1. Introduction

In recent years, an increasing interest was demonstrated for application of the fiber optic sensing technology for real time continuous monitoring of pipelines for detection and localization of leaks and damages, for intrusion detection in perimeter security systems, etc. For such applications, fiber optic sensors possess very attractive features such as a capability for distributed detection and measuring, safety of operation in hazardous environments and immunity of sensing optical cable to electromagnetic interference. Very low attenuation of modern optical fibers allows developing large scale (very long) multiplexed sensor systems and truly distributed fiber optic sensors.

Different sophisticated fiber optic sensing systems have been reported [1, 2]. Remarkable examples of the distributed fiber optic sensors are systems for strain and/or temperature measuring based on Brillouin or Raman scattering in optical fibers [2]. These sensors use short light pulses and high speed electronics, and are capable to provide precise measurements of temperature or/and strain at several thousand points along the fiber. However, because of low efficiency of non-elastic light scattering which results in very weak signals, a long averaging time, usually from several seconds to minutes, is required in order to obtain an acceptable sensitivity to an external influence (a reasonable signal to noise ratio (SNR) for each spatially resolved fiber segment). Therefore, these sensors are suitable mainly for measuring of static or slowly-varying parameters.

For detection of acoustical waves and vibrations, fiber optic interferometers are very appropriate choice because of very high sensitivity and compactness. Different configurations of multiplexed arrays of fiber optic interferometric sensors were developed for passive sonar applications. Being very sensitive to temperature variations, these sensors undergo a thermal drift of the “operating point”. That results in a variation of sensitivity and unacceptable distortions in measured acoustical spectra. Different solutions for this problem have been demonstrated, including a heterodyne-type interrogation of time-domain multiplexed receiving interferometers [3, 4]. Based on this approach, an intrusion detection system [5] and an array of fiber-optic interferometric microphones [6] for military applications have been reported recently. However, the necessity to use the sophisticated and expensive components results in a significant cost for the interrogation units [6].

For many applications, where the sensor has to detect a perturbation (without measuring its intensity spectrum) and to determine position of the perturbation along the fiber length, the system design can be much simplified, thus reducing the cost of the system. Recently, a phase-sensitive coherent OTDR system has been reported as an intrusion detection sensor [7]. Rayleigh backscattering in optical fibers is much stronger in comparison to non-elastic scattering and can provide much higher signal-to-noise ratio (SNR) even from a single light pulse. That opens a possibility to detect and localize changes in a spatial distribution of the fiber effective refractive index. The system utilizes probe light pulses from a highly coherent laser. Interference of light waves scattered from different sections of the fiber results in a noise-like OTDR trace. Local changes of the fiber refractive index lead to phase changes of interfering backscattered light waves. As a result, local changes appear in a corresponding interval of the OTDR trace. By subtracting a phase-OTDR trace from an earlier stored trace, a time varying perturbation of the fiber can be detected and localized. This system allows detection of simultaneous perturbations at many points along the fiber. However, the laser must satisfy very strict requirements on its intensity (no averaging is permitted), coherence length, and a very small drift of the optical frequency from pulse to pulse is required [7].

For location of non-concurrent perturbations (or a single event), several relatively simple systems have been proposed. Most recent approach is based on spectrum analysis of Polarization-OTDR system [8] and it utilizes a complicated signal processing algorithm. Other systems are based on different combinations of long-path fiber-optic interferometers such as a Sagnac loop interferometer, a Mach-Zehnder interferometer, double Sagnac interferometers, a ring Mach-Zehnder interferometer [9–12], etc. Two interferometers are required in order to compensate for influence of a disturbance frequency on a calculated position of the disturbance. A more sophisticated sensor employing dual-wavelength, 40-km long dual-Sagnac configuration and complicated signal processing was reported to be able to detect of multiple disturbances with different frequencies [10]. A hybrid configuration of Mach-Zehnder and Sagnac interferometers was used for detection of a broad-band vibrational disturbance simulating a leak from a high pressure pipe. The position of the disturbance was determined from the null-frequencies in the output spectra [13]. Similar approach based on appearance of nulls in the output power spectrum but in different experimental configurations was demonstrated for detection of a wideband perturbation [14].

For some applications, rare single events like a leak from a pressurized pipe, impacts on and digging near gas and oil pipelines have to be detected and localized. Usually, no exact measurement of the disturbance spectra is required. Acoustical waves generated by leaks (and by mechanical impacts) can propagate some distance in the pipe or in soil. In this case, instead of truly distributed sensing system, a serial array of low-reflecting interferometers can be used for detection and localization of vibrational disturbances. This approach has an advantage that only sensing interferometers have to be acoustically coupled to the pipeline. Interferometers can de formed by partial reflectors, such as low-reflective Bragg gratings, as it was done, for example, in [5]. In order to reduce complexity of the sensor system, a localization method different to time-domain reflectometry method should be employed.

In this paper we propose a new simple method for localization of disturbed interferometer and present first experimental results for laboratory testing of the sensor.

2. Principle of operation

The proposed fiber optic system for detection and localization of time-varying disturbance is based on a serial array of identical reflecting interferometers. The schematic diagram of the sensor is shown in Fig 1. Interferometers are formed in the core of the optical fiber by pairs of identical low-reflecting Bragg gratings. Therefore, all interferometers have overlapping reflection spectra. The Bragg gratings are isolated from the environmental perturbations and are serving here just as partial reflectors at the wavelength of the diode laser. CW light from the laser diode is intensity modulated. The output of the intensity modulator is coupled to the sensing fiber through a coupler and an optical circulator. Part of the modulated light power from the second output of the coupler is directed to the reference channel. Light waves reflected by the sensing fiber are directed by the circulator to the signal photo-detector. A simple signal processing allows to detect and to localize an interferometer affected by the time-varying disturbance.

Let us consider the principle of operation of the proposed sensor. The normalized optical power coupled to the sensing fiber can be presented as S(t)=1+Acos(ω_mt), where A is the index of intensity modulation and ω_m is the angular frequency of modulation. Let us suppose that only one interferometer is placed at some unknown distance along the whole fiber length. The interferometer can be considered as a reflector operating at the probe wavelength of the diode laser. By measuring the phase shift between reference and reflected signal channels, one can find the delay time that probe light takes to travel to the interferometer and back to the photo-detector, hence, the position of the interferometer can be determined. This principle works fine for one reflector and it is widely used in laser rangefinders. However, if many partial reflectors are placed along the fiber length, a single frequency modulation cannot be employed for measuring distance to one particular reflector. Multiple reflections with different intensities and delays will results in a photodiode signal at the modulation frequency but with unpredictable phase delay in respect to reference signal. Nevertheless, in case when one interferometer is affected by vibrational disturbance, while other ones are affected by slow-varying influences only (like temperature change), the position of the disturbed interferometer can be determined by analyzing different frequency components in the Fourier spectrum of the photodiode signal.

 

Fig. 1. Experimental setup.

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We consider, that perturbation of any interferometer in the array results in modulation of optical path difference, and correspondingly, in modulation of the interferometer reflectivity at the fixed interrogation wavelength. For any interferometer shown in Figure 1, we can write its normalized reflection as

Here L₀ is the optical length of the interferometer, L₀=2nl, n is the effective refractive index of fiber core, l is the length of interferometer, k is the propagation constant of probe light, λ is the wavelength of probe light. When a vibration perturbs one interferometer, dynamic deformation of the optical fiber will change the optical length of the affected interferometer:

where ω_s and ϕ_s are the angular frequency and phase of the disturbance, respectively. An amplitude of the optical length modulation δL=0.71εL₀≪L ₀, represents a contribution of the fiber axial strain, ε, including contribution of elasto-optic effect for a standard germanosilicate fiber [1]. Substituting (3) in (1) yields

For small disturbance δLk≪1, time-varying reflectance of the interferometer

Probe light is intensity modulated and we can refer it as

In our case, the signal is the probe light reflected by the perturbed interferometer with a respective phase delay due to the time traveled by light along the fiber. The signal can be presented as S_refl(t)=S(t)R_s(t). Substitution S(t) and R_s(t) from (5) and (6), taking into account the time of the probe light propagation, yields

where τ is time delay that probe light takes to travel from the modulator to the disturbed interferometer (or from the interferometer to the photo-detector).

For the sensor system with many interferometers in a long fiber, other interferometers as well as Rayleigh backscattering of the fiber itself will produce additional signals at the same modulation frequency, _m ω, but with different amplitudes and phases. For slowly-varying influences, such as temperature variations, the reflectivity of these interferometers can be considered as constants during the signal acquisition time. So, contribution of all additional backscatters can be represented as a single virtual reflector having slow-varying reflection coefficient and whose position along the fiber can slowly change. Then, the probe light power at the signal photo-detector can be written as

where a=1+cos(L₀k) and b=δLksin(L₀k), r is the effective reflection coefficient representing influence of other backscatters, ϕ_R(t) is slowly-varying phase delay of the effective backscatter. The first term in (8) does not depend on the time, the second and the fifths terms are signals at the probe light modulation frequency. The third term represents the disturbance at the baseband acoustic frequency, ω_s, and it can be used for detection of the event (alarm conditions). The fourth term contains two frequency components, ω_m-ω_s and ω_m+ω_s, due to product of terms at the modulation frequency and perturbation signal. In order to determine the position of the disturbed interferometer, we need to find a value of the time delay, τ, from the detected signal S_refl(t). The equation (8) contains 5 unknown parameters: τ, ϕ_s and ω_s, and also r and ϕ_R. Let us consider the complex amplitudes of 4 frequency components in the Fourier transform of the detected signal. The disturbance can be detected and its frequency, ω_s, can be easily determined from the power spectrum of the signal (8).

The complex amplitude at the disturbance frequency ω_s is

Here, two unknown are presented in the phase of this complex amplitude, τ and ϕ_s. The complex amplitude of the spectral component at the modulation frequency ω_m is

This spectral component is a superposition of the signals from the disturbed interferometer and all other backscatters in the fiber. It can not be used for localization. Moreover, special measures should be taken to avoid influence of this powerful but noisy component on the accuracy of localization.

The spectral component ω_m-ω_s has a complex amplitude

and, finally, the frequency component ω_m+ω_s has a complex amplitude

Together with (9), any of the later two spectral components, (11) or (12), can be used for the time delay determination. By measuring phases of complex amplitudes, (9) and (12), a system of two linear equations can be solved in respect to τ :

and then the distance to the perturbed interferometer can be calculated as

where ϕ_p is the phase difference between measured phases of spectral components (12) and (9), c is the speed of light and n is the effective refractive index of the fiber core.

To avoid 2π uncertainty in phase calculations, the modulation frequency must satisfy the following condition:

3. Experiment and discussion

In order to demonstrate functionality of the proposed method, 3 identical 1-meter long interferometers were formed in a 5 Km long standard telecommunication fiber (SMF-28e) at the distances of 3, 4 and 5 km from the light source, correspondingly. The interferometers were formed by imprinting equal low-reflective Bragg gratings (0.1% each) directly in the SMF-28 fiber without hydrogen loading. All gratings were centered at the Bragg wavelength of 1534.5 nm and had spectral bandwidth of approximately 0.1nm. The fiber remote end was immersed to avoid the Fresnel reflection. A DFB diode laser had CW output power of 5 mW and its wavelength was tuned by temperature adjustment into reflectance band of the Bragg gratings. Then, temperature stabilization of the lased diode was used to maintain the selected wavelength. An external electro-optic intensity modulator was used to modulate the probe light at a low frequency f_m=10 kHz. Since the intensity modulation was not synchronized with the signal acquisition, an additional reference channel was used to determine the phase delay of the probe light reflected from the sensing fiber. The photo-detector amplifier had a low pass filter with cutoff frequency of 50 kHz. In order to reduce the coherence length of the DFB laser to approximately 3 meters, a small amplitude direct modulation of the laser diode pump current was used at frequency of 250 KHz. Since this frequency is much higher than the cut-off frequency of the low-pass filter of the amplifier, this modulation did not affect operation of the sensing interferometers while efficiently reduced the noise related to coherent effects in Rayleigh backscattering.

In laboratory tests, the disturbance of the sensing interferometers was performed with a help of a piezoelectric actuator producing dynamic axial strain of the fiber section between Bragg gratings, as it is shown schematically in Fig. 2. The optical fiber was fixed to posts with a small tension in such a way that the Bragg gratings were outside of the strained section. The piezoelectric actuator being in mechanical contact with one post induced dynamic perturbation of the selected interferometer. In experiments, the perturbation frequency was of 1 KHz.

 

Fig. 2. Scheme for applying dynamic strain to a fiber interferometer.

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The output signals of the photo-detectors were captured with a digital oscilloscope using the sampling frequency of 100 KHz and the acquisition time of 20 ms. Then, digitized signals were transferred to a personal computer for signal processing.

Figure 3(a) shows the power spectrum of the photo-detector signal in the case when no dynamic strain was applied to any interferometer. A sharp peak at the modulation frequency contains an incoherent sum of the signals from all 3 interferometers and from Rayleigh backscatter. When a dynamic strain is applied to one of the interferometers, the power spectrum changes.

 

Fig. 3. Examples of a power spectrum of the photo-detector signal. (a). No dynamic strain was applied. (b). Vibration at frequency of 1 kHz was applied to an interferometer.

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Figure 3(b) shows a power spectrum of the 20 ms signal when a dynamic strain of 0.3µε was applied to the third interferometer, located at distance of 5 Km from the laser. One can observe all frequency components mentioned above, namely, ω_s, ω_m-ω_s, ω_m and ω_m+ω_s and represented by (9)–(12). For detection of the alarm event, the amplitude of the vibrational baseband signals, such as a spectral component at ω_s, are compared with a predetermined threshold level. If one or several frequency components of the baseband signal exceed the threshold, an alarm condition can be indicated and the localization of the disturbed interferometer can be performed.

From data presented in Fig. 3(b), signal-to-noise ratio for a baseband signal used for detection an event can be estimated as 52dB/Hz, and for sideband signals used for localization SNR=29dB/Hz. From these values, the disturbance detection has a strain threshold of 0.75nε/Hz ^1/2.

In order to determine the localization accuracy of the system, we performed 3 cycles of measurements, 25 measurements in each cycle. For comparison, the positions of the interferometers were measured with a commercial OTDR. These values are shown in Fig. 4 by dotted lines. The only difference between the cycles was in the position of the disturbed interferometer. In other words, during first 25 measurements we disturbed the interferometer located at distance of 5051 meters, next 25 measurements was for dynamic strain applied to the interferometer at distance of 4042 meters, and final 25 measurements were for distance of 3015 meters. For each acquired 20 ms signal, using the measured phases, we calculated the position of the disturbed interferometer. It should be noted, that no wavelength tuning was performed in order to compensate temperature fluctuation of the interferometer “operating point”. So, sometimes the second harmonic of the basic disturbance frequency was comparable or even higher than the first harmonic. In this case the component with the higher amplitude was used for localization. Fig. 4 demonstrates results of these measurements. For each cycle, an average distance was calculated (corresponds to averaging over 0.5 seconds) and these values are shown by solid lines.

 

Fig. 4. Positional results after a series of discrete 20-msec measurements (samples) of the position of a perturbed interferometer. Three different interferometers were excited one after another and series of 25 samples was taken for each position of the disturbance. Solid lines represent averaged result for each position of disturbance. For comparison, positions of the interferometers measured with OTDR are shown by dotted lines.

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Discrepancy between the location data obtained using the proposed technique (with 0.5 s averaging time) and with the OTDR measurements (averaging time of 1 minute) were 7, 19 and 32 meters for interferometers located at 3, 4 and 5 kilometers, respectively. Such a small averaging time makes possible location of disturbances in form of single impacts. Clear, that the system location accuracy will increase with longer averaging time.

Another experiment was performed with a serial array of 15 identical interferometers. The adjacent interferometers in the array were separated by 10 meters and each interferometer had the length of 1 meter. In difference with the first experiments, the Bragg gratings had 2.5 times lower reflectivity (0.04% each) and wider bandwidth (0.2 nm each). The array was placed at distance of 1 Km from the DFB laser, the total length of the fiber was approximately 3200 meters in this case. Two sets of measurements were performed, when dynamic strain was applied to the first interferometer and then to the last one. The distance between these two interferometers was 154 meters as measured with a tape-measure, and 153 m with OTDR. Using proposed technique, an averaged calculated distance between these two interferometers was found to be 156 meters (averaging over 1 second), what is in a very good agreement with independent measurements. So, we can conclude that the localization accuracy of the proposed technique is better than 10 meters.

The principle of operation of the sensor system allows detection and localization of narrow-band as well as wideband disturbances. The detection of the disturbance is based on the amplitude analysis of the baseband signal. In this paper, for simplicity, we presented an analysis for small amplitudes of single-frequency disturbances. Even in this case, a power spectrum of photo-detector signal can contain second and higher harmonics of the perturbation frequency since the working points of sensing interferometers are not stabilized. When amplitude of the disturbance is large, nonlinear distortions appear in the photo-detector signal. Nevertheless, every of the frequency components exceeding the established amplitude threshold level in the power spectrum can be used for localization of the perturbed interferometer utilizing the proposed algorithm. The localization procedure can be performed independently for each frequency component of the detected disturbance. In case of a single broadband perturbation, averaging of results obtained for different spectral components allows to increase the localization accuracy. Also, in some specific cases, localization of multiple simultaneous disturbances is possible. If two or more interferometers are disturbed simultaneously at different frequencies, they can be localized using corresponding frequency components.

When a frequency component, ω_s, of the perturbation exceeding the threshold is determined, the frequency component in side-band signal, which we use for localization, ω_s+ω_m, is also known. Therefore the localization can be performed even for low SNR of the sideband signal. The main source of noise in our experimental setup was the phase noise of the DFB laser diode, approximately $3\frac{\mathrm{mrad}}{\sqrt{\mathrm{Hz}}}$ for 1 meter long interferometer. We believe, so high noise level was coming from the pump current of the laser diode, since we used a simple current controller. Our estimations show that, if a low-noise laser will be used, the number of interferometers in the system can be well above 100, maintaining high accuracy of localization.

4. Conclusions

We present a new optical fiber system for detection and location of a time varying perturbation along the fiber. The system uses identical 1 meter long F-P cavities as sensor elements, formed by twin Bragg gratings of low reflectivity imprinted directly in the standard SMF-28e fiber without hydrogen loading. Localization accuracy about 10 meters has been demonstrated experimentally using 5 km long fiber. The system is relatively inexpensive since it is very simple in configuration and uses low-frequency components. First experimental verification of functionality of the sensor confirms its potential for application where a continuous monitoring of long pipe lines or perimeters is necessary for detection and localization of rare vibrational disturbances.