Identification and observation of the phase fading effect in phase-sensitive OTDR

Xiangge He; Min Zhang; Shangran Xie; Lijuan Gu; Fei Liu; Zhangyuan Chen; Qingchang Tao

doi:10.1364/OSAC.1.000963

1. Introduction

Phase-sensitive optical time-domain reflectometry (Φ-OTDR) is one of the key techniques to realize distributed acoustic sensing (DAS) [1]. In this system, sensitive acoustic detection is achieved via coherent interference between Rayleigh backscattered signal within pulses propagating along the sensing fiber. Due to the ability of detecting acoustic vibration with high sensitivity and with a distributed fashion, phase-retrieved Φ-OTDR system has attracted enormous research interests with several progresses reported in recent years [2–5], accompanied with notable attentions from industry applications [6]. As Φ-OTDR system exploits pre-installed optical fibers for acoustic sensing and detection, it is especially beneficial to applications in harsh environments, e.g. vibration monitoring in the oilfield. In this scenario, field tests of DAS applied in vertical seismic profile, micro-seismic monitoring, hydraulic fracturing monitoring, and reservoir surveillance have been reported [7,8].

The detected signal of Φ-OTDR contains the interference between backscattered light from different positions along the fiber. Since the scattering amplitude and phase shift of those Rayleigh scatters are randomly distributed over distance, the collected interference signal appears as intensity fluctuations termed as fading effects. A complete understanding of this fading effect is important for the application of Φ-OTDR system as it adds a key noise term limiting the system signal to noise ratio. The fading phenomenon was first predicted and reported by Healey, who revealed that the amplitude and phase variation of the backscattered light follows Rayleigh and uniform distribution respectively, resulting a jagged appearance in single-shot detection signal [9]. Shimizu et al. further studied the characteristics of this fading noise and proved that a frequency shift averaging technique can be used to reduce this noise [10]. However previous studies only analyzed the fading phenomenon for the intensity signal, namely intensity fading effect, which mixes the contributions from random scattering amplitudes and phase retardants, with the effects from each individual term unresolved.

Recently we reported a dual-pulse heterodyne Φ-OTDR system which can retrieve the acoustic-induced phase modulation in a distributed way [11]. In this system, two pulses with a fixed frequency difference form a moving interferometer along the sensing fiber, and the pure phase information is demodulated with heterodyne detection. Although several groups have observed the intensity fading effect [12–14], the phase fading effect has not yet been reported. Based on this technique, here we for the first time identify and observe the phase fading (in contrast to intensity fading) effect from the overall intensity fading signal in Φ-OTDR system, and show that the random phase retardants induced by the distributed Rayleigh scatters lead to a ripple-like fluctuation of the demodulated phase amplitude, on top of a smooth envelop contributed by the pulse-width averaging effect. The experimental observation is well supported by the numerical simulations from a generalized theoretical model for the phase fading effect also presented here.

2. Theoretical model of the dual-pulse heterodyne Φ-OTDR system

Figure 1

Fig. 1 The interference model for a backscattered heterodyne pulse pair in optical fiber.

Download Full Size | PDF

illustrates the interference model of the backscattered heterodyne pulse pair in an optical fiber. The horizontal axis represents position along the fiber and the vertical axis represents time. The heterodyne pulse pairs are periodically generated with a repetition rate of f_r. The pulse width is w and the spatial distance between the two pulses is L_d. The frequencies of two pulses are f₁ and f₂ respectively, the heterodyne frequency is therefore Δf = f₁-f₂. Here in Fig. 1 only one pulse pair propagating in the fiber is plotted and considered. Backscattered signal is detected by a photodetector and acquired by an analog-to-digital converter (ADC). The sampling rate of the ADC is f_a. Note that in this model we explicitly identify two time frames [12]: one is the fast-time t linked to the position z of the rear edge of the pulse via the relation z = tc/n, where c is the speed of light in vacuum and n is the effective mode index of the fiber; the other is the slow-time τ = 1/f_r, indicating the sampling time within each ADC sampling channel.

In principle only the backscattered light beams arriving at the photodetector at the same time can interfere with each other. As shown in Fig. 1, at the time moment t_j, the position of the rear edge of the pulse pair is z_j = t_jc/n. At the next moment t_{j + 1}, the backscattered light of the t_j pulse pair is Δz = Δtc/n backward, where Δz = z_{j + 1}-z_j and Δt = t_{j + 1}-t_j. Therefore the backscattered light at z_j + 2Δz of t_j pulse pair will reach z_{j + 1} at the moment t_{j + 1}, interfering with the backscattered light at z_{j + 1} of t_{j + 1} pulse pair. The blue arrows and dotted lines indicate the backscattered light reaching the input fiber endface at the same time, which can interfere with each other. The electric field of the light transferring in the fiber can be written as

E (z, t) = E_{0} e^{- \frac{α}{2} z} e x p {j [β z - 2 π f t + \int_{0}^{z} Φ (l, t) d l]}

where E₀ is the amplitude of the light field, α is the loss coefficient of the sensing fiber, β = 2πn/λ is the propagation constant of the fiber mode, λ and f represent respectively the wavelength and frequency of light. Φ(l, t) is the vibration-induced phase change at position l and moment t. For simplicity here we assume a linearly polarized light and ignore its polarization variation.

We then apply the discrete model of Rayleigh backscattering [15], in which case the backscattering process is described by a set of reflectors regarded as the resultant contribution of randomly distributed scatters within a particular length of fiber. The length of each reflector was set 1 cm in the simulation which is much shorter than the pulse length (10 m) to give high enough simulation accuracy. The reflectivity and phase shift of the reflector at position z, represented by r(z) and θ(z), can be simulated as Rayleigh and uniform density distributions respectively [15]

\begin{array}{l} P (r) = \frac{r}{σ^{2}} e x p (- \frac{r^{2}}{2 σ^{2}}) r > 0 \\ P (θ) = \frac{1}{2 π} - π < θ < π \end{array}

Note that each reflector contains a large number of scatters, the optical path within each reflector is therefore randomly introducing a uniform distributed phase retardant. Suppose that the extinction ratio of the pulses is high enough such that the background backscattered light (i.e. DC component) is negligible, the electric field of the backscattered pulse pair from position z written as

\begin{array}{l} E_{R S} (z, t) = E_{01} \int_{z}^{z + \frac{w}{2}} r (p) e^{j θ (p)} e^{- α p} e x p {j [2 β p - 2 π f_{1} t + 2 \int_{0}^{p} Φ (l, t) d l]} d p \\ + E_{02} \int_{z + \frac{L_{d}}{2}}^{z + \frac{L_{d} + w}{2}} r (p) e^{j θ (p)} e^{- α p} e x p {j [2 β p - 2 π f_{2} t + 2 \int_{0}^{p} Φ (l, t) d l]} d p \end{array}

where E₀₁ and E₀₂ are the field amplitude of the two pulses respectively. Note that Eq. (3) describes the backscattered field from each individual pulse pair and the fast-time frame t represents light propagating in the fiber. As Δf << f₁ and f₂, by omitting the optical frequency oscillation terms, the backscattered field considering the repeating pulse pairs can be expressed as

\begin{array}{l} E_{R S} (z, τ) = E_{01} \int_{z}^{z + \frac{w}{2}} r (p) e^{j θ (p)} e^{- α p} e x p [j 2 \int_{0}^{p} Φ (l, τ) d l] d p \\ + E_{02} \int_{z + \frac{L_{d}}{2}}^{z + \frac{L_{d} + w}{2}} r (p) e^{j θ (p)} e^{- α p} e x p [j 2 \int_{0}^{p} Φ (l, τ) d l] d p \cdot e x p [j (2 β z - 2 π Δ f τ)] \end{array}

here the position z relates to the different ADC sampling channels with the sampling time given by the slow-time τ. Equation (4) can therefore be used to simulate the scattered field from any ADC sampling channel of phase-retrieved Φ-OTDR system. The vibration-induced phase change Φ(l, τ) in Eq. (4) can be determined via experiment. Suppose that a fiber length L is under uniform acoustic driving and the total phase change at moment τ is ΔΦ(τ), Φ(l, τ) can be written as

Φ (l, τ) = {\begin{matrix} \frac{δ Φ (τ)}{L}, l_{1} \leq l \leq l_{2} \\ 0, o t h e r p o s i t i o n s \end{matrix}

where l₁ and l₂ are the beginning and ending positions of the phase change section and L = l₂-l₁. Using the heterodyne demodulation algorithm introduced in [11], we can demodulate the backscattered field described in Eq. (4), and further simulate the phase fading effect induced by random Rayleigh scatterings in the sensing fiber. In our simulation we neglect the contribution of laser-induced and environment-induced phase noises.

3. Phase fading effect

Figure 2(b)

Fig. 2 Numerical simulations of phase fading effect using experimental parameters. (a) Amplitude fluctuation of the retrieved phase signal over distance for uniform acoustic driving amplitude. (b) Spatial-temporal plot of the demodulated sinusoidal phase variation. (c) The demodulated time-domain phase signal at a position of 150 m. (d) Numerical simulations of phase fluctuation with different combinations of θ(z) and r(z) distributions.

Download Full Size | PDF

plots the numerically simulated phase demodulation signal over a specific range of sensing fiber, under a uniform acoustic driving amplitude at 300 Hz frequency. The simulation parameters are chosen the same as experiments described below. Figure 2(c) plots the time-domain trace retrieved at a specific position along the fiber, showing a perfect sinusoidal wave with a fixed amplitude. Figure 2(a) plots the amplitude of the demodulated phase signal over distance. It can be clearly seen that, even though the acoustic driving amplitude is fixed, the retrieved phase signal appears a fast amplitude fluctuation over distance, inducing the phase fading effect. To further identify the contributions of the reflectivity r(z) and phase retardant θ(z), we simulate the phase fluctuations using four combinations of r(z) and θ(z) distributions, as compared in Fig. 2(d). It can be seen that when both θ(z) and r(z) are constants (solid red), the phase fading effect disappears. The smooth envelop is simply caused by the averaging effect from the pulse width, as in our system the vibration range is 7 m while the spatial resolution is about 15 m. When only r(z) is set as Rayleigh distribution while θ(z) is kept as constant (dashed red), the demodulated result barely changes, meaning that a random distribution of r(z) introduces negligible phase fading noise. However, when θ(z) is set as a uniform distribution, no matter r(z) is a Rayleigh distribution or a constant value (dashed and solid blue), the phase amplitude appears significant ripple-like oscillations on top of the smooth envelop, which is the main feature of the phase fading effect. This comparison clearly identifies the key contribution of random phase retardant term (i.e. θ(z)) induced by distributed Rayleigh scattering on the phase fading effect.

We then conduct experiments to observe the phase fading effect. The experimental setup is shown in Fig. 3

Fig. 3 Experimental setup. OC, optical coupler; AOM, acousto-optic modulator; ADC, analog-to-digital converter; PZT, piezoelectric ceramic transducer; FRM, Faraday rotation mirror.

Download Full Size | PDF

and it contains three parts. The interrogator part includes a heterodyne pulse pair generation module and a detection module. The laser we used is a narrow linewidth CW laser at 1550.12 nm (NKT Koheras BasiK E15) and the linewidth is ~100 Hz. The duration of the pulse is T_p = 50 ns (w = cT_p/n) and the length of the delay fiber is L_d = 20 m. The shape of the pulses are rectangle. The sampling rate of the ADC is 100 MS/s. To mimic the acoustic vibration, a piezoelectric ceramic transducer (PZT) wrapped with a 7 m long fiber was driven by a signal generator with sinusoidal function. An interferometric configuration was used to calibrate the vibration-induced phase change from the PZT. This part is similar to the configuration in [16] and the arm length difference of the Michelson interferometer was 10 m. The same PZT was applied in the scattering configuration. The detailed configuration of this part can refer to [11] and the PZT was placed between two coils of single mode fibers (SMFs) with lengths of 150 m.

A sinusoidal signal with 200 mVpp and 300 Hz frequency was applied on the PZT. The value of phase change was measured as 1.74 rad using the interferometric configuration. Then we switched to the scattering configuration with the same sinusoidal signal applied on the PZT. In our dual-pulse heterodyne Φ-OTDR system, the two pulses are offset in both temporal and frequency domains, functioning similar as the sensing and reference arms of an interferometer. Therefore, our system can retrieve the phase difference between backscattered pulses as illustrated in Fig. 1. The spatial-temporal distribution of the demodulated phase signal is shown in Fig. 4(b)

Fig. 4 Experimentally observed phase fading effect. (a) 50 times of repeat measurements of the retrieved phase amplitude at different positions (grey solid) and their average (black solid). The color solid curve corresponds to the data presented in (b). The blue-dashed line represents numerical simulation using the same parameters as experiment. (b) Measured spatial-temporal plot of the retrieved phase variation induced by acoustic driving. (c) The time-domain phase signal at a position of 150 m.

Download Full Size | PDF

. It can be seen that the phase change covers a range longer than 7 m, mainly caused by the smoothing effect of the pulse pair. Figure 4(c) plots the retrieved phase signal at position 150 m showing a perfect sinusoidal signal. The gray curves in Fig. 4(a) plot the measured phase amplitude over position for 50 times repeat measurements, with the black solid curve representing its average. An obvious ripple-like fluctuation over distance in the averaged phase amplitude can be observed given the fixed driving amplitude of the PZT. The dashed-blue curve in Fig. 4(a) represents the numerically simulated phase fluctuations, showing a similar feature as the measurement, confirming our observation. The mismatch could be attributed by the difference between the simulated and actual distributions of r(z) and θ(z) along the fiber. Note that in the simulation the measured phase change amplitude from the interferometer configuration was used.

As a discussion, we propose an approach that can be used to suppress the observed phase fading phenomenon. It is worth to mention that although the phase fading effect is mainly contributed by the random phase θ(z), it is different from θ(z) itself, as it comes from the comprehensive interference of a vast number of backscattered light. Figure 5(a)

Fig. 5 (a) Numerical simulation of demodulated phase amplitude for 100 different sets of Rayleigh and uniform distributions of r(z) and θ(z). The red-solid curve is their average and the black-dashed line refers to the case of constant r(z) and θ(z). (b) Measured and simulated phase amplitude with and without moving average of 5 m of sensing fiber.

Download Full Size | PDF

(green dashed lines) plots the demodulated phase signal under 100 different sets of Rayleigh and uniform distributions of r(z) and θ(z), with the red solid line representing their average. As a comparison, we also plot the simulation result when both r(z) and θ(z) are constants (black dotted). It can be seen that the phase fading noise varies dramatically with the change of r(z) and θ(z) distributions and can be overcame by averaging over different distributions. This indicates that by averaging the demodulated phase signal along the fiber lengths the phase fading noise may be suppressed (with compromised spatial resolution). Figure 5(b) (blue solid) shows the experimentally measured phase amplitude with 5 m moving average. It can be clearly seen that the phase fading noise is smoothed compared to the case of without moving average. Numerical simulation using the same condition also predicts a similar suppression effect (red solid and dashed lines). This indicates that the phase fading effect in actual sensing fiber has a random distribution along the fiber length. A detailed analysis on the suppression technique will be presented elsewhere.

4. Conclusion

In summary, the phase fading effect in Φ-OTDR system is for the first time analyzed and observed. We show that the phase fading noise appears as ripple-like amplitude fluctuations over distance in the demodulated phase signal, and it is revealed to be mainly contributed by the random distribution of the Rayleigh-scattering-induced phase retardant. The analysis and results presented here represent an important step in understanding the fading effect, as well as paving the way towards the suppression of phase fading noises in Φ-OTDR systems.

Funding

China Postdoctoral Science Foundation (CPSF) (2018M631250).

References

1. X. Bao, D. Zhou, C. Baker, and L. Chen, “Recent development in the distributed fiber optic acoustic and ultrasonic detection,” J. Lightwave Technol. 35(16), 3256–3267 (2017). [CrossRef]

2. Z. Wang, L. Zhang, S. Wang, N. Xue, F. Peng, M. Fan, W. Sun, X. Qian, J. Rao, and Y. Rao, “Coherent Φ-OTDR based on I/Q demodulation and homodyne detection,” Opt. Express 24(2), 853–858 (2016). [CrossRef] [PubMed]

3. A. Masoudi and T. P. Newson, “High spatial resolution distributed optical fiber dynamic strain sensor with enhanced frequency and strain resolution,” Opt. Lett. 42(2), 290–293 (2017). [CrossRef] [PubMed]

4. P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9(1), 2509 (2018). [CrossRef] [PubMed]

5. Y. Muanenda, S. Faralli, C. J. Oton, and F. Di Pasquale, “Dynamic phase extraction in a modulated double-pulse ϕ-OTDR sensor using a stable homodyne demodulation in direct detection,” Opt. Express 26(2), 687–701 (2018). [CrossRef] [PubMed]

6. T. Parker, S. Shatalin, and M. Farhadiroushan, “Distributed acoustic sensing – a new tool for seismic applications,” First Break 32(2010), 61–69 (2014). [CrossRef]

7. A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, B. Kuvshinov, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014). [CrossRef]

8. M. Li, H. Wang, and G. Tao, “Current and future applications of distributed acoustic sensing as a new reservoir geophysics tool,” Open Petrol. Eng. J. 8(1), 272–281 (2015).

9. P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. 20(1), 30–32 (1984). [CrossRef]

10. K. Shimizu, T. Horiguchi, and Y. Koyamada, “Characteristics and reduction of coherent fading noise in Rayleigh backscattering measurement for optical fibers and components,” J. Lightwave Technol. 10(7), 982–987 (1992). [CrossRef]

11. X. He, S. Xie, F. Liu, S. Cao, L. Gu, X. Zheng, and M. Zhang, “Multi-event waveform-retrieved distributed optical fiber acoustic sensor using dual-pulse heterodyne phase-sensitive OTDR,” Opt. Lett. 42(3), 442–445 (2017). [CrossRef] [PubMed]

12. L. B. Liokumovich, N. A. Ushakov, O. I. Kotov, M. A. Bisyarin, and A. H. Hartog, “Fundamentals of optical fiber sensing schemes based on coherent optical time domain reflectometry: Signal model under static fiber conditions,” J. Lightwave Technol. 33(17), 3660–3671 (2015). [CrossRef]

13. A. Hartog and K. Kader, “Distributed fiber optic sensor system with improved linearity,” US Patent 2012/0067118A1 (2012).

14. J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express 24(12), 13121–13133 (2016). [CrossRef] [PubMed]

15. J. Park, W. Lee, and H. F. Taylor, “Fiber optic intrusion sensor with the configuration of an optical time-domain reflectometer using coherent interference of Rayleigh backscattering,” Proc. SPIE 3555, 49–56 (1998). [CrossRef]

16. F. Liu, S. Xie, X. Qiu, X. Wang, S. Cao, M. Qin, X. He, B. Xie, X. Zheng, and M. Zhang, “Efficient common-mode noise suppression for fiber-optic interferometric sensor using heterodyne demodulation,” J. Lit. Technol. 34(23), 5453–5461 (2016). [CrossRef]

Identification and observation of the phase fading effect in phase-sensitive OTDR

Abstract

1. Introduction

2. Theoretical model of the dual-pulse heterodyne Φ-OTDR system

3. Phase fading effect

4. Conclusion

Funding

References

Cited By

Figures (5)

Equations (5)

OSA Continuum