1. Introduction

In recent decades, fiber optic sensors have received considerable attention. Compared with traditional sensors, optical fiber sensors have obvious advantages, such as high sensitivity, immunity to electromagnetic interference and ease of application to networking etc [1–4]. Among all kinds of fiber optic sensors, interferometric fiber optical sensors, which measure the phase change caused by environmental influences (such as vibration) posed on the fiber, have very high sensitivity. So a wide range of researches and applications in terms of military sonar, seismic wave detection and underwater monitoring system have been conducted [5–8]. Usually, single sensor applications are only appropriate in very few instances mainly due to the high cost. So fiber optic sensors are more practical when organized in arrays of dozens to tens of hundreds, such as in earthquake forecasting, oil exploration, and security monitoring circumstances. Many multiplexing technologies including the time, frequency, coherence, and wavelength multiplexing have been proposed to support multi-sensors capability [9–13]. In time-division multiplexing (TDM) scheme, the sensors are sequentially addressed by using a pulsed input signal so that the “time of flight” of the optical pulses allows individual sensor signals to be distinguished. In wavelength-division multiplexing (WDM) scheme, it allows many TDM signals at different wavelengths to be combined in a single fiber. Furthermore, dense WDM (DWDM) technology can include more wavelengths and contribute to highly multiplexed systems. The hybrid multiplexing scheme based on TDM and DWDM is the first choice for large-scale arrays. The largest interferometric fiber-optic sensor array reported up to now is able to support a total number of 1024 sensors along one fiber pair, and can be expanded to interrogate 4096 sensors using 16 wavelengths in theory [12].

For large-scale sensor arrays which adopt TDM architecture, sensor-to-sensor crosstalk is one of the most intractable problems which not only influences the signal quality of an individual sensor but also determines the upper bound of the sensor number in the array. In general, ultra-narrow band linewidth light sources are used in large-scale sensor arrays by lending the benefits of their ultra-low phase noise, which are essential to improve the detection accuracy and dynamic range. However, these light sources simultaneously have rather long coherent length which is far longer than the fiber distance between adjacent sensors. This will result in severe coherent light overlapping and cause crosstalk if the optical pulse modulator (or light switch) needed by the TDM scheme is not ideal (with finite extinction ratio) [14, 15]. In the military field, the crosstalk between sensors is generally required to be less than −40 dB for high quality consideration. For an 8 sensors TDM system, to achieve the requirement, the extinction ratio of the optical pulse modulator must be less than −55 dB, which is very demanding for commercially available modulators.

According to the best of the author’s knowledge, there are generally two main methods to combat the crosstalk existing in the literatures. All the methods are discussed in the context of the ultra-weak fiber Bragg grating (FBG) sensor array, since the performance of this kind of array is seriously constrained by the multi-reflection induced crosstalk. The first method is to reduce the reflectivity of the FBG, however this requires the reflectivity down to 1%~5% and causes significant signal-to-noise problems [16]. The second method is the layer-peeling inverse scattering method which extracts the crosstalk-suppressed signal in an iterative manner according to the appearing orders of the sensors in the TDM array, but this method is rather computationally complicate [17]. Besides, all these methods are proposed to cope with the multi-reflection induced crosstalk, and it seems that there are no effective methods to cope with the pulse-modulator-induced crosstalk except improving the extinction ratio as high as possible. In this paper, aiming to thoroughly overcome the pulse-modulator-induced crosstalk problem, we propose a novel wavelength-cross-combination (WCC) method by re-organizing the architecture of the sensor array, which can theoretically eradicate the coherent superposition and thus reduce the crosstalk between sensors significantly.

Another key consideration for practical sensor array applications is the phase demodulation scheme which influences both the system performance and the implementation complexity significantly. Several widely used demodulation methods include: the phase-generator carrier (PGC) method [18, 19], the 3x3 coupling multi-phase detection method [20, 21], and the heterodyne demodulation method [22, 23]. In this paper, a so-called rectangular-pulse binary phase demodulation method [24] is utilized to support our sensor array prototype. Compared with other methods, it has the advantages of low operation complexity and excellent real-time capability. More importantly, since this demodulation method is based on the phase shifting principle and uses arctan phase calculation method, it can naturally eliminate the non-coherent light intensity crosstalk. When combined with the up-mentioned WCC scheme, both coherent and non-coherent sources of crosstalk can be theoretically removed and this results in very high-quality signal recovery.

To verify our method, a quasi-distributed fiber optic sensor array prototype based on hybrid TDM/DWDM technology is built and experimentally tested in this paper. In this system, 4 TDM time windows and 16 DWDM wavelengths are used to constitute the 64-sensors array. The proposed WCC technology is utilized to remove the coherent superposition crosstalk caused by the highly coherent light source and the rectangular-pulse binary phase demodulation method is used to retrieve the phase information. Experimental results showed that even utilizing an optical pulse modulator with the extinction ratio of less than 28 dB, the sensor array still realized the crosstalk of less than −60 dB. This method is also easy to scale up and provides a very valuable option for large-scale sensor array applications where low crosstalk and high sensitivity are of the top consideration.

2. Principle of the wavelength-cross-combination (WCC) method

In traditional TDM/DWDM schemes, demultiplexers are usually used first to separate the optical pulses of different wavelengths returning from the sensor array, and then to transfer the optical pulses of the same wavelength to the same photodetector (PD). In the following steps, the demodulation setup can resolve the TDM signals and fulfill phase retrieval. In practical sensor array applications, since the extinction ratio of the optical pulse modulator is not infinite, there exist coherent light overlapping chances if the used laser source has longer coherent length than the distance span of adjacent sensors. The WCC method is proposed here to thoroughly overcome this problem. Its basic idea is to reassign optical pulses of different wavelengths rather than of the same wavelength to the same PD to eliminate the possibility of coherent optical pulse overlapping and interference.

Here we use a conceptual N-time-windows TDM array shown in Fig. 1 as the explanation example. The term T_i (i = 1,…N) represents the i-th time window, during which the i-th light intensity can be sampled and the phase information can be retrieved. At T_i moment, the term A represents the amplitude of the optical pulse of the i-th time window while the term B represents the amplitude of the optical pulse from any other time windows. According to the definition of the extinction ratio, it exists: $\eta =B/A={10}^{-\frac{ER}{20}},$ where $\eta$ represents the light intensity ratio and ER represents the extinction ratio of the optical pulse modulator.

 

Fig. 1 N-time-windows TDM array.

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Assuming that the polarization direction of each beam is consistent, the final output light intensity $I_m$ corresponding to T_m (m = 1,2…N) can be expressed as:

To illustrate the WCC method, considering a N-time-windows TDM and M-wavelengths DWDM sensor array in the parallel network configuration [25] with the specific implementation structure shown in Fig. 2 as an example system, there are totally N$\times$M optical pulses which need to be discriminated and phase demodulated.

 

Fig. 2 An example system of N-time-windows TDM and M-wavelengths DWDM sensor array.

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Under the WCC configuration mode, N wavelength demultiplexers (DMUXs) are used to separate the light pulses of different wavelengths while M multiplexers (MUXs) are used to recombine these pulses. Assuming that $S_{ij}$ represents the optical pulse belonging to the i-th time window while having the j-th wavelength ($1\le i\le N,1\le j\le M$) and $Mu{x}_j$ represents the j-th MUX, the specific combination pattern corresponding to the sensor array architecture of Fig. 2 is depicted in Fig. 3 and expressed as:

 

Fig. 3 WCC-method-based combination pattern.

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According to the above method, the light pulses of different wavelengths are combined to the same MUX, resulting in an overall reassignment for all the optical pulses.

Corresponding to each PD, the light path contains N optical pulses which come from T₁, T₂, …, T_N respectively with mutually different wavelengths. By using this recombination technique, no matter how long the coherent length of the laser source is, there won’t be any coherent superposition crosstalk between the two arms of T_m and the ones of any other time windows. So Eq. (2) can be converted to

This means that the coherent superposition crosstalk between different TDM time windows is completely removed, remaining only non-coherent superposition crosstalk with a much smaller order of ${\eta }^2$.

Generally, the specific combination pattern of the TDM/DWDM scheme may differ corresponding to the specific sensor array architecture (not comply with the one shown in Fig. 2), however the WCC method can still be applied by properly adjusting the combination relationship in Fig. 3. Finally, we point out that in order to completely avoid possible coherent overlapping, M must not be smaller than N which gives M$\ge$N. It guarantees that the wavelengths combined to the same MUX are definitely different with each other.

3. Binary rectangular pulse phase modulation

A modulation method based on binary rectangular pulse phase modulation is used in this paper. The key implementation element is the rectangular-pulse binary phase modulation imposed on the laser source, through which three phase-shifting steps of $\text{-}\pi /2$, 0, and $\pi /2$ radians can be realized at the output, and subsequently the phase information that reflects the imposed measurand on the fiber sensor can be obtained via an orthogonal arctan demodulation algorithm. The implementation schematic of the method is shown in Fig. 4. The output light intensity $I_d$ is expressed as follows

 

Fig. 4 Implementation schematic of binary rectangular pulse phase modulation method.

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Assuming that the length difference of the arms is $l$, it holds that $\tau =2nl/c$,where $n$ is refractive index of optical fiber, and $c$is the speed of light. According to the timing shown in Fig. 5(a), ${\phi }_p(t)$ in one period can be expressed as:

 

Fig. 5 Time and phase relationships between the modulated phase terms ${\phi }_p\left(t\right), {\phi }_p(t-\tau )$, and ${\phi }_p(t)-{\phi }_p(t-\tau )$. (a) ${\phi }_p(t)$; (b) ${\phi }_p(t-\tau )$; (c);${\phi }_p(t)-{\phi }_p\left(t-\tau \right)$ (d) Sampling timing for the three phases.

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Assuming that the vibration period of the measurand signal is $T_1$, since $T<<T_1$ holds true in practical system, it can be considered that the vibration signal remains unchanged over the time period $0<t<T$, which guarantees the PD can detect the light intensity stably. Subsequently, the three light intensities $I_{d1}$, $I_{d2}$, $I_{d3}$ corresponding to the three points P₁, P₂,and P₃ are obtained. The time terms $t_1$, $t_2$, $t_3$ represent the time intervals between the corresponding points P₁, P₂, P₃ and the rising edge of the reference pulse shown in Fig. 5(d). Using the orthogonal arctan demodulation algorithm, can be calculated as follows:

When the modulation method is applied to a TDM sensor array, the required timing diagram is shown in Fig. 6. The three phase-shift intensity signals $I_{m1},$ $I_{m2},$ $I_{m3}$ corresponding to T_m $(m=1,2,\mathrm{...},N)$ need to be sampled to demodulate the phase signals. After applying the WCC method, the light intensity $I_m$ from Eq. (3) can be expressed as:

 

Fig. 6 Pulse train and sampling timing for the TDM array.

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It indicates that is${\eta }^2{\displaystyle \sum _{k=1,k\ne m}^N\cos (\frac{4\pi nl}{\lambda }+{\phi }_{ks}-{\phi }_{kr})}$ a constant value commonly existing in $I_{m1}$, $I_{m2}$, $I_{m3}$. According to Eq. (7), the demodulated phase signal won’t be affected by this constant value, which means that the phase demodulation technology naturally eliminates the non-coherent optical pulse superposition crosstalk. When combined with the WCC technology, the crosstalk between sensors can be thoroughly eradicated in theory.

4. Sensor Array Prototype Composition

To valid the proposed WCC method, a sensor array prototype is built up whose overall structure is depicted in Fig. 7. It consists of four main parts: laser source launching module, sensor array module, signal receiver and recombination module, and FPGA control terminal. The laser source launching module generates the phase modulated optical pulses which are fed into the sensor array. The sensor array module is an all optical fiber network that organizes all sensors in a particular form to support the TDM and DWDM scheme. The signal receiver and recombination module receives the returning light pulses from the sensor array and converts the light signals to electrical signals. The FPGA control terminal drives the timing signals to the laser source launching module and fulfills the phase demodulation task after receiving the signals from the signal receiver and recombination module.

 

Fig. 7 The structure of the sensor array prototype.

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4.1 Laser source launching module

The structure of the laser source launching module is shown in Fig. 2(a) above. The laser light source is made up of M lasers with different center wavelengths (${\lambda }_1,{\lambda }_2,\mathrm{...},{\lambda }_M$). The light pulses are generated by utilizing an optical pulse modulator which is then rectangular-pulse binary phase modulated by a phase modulator. The light pulses are then conducted into N TDM paths T₁, T₂, …, T_N through a 1 × N coupler. In each path, there is a delay fiber to generate time delay and an EDFA to compensate for the loss of energy which ensures that the power of the corresponding sensor array is strong enough to be detected. The lengths of delay fibers corresponding to the T₁, T₂, …, T_N paths are 0, $\Delta L$, $2\Delta L$, …,$(n-1)\Delta L$. By using this configuration, N optical paths having N different time delays while containing M different wavelengths are generated.

4.2 Sensor array module

The specific structure of the sensor array is shown in Fig. 2(b) above. In the sensor array, there are two common telemetry fibers used for multiplexing; the pulses of each wavelength are separated from one telemetry fiber by an optical drop multiplexer (ODM), travel into each individual sensor, carry the measurand information and then travel back to another telemetry fiber through an add multiplexer (OAM).

The implemented structure has three merits. Firstly, the light pulses of each wavelength reach the receiver end experiencing the same optical path, so there is no delay in time between the received pulses of different sensors; secondly, the energy loss of the light pulses corresponding to each wavelength is almost the same; lastly, if the telemetry fiber is cut off, only the pulses corresponding to the ODAM after the breakpoint will be lost. The sensor in the array is actually an implementation of a non-balanced fiber Michelson interferometer as shown in the dashed box in Fig. 2. The unbalanced arm configuration helps realize the binary rectangular pulse phase modulation and more details can be found in [24].

4.3 Signal receiver and recombination module

The structure of the signal receiver and recombination module is shown in Fig. 8, which is the core component to realize the WCC method. The returned light pulses from the N sensor array modules each containing M wavelengths travel into N DMUXs to be separated and then into M MUXs to be recombined according to the principle illustrated in Fig. 3. There are totally M PDs, each one of which is responsible for N optical pulses with different wavelengths, to convert all the N × M optical pulses into digital values for the FPGA control terminal.

 

Fig. 8 The structure of the signal receiver and recombination module.

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4.4 FPGA control terminal

The structure of the FPGA control terminal is shown in Fig. 9, which includes an FPGA chip, several ADC chips, and some necessary analog circuit chips [26]. Its main functions are as follows: 1. generating voltage signals for the modulation of the optical pulse modulator and phase modulator; 2. generating reference pulse and precise control of synchronization to obtain the three phase-shift signals of all the sensors for demodulation; 3. calculating the phase signals in real time and sending the results through the USB interface to the PC.

 

Fig. 9 The FPGA control terminal.

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5. Experiments and results

5.1 Experimental setup

In the sensor array prototype realized in this paper, N is set as 4 while M is set as 16 resulting in totally 64 optical pulses. The photograph of the realized system is shown in Fig. 10. In this photograph, A is the monitor screen; B is the personal computer (PC); C is the optical case, including the laser source launching module (excluding the light sources) and the signal receiver and recombination module; D is the combined laser light sources with 16 different wavelengths; E is the FPGA control terminal; F is the power supply for all the active devices; and G is the sensor array module.

 

Fig. 10 Photograph of the system. (a) Front side; (b) Back side.

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On the actual implementation, the light sources are made up of 16 low phase noise lasers (LN Solutions Inc. LN Focus) with different wavelengths ranging from 1549.3 to 1561.3 nm. The lasers have a wavelength interval of 0.8 nm and own a very narrow linewidth of less than 1 KHz. An electro-optic modulator (Boston Applied Technologies Inc. NANONA^TM) is used to generate an optical pulse (extinction ratio below 28 dB). The width of the modulated light pulse is 400 ns and the repetition frequency is 500 KHz. The phase modulator (PHOTLINE Inc. with series number MPZ-LN-10) is used to generate the phase modulated pulses with a width of 28 ns and a repetition frequency of 500 KHz. The modulator has a linear and stable phase versus voltage response curve [27]. The applied 2.5 V to the modulator generates the shifted phase of $\pi /2$ needed in the sensor array.

The step length of the delay fiber $\Delta L$ is set as 100 m corresponding to a delay of 500 ns, so the obtained delays for T₁, T₂, T₃, T₄ are 0 ns, 500 ns, 1000 ns, 1500 ns respectively. The power of each port is amplified by an EDFA up to about 48 mW to balance the optical loss when travelling through the sensor array. As for each specific fiber optic sensor, the length of the reference arm is 7.2 m while that of the signal arm is 10 m, leading to $l\text{=}$2.8 m. The sensor acts as a double-end-fixing acceleration sensor.

5.2 System functionality validation experiments and results

To verify that this sensor array prototype can function precisely and reliably, the sensors were first placed on a vibration table (Yangzhou YMC Technology Co., Ltd. VT80), which generated continuous vibrations with constant acceleration. The intermediate light intensities and demodulated phase results were transferred to PC for further analyzing. Taking the No.1 sensor as the example, the received light intensity is shown in Fig. 11(a). The sampled light intensities$I_1$, $I_2$, $I_3$ corresponding to the three phase-shifting steps are shown in Fig. 11(b), and the relative relationships between them are consistent with Eq. (9). By applying that$I_{\text{s}}=I_1-I_3$,$I_{\mathrm{c}}=2I_2-(I_1+I_3)$, the corresponding Lissajous figure and its fitting curve are depicted in Fig. 11(c). The exact circle shape in the figure further certificates the correct phase relationship as defined by Eq. (9). Using these light intensities, the demodulated vibration signal is depicted in Fig. 11 (d), which shows excellent agreement with its theoretical expectation.

 

Fig. 11 (a) Light intensity versus time; (b) Three phase-shifting steps $I_1$,$I_2$, $I_3$; (c) Lissajous curves of $I_{\text{s}}$and$I_{\mathrm{c}}$; (d) Experimental result of the demodulated phase shifts.

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5.3 Crosstalk experiments and results

To validate the effectiveness of the proposed WCC method on suppressing the crosstalk, two sensors belonging to the first two TDM time windows were chosen for the following experiments. Sensor 1 corresponding to wavelength ${\lambda }_1$ was placed in a quiet environment, while sensor 2 corresponding to wavelength ${\lambda }_2$ was placed on the vibrating table which generated a stable vibration signal at 100 Hz.

The tested results are shown in Fig. 12. The phase amplitude of sensor 2 at 100 Hz was 6.8 rad, while the phase amplitude of sensor 1 at 100 Hz was 0.0067 rad. The crosstalk was calculated as [16]: 20log₁₀ (0.0067/6.8) = −60 dB. Because the sensor 1 was not placed in an absolutely quiet environment, there existed some noise power baseline, so the actual crosstalk should be smaller than −60 dB. Considering that the extinction ratio of the used electro-optic modulator is less than 28 dB, it proves that the WCC method can greatly reduce the crosstalk between sensors which significantly improves the accuracy of the signal.

 

Fig. 12 (a) Vibration signal of the sensor 2; (b) Frequency spectrum of the Sensor 2; (c) Vibration signal of the sensor 1; (d) Frequency spectrum of the Sensor 2.

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5.4 Phase resolution and field vibration experiments and results

In this section, the 64 sensors were put in a relatively quiet environment to test the phase resolution. Each sensor has a quite similar phase noise behavior and the typical time domain and frequency domain noise curves are depicted in Fig. 13. The calculated phase resolution according to this figure is 4 × 10⁻⁴ rad/√Hz@100Hz. The main reason contributing to this resolution value is the not strictly quiet environment and we plan to find other ideal places such as an isolated cave to re-perform this experiment. One may also notice that the noise phase floor is smaller than that shown in Fig. 12(a). The reason is caused by the not exactly equal testing conditions, since the use of the vibration table in the crosstalk experiment inevitably brings more noise to the sensor under test through environmental coupling.

 

Fig. 13 (a) Time-domain curve of the system noise; (b) the power spectrum of the system noise.

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Finally to carry on the field vibration test of the sensor array, the 64 sensors were fixed steadily to the ground. All the sensors were closely arranged to form a 4$\times$16 rectangular grid region. A hammer was used to strike the ground fiercely to simulate the seismic wave source. The specific configuration of the experiment is shown in Fig. 14.

 

Fig. 14 The sensors deployment of the vibration experiment.

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By collecting the seismic wave induced phase data utilizing the sensor array, the calculated vibration curves of the 64 sensors are depicted in Fig. 15. All the sensors show a vibration amplitude of about 1 rad and a main pulse duration of about 50 ms. By applying the Fourier analysis, the seismic waves are found to contain a frequency range of (5 Hz, 150 Hz). Based on the propagation delay time, all the 64 sensors can be divided into 4 groups corresponding to the 4 columns in Fig. 15. The discontinuous sensor numbers are 17, 33 and 49 and conform to the first deployed sensor number in each sensor column. Within each sensor group, the propagation delay time increases weakly with the sensor number and accords with the fact that the sensors of larger numbers are farther to the seismic source in distance. More accurate analysis of these signals requires professional geophysics knowledge and is beyond the scope of this paper.

 

Fig. 15 Vibration phase signals of the 64 sensors.

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5.5 Conclusion

Due to practical device performance limitation, light overlapping induced crosstalk between different sensors is one of the main obstacles that influence the overall performance of the TDM/DWDM sensor array system. To overcome this problem, a high-quality hybrid TDM/DWDM-based fiber-optic sensor array with extremely low crosstalk based on a novel WCC method is proposed and experimentally demonstrated. Experimental results indicate that even utilizing an optical pulse modulator with less than 28 dB extinction ratio, the obtained crosstalk between adjacent sensors in the system is less than −60dB. In addition, this method can be easily extended to be applied in large-scale TDM/DWDM system. Although costing more passive optical devices such as DMUXs and MUXs, this method provides an excellent choice for the practical applications where the sensing performance is of the top consideration.