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Abstract
In conventional heterodyne phase-sensitive optical time domain reflectometry (Φ-OTDR), the optical path difference (OPD) between sensing and reference arms deteriorates the signal-to-noise ratio (SNR). We counteract this effect by introducing a loop path in reference arm. This facilitates the use of laser source with low coherence length. Compared with an ordinary Φ-OTDR system, SNR increased from ~1 dB to 5 dB. Regardless of OPD compensation features, the probability to getting a better output increases by generation of multiple reference beams (and consequently multiple beat signals), as compared to conventional systems. The method is cost efficient and suitable for practical purposes.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past several decades, optical time domain reflectometry (OTDR) has been used for remote sensing of fiber losses, locating faults, and distributed sensing. An improved technique, called phase sensitive optical time domain reflectometry (Φ-OTDR) [1], uses narrow linewidth lasers [2] to enhance the sensitivity and working length. However, Φ-OTDR exhibits several types of noises. Conventionally, this issue can be resolved by implementing highly coherent lasers with better frequency stability and narrower linewidth, such that the coherence length exceeds the optical path difference (OPD). This would ensure that phase noise does not affect the system output. Several studies have pointed out that a laser linewidth in the kHz range is required to develop a practical Φ-OTDR system [3–5]. An alternate method was recently proposed by Zabihi et al. [1], which was based on predicting the defected output areas and using an additional probe laser to reconstruct these areas. Although this method shows potential, implementing a system with multiple probe lasers is expensive. Some other studies applied severe constraints on the laser source itself, rather than focusing on reduction of OPD [6]. For example, Shimizu et al. [7] proposed noise mitigation in the signal processing stage by using frequency shift averaging (FSA), which improved the output quality. However, for real-time measurements, such lengthy mathematical process can be time-consuming and noise suppression before signal processing is always better. We recently proposed the use of two beams in the sensing arm to reduce the noise [8]. However, it is not always feasible to increase the reference arm length to be equal to the sensing arm length. Particularly for long-range sensing, it is not easy to use a fiber of several tens of kilometers length on the reference side to reduce OPD. Even the use of two-beam method [8], while is based on the detection of vibration events in the vicinity of the near end in sensing arm, would result in a large OPD. Bin Wang et al. [9] proposed a technique based on optical fiber delay loop consisting of a delay fiber and a frequency shifter. Although this technique was focused on frequency domain measurements, i.e., optical frequency domain reflectometry (OFDR), it can be extended to OTDR as well.
Healey et al. [10] confirmed that the noise in Rayleigh backscattering (RBS) and speckle-like phenomenon is not stationary. Therefore, the output obtained by reflectometry techniques is highly variable. Further, several factors may contribute to the noise and fading, such as amplitude fluctuations, state of polarization, and external environment, which in turn can affect the output. Therefore, a single output signal might not provide effective information in a specific sweep. To this end, beat signals may be used to improve the output quality.
Here, we propose a technique to mitigate the phase noise and enhance the output signal-to-noise ratio (SNR) by reducing the OPD between the reference and sensing arms. Further, we generate more than one beat frequency to facilitate the selection of the best output. The advantage of this technique is that we do not need a laser source of very high coherence length, and it can be implemented with a relatively high linewidth laser and cost-efficient elements.
2. Principle
Consider a heterodyne Φ-OTDR system (Fig. 1), where the angular frequency and electric field of the laser are and respectively. The backscattered electric field, which is shifted to by a modulator, can be expressed as [11]:
where and are the amplitude and phase of the backscattered signal, respectively. is proportional to the square root of the backscattered power from the position (is the group velocity).The termis the phase noise of the laser, which is a random function of distance. This phase noise arises because the practical single-frequency lasers are not fully monochromatic [12], which leads to their finite linewidth. The origin of the phase noise is quantum noise associated with optical losses and spontaneous emission of the gain medium into the resonator modes. Additional factors, e.g., vibrations of the cavity mirrors or temperature fluctuations, may also contribute to it. Phase noise may occur in the form of a continuous frequency drift or as sudden phase jumps [12].
Fig. 1 Schematic of traditional heterodyne detection. AOM: acousto-optic modulator, C: circulator; BPD: balanced photodetector, FUT: fiber under test.
Considering the effect of the phase noise, the output electric field at the detector can be given by
and the photocurrent can be expressed aswhere Rd is the detector responsivity. Using a filter to select the intermediate frequency () only, the following signal is obtained [11]:For a heterodyne Φ-OTDR system, as the OPD between the sensing and reference arms increases, the probe light deviates from the reference light (local oscillator) and the detection signal exhibits effects of phase noise [13,14]. Consequently, the demodulation recognizes these noises as disturbance events. If OPD is decreased, the phases of the probe beam and the local oscillator become nearly equal. This causes a similar level of laser noise in both the beams, and the term is therefore suppressed. This implies a much better vibration detection mechanism.OPD can be decreased by guiding the reference light through a longer fiber. Figure 2 illustrates a scheme where the incoming reference light passes through a 2 × 2 coupler in a loop path. There is a fiber coil inside the loop, which introduces a delay and therefore, the length of the reference arm is increased by a fixed amount in each circulation. Acousto-optic modulator (AOM) also creates a new frequency in each loop. An erbium doped fiber amplifier (EDFA) and a bandpass filter (BPF) are used for amplification and reduction of amplified spontaneous emission (ASE) noise, respectively. Therefore, this design can be used to compensate a part of OPD in every circulation.
To get better insights, we analyze the loop function when a light beam of amplitude A and initial frequency f propagates in the loop. We consider the fiber length delay in the loop to be Lʹ. As the light beam propagates in the first loop, it beats with the backscattered light from the FUT after t = Lʹ/Vg (seconds). Its highest frequency component is f2, which is the frequency shift of the AOM in the loop. The input () and output () fields of the first loop can be written as follows:
Here, g is the loop gain that includes the effect of AOM, BPF, fiber losses, and EDFA gain. Similarly, for the second loop, we can writeThis beam has 2f2 as the highest frequency component. The 2f2 frequency beats with backscattered light at t = 2Lʹ/Vg. Using above equations, the general form of the loop’s output can be expressed aswhere m represents the numbers of circulations in the loop. This recursive process continues as long as the time m × Lʹ/Vg is less than the pulse width of AOM in the loop. The number of generated frequencies can also be obtained by dividing pulse width of AOM with the delay time in the loop. This structure generates several frequencies and the higher frequency implies more circulation in the loop.The structure shown in Fig. 2 can be placed in the reference arm of a heterodyne Φ-OTDR system to reduce the OPD as it adds a specific length to the reference arm in each circulation (Fig. 3). The output of the first loop with f2 frequency beats with backscattered light from FUT after a time interval of Lʹ/Vg seconds and therefore, the beat frequency is f1-f2. Here, f1 is the frequency shift of the AOM1 that is located in the sensing arm. The signal with f1-f2 frequency corresponds to the compensation of OPD after Lʹ. Similarly, after the completion of the mth loop, the ‘m × f2’ frequency component beats with backscattered light, and the beat frequency is . An absolute value is considered here because the beat frequency appears in a cosine function. This beat frequency is created after tb = m × Lʹ/Vg and the compensated OPD is m × Lʹ. The number of circulations in the loop, m, can be controlled by the pulse width of AOM2. Note that m × Lʹ must not be larger than L, which is the total length of the FUT. Using the above argument, we can rewrite Eq. (3) and Eq. (4) as
The heterodyne output contains multi-frequency components. Each of these components is created after a specific time and after passing through the loop for one or more times. Therefore, the output current is a function of both time and loop number. However, the probe frequencies must be selected properly to have a minimum possible phase correlation among themselves. The following condition must be satisfied to ensure that the probe beams are independent, i.e., there is no phase correlation between two generated frequencies [7]:
A proper selection of f2 is crucial for implementation of the loop structure. Here, we want to introduce several reference light beams for different OPD compensations. As regards the perturbation location and required time for receiving RBS light from perturbation, one or more compensated beat signals may provide better SNR while others might be futile. The futility of a beat signal may be attributed to its generation time. If the generation of a reference frequency takes similar or more time than that taken in the round trip of probe light in the perturbation area (tFUT), then that frequency does not provide any useful information.3. Signal processing scheme
Figure 4 illustrates the signal processing scheme. We used multi-frequency I/Q demodulation to detect and extract different beat frequencies obtained from BPD [15].
The frequency of each I and Q element is equal to one beat frequency. Each of these elements passes through a lowpass filter (LPF) with a bandwidth suitable for the probe pulse width. Finally, an amplitude demodulation (AM) is performed to extract the vibration location. We apply the mean-square method for locating the vibration to increase the SNR [16]. This method involves evaluating the change in amplitude of the Rayleigh backscattering signal within a time window. The mean-square method can be mathematically expressed as:
where K is the number of consecutive traces sampled within the time window. In regression analysis, the term mean-square is sometimes used to indicate the unbiased estimate of error variance, which is different from S in Eq. (12).4. Experimental system
Figure 5 shows the schematic of our Φ-OTDR system. We tested several configurations to obtain the output SNR with different OPD compensations. The procedure and significance of generating multiple beat signals will be clear from the details of the two experiments discussed below. Comparing the results of these experiments provides useful insights on the dependence of loop frequency and reference length on SNR.
Fig. 5 Schematic of Φ-OTDR system with a loop in the reference arm. AOM1,2: acousto-optic modulator, EDFA1,2: erbium doped fiber amplifier, Cir: circulator, FUT: fiber under test, PZT: piezo-electric transducer, BPD: balanced photodetector, BPF: bandpass filter, DAQ: data acquisition card.
The details of the first experimental configuration are as follows. We employed a relatively low coherence CW laser source of 1550.12 nm wavelength and 1 MHz linewidth. A laser with 1 MHz linewidth is not appropriate for Φ-OTDR systems, since a kilohertz laser source must be included in order to avoid phase noise problems while maintaining the desired coherence length [13]. However, here we aimed to construct a practical system with minimum requirements and a moderate laser source. The laser beam was split into two parts, one for detection (sensing) and other as a reference beam, to build a coherent heterodyne system. An AOM (AOM1) with a frequency shift of 150 MHz was placed in the sensing arm to shape the CW probe beam into a pulsed beam. The repetition period and pulse width of the pulsed beam were 95 μs and 200 ns, respectively. A pulse generator was used to create the pulses. The modulated pulse was then amplified by an EDFA and passed through a bandpass filter to mitigate the unwanted ASE noise. The probe pulse was sent through the circulator to FUT, which consisted of two pieces of fiber, FUT1 and FUT2 (of 3 and 5 km lengths, respectively). A PZT transducer with 10 m fiber coil was placed between these two pieces to generate vibration. In the loop, we used a 40 MHz AOM (AOM2) to shape a pulsed beam (with 70 µs pulse width and 95 µs repetition period). This pulse was then passed through an EDFA, bandpass filter, and a delay line (2 km fiber). The backscattered light and the reference light interfered at the coupler generating several beat frequencies, which were detected by a balanced photodetector (BPD). Finally, the output signals were simultaneously recorded on an oscilloscope (OSC), which was synchronized with AOM1 and AOM2 by the pulse generator. The sampling rate of the data acquisition card (DAQ) was set to 2 GHz to capture the highest frequency in the system. Note that the repetition periods of AOM1 and AOM2 must be longer than the round-trip time of the light beam through the entire FUT (i.e., FUT1 + FUT2). The pulse width of AOM1 was 200 ns for all experiments, which provided a reasonable spatial resolution. However, the pulse width of AOM2 depended on Lʹ and the number of reference frequencies needed for covering the entire FUT length.
In this experiment, the loop generated seven frequencies: 40, 80, 120, 160, 200, 240, and 280 MHz that interfered with the 150 MHz backscattered light from the sensing arm and generated beat frequencies of 110, 70, 30, 10, 50, 90, and 130 MHz, respectively (Table 1). As shown in this table, the 110 MHz frequency has the highest amplitude and compensates OPD for 2 km while the 130 MHz has the lowest amplitude. It is important to note that depending on the vibration location, some of the beat frequencies do not play any role in our vibration detection scheme because they are created after the probe pulse has already passed through the vibration area. Here, the vibration point is at 3 km, i.e., the time needed to receive the backscattered light of PZT (tFUT1) is 30 µs, and in the meantime, only 110 MHz and 70 MHz frequencies have been generated. Figure 6 shows the vibration location for this system as well as that for a traditional system, which has the same sensing arm but no loop in the reference arm. The traditional system had 150 MHz as its only beat frequency.
Table 1. Frequencies generated by the loop in the Φ-OTDR system with 8 km sensing fiber. tFUT is the time required for receiving the backscattered light from the perturbation point. *Valid beat signal is a signal that carries information about the vibration location.
Fig. 6 Contrastable 3D plot of the seven frequencies generated in our system with 8 km sensing fiber, as well as that of the output of a traditional system.
Since the amplitudes of the first two loop frequencies in the power spectrum are almost the same, the only factor that governs the SNR enhancement is OPD. As shown in Fig. 6, SNR improves from 110 MHz to 70 MHz, which are the first and second beat signals. We call these signals as valid beat signals. Any further frequencies are useless because they have been injected into the circulator at the same time or after the time when the perturbation backscattered light beams reached the BPD. Gray plots in Fig. 6 show the beat frequencies that do not provide useful information. As expected, there are no detectable peaks in the gray plots from the 3rd to 7th loop. Figure 7 illustrates seven generated frequencies and the regions over which each given beat signal cannot provide any information on perturbations. We have highlighted these regions with gray boxes and call them blind regions.
Fig. 7 2D plots of seven generated frequencies and output of the traditional system. Gray boxes show the area that each beat frequency is blind.
We designed the second experiment to observe the evolution of SNR in a system with short loop delay. We considered Lʹ = 1 km which resulted in a 5 µs delay in every circulation. The lengths of FUT1 and FUT2 were set as 3 and 1 km respectively. A pulse of 50 µs repetition period and 35 µs width was sent through AOM2. The short length of the delay fiber caused the generation of five valid reference frequencies out of the total seven frequencies (Fig. 8). Table 2 shows each of these loop frequencies.
Fig. 8 Performance of the seven frequencies generated in our system with 4 km sensing fiber, as well as that of the output of a traditional system.
Table 2. Frequencies generated by the loop in the Φ-OTDR system with 4 km sensing fiber.
Although our FUT is not that long, the perturbation information in beat frequencies of 110, 70, 30, 10, and 50 MHz could be obtained due to the short delay fiber. The 90 MHz and 130 MHz frequencies did not provide the vibration location because they had been generated at the same time or after the time when the probe pulse passed through the PZT. As expected, there is no detectable peak in these two beat signals (6th and 7th loops in Fig. 8). Figure 9 confirms that whenever the vibration event is in the blind region, the beat signal is invalid.
Fig. 9 2D plots of seven generated frequencies in a system with 4 km sensing fiber and output of the traditional system. The gray boxes denote the area where each beat frequency is blind.
5. Results and discussion
To validate the use of the loop structure, we measured the SNR in a traditional Φ-OTDR system without the loop in reference arms. Figure 10 compares the valid beat frequencies and the relevant SNRs of the traditional and proposed system for the first two experiments.
For the first experiment, the SNR increases in the presence of the loop from 20.7 dB to 21.9 dB. Further, the SNR in traditional system is only 19.9 dB SNR. In the second experiment, SNR increases from 22.4 dB to 24.4 dB for the first two circulations, while SNR in the traditional system is only 19.9 dB. Similar to the first experiment, we observe an incremental trend in SNR from 110 MHz to 70 MHz, which means the amplitudes of the loop outputs are relatively high. However, a gradual decrease in amplitude negated the OPD compensation, and the SNR decreased below the output of the traditional system.
Due to the non-stationary behavior of our beat signals, we tested several configurations with uncorrelated and different FUT1, FUT2, Lʹ, and pulse width to obtain a concrete conclusion. The results are listed in Table 3 (including the first two experiments).
Table 3. Results of the seven experiments.
All the experiments proved that if there are enough beat signals, there is a high possibility to obtain one or more output signals where an appropriate tradeoff between the amplitude of reference light and compensated OPD is achieved. This facilitates the selection of the output signal with SNR much higher than that in a traditional system. The required number of circulations and the resulting beat signals that exhibit enhanced SNR varies according to the vibration location, loop parameters, EDFA performance, laser linewidth, stability of laser wavelength, and other external parameters. We achieved an enhanced SNR using the loop structure in six experiments. SNR decreased in the third experiment only. A possible reason is the presence of only one valid beat signal. For an appropriate selection of parameters, following considerations must be taken into account. Number of reference frequencies can be measured from
and the pulse width of the AOM in the loop isFigure 11 shows the improved output SNR in all the seven experiments that are compared with the SNR of a traditional system (black bars with 150 MHz beat frequency). We obtained one or more outputs with enhanced SNR in all the experiments, except in the third one. Moreover, all enhancements were restricted to the initial four loops, i.e., from first to fourth. It can be explained by focusing on improvement of SNR in our Φ-OTDR system by considering two contradictory factors: “inevitable amplitude reduction in loop frequencies” and “increase in length of the reference arm.” While the first one decreases the SNR, the second one increases it. This implies that the higher frequencies should provide lower OPD and consequently, a better SNR. However, here the effect of attenuation must be taken into account. Lower frequencies show higher amplitudes because they remain in the loop for a longer time; therefore, they are amplified in each cycle by EDFA. This implies that although more circulation in the loop increases the reference length, it decreases the amplitudes of higher frequencies. Figure 12 shows the output of the loop as a function of frequency.
With increase in time, more frequencies appear at the output until the pulse of AOM2 becomeszero. This plot corresponds to an arbitrary loop with 35 µs pulse width and 1 km long delay fiber. For this length of delay, a new frequency was generated every 5 µs, and there were seven independent frequencies in total. The upshift frequency of AOM2 was 40 MHz.
Here, the peak amplitude reduces gradually from −15 dBm in the first frequency to −28 dBm in the seventh one. Consequently, we cannot expect a linearly increasing rate for SNR in the entire system due to the tradeoff between reduction in amplitude of the loop frequencies and OPD compensation by the delay fiber in the loop.
To sum up, in six out of seven experiments, i.e. in 85% experiments, we achieved improvement in system performance with minimal required equipment.
6. Conclusion
We demonstrated that a loop structure in heterodyne Φ-OTDR systems enhances the SNR in the vibration location measurements. By circulating the reference light beam through this loop, we can add more fiber length to the reference arm in each cycle and therefore, decrease the OPD between the sensing and reference arms. In other words, system with cyclic loop offers different reference arm lengths for each sweep of probe pulse in FUT. These various arm lengths provide OPD compensation with different values. Additionally, a new beat signal is generated with each circulation in the loop, which provides more scope for choosing the best possible output. Consequently, we do not require highly coherent lasers because the noise in the system can be reduced to some extent by mitigating OPD. This method simplifies the system requirements. Therefore, it is cost efficient and is suitable for practical purposes. To the best of our knowledge, no former study has reported such high level of OPD compensation in heterodyne systems with very simple equipment.
Funding
National Natural Science Foundation of China (61627816); Key Research and Development Program of Jiangsu Province (BE2018047); Natural Science Foundation of Jiangsu Province (BK20180328); Fundamental Research Funds of the Central Universities (021314380095, 021314380136, and 021314380116); Chinese Scholarship Council (2017GXZ022724).
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