1. Introduction
Conventional optical time domain reflectometry (OTDR) has been widely used in optical fiber communication to detect fault events of fiber links. The working principle is to measure the index of fraction changes [
1,
2,
3]. However, only static changes can be discerned, such as the fiber attenuation, splice and connector loss and break points. Dynamic events cannot be determined by using conventional OTDR. Moreover, its spatial resolution is generally tens of meters, which is not enough to locate the position of a fault precisely. With the capability of telling the type and exact position of an intrusion simultaneously, phase-sensitive optical time domain reflectometry (Ф-OTDR) has attracted much attention since its invention [
4]. Furthermore, Ф-OTDR has many field applications such as in the health monitoring of large-scale structures, including borders, bridges, tunnels, oil pipes and so on [
5,
6].
There are two typical signal detection schemes in the Ф-OTDR system including direct detection [
7,
8,
9,
10] and coherent detection [
11,
12,
13,
14,
15,
16,
17,
18,
19,
20]. In the direct detection scheme, the setup is simple; only the intensity of the optical signal is detected by using a high-sensitivity photodetector. However, the sensing distance is limited (without amplification). To achieve a longer sensing distance, a complex structure and high cost (extra pump laser) are necessary for the direct detection scheme [
9,
10]. Different from the direct detection technique, local light and a balanced photodetector are used to implement the longer sensing distance in the coherent detection scheme. This greatly reduces the complexity and the cost of the whole system. Up until now, there were three kinds of signal demodulation methods for the system based on coherent detection, including the zero-span function of the electrical spectrum analyzer (ESA) [
11,
12], heterodyne detection [
13,
14,
15,
16,
17,
18] and digital coherent detection [
19,
20]. In previous reports, the zero-span function of the ESA was used to eliminate all the other unwanted electrical components to obtain a pure signal [
11,
12]. However, it is not practical in real-time monitoring and the ESA increases the cost of the system greatly. In the heterodyne demodulation scheme, a stably local electrical signal mixes with the beat signal where its frequency strictly equals the frequency shift caused by the acoustic-optic modulator (AOM) [
13,
14,
15,
16,
17,
18]. However, this synchronous demodulation scheme is sensitive to the variation of the beat signal, and typically a frequency locked loop is needed. The instability of the beat signal makes the signal-to-noise ratio (SNR) of the detection system fluctuate because of the frequency drift of the laser and the AOM [
16,
17]. For the demodulation method of digital coherent detection, a data acquisition card (DAQ) with an ultra-high sample rate and a large amount of storage is necessary. That makes too much unnecessary data be stored and processed. Although it can get a better performance in demodulation, it takes much more time and cannot realize real-time monitoring [
19,
20].
In this work, a self-mixing signal demodulation scheme has been proposed for the coherent Ф-OTDR system. It extracts the intrusion signal from the beat signal by mixing the beat signal itself, which avoids generating a local signal and a frequency locked loop compared to the heterodyne detection. More importantly, it eliminates the residual frequency (caused by the instability of the beat signal) to achieve a pure signal. Thus, it greatly improves the demodulation performance. The experimental results prove the feasibility of this technique by simultaneously determining the frequency and location of the vibration intrusion. A 10 m spatial resolution has been achieved on a 42.5 km fiber link. In addition, the detectable frequency range from 8 Hz to 980 Hz and a high SNR of 21.4 dB have been implemented in this work.
2. Principle
The phase of the backscattered Rayleigh light carries the vibration information when an optical pulse from a high-coherence laser source is injected into a sensing fiber [
7,
8,
17,
21]. The optical signals will interfere with each other within one pulse duration. They will interfere when the backscattered signal of the pulse leading edge (embracing the vibration information) meets with the signal behind it which has no vibration information [
8,
17,
21]. The evolution of the backscattered Rayleigh light within a one-pulse duration is shown in
Figure 1, including the unmodulated, partly modulated and completely modulated signal [
8,
17,
21]; the part of the signal with the vibration information is called modulated (orange part) while that without vibration information is called unmodulated (blue part). It means that the phase difference of two backscattered signals within a one-pulse duration reflects the external information (vibration/strain). The backscattered Rayleigh light returns to the end of the pulse light injection, which can be described as:
The phases of two backscattered optical signals are φ1(t) which carries vibration information and φ0(t) which is the normal backscattered one (without vibration information). ER1(t) and ER0(t) are the amplitudes, correspondingly, and fc is the center frequency of the light output from the laser source.
For the direct detection method, these two parts will interfere at the photodetector. The output of the photodetector
Idirect(
t) is expressed by [
21].
To realize long-distance sensing with a satisfying SNR, the Ф-OTDR system based on coherent detection has been proposed [
11,
12,
13,
14,
15,
16,
17,
18,
19,
20]. As shown in
Figure 2a, the pulse probe light modulated by an AOM is injected into a sensing fiber to detect the external vibration/intrusion. The backscattered Rayleigh light can be described as
ER1(
t)
expi(
2π(
fc +
∆f)
t +
φ1(
t)) +
ER0(
t)
expi(
2π(
fc +
∆f)
t +
φ0(
t)), and
∆f is the frequency shift introduced by the AOM. The backscattered Rayleigh light combines with a continuous wave (CW) local light by a 3 dB coupler before it falls on the balanced photodetector. The CW local light
ELO(
t)
expi(
2πfct) is split from the coherent laser through a 90:10 coupler. The coupled light is detected by a balanced photodetector. The detected current
Icoherent is proportional to the optical power.
where
ELO(
t) is much larger than the
ER1(
t) and
ER2(
t), and
θ(
t) is the relative polarization angle between the backscattered light and the CW local light.
In previous reports [
13,
14,
15,
16,
17,
18], the schematic diagram of coherent Ф-OTDR based on heterodyne detection is illustrated in
Figure 2b. The AC component of
Icoherent(
t) in Equation (3) can be obtained by passing through a carefully selected electrical bandpass filter or high-pass filter, which can be rewritten as:
In the heterodyne detection scheme, a local electrical oscillator with extremely stable frequency
∆f is necessary to obtain the demodulated signal of
2ELO(
t)
cosθ(
t)[
ER1(
t)
cosφ1(
t) +
ER0(
t)
cosφ0(
t)]. Meanwhile, the frequency
∆f must be equal to the center frequency of the beat signal. Unfortunately, the center frequency is unstable because of the frequency drift of the local light and the jitter of the AOM driver [
13,
14,
15,
16,
17,
18]. Although the local electrical oscillator is stable enough, the demodulated signal cannot eliminate the frequency component completely, as illustrated in
Figure 2c. Thus, a typical frequency locked loop is needed to follow the beat signal variation tightly [
13,
14,
15,
16,
17,
18]. In addition, the demodulated signal does not contain a phase difference since the two components in Equation (4) do not interfere with each other. That makes further data processing necessary (to realize the precise location and frequency measurement).
Compared to the heterodyne detection method, the self-mixing demodulation technique extracts the intrusion signal from the beat signal by mixing the beat signal itself, as shown in
Figure 2d. It avoids generating a local electrical signal and setting up a frequency locked loop in addition. More importantly, although the frequency of the beat signal is unstable, it can demodulate the beat signal completely (without residual frequency) and obtain the phase difference.
Figure 2e shows the demodulated result in the situation of the beat signal instability. Obviously, there is no residual frequency left since the mixing signals are split from the same signal. Therefore, this method of self-mixing can overcome the defect in heterodyne detection. The demodulation result of
Sself-mixing(
t) can be described as:
The vibration information can be extracted by using a deliberately selected low-pass filter with suitable cutoff frequency.
For a stable laser, the
ELO(
t) is almost a constant, and the change of the relative polarization angle
θ(
t) is a slow change process compared with the dynamic measurement [
12,
13]. Therefore, the coefficient 2[
cosθ(
t)
ELO(
t)]
2 is a slowly varying variable. It can be considered as a constant in comparison with the vibration signal. Compared to
Idirect(
t) in Equation (2), only the coefficients are different. So the self-mixing scheme can extract the vibration information modulated on the optical signal in theory.
4. Experimental Results
A vibration with a frequency of 300 Hz was applied to the sensing fiber. Three hundred consecutive traces were sampled by an oscilloscope (with a sample rate of 100 MS/s). By calculating the auto-power spectrum of vibration along the sensing fiber, the vibration with a frequency of 300 Hz appears at 40.45 km clearly, as illustrated in
Figure 4a.
Figure 4b,c show the time domain signal and the corresponding frequency spectrum at the test point, respectively. Limited by the performance of the vibration actuator (PZT) and non-treatment of the signal, the time domain curve is slightly fluctuant. Note that all results are not processed with the filtering algorithm. Obviously, the demodulation results are in good agreement with the applied vibration signals.
By subtracting the amplitude traces from the first trace and computing the sum of the absolute amplitude change [
11,
12], the vibration location curve is shown in
Figure 5a. The achieved SNR of the intrusion signals reaches up to 21.4 dB at the vibration position of 40.45 km (the SNR is calculated as the ratio between the peak intensity of the vibration signal and the root-mean-square intensity of the background noise) [
11]. The vibration was applied along 1.5 m of fiber at the vibration position. In the experimental results, one point represents one meter since the sample rate of 100 MS/s was used in these experiments.
Figure 5b shows that the full width of the vibration location is about 12 m (40,446–40,458 m). That means the spatial resolution is ~12 m without any further processing [
22]. Considering the pulse-broadening caused by the AOM (the optical pulse modulated by the AOM has a rising edge over 10 ns), it is in good agreement with the probe pulse width of 100 ns [
22].
Restricted by the fiber length of 42.5 km, the pulse repetition of 2 kHz was used in the experiment. Therefore, the maximum frequency response is 1 kHz according to the Nyquist theorem. To identify the capability of broadband measurement, the vibration signals with a frequency from 8 Hz to 980 Hz were applied on the sensing fiber separately.
Figure 6a shows the normalized power spectrum with a frequency range from 8 Hz to 980 Hz.
Figure 6b,c show the details of the applied minimum and maximum frequency, respectively.
6. Conclusions
In this paper, we propose a self-mixing method to extract the vibration signal modulated in the Rayleigh backscattered signal in the coherent Ф-OTDR system. Compared to previous methods, the self-mixing demodulation technique extracts the intrusion signal from the beat signal by mixing the beat signal itself, which avoids generating a local signal and a typical frequency locked loop as well. More importantly, this method can eliminate the residual frequency caused by the frequency drift of the local oscillator and the AOM driver. Thus, a superior demodulated signal can be achieved with this method.
In this work, we have experimentally demonstrated the demodulation capability of the self-mixing method. With 100 ns pulse-width modulated light, the spatial resolution of 10 m has been achieved. The vibration location on a 42.5 km fiber has been precisely obtained with a satisfying SNR of 21.4 dB. Meanwhile, more than 10 vibration signals with different frequency from 8 Hz to 980 Hz were measured accurately.