1. Introduction

Scattering of light is widely used for imaging [1] and distributed optical fiber sensing, with the latter mainly uses Rayleigh [2,3], Brillouin [4–6], Raman [7] scattering or their combination [8] in optical fibers. As a distributed optical fiber sensing technology based on Rayleigh scattering, phase-sensitive optical time domain reflectometer (Φ-OTDR) has a high sensitivity up to the nano or even pico strain scale, which is usually used for weak vibration event detection [8–10] and has a great prospect for applications in seismic wave detection [11,12] and oil and gas exploration [13].

Quantitative analysis for amplitude and frequency of vibration event can be achieved by the Φ-OTDR system through analyzing the phase difference between two reference positions before and after the vibration region. It derives the dynamic process of phase in the vibration region over time. However, the phase depends entirely on the strength of the Rayleigh backscattering (RBS) signal at the reference position. Since the refractive index of the sensing fiber and positions of internal scattering points are all randomly distributed, the coherent constructive and destructive interferences of the RBS signal are both random. When the signal is very weak, the demodulated phase will have serious distortion, which is the fading effect. Due to the fading effect of the Φ-OTDR system, the RBS light intensities at certain locations of the fiber will be extremely low, where the phase can be easily distorted. This results in the inability of the system to correctly reflect the external vibration events, making it being frequently misrepresented in practical applications such as structural health monitoring.

Therefore, it is important to study the methods for suppression of fading effect in Φ-OTDR systems, on which many efforts have been made up to now. Pan et al. proposed the digital coherent detection employed into the Φ-OTDR with a high SNR [14]. Zhou et al. pointed out that RBS signals with different frequencies have different distributions of fading locations [15]. A. E. Alekseev et al. used a multimode fiber as the sensitive element for RBS signals, suppressing fading effects through joint and independent analysis techniques, thus, enhancing the sensitivity of the system to external vibration signals [16]. He’s group proposed the use of linear chirp pulses, obtaining multiple RBS signal intensity profiles by bandpass filtering, and suppressed the fading effect using the rotating vector sum method with remarkable results [17]. Cai’s research group suppressed the fading effect by differential phase-shifted pulse technique without sacrificing vibration response bandwidth [18]. Wu et al. proposed a spectrum extraction remixing scheme to suppress the fading effect by multiplexing the flanks of a single pulse with the main flanker, in which no complicated pulse modulation is required, and the signal processing executed in digital domain is simple [19]. M. Zabihi et al. simultaneously accessed three acoustic optic modulators (AOM) with different frequency shifts in the Ф-OTDR system to suppress the fading effect by frequency division multiplexing [20]. Liu et al. proposed a fading free distributed acoustic sensor assisted with the scattering enhanced optical fiber and double wavelength lasers. The random polarization fading is effectively eliminated by synthesizing the scattering signals of two lasers [21]. Subsequently, Zhao et al. proposed the use of a few-mode fiber as a sensing medium for Φ-OTDR system and multiplexed RBS signals of different modes to suppress the fading effect in the system [22]. Moreover, He et al. proposed the phase-shift transform and demonstrated to suppress the fading effect in Φ-OTDR [23], and Qian et al. used the multi-frequency decomposition (MFD) scheme to suppress the fading effect [24]. For the two methods mentioned in Refs. [23] and [24], the phase shift transform method requires an auxiliary polarization diversity detection or multiple transforms, and the MFD method decomposes the detected signal into a large number of components with different amplitude fluctuations by setting an appropriately sized sliding window, and performs short-time Fourier transform on the detected signal.

This paper presents an innovative method for fading suppression in the Ф-OTDR system using an optical frequency comb, which is based on the use of a phase modulator. As a proof of concept, we demonstrate experimentally that using an optical frequency comb composed by a center frequency of 200 MHz and its ±1st, ± 2nd and ±3rd order sidebands with intervals of 40 MHz, the probability density of occurrence of fading effects can be effectively suppressed to 0.08%. This method does not sacrifice the response bandwidth and spatial resolution of the system; moreover, the number and interval of modulated frequencies can be flexibly controlled, and the phase delay can be precisely controlled.

2. Theory

In the Φ-OTDR system based on the outlier detection structure, the phase is accumulated with the sensing distance. By making a difference between the phase of two positions in the front and rear of the vibration region in the sensing fiber in a stable state, the phase introduced in the vibration region can be obtained. In our method, the phase modulator in the system generates a continuous light in the form of a frequency comb, which is then modulated into a pulsed probe light and injected into the sensing fiber to produce different RBS intensity distributions.

The principle of generating an equal-amplitude optical frequency comb through phase modulation is as follows [25]:

First, we define V_m as the modulation voltage amplitude, V_π as the half-wave voltage of the phase modulator, and γ as the modulation index with the relationship of:

For any periodically modulated signal m(t) with a fundamental frequency f_m, the Fourier series expansion is:

Then a continuous light in the form of a frequency comb can be produced under the modulation of m(t) with the time domain expression as:

By using an AOM with a frequency shift of Δf, a single probe pulse can be achieved in the form of an optical frequency comb which contains multiple frequency components with equal amplitudes as:

After coherent detection, the RBS signal, which is generated by the pulsed probe light injected into the fiber, contains multiple frequency components of ± nf_m-Δf, and its frequency interval f_m is determined by the pulse width τ of the probe light. To avoid spectral overlap, it is usually necessary to satisfy f_m> 4/τ. The RBS signal is filtered by a digital bandpass filter with a frequency range of [nf_m-Δf-1/τ, nf_m-Δf + 1/τ], so that only a single measurement is needed to obtain the RBS signal with multiple frequency components.

3. Experimental setup

The experimental setup of the Φ-OTDR system is shown in Fig. 1. The continuous light output from a narrow linewidth laser (NLL) with a linewidth of 3 kHz and a central wavelength of 1550.12 nm is divided into two branches by a 90:10 optical coupler (OC1). In the upper branch, the continuous light (90%) is firstly modulated by a phase modulator (PM) to contain multiple frequencies, and then modulated into a pulsed probe light with a width of 100 ns and a repetition frequency of 10 kHz (100 µs) by an AOM with a 200 MHz downshift frequency. The pulsed probe light is amplified by an Erbium-doped fiber amplifier (EDFA) and then injected into the fiber under test (FUT) with a total length of about 4 km through an optical circulator. A piezoelectric ceramic (PZT) wrapped with a 20 m fiber is located near 2 km of the FUT and is used to generate the vibration signal. In the lower branch, the continuous light (10%) is used as a reference light passing through the polarization controller (PC), coherently coupled with the RBS signal by a 50:50 optical coupler (OC2); then the photoelectric conversion is performed by a balanced photodetector (BPD) with an operating bandwidth of 350 MHz, and finally a real-time dynamic acquisition by an oscilloscope (OSC) with a distance sampling rate of 2 GSa/s and a time sampling rate of 10 kHz. The modulation signal of the PM, the acquisition trigger of the OSC, and the excitation signal of the PZT are all provided by the arbitrary waveform generator (AWG).

 

Fig. 1. Experimental setup. NLL, narrow linewidth laser; OC, optical coupler; PM, phase modulator; AOM, acoustic optical modulator; EDFA, Erbium-doped fiber amplifier; CIR, circulator; PC, polarization controller; FUT, fiber under test; PZT, piezoelectric ceramic; BPD, balanced photodetector; AWG, arbitrary waveform generator; OSC, oscilloscope.

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4. Results and discussions

First, the sensing fiber was placed in a soundproof box to exclude the influence of ambient waves on the experimental results, to facilitate an accurate assessment of the fading effect in the system, and to analyze the suppression effect of the proposed scheme on the fading effect.

Second, to avoid spectral aliasing and deterioration of the RBS signal quality, the modulation frequency of the PM was set to 40 MHz, so that the modulated signal contains the fundamental frequency (±40 MHz), the second and the third harmonics (±80 and ±120 MHz). The continuous light output from the NLL with the frequency f_c is modulated sequentially by the PM into the form of an equal-amplitude optical frequency comb and by the AOM to obtain a downshift of 200 MHz, with seven frequency components of f_c± n40-200 MHz, n = 0, 1, 2, 3.

Finally, the RBS signal detected after coherent beat frequency contains seven frequencies: 80, 120, 160, 200, 240, 280 and 320 MHz, respectively. Figure 2 shows the RBS intensity distributions in a length range of 100 m where (a) is the local amplification of the RBS signal and (b)-(h) are for its seven frequency components, respectively.

 

Fig. 2. Time domain intensity distributions of the RBS signal. (a) local amplification of the RBS signal; (b)∼(h) local amplifications of its 80, 120, 160, 200, 240, 280, and 320 MHz components, respectively.

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The spectrum of the RBS signal is shown in Fig. 3. It can be visualized that it mainly contains seven frequency components of 80, 120, 160, 200, 240, 280, and 320 MHz, which is consistent with the theoretical analysis results.

 

Fig. 3. Frequency spectrum of the RBS signal.

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Figure 4 shows the normalized intensity distributions of the seven frequency components of the RBS signal in the sensing range of 150-250 m. It can be obviously seen from the figure that those points with very low intensity for 80, 120, 160, 200, 240, 280, and 320 MHz do not overlap one another, which indicates that the distribution of their fading locations is not consistent, therefore the fading effect can be adequately suppressed by mixing of these frequencies.

 

Fig. 4. Normalized intensity distributions of the seven frequency components.

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After eliminating the environmental interference, the intensity distribution of the RBS signal in the Φ-OTDR system remains unchanged, i.e., the distribution of the fading position remains unchanged, which facilitates our discussion of the fading effect. The differential phase obtained from the Hilbert transform [26] is unwrapped, and the results are shown in Fig. 5.

 

Fig. 5. Differential phase distributions of the seven frequency components filtered at their respective center frequencies.

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The large phase differences at the starting end of the sensing fiber shown in Fig. 5 are mainly due to the time delay introduced by the digital bandpass filtering of the RBS signal, which is partially ignored. In spite of this, Fig. 5 shows that the fading effect causes phase difference distortions at many locations for each of the 80, 120, 160, 200, 240, 280, and 320 MHz components. Fortunately, their distortion points do not overlap one another, which is consistent with the results shown in Fig. 4.

With a spatial resolution of 10 m as the interval for phase reconstruction, the normalized intensities of the 80, 120, 160, 200, 240, 280, and 320 MHz components were statistically analyzed, with the value of 0.1 used as the threshold to judge the existence of fading effect [20]; and the probabilities of cumulative occurrence of the normalized intensities measured in this experiment were simultaneously calculated. The statistical results are shown as the solid curves in Fig. 6, where the vertical dashed line shows a normalized intensity of 0.1, indicating the fading probability density of each frequency component is mainly distributed in the range of 5.49%-9.83%.

 

Fig. 6. Probability density of the RBS signal and its seven frequency components.

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After suppressing the fading effect by amplitude evaluation, the correction result is shown as the green dashed line in Fig. 6, and the fading probability density is as low as about 0.08%. This indicates that the corrected phase fidelity is improved from 90.17%-94.51% to 99.92% compared to those of the single-frequency RBS components. If polarization diversity is used to exclude the calculation error caused by polarization attenuation, an even higher phase fidelity can be expected.

The above experimental results fully corroborate the feasibility of using a phase modulator to generate an equal-amplitude optical frequency comb, as well as sufficient suppression of the fading effect with the amplitude evaluation method.

To verify the ability of the system to extract actual vibration signals, a 20 Hz triangular wave vibration generated by a piezoelectric ceramic was applied at the 2 km position on a sensing fiber with a length of 4 km. The extracted differential phase distribution and the frequency spectrum of the vibration signal are shown in Fig. 7(a) and Fig. 7(b), respectively, which indicates that the vibration is located at the position of 2 km. Furthermore, as it is illustrated in Fig. 7(a), there are approximately ten periods for the periodic triangular waveform within 500 ms; and the spectrum in Fig. 7(b) show a central frequency of 20 Hz, which are consistent with the 20 Hz frequency of the vibration signal provided by the piezoelectric ceramic. The system has shown the ability of highly-fidelity extraction for the actual vibration signal.

 

Fig. 7. Results of high-fidelity phase extraction for a 20 Hz vibration signal (a) Differential phase distribution; (b) Frequency spectrum.

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5. Conclusion

In this paper, a novel method for fading suppression in Φ-OTDR system based on phase modulated optical frequency comb is proposed and demonstrated. In our scheme, a continuous light in the form of an equal-amplitude frequency comb is generated by a phase modulator and then modulated into pulsed probe light to obtain backscattered Rayleigh light of different intensity distributions for each frequency component. The fading effect is almost completely suppressed without sacrificing the response bandwidth and spatial resolution of the system with our method. It is experimentally verified that by using an equal-amplitude optical frequency comb containing seven frequency components, the fading probability density is sufficiently reduced to as low as 0.08% and high-fidelity phase extraction is achieved.

The scheme features a flexible and controllable number of frequencies, precise control of the phase delay, and a larger modulation bandwidth than, for example, conventional methods based on the use of AOM to suppress the fading effect, which provides a new way for high-precision measurement of vibration signals.