Polarization fading elimination for ultra-weak FBG array-based &#x03A6;-OTDR using a composite double probe pulse approach

Feng Wang; Yu Liu; Tao Wei; Yixin Zhang; Wenbin Ji; Ming Zong; Xuping Zhang

doi:10.1364/OE.27.020468

1. Introduction

The phase-sensitive optical time domain reflectometer (𝜙-OTDR) was first proposed by Lee and Taylor in 1993 [1]. With the help of the interference phenomenon among Rayleigh backscattering light, the 𝜙-OTDR is sensitive to vibrations and can be used for security applications, pipeline monitoring, and interpretation of seismic measurements [2–7]. Recently, ultra-weak FBG (UWFBG) array based 𝜙-OTDR was proposed towards the application of high performance distributed vibration sensing [8–13]. In this technique, the UWFBG array embedded in the fiber is used as a set of “weak mirrors” to provide a stable and large reflected light signal at the specified locations of the fiber. The interference signal associated with the UWFBG can be processed to measure the distributed external perturbations along the fiber. In 2015, Chen Wang et. al demonstrated a distributed acoustic measurement system using 500 identical UWFBGs with an equal separation of 2m based on 𝜙-OTDR technique. The system achieved an acoustic phase sensitivity of around −158dB (re rad/μPa) with a relatively flat frequency response between 450Hz to 600Hz [11]. In 2018, Ciming Zou et. al proposed a hydroacoustic sensing array based on ultra-weak Fiber Bragg Gratings. Experiment testing demonstrates a minimum detectable hydroacoustic pressure of 2239μPa/√Hz, and exhibits a particularly large response in the very low frequency region [13]. In the same year, Tao Liu et. al proposed a double-optical-pulse technique for UWFBG array to realize the distributed vibration measurement. The minimum detectable fiber length variation was 14.85nm, the sensing frequency could be as low as 0.2 Hz with the SNR of 18 dB [12].

However, polarization fading is an important challenge which severely limiting the performance of 𝜙-OTDR. The polarization fading phenomenon arises from the mismatch of the states of polarization (SOPs) of two coherent light beams. Ideally, when the SOPs of two beams are identical, a perfect interference signal is generated. Unfortunately, in reality, the SOPs of these two beams are different, resulting in a degraded interference signal with decreased visibility. Under the worst case scenario, when the SOPs of these two beams are orthogonal, the interference signal vanishes.

Several approaches have been proposed to overcome this limitation. These techniques include the use of manual/automatic polarization controllers in the arms to match the SOPs [14], and polarization diversity detection schemes [15–17]. These methods effectively tackle the polarization mismatch between the reference light beam and the scattered optical signal. However, for the traditional 𝜙-OTDR based on normal signal mode fiber, all of the techniques are not capable of eliminating the polarization fading during the generation of the scattered signal. The scattered signal can be viewed as a superposition of massive amount of scattered pulses with differing polarization states. In order to fundamentally tackle this challenge, one alternative approach is through the adoption of polarization-maintaining (PM) fiber [18] for both reference and sensing fibers. The trade-off is apparently a significant cost increase.

In this paper, based on the unique nature of the UWFBG array in generating the optical signals, we propose to use a new method, namely composite-double-probe-pulse (CDPP), to eliminate the influence of polarization fading. The CDPP is composed of two optical pulses with different modulation frequencies, and one of the optical pulse is composed of two continuous short-pulses whose SOPs are orthogonal to each other. Using only direct detection the influence of polarization fading can be eliminated thoroughly while achieving quantitative measurement and maintaining the high SNR characteristic of the UWFBG array simultaneously.

2. Principle

The profile of the proposed CDPP is shown in Fig. 1. The CDPP is composed of two optical pulses. The first optical pulse is a single pulse and the second optical pulse is a composite pulse constructed by two short pulses with equal width and orthogonal SOPs. In other words, the width of the first pulse is equal to the combined width of the second composite pulse. The spatial interval between the first and the second optical pulses is equal to twice that of the spatial interval between neighboring UWFBGs. When the CDPP interacts with a pair of UWFBGs in the array, the optical signal from the second pulse reflected by the front UWFBG will join with the optical signal from the first pulse reflected by the rear UWFBG. Then, the overlapped reflection signal will propagate back together, and eventually collected by the detector. It is worth noting that the frequencies of the first probe pulse and the second probe pulse are different.

Fig. 1 The profile of the CDPP.

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Jones representation can be used to describe this process. The electric field of the first optical pulse is

E_{1} = A_{0} e^{j (ω_{1} t + ϕ_{1})} [\begin{array}{l} \sqrt{P_{1 x}} \\ \sqrt{1 - P_{1x}} e^{j Δ ϕ_{1}} \end{array}],

and the electric fields of the two short optical pulses in the second optical pulse are

E_{2}^{'} = A_{0} e^{j (ω_{2} t + ϕ_{2}^{'})} [\begin{array}{l} \sqrt{P_{2 x}} \\ \sqrt{1 - P_{2 x}} e^{j Δ ϕ_{2}} \end{array}]

and

E_{2}^{' ​'} = A_{0} e^{j (ω_{2} t + {ϕ^{″}}_{2})} [\begin{array}{l} \sqrt{1 - P_{2 x}} \\ \sqrt{P_{2 x}} e^{j (Δ ϕ_{2} - π)} \end{array}]

respectively. In Eqs. (1) and (2), A₀ is the amplitude, ω₁ and ω₂ are the angular frequencies,

ϕ_{1}

,

ϕ_{2}^{'}

and

ϕ_{2}^{' ​'}

are the initial phases.

p_{1}_{x}

is the power of the first pulse in horizontal polarization direction (x-axis), and

p_{2 x}

is that of the front short pulse, which is the first half of the second optical pulse, shown in Fig. 1.

Δ ϕ_{1}

,

Δ ϕ_{2}

,

Δ ϕ_{2} - π

are the initial phase differences between the horizontal and vertical polarization directions for all three electric fields. Apparently,

E_{2}^{'}

and

E_{2}^{' ​'}

are orthogonal to each other [16].

When the CDPP interacts with a UWFBG pair, the optical signal from the second pulse reflected by the front UWFBG overlaps with the optical signal from the first pulse reflected by the rear UWFBG. This process can be described rigorously as follows. Assuming a fiber section with a length of z₀, the transmission matrix is expressed as:

J_{F} = (\begin{matrix} α + i β \cos 2 q & - γ + i β \sin 2 q \\ γ + i β \sin 2 q & α - i β \cos 2 q \end{matrix})

where

\begin{array}{l} α = \cos Δ \\ β = δ z_{0} / 2 \cdot \sin Δ / Δ \\ γ = ρ z_{0} \cdot \sin Δ / Δ \end{array}

with

Δ = z_{0} {(ρ^{2} + δ^{2} / 4)}^{1 / 2}

where

δ

is the linear birefringence,

ρ

is the circular birefringence,

q

is the angle between the fast axis of the linear birefringence with respect to the chosen axes Y. And for a backward transmission, the transmission matrix is:

J_{B} = (\begin{matrix} α + i β \cos 2 q & γ + i β \sin 2 q \\ - γ + i β \sin 2 q & α - i β \cos 2 q \end{matrix}) .

Thus the transmission matrix of the round-trip in a fiber section can be deduced as:

J_{R} = J_{B} \cdot J_{F} = (\begin{matrix} (α^{2} + γ^{2} - β^{2}) + i \cdot 2 β \sqrt{α^{2} + β^{2}} \cos (2 q - Φ) & i \cdot 2 β \sqrt{α^{2} + β^{2}} \sin (2 q - Φ) \\ i \cdot 2 β \sqrt{α^{2} + β^{2}} \sin (2 q - Φ) & (α^{2} + γ^{2} - β^{2}) - i \cdot 2 β \sqrt{α^{2} + β^{2}} \cos (2 q - Φ) \end{matrix}),

where

Φ = \arctan (γ / α)

. Comparing Eq. (5) with Eq. (4), it can be found that the transmission matrix of the round-trip has similar form as that of the forward transmission matrix without circular birefringence. This is because a reciprocal fiber can be equivalent to a series combination of a linear retarder and a circular retarder, and the round-trip passage would cancel the effect of the circular retarder and double the effect of the linear retarder. So we define an equivalent round-trip transmission matrix for the fiber section between the two adjacent UWFBGs as

J_{R} = J_{B} \cdot J_{F}

, where

\cos ϕ = α^{2} + γ^{2} - β^{2}

,

\sin ϕ = 2 β \sqrt{α^{2} + β^{2}}

and

θ = 2 q - Φ

[19].

When the reflected signals from adjacent UWFBGs overlap with each other, the intensity of the signals are

I_{1} = (J_{R} E_{1} + M E_{2}^{'}) {(J_{R} E_{1} + M E_{2}^{'})}^{*}

I_{2} = (J_{R} E_{1} + M E_{2}^{' ​'}) {(J_{R} E_{1} + M E_{2}^{' ​'})}^{*}

where

M = [\begin{array}{l} - r, 0 \\ 0, r \end{array}]

is the reflection matrix, and r is the reflectivity. In Eqs. (6) and (7),

I_{1}

is the coherent result between the reflected first optical pulse and the front part of the reflected second optical pulse, and

I_{2}

is the coherent result between the reflected first optical pulse and the rear part of the reflected second optical pulse.

Rearranging Eqs. (6) and (7), we can obtain

\begin{array}{l} I_{1} = 2 A_{0}^{2} r^{2} + A_{0}^{2} r^{2} \sqrt{P_{1 x} (1 - P_{1 x})} \sin 2 θ \sin Δ ϕ_{1} (cos 2 ϕ - \sin 2 ϕ) \\ + 2 A_{0}^{2} r^{2} \sqrt{B_{1}^{2} + B_{2}^{2}} \cdot \sin [Δ ω t +(ϕ_{1} - ϕ_{2}^{'}) + γ_{1}] \\ I_{2} = 2 A_{0}^{2} r^{2} + A_{0}^{2} r^{2} \sqrt{P_{1 x} (1 - P_{1 x})} \sin 2 θ \sin Δ ϕ_{1} (cos 2 ϕ - \sin 2 ϕ) \\ + 2 A_{0}^{2} r^{2} \sqrt{B_{3}^{2} + B_{4}^{2}} \cdot \sin [Δ ω t +(ϕ_{1} - ϕ_{2}^{' ​'}) + γ_{2}] \end{array}

with

\begin{array}{l} B_{1} = (C_{2} \cos δ ϕ + C_{1}) \cos ϕ + C_{2} \sin ϕ \cos 2 θ \sin δ ϕ - (C_{3} \sin Δ ϕ_{2} + C_{4} \sin Δ ϕ_{1}) \sin ϕ \sin 2 θ, \\ B_{2} = - C_{2} \sin δ ϕ \cos ϕ + (C_{2} \cos δ ϕ - C_{1}) \sin ϕ \cos 2 θ - (C_{3} \cos Δ ϕ_{2} + C_{4} \cos Δ ϕ_{1}) \sin ϕ \sin 2 θ, \\ B_{3} = (C_{4} \cos δ ϕ^{'} + C_{3}) \cos ϕ + C_{4} \sin ϕ \cos 2 θ \sin δ ϕ^{'} - (C_{1} \sin (Δ ϕ_{2} - π) + C_{2} \sin Δ ϕ_{1}) \sin ϕ \sin 2 θ, \\ B_{4} = - C_{4} \sin δ ϕ^{'} \cos ϕ + (C_{4} \cos δ ϕ^{'} - C_{3}) \sin ϕ \cos 2 θ - (C_{1} \cos (Δ ϕ_{2} - π) + C_{2} \cos Δ ϕ_{1}) \sin ϕ \sin 2 θ, \\ C_{1} = \sqrt{P_{1 x} P_{2 x}}, C_{2} = \sqrt{(1 - P_{1 x}) (1 - P_{2 x})}, \\ C_{3} = \sqrt{P_{1 x} (1 - P_{2 x})}, C_{4} = \sqrt{(1 - P_{1 x}) P_{2 x}}, \\ δ ϕ = Δ ϕ_{1} - Δ ϕ_{2}, δ ϕ^{'} = Δ ϕ_{1} - Δ ϕ_{2} + π, \\ Δ ω = ω_{1} - ω_{2}, \\ γ_{1} = arc \tan \frac{B_{1}}{B_{2}}, \\ γ_{2} = arc \tan \frac{B_{3}}{B_{4}} . \end{array}

Thus, the visibilities of

I_{1}

and

I_{2}

can be deduced as:

\begin{array}{l} V_{1} = \frac{\sqrt{B_{1}^{2} + B_{2}^{2}}}{1 + \frac{1}{2} \sqrt{P_{1 x} (1 - P_{1 x})} \sin 2 θ \sin Δ ϕ_{1} (\cos 2 ϕ - \sin 2 ϕ)} \\ V_{2} = \frac{\sqrt{B_{3}^{2} + B_{4}^{2}}}{1 + \frac{1}{2} \sqrt{P_{1 x} (1 - P_{1 x})} \sin 2 θ \sin Δ ϕ_{1} (\cos 2 ϕ - \sin 2 ϕ)} . \end{array}

Since

\begin{array}{l} V_{1}^{2} + V_{2}^{2} \\ = \frac{B_{1}^{2} + B_{2}^{2} + B_{3}^{2} + B_{4}^{2}}{{(1 + \frac{1}{2} A_{0}^{2} r^{2} \sqrt{P_{1 x} (1 - P_{1 x})} \sin 2 θ \sin Δ ϕ_{1} (\cos 2 ϕ - \sin 2 ϕ))}^{2}} \\ = 1, \end{array}

it means that the visibilities of I₁ and I₂ are complementary for each other. When the visibility of I₁ is relatively large, the visibility of I₂ is small, and vice versa. Therefore, no matter how the SOP of the first optical pulse changes, this design always generates high quality interference signal with at least one of the short optical pulses in the CDPP.

3. Experiment results and discussion

An experiment was conducted to verify the proposed method, shown in Fig. 2. The linewidth of the laser source at the wavelength of 1550 nm is 100 Hz. Its output was split into two beams by a 1 × 2 fiber coupler1. The two beams were modulated into two optical pulses respectively by the AOM1 and AOM2, whose driving frequencies were 40 MHz and 200 MHz respectively. The pulse width of the first pulse was 300 ns, and the pulse width of the second pulse, when it is generated, was 150 ns. In order to form the second pulse as desired in Fig. 1, the generated second pulse from AOM2 was firstly divided into two pulses by PC1 and PBS1. The PC1 is used to adjust the SOP of the lightwave before inputting into the PBS1 to guarantee that the intensities of the beams in the two arms of PBS1 equals to each other. A delay fiber with 30 m length was inserted into one output arm of the PBS1 to introduce 150 ns time delay difference between the two short pulses. Then, the two pulses were combined via PBS2.The PC2 after the delay fiber was used to align the SOP to be parallel to the slow axis of the input arm of PBS2. So, the optical pulse output from the PBS2 was composed of two successive 150 ns short pulses with orthogonal SOPs as shown in Fig. 1. In this experiment, the total length of UWFBG array was 4.5 km, and the spatial interval of the UWFBG array was 50m. For the fabrication of the UWFBG array, one can refer to [20]. Accordingly, we set the time delay between the first and the second optical pulse to be 500 ns to match with the spatial interval. The average reflectivity of the UWFBG array was about −40 dB. The insertion loss of the AOM1 and AOM2 were 5 dB and 6 dB respectively, the coupling ratio of the coupler2 was 50%:50%, and the additional insertion loss of the two PBSs were 1 dB. In order for the optical pulses in the CDPP to have similar peak power, the coupling ratio of the first coupler was chosen to be 30%:70%. The peak power of the CDPP was about 3 dBm and was amplified to 15 dBm with an EDFA. Its repetition rate was 10 kHz. The returned coherent signal was received by a photodetector with 350 MHz bandwidth. A data acquisition card (DAQ) with a sampling rate of 500 MSa/s was used to convert the electric signal into digital form and send them to a computer for further processing.

Fig. 2 The experiment setup using the CDPP.

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At the beginning of this experiment, a PD was set after the coupler2 to monitor the CDPP whose temporal profile is shown in Fig. 3. It can be seen that the second optical pulse is composed of two short optical pulses whose width are both about 150 ns. The time interval between the first and the second optical pulses is about 500 ns. The rising edge and trailing edge of the first optical pulse are slower than that of the second optical pulse, because the first optical pulse was modulated with a 40 MHz AOM. However, most part of the two optical pulses can overlap together when the CDPP was reflected from the UWFBG array.

Fig. 3 The temporal profile of the CDPP in experiment.

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In this experiment, the fiber under test was winding around a PZT at a location of around 4.1 km. The PZT was driven by a 30 Hz sinusoidal signal. The obtained temporal trace is shown in Fig. 4. It can be seen that there are many peaks in the trace, each of which is a coherent superposition between two optical pulses reflected from a UWFBG pair. Due to the fact that two optical pulses in the CDPP have different frequencies, each peak has obvious oscillation at 160 MHz (the modulation frequency difference between the two optical pulses). Meanwhile, each peak has two parts which are related to the front part and rear part of the second optical pulse, respectively. And the visibilities of the two parts are different in different peak. In the insets in Fig. 4, signals are enlarged to show three typical cases: 1) the visibility of the front (left) part is larger than that of the rear (right) part, 2) the visibility of the front part is smaller than that of the rear part, and 3) the visibilities of both parts are similar. These signals demonstrate that due to the reflected signal of the first optical pulse undergoes an extra round-trip in the fiber section between two adjacent UWFBGs than that of the second optical pulse, their SOPs may have various different relationships. No matter what SOPs of the first optical pulse and the second optical pulse are given at the input end, as long as each of them has single SOP, the polarization fading may occur for some UWFBG pairs. Then the sensitivities for these positions deteriorate dramatically.

Fig. 4 Temporal trace obtained with the CDPP in the UWFBG array.

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However, as explained in the principle, the visibility between the two parts of each peak should be complementary for each other. In the experiment, we have gathered the signal in Fig. 4 for 0.5 s. So we choose five traces at 0.05 s, 0.15 s, 0.25 s, 0.35 s and 0.45 s respectively to compare the visibilities between the front part and rear part of the peak at 4.1 km. The results are shown in Fig. 5. It can be seen that the visibilities of the two parts change conversely and the square sum of the visibilities at any time is 0.93~0.98. So when using the CDPP proposed in this paper, at least one part of each peak has sufficiently high visibility. Since the interference signal is a beat signal with an intermediate frequency (IF) of 160 MHz, it is easy to demodulate its phase directly by using the IQ demodulation method. The process of the phase demodulation is shown in Fig. 6 and the detailed introduction can be referred from [21]. In the peak at 4.1 km, we demodulate the phase change induced by the vibration from the rear part whose amplitude is larger than the front one. The final demodulated result is shown in Fig. 7. In Fig. 7, there exist 15 batches of signals, and the time duration of each signal is 0.5 second. It can be seen that the demodulated signal restores the driving signal accurately.

Fig. 5 The variations of the visibilities for the front part and the rear part of the peak at 4.1 km.

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Fig. 6 The process of the phase demodulation.

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Fig. 7 A demodulated sinusoidal signal with a frequency of 30Hz.

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In the following experiments, the amplitude of the sinusoidal driving signals was swept from 1V to 10V with 1V step and the corresponding phase signal was measured for each driving signal. The results are shown in Fig. 8, where the discrete points in black represent the measured data and the blue curve is the linear fitted curve. The R-square is 0.9981, and the standard deviation is 0.032 rad, which corresponds to an optical path measurement uncertainty of 3.8 nm. So it demonstrates the setup can achieve good linear measurement.

Fig. 8 Demodulated phase information with different function generating voltages at 30Hz.

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In practice, the SOP of the optical pulse may vary continuously due to the influence of external circumstance. So the visibilities of the two parts in each interference peak may vary with time. When the visibility of one part becomes very small, it will induce significant error in the IQ demodulation process. On the contrary, the visibility of the other part will become large at the same time. So we need to shift the objective signal to be demodulated from one part to the other part of the interference peak. However, since the second optical pulse is constructed by combining two orthogonal short optical pulses, there is an inevitable phase discontinuity between the two parts of each interference peak in the reflected signal. So in order to measure the external perturbation continuously during the shifting, the phases demodulated from the two parts should be identical with each other in a same temporal trace.

Figure 9 shows an example of the temporal trace in which both parts of the interference peak have moderate visibilities for the demodulation of phases. Since the PZT was located between the two UWFBGs generating the interference peak, both parts of the interference peak were modulated by the vibration. According to the process of phase demodulation in Fig. 6, the phases of the two parts can be obtained respectively. Then we measured the signal for 0.5 s and the phase evolutions of the two parts during this period are shown in Fig. 10. From the figure, we can see that the results obtained from the two parts have the same profile including the amplitude, frequency and waveform. The only difference is the initial phase (amplitude offset) which is induced by the position difference of the selected points and the phase discontinuity between the two parts of the interference peak. Thus, before shifting the objective signal from one part to the other, demodulating the phases of both parts in parallel for a short period to obtain two phase traces and to align them together can make us measure the external perturbation continuously after the shifting.

Fig. 9 The phase demodulated by subtracting the interference signals on the adjacent gratings.

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Fig. 10 The results of phase demodulation after subtracting the phase of the adjacent gratings.

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4. Conclusion

An interrogation method by a composite-double-probe-pulse for UWFBG array is proposed. The CDPP is composed of two optical pulses with different frequencies and one of the optical pulse is composed of two continuous short-pulses whose SOPs are orthogonal to each other. The proposed method is free of polarization fading which deteriorates the performance of 𝜙-OTDR severely, and can achieve quantitative measurement with only direct detection. The experiment result shows that this novel method can achieve good performance. The influence of polarization fading is eliminated for all the positions along the UWFBG array. And the disturbance signal applied on the fiber can be accurately demodulated at the same time.

Funding

National Natural Science Foundation of China (NSFC) (61627816), the Key Research and Development Program of Jiangsu Province (BE2018047), the Natural Science Foundation for Young Scientists of Jiangsu Province (BK20180328) and the Fundamental Research Funds for the Central Universities (021314380116).

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Polarization fading elimination for ultra-weak FBG array-based Φ-OTDR using a composite double probe pulse approach

Abstract

1. Introduction

2. Principle

3. Experiment results and discussion

4. Conclusion

Funding

References

Cited By

Figures (10)

Equations (13)

Optics Express