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Abstract
This article discovers that the excessive correlation between the selected temporal sensing sequences will lead to phase demodulation failure in the demodulation process of direct detection Φ-OTDR in certain duration, which reduces the quality of demodulated phase. Besides, we also first discover a phase polarity flipping phenomenon in the demodulation process, which will introduce additional errors and further degrade the quality of demodulated phase. In order to obtain the real phase change caused by external intrusion, a high-quality phase demodulation strategy with multi-position compensation based on leveraging the information redundancy between each Rayleigh back-scattered temporal sequence is proposed. The optimal demodulation position is selected by calculating the cross-correlation between temporal sensing sequences. The phase demodulation failure is then compensated by phase demodulation results from multiple positions. At the same time, the phase polarity change is also determined and corrected. The experimental results show that this strategy can effectively suppress the waveform distortion and improve the signal-to-noise ratio of the demodulated phase. This scheme can effectively improve the demodulation effect and detection performance of direct detection Φ-OTDR and may promote its application.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The phase-sensitive optical time-domain reflector (Φ-OTDR) was first proposed by Taylor et al in 1993 [1]. It has gained significant attention in recent years and has become a popular choice for distributed sensing. The Φ-OTDR has found applications in various fields, including pipeline safety monitoring, structural safety monitoring of buildings and bridges, perimeter security, and transport tracking [2–11]. The Φ-OTDR stands out from other conventional OTDR by using a highly coherent laser source, which gives coherence to the Rayleigh back-scattered light (RBS). By monitoring changes in the RBS, external intrusion events along the sensing fiber can be detected and located. If more information about these intrusion events is desired, the waveform of the external vibrations carried by the RBS needs to be further demodulated. However, the non-linear relationship between the intrusion waveform and the intensity of RBS will introduce distortion in reproducing the vibration waveform of the intrusion. In order to mitigate this effect, accurate demodulation of the phase of the RBS light waveform is required.
Different countermeasures and optimizations have been proposed for phase demodulation. Pan et al. introduced local oscillation light into the original structure and performed coherent detection at the detector to obtain the I/Q component for phase demodulation [12]. Local oscillators and high-speed acquisition devices are necessary for this method, which makes the sensing system complex and expensive. Fang et al. applied phase-generating carrier (PGC) modulation by using an unbalance Meckelsen interferometer structure and a phase modulator [13]. Masoudi et al. proposed a phase-demodulation structure based on local oscillator and a 3 × 3 coupler to obtain intensity signals from three channels that are 120° apart from each other [14,15]. This scheme requires the use of three synchronous photodetectors, three channels of synchronous data acquisition and an interferometer structure to ensure correct demodulation. Alekseev et al. used a sequence of three consecutive double pulse pairs as detection pulses, where the three pulses correspond to different phase values [16]. An external disturbance causes a change in the phase between the three pulses, and by extracting this phase change, the perturbed signal information can be measured quantitatively. However, this solution requires high accuracy in the configuration of the cells. Yu et al. constructed a simultaneous acquisition type outlier detection structure that can simultaneously obtain the required two I/Q components [17]. This method can reduce system error and demodulate the differential phase, but it increases the cost of the system due to the need for multiple filters and couplers, as well as a high-speed acquisition card.
Those methods can effectively extract intrusion phase, but they require additional hardware equipment, which increases the system complexity and cost. The width of the detection pulse allows the observer to obtain an effective vibration signal not only at the point of intrusion but also at a section of its surrounding spatial location with a wealth of information, which makes it possible to implement phase demodulation for direct detection Φ-OTDR with single detection channel. Sha et al. proposed a sum-and-difference method to construct two orthogonal components from two RBS temporal sensing sequences and perform I/Q demodulation for phase extraction [18]. This method can demodulate the correct phase information without adding any additional equipment, but the coherent fading, extremely small sum or difference components and laser frequency drift result in distortion to the demodulation results. In 2020, another improved demodulation method was proposed in [19], which revealed the different functions of two types of local extreme points in light intensity waveforms. With the information supplied by these two types of local extreme points, the intrusion phase can be then successfully reproduced. This method does not need to calculate the sum and the difference components, but requires high signal quality to precisely determine the type of each local extreme point. Although these methods can obtain the correct phase waveform, the coherent fading and time-varying signal-to-noise ratio (SNR) make the demodulation quality unstable in a long duration. In order to obtain the intrude waveform with high quality in a long duration, we did deep research into the phase demodulation process for direct detection Φ-OTDR. Through theoretical analysis, we point out the specific reasons for the occurrence of minimum points in sum and difference components and first point out the phase reversal phenomenon caused by coherent fading in Φ-OTDR. By utilizing the redundant information in the signals collected from multiple locations, this article proposes a more reliable phase demodulation compensation scheme. The correctness and the effectiveness of the method are demonstrated through experiments. The experiment results show that this method can cope with the occurrence of minima value problem and phase reversal in various intrusion scenarios. Through this compensation method, the distortion of demodulated phase can be improved and will promote the field application of low-cost direct-detection Φ-OTDR.
2. Principle and method
2.1 Phase demodulation principle
In direct detection Φ-OTDR, the Rayleigh back-scattered optical intensity signal from the detector can be expressed as, [18]
where Z denotes the spatial location, ${D_Z}$ is the direct current (DC) component, ${A_Z}$ is the amplitude of alternating current (AC) component, $\theta (t)$ is the optical phase change caused by the intrusion at the position Z which contains the information of the intrusion event, ${\psi _Z}$ represents the initial phase which is determined by the working state of the system. Then, the AC and DC components are removed by fitting the upper and lower envelopes of ${I_Z}$. The normalized signal can be then expressed as,Then select two spatial locations m and n that are affected by the intrusion and compute the summation and disparity of their temporal sequences. The outcome can be represented using the sum-difference product formula as,
Since ${\psi _m}$ and ${\psi _n}$ are both slowly varying components compared to the rapidly varying phase $\theta (t)$, the $\cos (({\psi _m} - {\psi _n})/\textrm{2})$ and $\sin (({\psi _m} - {\psi _n})/\textrm{2})$ in Eq. (3) will form an envelope of the overall waveform, which can be removed by fitting the envelope. The signal after de-enveloping is expressed as,
As Eq. (4) gives out two quadrature components of $\theta (t)$, $\theta (t)$ can be then demodulated by the basic I/Q demodulation algorithm.
2.2 Sum and difference close to zero
In the process of de-envelopment, when the value of $({\psi _m} - {\psi _n})/\textrm{2}$ approaches kπ/2, where k is an integer, the Sum(t) or Diff(t) will approach zero as $\cos (({\psi _m} - {\psi _n})/\textrm{2})$ or $\sin (({\psi _m} - {\psi _n})/\textrm{2})$ approaches zero. When the absolute value of the sum or difference in Eq. (3) is too small, the de-envelopment process will introduce a very large error, resulting in a significant distortion of the phase demodulation result at that moment. This distortion is characterized by a significant decrease in the SNR of the demodulation result. The specific definition of SNR is shown in the following equation, where E is the signal power and N is the noise power.
Based on the demodulation process described in Section 2.1, when the cross-correlation between the two Rayleigh back-scattered temporal sequences selected for phase demodulation is too high, the value of $\cos (({\psi _m} - {\psi _n})/\textrm{2})$ or $\sin (({\psi _m} - {\psi _n})/\textrm{2})$ will tend to zero. Figure 1 shows the waveforms of two temporal sequences with high cross-correlation (Fig. 1(a) for high positive cross-correlation and Fig. 1(b) for high negative cross-correlation) and their corresponding sum and difference results (Fig. 1(c) and Fig. 1(d)). As shown in Fig. 1, the temporal sequences of the M position and N position show a high positive cross-correlation between 0.2s and 0.3s (Fig. 1(a)), resulting in the corresponding Diff curve keeps a low value (Fig. 1(c)), while they show a strong negative cross-correlation between 1s and 1.1s (Fig. 1(b)), resulting in the corresponding Sum curve keeps a low value (Fig. 1(d)).
Fig. 1. Temporal sequences after de-envelopment at two different locations in different time periods(a)(b) and the corresponding sums and differences(c)(d).
2.3 Positive and negative polarity change of demodulated phase waveform
Since ${\psi _m}$ and ${\psi _n}$ are still time-varying quantities, the positivity and negativity of $\cos (({\psi _m} - {\psi _n})/\textrm{2})$ and $\sin (({\psi _m} - {\psi _n})/\textrm{2})$ may change over an extended period of time, which introduces additional error into the demodulation. Table 1 shows the relationship between the phase value $({\psi _m} - {\psi _n})/\textrm{2}$ and the polarity state of the corresponding sine part, cosine part, sum part (Sum(t)) and difference part (Diff(t)). k is an integer in Table 1. When the phase value $({\psi _m} - {\psi _n})/\textrm{2}$ varies from one section to another adjacent section, the sign of the sum part and the difference part will change in the opposite direction. However, this phase variation and the corresponding sign change phenomenon have not been considered in Eq. (3) and Eq. (4), which will introduce additional polarity flipping and distortion in the demodulated phase. To eliminate this impact, Eq. (3) should be revised to,
Table 1. Polarity state change with phase value
These two problems described in Section 2.2 and Section 2.3 occur simultaneously in the demodulated results. The fact that the summation and differential parts become close to 0 is only a necessary condition for the phase invert, and another judgement is needed to further determine whether the phase is inverted or not.
2.4 High quality phase demodulation method
The $\psi ({z_i},t)$ in Eq. (6) varies in both spatial and temporal directions, which makes the cross-correlation between different temporal sequences constantly change over time. In this paper, we utilize the information redundancy between the temporal sequences from multiple sensing positions and propose a high-quality phase demodulation method based on multi-point compensation.
Within the vibration influence range, an arbitrary position is selected as the basic position B for phase demodulation, and its temporal sequence is noted as ${I_B}$. Then, select another temporal sequence (from position S) within the vibration influence range with the weakest cross-correlation with ${I_B}$, denoted as ${I_S}$.The demodulation process described in Section 2.1 is applied to ${I_B}$ and ${I_S}$ to obtain the base demodulation result, denoted as Basic-Phase. The cross-correlation between ${I_B}$ and ${I_S}$ is also a function of time, and the overall weaker cross-correlation coefficient only guarantees better demodulation results at most moments. However, there are still moments with high local cross-correlation, which can lead to local distortion of the demodulation results. Since all positions in the vibration-affected region receive the same phase waveform of the external disturbance, an additional temporal sequence from this vibration-affected region, denoted as ${I_\textrm{C}}$, can be introduced to compensate the Basic-Phase. The compensation sequence ${I_\textrm{C}}$ will be selected from all the remaining available temporal sensing sequences. We hope that the cross-correlation between ${I_\textrm{C}}$ and ${I_B}$ is not too large to avoid large-scale distortion and compensation failure. At the same time, we also want that the cross-correlation between ${I_\textrm{C}}$ and ${I_B}$ is different from the cross-correlation between ${I_\textrm{S}}$ and ${I_B}$, otherwise it will cause the two demodulation results to be too similar to compensate. Therefore, we choose the temporal sequence with moderate cross-correlation with ${I_B}$ as the compensation source and a judging function ($Scor{e_z}$) is defined to help find the compensation sequence,
where ${D_{S,z}}$ denotes the distance between the position z and the position S, K is a weight, $Xcor{r_{B,z}}$ denotes the absolute value of the cross-correlation between ${I_B}$ and ${I_z}$, and $\overline {Xcorr} $ represents the median value of all $Xcor{r_{B,z}}$. The reason for using sigmoid function is that when the cross-correlations for different positions are similar, $Scor{e_z}$ can pay more attention to the distance. The weight coefficient K is used to adjust the influence of the sigmoid function. A higher value of $Scor{e_Z}$ indicates a better compensation effect of ${I_Z}$. The demodulated phase based on ${I_\textrm{C}}$ and ${I_B}$, which denoted as Comp-Phase, is then used to compensate the local distortion of Basic-Phase through locally replacing Basic-Phase with Comp-Phase. In the compensation process, firstly calculate the cross-correlation between Basic-Phase and Comp-Phase step by step with a small window length L, whose results are denoted as X. The X array can be then used to determine if a demodulation failure has occurred. If ${X_i} \ast {X_{i + 1}} < 0$, it means the phase polarity is reversed after that time stamp, and this time stamp will be denoted as Tag1. Besides, if ${X_i}$ is far from 1, it means there is a demodulation failure at that time stamp, which is usually caused by coherent fading problem, and this time stamp will be denoted as Tag2. Furthermore, we also calculate the local SNR to determine whether demodulation failure occurs in Basic-Phase or Comp-Phase. The failure is attributed to the demodulated phase with the lower SNR.The correctness and compensation process are as follow. The phase inversion problem is firstly corrected by using Tag1. Since it is not possible to determine if a phase reversal has occurred at the beginning, we assume that the phase in the first window is not reversed. By reversing the phase between Tag1(k)∼Tag1(k + 1), where k is odd, we can correct the phase with invert operation. Then locally replace the Basic-Phase with Comp-Phase when $Ta{g_2}$ is marked. Through this way, the demodulation distortion caused by the extremely small sum and difference value can be compensated. The specific flow of the method is shown in following pseudo code (Algorithm 1) and the corresponding flow chart is shown in Fig. 2. It needs mention that if both the Basic-Phase and Comp-Phase suffer phase fading at the same specific time, the compensation may also fail. Thus, the proposed method tried to reduce the probability of simultaneous phase fading of Basic-Phase and Comp-Phase by choosing the most suitable compensation sequence with the maximum $Scor{e_z}$.
Algorithm 1. Multi-point compensation method
3. Data collection and reliability verification
3.1 Experiment setup and data collection
The experiment setup is shown in Fig. 3. An ultra-narrow linewidth laser with a linewidth of 3kHz is used as the light source. The continuous probe light is modulated into pulses by an acousto-optic modulator (AOM) and enhanced by an erbium-doped fiber amplifier (EDFA). The repetition frequency of the probe pulses is set to 20kHz with a pulse width of 100 ns. The probe pulsed light is then injected into a 1 km long sensing fiber through an optical circulator. RBS is collected by a detector (PD) through a circulator, and the signals are acquired by an acquisition card (DAQ) with an acquisition speed of 100 MS/s, corresponding to approximately 1 m per sampling point. A piezoelectric transducer cylinder (PZT) with a radius of 3 cm is placed at 115 m of the sensing fiber to sever as the vibration source. There are 15 m the sensing fiber wounded on the PZT. Different kinds of waveforms are generated by a signal generator to drive the PZT.
Six kinds of external vibration signals are applied to the PZT respectively: 120 Hz, 125 Hz, 173 Hz and 200 Hz single frequency sinusoidal vibration, 174 Hz amplitude-modulated (AM) sinusoidal vibration with 20 Hz modulation frequency and 95% modulation depth, 120Hz∼200 Hz frequency-modulated (FM) vibration with 0.5s modulating length. These frequencies are often detected in the long range and buried fiber sensing applications, such as long range pipeline monitoring. The drive voltage is all set to 5Vp-p. The length of data collected are shown in Table 2. The data per second and within [115 m,129 m] is used as one data sample. In order to ensure the reliability of our method, all of the data is divided into two sets. The validation set is used to valid the correctness and effectiveness of our analysis and compensation method, such as the relationship among cross-correlation value, SNR and demodulation quality, and the rationality of Scorez. The test set is used to demonstrate the performance of our high-quality demodulation method.
Table 2. Data distribution
3.2 Relationship between cross-correlation and demodulation quality
In this section, we verified the relationship between cross-correlation value and demodulation quality. SNR is used to evaluate the demodulation quality. This validation is taken on the validation set in Table 2. There are 15 temporal sequences in each data sample. The temporal sequence from 115 m is selected as the basic sequence. Then calculate the cross-correlation and perform the basic phase demodulation process between each temporal sequences from 116 m to 129 m and the basic sequence. The absolution value of cross-correlation and SNR of the demodulated phase are then recorded. The SNR distribution with respect to different cross-correlation value are shown in Table 3.
Table 3. SNR distribution of the demodulated phase
From Table 3, it can be seen that when the cross-correlation decreases from 1 to 0.6, the SNR increases, and when the cross-correlation is lower than 0.6, the SNR value stabilizes with minor fluctuation. Based on this result, we can conclude that when the cross-correlation is high, the cross-correlation becomes significantly negatively related to the SNR of the demodulation result and we can use the cross-correlation to predict the demodulation quality. However, when the cross-correlation falls below a certain threshold, the relationship between cross-correlation and SNR weakens significantly. But it is still possible to select the temporal sensing sequence with the lowest cross-correlation as the ${I_S}$ to avoid large demodulation distortions.
3.3 Relationship between scorez and compensation ability
Similar validation is also taken one the validation set to show the relationship between the Scorez and the compensation ability of compensation sequence. The compensation time refers the total length of the part in Basic-Phase that are replaced by Comp-Phase. When the local SNR in Comp-Phase is higher than the corresponding part in Basic-Phase, this part of Basic-Phase will be replaced by the corresponding part in Comp-Phase. Thus the total compensation time can somehow show the compensation ability of compensation sequence. The temporal sequence from 115 m is selected as the base sequence ${I_B}$ and another temporal sequence with the minimum cross-correlation value (with ${I_B}$) is selected as the initial demodulation sequence ${I_S}$. The remaining 13 other temporal sequences in that data sample are used as the potential compensation sequences. The compensation evaluation Scorez is calculated for each potential compensation sequence. The weight K is set to be 0.1 and L is set to be 0.1s here. Then the compensation demodulation process is taken for each potential compensation sequences (with ${I_B}$ and ${I_\textrm{S}}$), respectively. The average value of ${X_i}$ is set to be threshold to determine whether the $Ta{g_2}$ should be marked or not. At the same time, the SNR of each length of $Ta{g_2}$ should be calculated to judge that the Comp-Phase is qualified or not. The total compensation time and the corresponding Scorez rank in one data sample are recorded for each potential compensation sequence and shown in Fig. 4. In Fig. 4, the horizontal axis refers to the arrangement of Scorez from large to small. Thus, the first rank of Scorez means the largest one. From Fig. 4, we can see that the total compensation time is inversely proportional to rank of Scorez, which means that the Scorez can effectively predict the compensation ability of the potential compensation sequences.
4. Phase demodulation and compensation tests
In this section, the effectiveness of phase demodulation and compensation will be tested. In order to avoid the reuse of the above-mentioned validation set, the test set is used in this demodulation performance testing session, as shown in Table 2. In addition to SNR, the signal-to-noise-and-distortion ratio (SINAD) is also introduced to evaluate the demodulation quality from waveform distortion aspect. SINAD can show the distortion of the signal and is defined as Eq. (10),
where D is the harmonic power.4.1 Single frequency waveform tests
An 1 second 173 Hz single frequency demodulation is randomly selected illustrated as an example to show the demodulation and compensation effect. The temporal sequence (115 m) is selected as the base sequence ${I_B}$ and another temporal sequence with the minimum cross-correlation value (with ${I_B}$) is selected as the initial demodulation sequence ${I_S}$ (129 m).
In order to valid the compensation ability of different compensation sequences, three different compensation sequence selection strategies are applied. Strategy 1: select the temporal sequence which has the minimum Scorez as the compensation sequence. Strategy 2: select the temporal sequence which has the medium Scorez as the compensation sequence. Strategy 3 (ours): select the temporal sequence which has the maximum Scorez as the compensation sequence. Figure 5 shows the demodulation and compensation process of the 173 Hz single frequency waveform. Figure 5(e) shows the Scorez rankings. A higher rankings indicating larger Scorez values. Then the 128 m temporal sequence (black dot in Fig. 5(e)) is chose based on Strategy 1, 116 m temporal sequence (purple dot in Fig. 5(e)) is chose based on Strategy 2 and 119 m temporal sequence (red dot in Fig. 5(e)) is chose based on Strategy 3. Figure 5(a) shows the Basic-Phase and Fig. 5(b)∼(d) show the Comp-Phase based on those 3 strategies. From Fig. 5(a), it can be easily found that there are four failure sections in Basic-Phase around about 0.5s, 1.4s, 2.5s and 2.8s, which are marked by red rectangular boxes. The Comp-Phase of Strategy 2 (Fig. 5(c)) suffers large amount failure due to the high cross-correlation and not suitable for compensation usage. The Comp-Phase of Strategy 1 (Fig. 5(d)) and Strategy 3 (Fig. 5(b)) suffers less failure. Thus, we can conclude that a low Scorez of Strategy 1 implies minimal alterations in comparison to the Basic-Phase and fails to yield the desired level of compensation. In contrast, the Comp-Phase of Strategy 3, which has the maximum Scorez, can give the best compensation as it doesn’t suffer the same failure periods as the Basic-Phase.
Fig. 5. Demodulation results (a∼d), cross-correlation and SNR(e), and the demodulation quality evaluations(f∼h) for 3 different strategies of 173 Hz single frequency demodulation.
Figure 5(f)∼(h) show the comparison of the compensated phase quality based on those 3 strategies. The compensation times are 0.15s, 0.35s, 0.5s respectively, and their corresponding SNR values are 29.59 dB, 30.22 dB, 32.3 dB. Compared to the SNR of Basic-Phase, 28.29 dB, SNR improves 1.3 dB, 1.93 dB, 3.01 dB respectively. And the SINAD also improves from 17.42 dB to 17.93 dB, 18.38 dB, 20.11 dB with 0.51 dB, 0.96 dB and 2.69 dB improvement in three different situations. It can be seen that the Strategy 3 offers the best compensation effect.
Figure 6 shows the waveform details and phase polarity state of the demodulation and compensation (under Strategy 3) waveforms. The phase polarity flipping phenomenon can be observed in the insert figure in Fig. 6(a). At first, the Basic-Phase has the same phase polarity as the Comp-Phase. However, after a distortion section, the Basic-Phase and Comp-Phase are with the reversed phase. If phase polarity flipping has not been corrected, the compensated result will show additional distortion, as shown in Fig. 6(b). And Fig. 6(c) shows the compensated results after phase polarity correction. Figure 6(d∼f) further show the phase polarity state change with time in Basic-Phase, Comp-Phase and the final compensated phase. It can be seen that the phase polarity state changes with time both in the original Basic-Phase and Comp-Phase but becomes constant after correction.
Fig. 6. Detailed waveform information (a∼c) and the corresponding phase polarity state (d∼f) of 173 Hz single frequency demodulation.
Then this method is applied to the whole single frequency vibration data in the test set and Table.4 shows the average quantitative evaluations, including SNR, SINAD, the number of fading and the compensation time in one second. From Table 4, the SNR and SINAD have got 4.30 dB and 2.63 dB improvement, respectively, and the fading number decreases a lot.
Table 4. Average compensation improvement for single frequency vibration
4.2 Chirp waveform tests
The same method is used to operate on the FM vibration. The FM vibration sweeps from 120 Hz to 200 Hz with 0.5s modulation length. Figure 7(a) and Fig. 7(b) demonstrate the Basic-Phase and its compensated results of FM vibration. The red line in Fig. 8 represents the phase polarity state. Based on the red line, the Basic-Phase experiences phase inversion for 0.95 seconds and phase distortion for 0.6 seconds within the selected 3-second time period. After compensation, the phase distortion and inversion are improved. Wavelet analysis shows that the energy distribution over time is consistent with the imposed external vibration as shown in Fig. 7(c) and Fig. 7(d). After compensation, the energy distribution is more concentrated at 0.2s, 1.5s, 2s and 2.5s places, and the frequency shift is much more clearly, as indicated by the red boxes in Fig. 8. Besides, the SNR is improved from 31.38 dB to 33.16 dB with 1.78 dB improvement. And the SINAD is improved from 15.71 dB to 17.76 dB with 2.05 dB improvement. It shows that the compensation method can also work well to enhance the quality of the FM demodulation.
Fig. 7. FM vibration demodulation and wavelet analysis. (a) Basic-Phase, (b) the compensated result, (c) wavelet analysis of Basic-Phase and (d) wavelet analysis of the compensated result.
Then this method is applied to the whole FM vibration data in the test set and Table 5 shows the average results. From Table 5, the SNR and SINAD have achieved 2.10 dB and 0.68 dB improvement, respectively, and the the number of fading decreases from 1.50 to 0.50 times per second.
Table 5. Average compensation improvement for FM vibration
4.3 Amplitude-modulated waveform tests
The same method is used to operate on the AM vibration. The AM vibration is 174 Hz basic frequency with 20 Hz modulation frequency and 95% modulation depth. Figure 8(a) demonstrates the Basic-Phase and its phase polarity corrected results of AM vibration. Figure 8(b) demonstrates the Comp-Phase and Fig. 8(c) shows the compensated phase. It can be seen that the distortion at the head of Basic-Phase is compensated and the phase polarity has also been corrected. The SNR is improved from 31.22 dB to 34.43 dB with 3.21 dB improvement. And the SINAD is improved from 23.28 dB to 24.02 dB with 0.74 dB improvement. Then all of the AM data in the test set are used for evaluation and the results are shown in Table 6. From Table 6, the SNR and SINAD have got 2.94 dB and 2.15 dB improvement, respectively. And the number of fading decreases from 1.88 to 0.38 times per second. The results show that the proposed method can also improve the demodulation quality of AM vibration.
Table 6. Average compensation improvement for AM vibration
5. Conclusion
In this paper, a high-quality phase demodulation strategy is proposed for direct detection Φ-OTDR. Depth analysis of the reasons for demodulation failure is conducted and it is pointed out for the first time that the phase reversal problem may occur during the demodulation process when the sum and difference intermediate variable crosses a very small value. To address this problem, this paper uses the redundancy information between each temporal sensing sequence to discriminate the demodulation phase reversal, and proposes a multi-position demodulation compensation scheme to improve the quality of the demodulated phase. It is demonstrated experimentally that the scheme can significantly improve the quality of demodulation and reconstruct a more realistic intrusion phase under different intrusion waveforms. Furthermore, the scheme successfully overcomes the phase inversion problem and reduces the effect of coherent fading issue. The improved demodulation performance of direct detection Φ-OTDR will increase its reliability and may promote its field applications.
Funding
National Natural Science Foundation of China (61801283); Basic and Applied Basic Research Foundation of Guangdong Province (2021A1515012001).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data will be made available upon reasonable request.
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