ is the fiber length. The maximum update rate is also the maximum rate with which the measured acoustic signals are sampled. Hence, in accord with Nyquist criterion, the maximum measurable acoustic frequency is given by: $c/4L$. The minimum measurable radial velocity, ${v}_{\mathrm{min}}$, is the velocity whose Doppler shift equals the frequency resolution $\Delta f$. Using Eq. (4) we obtain: ${v}_{\mathrm{min}}\approx {v}_{s}\Delta f/{f}_{\text{signal}}={v}_{s}/\left(T{f}_{\text{signal}}\right)$ where $T$ is the time window used in the STFT. $T$ is chosen to satisfy the requirement that the radial velocity will remain roughly constant within the FFT window. Combining the above results we obtain expression for ${v}_{\mathrm{min}}$:

Note that this expression is for the radial velocity, while the minimum total velocity can be much larger depending on the direction of the target. It can be seen that ${v}_{\mathrm{min}}$ increases linearly with the fiber length.Finally, it is of interest to discuss the computational complexity of the proposed method and the feasibility of real time operation. The processing of the raw data was performed in two stages. First, the received samples were Fourier transformed (to obtain the Rayleigh profile of the sensing fiber) and the phase information was obtained. This part is extremely efficient and can be performed faster than a scan period (namely, in real time). The second stage involved collecting phases from multiple scans to allow spectral analysis of the received acoustic signal, detection of spectral peaks which corresponded to the source and execution of the Doppler tracking algorithm. This stage has an intrinsic delay as it requires collection of data from a number of scans to enable spectral tracking but, again, the algorithm itself is not computationally intensive. Considering the fact that the second processing phase is performed per target (i.e. not over the entire collected data) it is expected that real time implementation of the method will be indeed feasible.

In summary, a new Doppler-based DAS tracking method was proposed and demonstrated experimentally. Tracking of a narrowband acoustic source was successfully implemented. The new method can find applications in detection and localization of targets in air and water.

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