Dynamic Phase Demodulation Algorithm for Phase-Sensitive OTDR With Direct Detection

A dynamic phase demodulation algorithm for direct detection <inline-formula> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula>-OTDR is proposed and experimentally demonstrated. It offers a way for single channel direct detection <inline-formula> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula>-OTDR, which is the simplest and most cost-effective structure, to realize phase demodulation. Through making use of the redundant information between the sensing series from the vibration impacted region, the local extreme points(LEP) of the sensing series can be divided into two types. The second type LEP offers light phase quadrant information, and then the phase can be further reconstructed through anti-trigonometric function. Single frequency and amplitude-modulated waveforms have been correctly demodulated. The demodulated phase amplitude agrees well with theoretical value, which shows a potential application in strain measurement.


I. INTRODUCTION
Phase-sensitive optical time domain reflectometry ( -OTDR) was first proposed in 1993 [1]. Compared to conventional OTDR, -OTDR employs highly coherent laser source, which makes the Rayleigh backscattered traces(RBT) coherent and can respond to external vibration. Due to its dynamic vibration detecting ability, -OTDR has been widely investigated and applied in fields, such as monitoring safety and integrity of long pipelines, railway infrastructures and health monitoring of huge structures [2]- [9]. The intensity of backscattered light carries the waveform information of the external vibration. Some technologies have been studied to improve the performance of intensity signal. Alekseev et al. [10] applied a chirp probe pulse under specific law against the self-phase modulation(SPM) effect to improve the contrast of the intensity signal. But this technique can only fully compensate SPM at one certain sensing position. Pastor-Graells et al. [11] applied liner chirp probe pulse in -OTDR and realized temperature and strain measurement through trace to trace comparison. However, the trace to trace comparison reduces the frequency response and a GHz sampling equipment is necessary required in [11], The associate editor coordinating the review of this manuscript and approving it for publication was Muguang Wang . which is expensive. Bhatta et al. [12] applied correlation method into chirp-pulse -OTDR and increased the maximum detected strain to about 1000 micro-strain. But the maximum strain is still limited by the frequency band of the chirp pulse, which is 150MHz frequency shift for 1 microstrain. Moreover, due to the nonlinear effect of interference, the intensity signal is distorted. In order to retrieve the external vibration waveform, phase demodulation needs to be applied. Masoudi et al. [13] and Masoudi and Newson [14] proposed a phase demodulation -OTDR structure based on local oscillator and 3×3 coupler. This scheme requires the use of three photo-detectors working in synchronization and an extra interferometry with thermal isolation for stable demodulation. Another way to retrieve the light phase is through I/Q (In phase and Quadrature) demodulation. Wang et al. [15] used a 90 • optical hybrid to generate the I/Q components and utilized two detectors and two-channel synchronous acquisition. Pan et al. [16] applied a local oscillator and detected the coherent light with certain beat frequency through a high speed data acquisition equipment, which is costly. The light phase was then obtained through digital I/Q demodulation. Fang et al. [17] applied phase-generated carrier (PGC) modulation in -OTDR, which required an unbalanced Michelson interferometry, and then obtained the light phase through PGC demodulation process. Muanenda et al. [18] applied homodyne detection to stabilize the demodulation, which requires an extra intererometry and phase modulator at the head end. Liu et al. [19] applied heterodyne detection to obtain the I/Q components and demodulated the differential phase, which requires two channel synchronous coherent detection and acquisition. He et al. [20] applied self-mixing demodulation with heterodyne detection to stabilize the frequency mixing procedure. Jiang et al. [21] applied Kramers-Kronig receiver in -OTDR and realized phase retrieving with one-channel heterodyne detection. Generally, the phase demodulation methods in the literature require coherent detection, extra interferometry or multi-channel synchronous detection and acquisition system, which makes the sensing system more complex and costly.
In -OTDR, the phase change caused by external vibration can be detected in a region around the vibration position due to the width of probe optical pulse. Thus, all the sensing series from that impacted region can be used for retrieving the light phase. The redundancy information between these sensing series gives the possibility for dynamic phase demodulation through only one channel direct detection. Sha et al. [22] proposed a demodulation method based on two sensing series from the vibration impacted region with one channel direct detection. Through summation and difference of the sensing series, the IQ component of the extra phase and initial phase can be obtained. However, once the difference component is too small, the phase demodulation will fail. Besides, these two sensing series used for demodulation needs to be carefully chose to avoid coherent fading. This paper proposes a dynamic phase demodulation algorithm for -OTDR with only one-channel direct detection, which is the simplest and most cost-effective -OTDR structure. Through analyzing and inspecting the redundancy in the sensing series from the vibration impacted region, the phase quadrant information can be retrieved. Combined with the phase quadrant information, light phase could be demodulated through inverse cosine operation of the normalized intensity. As there is no subtraction operation in the algorithm, the small-amplitude problem can be avoided. Experiment results show that the algorithm can correctly extract the dynamic phase waveform for single frequency vibration, amplitude-modulated vibration and chirp vibration. The measured phase amplitude agrees well with the theoretical calculated value, which shows that this algorithm can be further used for strain or temperature detection.

II. PRINCIPLE
In -OTDR structure, the Rayleigh backsacttering light is formed from multiple scatters and can be described as [22], where z M represents the spatial distance from the optical detector, the marker M means the M-th scatter is at the position z M , N is the total number of scatters from z M to z M + SR, SR is the spatial resolution(SR) of -OTDR, which is half of the probe pulse length in optical fiber, α is the attenuation coefficient of optical fiber, e k and ϕ k are the amplitude and optical phase change caused by the k-th scatter, K and ω are the wavenumber and angular frequency of probe light and E 0 is the initial amplitude of probe pulse. As the addition is within the range of SR, which is half of the pulse width and rather short, the term of attenuation can be ignored.
If a perturbation appears at z M 1 , the Rayleigh backscattering trace(RBT) in the section ([z M 1 , z M 1 + SR]) can be described as a sum of two terms [22], where θ(t) is the optical phase change caused by the perturbation at z M 1 .
The light intensity acquired at the head of the fiber can be expressed as [22], where, In Eq. (3), the four quantities A 1M , A 2M , ψ 1M and ψ 2M are a result of the scattering profile, which determined by the sensing fiber. Their values are stochastic and unable to be obtained. However, once the sensing fiber and the source laser is assigned, those four quantities are determined. They are supposed to be constant if the whole sensing system is in an ideal condition. However, in the practical situation, those four quantities will be affected by the environmental temperature fluctuation, laser frequency drift, and laser power fluctuation, which leads to a slowly drift of those four quantities. But they can still be treated as a constant parameter in a short time range, for example, in 0.1 second. In order to simplify the analysis, the intensity in Eq. (3) can be rewritten to be, where θ (t) is the derivative of θ(t). Let Eq.(9) to be zero, the local extreme points(LEP) of I M (t) can be obtained. These LEPs can be expressed as, Eq. (10) shows that there are two types of LEP. The first type of LEP (LEP-I) is inherited from the phase change caused by the perturbation. These LEPs have has nothing to do with the distance mark M, which means they appear at the same moment for different sensing positions, which is in the range of [z M 1 , z M 1 + SR]. The second type of LEP (LEP-II) is determined by both the phase change θ(t) and the initial phase ψ M . For different sensing positions, their initial phases ψ M are different. Thus, the occurrence moments of LEP-II are different for different sensing positions. Fig.1 gives an example shows the difference between LEP-I and LEP-II. LEP-Is always occur at the same time and LEP-IIs occur at different time.
As LEP-I and LEP-II have different origins, they can be separated through inspecting multiple sensing series in Through inverse cosine, the phase in Eq. (12) can be expressed as, In order to gain θ(t), i and n are still needed to be determined. Considering θ(t) is the phase change caused by extra perturbation, it can be regarded as a continuous function. Firstly, the parameter i is determined. Assume the set of LEP-II is {t 1 , t 2 , t 3 , . . .}. These LEP-IIs divide the whole time into several subsections. In each subsection, for example [t 1 , t 2 ], the parameter i keeps the same. And for every adjacent subsections, for example [t 1 , t 2 ] and [t 2 , t 3 ], their parameter i are different. Assuming the parameter i is 1 in the first subsection [0, t 1 ], the parameter i in the rest subsections can be determined one by one. After the parameter i is obtained, the parameter n can be determined by a traditional phase unwrapping operation, such as the unwrap function in Mat-Lab. Considering the initial phase ψ M is a slow varying drift and the perturbation phase change θ(t) is an fast oscillation, they can be further separated by a high pass or low pass filter.
The algorithm flow is shown in Fig.2. It should notice that this algorithm using the sensing series within the SR of -OTDR. Thus the SR of this algorithm is the same as the SR of -OTDR. And the vibration is located by the intensity trace before phase demodulation.

A. EXPERIMENT SETUP
The experiment system setup is shown in Fig.3. An ultra narrow line width laser with 3kHz line width is used as the light source. The continuous probe light is then modulated into pulses by an AOM and boosted by an Erbium doped fiber amplifier (EDFA). The repetition rate of the probe pulse VOLUME 8, 2020  is set to be 20kHz, with 200ns pulse width, corresponding to 20m SR. A fiber Bragg grating (FBG) is employed to remove the amplifier spontaneous emission (ASE) noise from EDFA. The probe pulse light is then injected into a 1km long sensing fiber through an optical circulator(Cir.2) and the RBT is detected by a photo detector with 400MHz bandwidth. The detector's signal is sampled by a 100MS/s data acquisition card (DAQ), corresponding to about 1m per sampling point. One piezoelectric transducer cylinder (PZT) with 1.25cm radius and 1.05m optical fiber glued on its outside is placed at 200m away from Cir.2 and is applied as a perturbation source. The attached fiber is pre-tensioned when we glue it. The PZT is then driven by a signal generator. The vibration amplitude of the PZT under different driving voltages and frequencies have been measured by a laser displacement sensor (Made by Keyence ) and is shown in Fig.4. From Fig.4, the vibration amplitude is tens of nanometer. In the experiment, the driving voltage is set to be 6Vp-p. In order to demonstrate the performance of this phase extraction method, different driving signals are applied to PZT to generate different kinds of vibration waveforms.

B. SINGLE FREQUENCY WAVEFORM EXPERIMENT
The sinusoidal driving signal with 100Hz frequency and 6Vpp amplitude is applied. As the spatial sampling distance is  1m, the 1.05m fiber attached on the PZT can be regarded as one point. The sensing series obtained between 200m and 220m are extracted for phase demodulation. Before sending these sensing series into phase demodulation process, a signal prepossessing based on moving average method [23] is applied to eliminate the high frequency random noise. Through moving average method, the signal to noise ratio (SNR) of the sensing series are improved from ∼0.46dB to ∼15.61dB (SNR is calculated through power spectrum density). Fig.5 shows two sensing series extracted from 203m and 206m positions and their details. In the detailed figure, the LEP-I and LEP-II can be separated through inspecting their occurrence moment in two sensing series. In fact, multiple sensing series are applied to figure out whether one LEP belongs to LEP-I or LEP-II. With the help of applying more sensing series, LEP-I extraction process become more reliable. Even one or two sensing series have similar initial phase and similar appearance, the LEP-I can still be recognized through inspecting other sensing series. Fig.6(a) shows the demodulated phase of sensing series at 203m using the proposed method. The SNR of the demodulated phase is ∼16.82dB, which is ∼1.31dB improved compared with the intensity sensing series. And Fig.6(b) shows the Fast Fourier Transform(FFT) results of the original sensing series and its demodulated phase. In time domain, the amplitude of the demodulated phase can be read, which is about 3.48 rad. In frequency domain, the original sensing series shows a similar amplitude (0.95 and 0.88) for 100Hz and  200Hz, which indicates a strong second harmonic generation. In the FFT result of demodulated phase, the 100Hz frequency component (1.47) is more than 8 times larger than the 200 Hz frequency component (0.17), which indicates a strong suppression of nonlinear. Considering that the vibration amplitude of PZT is 9.01nm and the radius is 1.25cm, the strain on fiber is 0.7208nε. The phase change can be determined by the strain of fiber through the following equation [18], where, ε is the strain on fiber, L is the fiber length under strain, n is the refractive index and λ is the wavelength. Note that L is 1.05m, n is 1.47 and λ is 1550nm. The phase change calculated through Eq.(14) is 3.51 rad. The demodulated result (3.48 rad) agrees well with the theoretical calculated value (3.51rad). Fig.7 shows more demodulated phase amplitude under 6∼10Vp-p PZT driving voltages with different frequencies.
The amplitude of demodulated phase shows a linearity with respect to voltage and basically agrees with the vibration amplitude of PZT, which shows the effectiveness of the proposed algorithm and its potential used in strain measurement.

C. AMPLITUDE-MODULATED WAVEFORM EXPERIMENT
The driving signal with 200Hz carrier frequency, 10Hz modulation frequency and 100% modulation depth is then applied. The driving voltage is still set to be 6Vp-p and other parameters also keep the same. The sensing series obtained between 200m and 220m are extracted for phase demodulation and a denoised procedure based on moving averaging is applied (with SNR improved from ∼1.40dB to ∼15.80dB). Fig.8 shows the sensing series and their details in the dashed box the from 208m and 212m positions. The details show the LEP-Is and LEP-IIs. In fact, multiple sensing series are applied to help determine the type belonging of each LEP. Fig.9 shows the demodulated phase and its FFT from the sensing series from 212m. The SNR of the demodulated phase is ∼17.11dB, which is ∼1.31dB improved compared with the intensity signal. The waveform of the demodulated phase shows an amplitude-modulated appearance, which shows a 3.73 rad maximum amplitude. The FFT result shows that the demodulated phase has three main frequencies, 200.0Hz, 190.2Hz and 209.9Hz. The 200.0Hz frequency equals to the carrier frequency of the PZT driving signal. The 190.2Hz and 209.9Hz frequencies with similar amplitude are the side bands due to modulation, which indicates the modulation frequency is 9.85Hz, corresponding to the 10Hz modulation frequency of PZT driving signal. The error is mainly due to the analysis precision of FFT. Once a longer data is applied, the frequency precision can be improved.

D. CHIRP WAVEFORM EXPERIMENT
The PZT driving signal is set to be a chirp waveform. The chirp range is from 50Hz to 200Hz and the repetition time is 500ms. The driving voltage is 6Vp-p. The sensing series obtained between 200m and 220m are extracted for phase demodulation and a denoised procedure based on moving averaging is applied (with SNR improved from ∼3.24dB to ∼17.20dB). Fig.10(a) shows the intensity sensing series from 203m position. The insert figure illustrates the its details, which shows a sinusoidal form. However, with the help of other sensing series, it can be found that the some of the LEPs in 203m sensing series belong to LEP-II, which are showed in Fig.10(b). In this case, the intensity sensing series shows a sinusoidal form, but its frequency is twice as much as the frequency of PZT driving signal. VOLUME 8, 2020    .11 shows the demodulated phase and its short time Fourier transformation(STFT) result. The demodulated phase shows a chirp appearance, with 3.66 rad amplitude in average and 501.1ms repetition time, which agrees well with the driving signal. The SNR of demodulated phase is ∼18.75dB, which is ∼1.55dB improved compared with the intensity signal. The lower frequency part shows a higher amplitude and the higher frequency part shows a lower amplitude. This amplitude fluctuation maybe due to the frequencies response difference of PZT. Fig.11(b) shows the frequency repeatedly sweeps from 50Hz to 200Hz, which agrees well with the chirp PZT driving signal.

IV. DISCUSSION
The SNR of the sensing series send to phase demodulate is important to ensure the LEPs can be found accurately. Usually, these sensing series contain high frequency noise and need to be smoothed through denoise method, such as moving average to remove the out-band noise and wavelet denoising to remove the in-band noise. Based on experience, these denoised signals should reach at least ∼15dB SNR before sending to demodulation. The low SNR may cause demodulation failure. As the LEPs need to be find one by one, the length of sensing series should longer than one period of the vibration.
Another concern is about the coherent fading problem in -OTDR. When the sensing series face a full coherent fading, little information can be delivered to the intensity series. Thus, the demonstration will fail. For those cases with a certain extent of coherent fading, which means some vibration information can still be delivered to the sensing seires, the phase demodulation could work if the SNR requirement is satisfied.

V. CONCLUSION
This paper proposed a dynamic phase demodulating algorithm for -OTDR system with direct detection, which is basically the simplest -OTDR structure. Without additional detectors, interferometry, optical hybrid or super-high speed acquisition card, the proposed demodulating algorithm can help reduce the cost of the sensing system. Taking advantage of the redundant information between each sensing series, two types of LEP can be distinguished. LEP-II will help to find the envelop of the sensing series and offer the quadrant information in inverse cosine processing. Besides, the algorithm avoids subtractions between each RBT, which gets rid of the demodulating failure caused by small subtraction result during the demodulation. The algorithm was applied to measure sinusoidal dynamic phase change, amplitude-modulated phase change and chirp phase change, demonstrating its capability in dynamic phase measurement.