A phase demodulation method specially developed for direct detection φ-OTDR is proposed and demonstrated. It is the only method to date that can be used for phase demodulation based on pure direct detection system. As a result, this method greatly simplifies the system configuration and lowers the cost. It works by firstly deriving a pair of orthogonal signals from the single-channel intensity and then realizing phase demodulation by means of IQ demodulation. Different forms of PZT induced vibration are applied to the fiber and the phase is correctly demodulated in each case. The experiment results show that this method can effectively perform phase demodulation with extremely simple system configuration.
© 2017 Optical Society of America
Phase sensitive OTDR (φ-OTDR), known as a popular kind of Distributed Optical Fiber Sensor (DOFS), was initially proposed and demonstrated by Taylor et al. in 1993  and has attracted extensive research interests these years [2–10]. As opposed to the conventional OTDR where broadband light source is used, φ-OTDR employs ultra narrow line width laser to launch highly coherent probe pulses. By monitoring the changes in the pattern of the Rayleigh backscattered (RBS) traces, also known as coherent Rayleigh noise (CRN), dynamic perturbations along the sensing fiber can be detected and located. Nowadays, φ-OTDR has been broadly employed for distributed vibration (acoustic) sensing in both fields of academic research and industrial application [7–10], typically in the field of pipeline integrity monitoring and structural health monitoring (SHM). Its effect is like the deployment of hundreds of tiny acoustic sensors along the sensing fiber with a common frequency response and stochastic sensitivity. It can be readily understood that the better each tiny acoustic sensor reproduce the exact external vibration waveform the better is the overall performance of an φ-OTDR. In the ideal case, the sensor can act as a series of telephones with a common monitor point with which one can hear what happened at any locations along the fiber. However, as is well-known, a basic problem preventing this ideal condition from happening is that the direct response of each tiny sensor is nonlinear [11–22]. Therefore the sensing result is distorted which leads to a worse reproduction of the vibration waveform of interest. However, this kind of nonlinear distortion is possible to eliminate if the phase of the RBS light wave of each tiny sensor can be correctly demodulated. In the literature, several techniques have been proposed to realize phase demodulation with various implementations [11–22]. It is worth noting that IQ demodulation is a commonly used technique at the final stage of phase demodulation in almost each of these works [11–22]. This is due to the fact that one cannot determine the phase value of an oscillation only by knowing its intensity. While, if two or more intensity signals of the same oscillation with a known relative phase shift are obtained, phase is then ready to be determined. In IQ demodulation (In phase and Quadrature), this phase shift is 90 degree, making the two intensities orthogonal to each other. It is obvious that the use of IQ demodulation requires two signals, and the methods in the literature [11–22] are essentially different ways of obtaining these IQ components . utilizes a 90° optical hybrid to generate the IQ components, where dual-channel coherent detection and synchronous data acquisition are indispensible . obtains the IQ components by means of digital coherent detection. Local oscillator and high speed data acquisition equipment are necessary for the method to work . realizes phase demodulation using the phase-generated carrier technique (PGC) which requires using an unbalanced Michelson interferometer (MI) structure and a phase modulator. IQ components are obtained through complex computer processing [19,20]. uses a 3 × 3 optical hybrid to simultaneously obtain three channels of intensity signals which are mutually 120° out of phase. The method needs three identical-characteristic photo detectors, three channel synchronous data acquisition and an interferometer structure, which greatly increase the system complexity. Besides, J.P. Dakin et al. proposed a dual-pulse phase demodulation scheme in 1990 , which was further developed in 2008 in . The two pulses within the same group need to have a frequency difference so that a beat signal can be generated and processed to obtain the IQ components. Additional optical structure and challenging control over the timing of the pulse pair are required. In general, although the works mentioned above are proved with good performance, they cannot be used under the circumstance of fundamental direct detection φ-OTDR, i.e., the system that does not involve coherent detection, optical hybrid or interferometer structure. The methods in the literature more or less have to rely on additional optical components and structures to realize phase demodulation, which will inevitably increase the system complexity and cost.
This paper proposes a method with which one can extract the phase information from a direct detection based system. It greatly simplifies the system configuration and thereby lowers the cost, such as omitting the requirement for multi-channel synchronous signal detection, optical hybrid, interferometer structure, coherent detection and high speed data acquisition. More importantly, this method provides a solution of phase demodulation under the circumstance of direct detection scheme, for which the methods in the references [11–22] are not available. The method proposed in this paper firstly derives a pair of IQ components from the intensity and then implement phase demodulation by means of IQ demodulation. In order to examine the correctness, various vibration waveforms, including single frequency harmonic vibration, amplitude modulated sinusoidal vibration and chirped vibration, are induced by a PZT tube to a certain part of the fiber and the corresponding phase terms are correctly demodulated.
The proposed method can be implemented in two fundamental schemes, i.e., single-pulse or dual-pulse according to different application situations. In the single-pulse scheme, the system launches one pulse per period to obtain conventional RBS traces. The trace can be considered as the sum of three sections as shown in Fig. 1 (left). In the dual-pulse scheme illustrated in Fig. 1 (right) and Fig. 2, two rectangular pulses with a certain interval are launched in each period. The two individual RBS light fields interfere to produce the final RBS intensity trace. Detailed theoretical derivation and explanation in each case are provided below.
2.1 Single-pulse probe scheme
In the case of a relatively small perturbation with longitudinal range less than 5m, a conventional single-pulse probe scheme can be used. The scenario is illustrated in Fig. 1 (left). The pulse width needs to be set at least ten times longer than the range of the disturbance. This can be conducted by firstly determining the location and range of a disturbance through moving differential or other locating algorithms and subsequently setting an appropriate pulse width. After that, two intensity evolutions versus time at two different locations nearby the disturbance are extracted from the raw data for post processing. The two intensity evolutions, respectively denoted as , can be expressed as:Eq. (3)’s influence upon the total electric field is tiny and negligible. As a result of the external disturbance, there will be a common round trip phase modulation acting on each of the individual RBS light waves that are scattered downstream from the disturbing location. The phase modulation, denoted by, is an accumulation of the distributed phase change occurring in the entire disturbing range. The resultant electric field can be expressed as a sum of two terms:
As can be seen from Eq. (6) and Eq. (7), the four quantities are essentially a result of the specific scattering profile in the absence of disturbance. Their values are stochastic and unable to be determined, but are supposed to be constant in the ideal condition. However in the practical situation, these four quantities would inevitably slowly drift rather than being perfectly constant, which might be a result of the inevitable laser frequency drift and environment temperature fluctuation. For the convenience of description, the intensity in Eq. (8) is written equally in the following form,
In which and are slowly varying quantities, is the phase to be demodulated. The phase is thereby demodulated in three steps. Firstly, are eliminated. This could be done by fitting the upper and lower envelops of . can be estimated by the envelope average, can be estimated by the envelope difference considering the slowly varying property of with respect to. As a result, becomes 0 and becomes 1. The processed signal can thereby be expressed as,
Secondly, the sum and difference of the two processed intensities are calculated, which is
The first terms on the right hand side in the two equations in Eq. (11) can be eliminated in the same way as described in step 1 by envelope fitting, in that they are slowly varying compared with the second term, and thereby yields:
Thus, a pair of orthogonal signals containing the phase modulation of interest and an undesired drift term is achieved. The phase with drift could thus be demodulated using the IQ demodulation as described in Eq. (13). Due to the frequency difference between the fast oscillating phase modulation and the slow varying drift, they can be further separated by high pass or low pass filter.
2.2 Dual-pulse probe scheme
In the case of a relatively large disturbance range, the dual-pulse probe scheme can be used, in which one probe signal consists of two individual rectangular pulses, with the same peak power, same pulse width, same optical frequency and a certain interval. The scenario is shown in Fig. 1 (right) and Fig. 2. Note that this kind of dual-pulse probe signal can be easily generated by appropriately adjusting the trigger signal of the acoustic optic modulator. The resultant RBS light field is essentially an addition of the RBS light waves respectively generated from the two pulses, denoted as trace 1 and trace 2. In the normal state of φ-OTDR, nonlinear effects are detrimental and designed to be prevented. Thus there is no evident nonlinear coupling between trace 1 and trace 2. As illustrated in Fig. 2, trace 1 is approximately the same as trace 2 except a time delay which equals the time interval between the pulse pair. Upstream, center and downstream regions are respectively marked in green, red and orange. Section A denotes the part of trace subjected to disturbance, section C denotes the time delay between the two traces and section B denotes the critical part of trace where the interference occurs between the downstream part of trace 1 and the upstream part of trace 2. Within the range of this particular section B, the resultant RBS light field can be expressed as the sum of two terms, one with no phase change and the other with a common phase change, as described in Eq. (5). Therefore, the same three-step demodulation procedure used in case 1 can be applied here using two adjacent intensity evolutions extracted from section B. Note that as long as the pulse pair interval (section C) is set longer than the disturbance length (section A) and within the range of coherent length, section B will exist and phase demodulation in this case can be conducted.
3. Experiments and results
The experimental setup is shown in Fig. 3. An Ultra Narrow Linewidth Laser (NLL, 100Hz) emitting 1550.147nm highly coherent light is used as the light source. An Acoustic Optic Modulator (AOM) with 200MHz frequency shift chops the continuous light into probe pulses. An Erbium Doped Fiber Amplifier (EDFA) is used to compensate the power loss. The amplified probe pulses are injected into the Fiber under Test (FUT) through port 1 of an optical circulator. The RBS light wave is directly routed to a PIN Photo Detector (PD) through port 3 for intensity detection. An NI-5122 Data Acquisition Card (DAC) with 50MS/s sampling rate is used for data acquisition. The intensity evolution versus time is recorded and processed in a Personal Computer. Function Generators (FG) are employed to provide driving signals for the Piezoelectric Transducer (PZT) tube and the synchronizing trigger signals for AOM and DAC. The FUT is 1700m long, with 2m of it wrapped around the PZT tube at around 160m. The pulse repetition rate is set to 5 KHz.
In order to demonstrate the correctness of the method to perform phase demodulation, different driving signals are applied to PZT to generate vibrations in different waveforms.
3.1 Single-frequency vibration test
Firstly applied is a sinusoidal driving signal with 170Hz frequency and 1Vpp amplitude. The pulse width is set to 200ns, resulting in a 20m interfering cell. The length of the fiber wrapped on the PZT is 2m, indicating a perturbation range which is 1/20 of the pulse width. This condition thereby meets the assumption of case 1 described in the theoretical part. The intensity evolution is continuously detected and sampled in 11 seconds. The time signal at 162m, which is within the range of half pulse width, is extracted as the source signal for phase demodulation. The phase demodulated using the proposed method is shown in Fig. 4. From Fig. 4 (left) and the inset, it can be recognized that the demodulated waveform is basically a constant amplitude sinusoid with certain spikes and drift. Figure 4 (right) shows the intensity signal and the corresponding demodulated waveform for comparison in detail. The demodulated waveform is found to be closer to the applied sinusoidal driving signal and its constant amplitude is consistent with the fact. On the other hand, obvious nonlinear distortions can be observed in the intensity signal, and the envelope that changes over time is misleading considering that the applied vibration is with constant amplitude.
3.2 Amplitude-modulated vibration test
For the demonstration of case 2, the dual-pulse probe scheme is adopted in the following experiments. The pulse width and interval are respectively set to 200ns and 800ns. An amplitude modulated signal with 110Hz carrier frequency, 3.5Vpp amplitude, 70% modulation depth and 200ms modulation period is applied. Figure 5 (left) shows 200 overlapped directly detected intensity traces. As a result of the applied dual-pulse probe scheme, two end reflection peaks can be clearly observed. The inset shows the vibration location is around 160m. To distinctly determine the perturbation range, global FFT is performed and the result is plotted in Fig. 5 (right). The spatial energy distribution shows that the disturbance range is from 160m to 240m. Besides, several higher order harmonic components are present due to the high strain that is applied to the fiber.
Note that according to Fig. 2, the pulse interval should theoretically be set longer than the perturbation range which is 2m in this case. Since the interval is set to 800ns, section B is supposed to start from 162m (160 + 2) to 240m (160 + 80). Namely, any intensity signals within this range can be used for phase demodulation. As an arbitrary choice, intensity signals at 178m and 182m, which are approximately in the middle of section B, are selected as the two source signals for phase demodulation. It should be noted, which has also been proven by experiments, that alternative choices of pulse pair interval are also available as long as they are greater than the 2m perturbation range. Intensity signals from other positions in section B can also be used. The 200ns pulse width and 800ns pulse interval are just one of the many available parameter choices.
The intensity evolution versus time at location 178m and 182m which are extracted as the two source intensity signals for demodulation, are shown in Fig. 6. Due to the interference induced nonlinearity, the intensity signals are severely distorted and none of the characteristics of the applied AM vibration can be observed. The signal drift and envelope fluctuation are firstly eliminated through upper and lower envelope fitting. Figure 7 shows the processed waveforms which are with constant amplitude and zero drift. Then the two waveforms are added together to yield a sum and subtracted to yield a difference, respectively shown in Fig. 8. It is clearly observed that the sum and difference waveforms exhibit obvious envelope fluctuation, for which can be accounted by the first terms on the right hand side in Eq. (11). This fluctuation is essentially a result of the laser frequency drift and environment temperature change. The fluctuation is eliminated again through envelope fitting and consequently leads to a pair of orthogonal signals which can be described by Eq. (12).
Lastly, the phase with drift is demodulated by means of IQ demodulation and unwrapped with the “unwrap” function in Matlab. The demodulated waveform is shown in Fig. 9 (left), which is found to be an amplitude modulated sinusoid with certain spikes and significant drift. This result is in great consistence with the theoretical analysis in that the oscillation and drift in the waveform can be respectively explained by the first and second terms on the left hand side in Eq. (13). The explicit waveforms plotted in the insets have rather high signal to noise ratio. In order to perform a quantitative comparison between the applied PZT driving signal and the demodulated waveform, a segment randomly selected from 9.25s to 9.5s is zoomed in and shown in Fig. 9 (right). It is clear that the peak and valley amplitude are respectively 13 rad and 3 rad, indicating a 76.92% modulation depth. And the interval between the two envelope peaks is 200ms. Thus, each parameter of the demodulated waveform agrees well with the PZT driving signal. Additionally, an AM signal with a different set of parameters as 70% modulation depth, 2Vpp peak amplitude and 15Hz modulation frequency is applied to PZT. The two intensity signals at 178m and 182m, used as the input of demodulation, are shown in Fig. 10. The demodulated waveform is shown in Fig. 11 (left). As can be seen in Fig. 11 (right), the peak and valley amplitudes of the demodulated waveform are measured to be 8 rad and 3 rad, implying a 62.5% modulation depth. The peak interval is 64ms, indicating a 15.625Hz modulation frequency. Therefore, with the measurement results listed above, the demodulated waveform is well in consistence with the PZT driving signal, and high quality waveform restoration is achieved as shown in Fig. 11 (right).
3.3 Chirped vibration test
As an investigation on the frequency response of the method, chirp signals are applied to the PZT tube. The chirp range is set from 50Hz to 200Hz, and the repetition rate is set to 10Hz. The intensity evolutions at location 178m and 182m are used for demodulation and the raw waveforms are shown in Fig. 12. Phase is demodulated with the same procedure and the result is shown in Fig. 13. It shows a well restored chirped waveform with certain spikes and drift. Similarly, this result can be well explained by the theoretical analysis, where the chirped oscillation and the drift correspond respectively to the first and second term on the left hand side in Eq. (13). Figure 14 (left) shows the demodulated waveform from 4.2s to 4.4s. The chirp period is measured to be 103ms which agrees well with the 10Hz repetition rate of the driving signal. In order to inspect the demodulation result in terms of time-frequency characteristic, wavelet analysis is adopted. The energy distribution versus time and frequency is shown in Fig. 14 (right). The frequency of the signal is found to repeatedly sweep from about 50Hz to 200Hz. Therefore, the method correctly reproduced the waveform of the chirped vibration with the waveform parameters in consistence with the given experiment condition.
3.4 Multiple-amplitude sinusoidal vibration test
In addition, sinusoidal driving signal with amplitude varying from 0.5V to 5V with 0.5V interval are successively applied to PZT. The corresponding phase variations are demodulated and the amplitude of phase are measured. Figure 15 shows a plot of the demodulated phase amplitude versus the applied driving signal amplitude. It shows that from 1.5V to 5V, the phase amplitude increases linearly with the vibration amplitude. The nonlinear behavior below 1.5V may be due to the fact that the fiber on the PZT is not wrapped sufficiently tight. The deformation could not be completely transferred to the fiber when the applied driving signal is too small. This partly accounts for the relatively low quality waveform obtained in experiment 1 where the amplitude of the PZT driving signal is set to 1V. This part of the experiment shows that the demodulated waveforms are proportional to the external vibrations.
According to the experiment results presented above, the method is proven to perform phase demodulation based on the fundamental direct detection φ-OTDR. Coherent detection in the entire process is not required. At the same time, it must be clearly stated here that the direct phase measurement of the RBS field was not conducted. Precise measurements of PZT deformation were also not performed. This is due to the great difficulty in the direct measurement of these two quantities. However, the agreement between the PZT driving signal and the demodulated waveform should also be able to prove the correctness and feasibility of the method.
In addition, some issues are analyzed in particular. Firstly, it is observed from all the demodulation results that the spikes, which are actually demodulation failures, are always present. More or less, the spikes bring about distortions and deteriorate the demodulation waveforms. Two reasons can account for the emergence of the spikes.
First is the presence of coherent fading. As is well known, coherent fading is an intrinsic phenomenon of φ-OTDR which is caused by the stochastic interference between individual RBS light pulses [23–25]. It can be explained by Eq. (9). When happens to be in the vicinity of kπ where k is an integer, the intensity does not noticeably change with respect to the phase variation. In this case, φ-OTDR is less or even not sensitive to the external perturbation. Although many researches have spend efforts trying to overcome this drawback, it cannot be completely solved. Intuitively, the method proposed in this paper would fail to restore the perturbation waveform as a result of the little or zero information that is delivered in the intensity signals. This is reasonable in theory and can be explained by the experiment results shown in Fig. 16. Figure 16 (left) shows a segment of 19s intensity evolution which is the sensing result of sinusoidal PZT vibration. The signal from 0s to 7s is subjected to coherent fading, which could be readily discriminated by the small amplitude and the chaotic waveform exhibiting no characteristic of the applied sinusoidal vibration. The waveform after 7s is free of coherent fading. The inset in this part shows normally distorted intensity signals. This half-fading, half-normal intensity signal is used as one of the inputs for phase demodulation, and the result is shown in Fig. 16 (right). It is clearly observed that the first half of the demodulated waveform exhibits chaotic vibration pattern giving no useful information, yet the second half exhibits the correct sinusoidal waveform. This proves that the coherent fading is one of the factors that can cause demodulation failure.
Another reason is the presence of small amplitude in the sum or difference signal. Figure 17 shows three plots that respectively presents the sum, difference and the corresponding demodulated waveform. The red frames highlight the parts of the difference signal that suffer from small amplitude and the simultaneous occurrence of the demodulation failure. The synchronization between the presence of small amplitude and the occurrence of demodulation failure proves the presence of small amplitude to be another reason for demodulation failure. This also agree with the theory derived above. When the amplitude of the sum or difference intensity is too small, the first terms on the right hand side in Eq. (11) is fading. Hence errors are being introduced when the envelope fluctuation is eliminated with a large compensating factor.
This paper proposed a phase demodulation method that can be used in the φ-OTDR system without coherent detection. As opposed to the existing phase demodulation techniques in the literature which have to rely on coherent detection, optical hybrid, interferometer structure or multi-channel synchronous signal detection, none of the above is required in this method. Consequently, it greatly simplifies the system configuration and lowers the cost. More importantly, in the case where coherent detection or complicated system implementation is not available, this method is the only method to date that can be used for phase demodulation. Successful phase demodulation experiments have been performed using the proposed method in the case of single-frequency vibration, amplitude-modulated vibration and chirped vibration. The experiment results can be well explained by the theoretical analysis. The demodulated phase waveform is proven to be proportional reproduction of the disturbance waveform, which is linear and less distorted.
National Natural Science Foundation of China (No. 61304244, 61374219); Natural Science Foundation of Tianjin (No. 14JCQNJC04900, 14JCZDJC32300); Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130032130001).
We are thankful for the financial support.
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