1. Introduction

The interferometric fiber Bragg grating (FBG) array based on the Fabry-Perot (F-P) cavity can detect weak signals by phase-matching methods, which has the advantages of high sensitivity, large dynamic range, simple optical structure, and high reliability [1–3]. As a typical fiber-optic hydrophone system with high detection sensitivity, it is widely used in fields facing harsh environments, such as underwater detection and seabed seismic monitoring [2–4].

In practical applications, multipair FBGs are integrated into a large-scale sensor array by utilizing multiplexing schemes, where time-division multiplexing (TDM) and wavelength-division multiplexing (WDM) have been widely used [5,6]. However, multiple reflections between the FBGs could delay some forgoing signals, which might arrive during the time window allotted to downstream FBGs and eventually be detected by other sensors in the array. Therefore, the crosstalk has greatly limited the multiplexing capability and detection sensitivity of the system. According to the generation mechanism, crosstalk can be divided into the TDM crosstalk induced by multiple reflections of light and WDM crosstalk caused by insufficient isolation of WDM devices. The TDM crosstalk problem was first raised by A. D. Kersey et al. and its causes and influencing factors were theoretically deduced and experimentally verified [7]; C. C. Chan et al. further investigated the crosstalk in various applications of fiber grating TDM structures [8,9]; H. Lin et al. conducted a detailed analysis of crosstalk in path-matching interferometric FBG sensing systems and derived the crosstalk level [10]; In Ref. [11], the level of WDM crosstalk decreased linearly with the isolation between WDM multiplexers and increased with the number of multiplexed channels. Since then, many teams have investigated in depth the principles and methods to suppress the traditional TDM and WDM crosstalk, achieving good suppression by targeting the crosstalk caused by the FBG itself. However, in practical applications, the crosstalk phenomenon does not disappear even when the problem of the FBG itself is solved. We recently found in experiments for the first time a special crosstalk case called the false crosstalk. This crosstalk was not related to the optical performance of the device but was involved with the optical position of the sensor in the array, which also varied with the leading fiber length.

This paper focused on the false crosstalk phenomenon caused by the different optical positions of the sensors. Theoretical model and simulation results showed that if the leading fiber was longer than a certain threshold, the Rayleigh backscattering (RB) noise near the collision point would generate the crosstalk. For a 2TDM structure, when the leading fiber length was over 172.8 m, the false crosstalk would appear. In addition, the false crosstalk affected TDM and WDM structures simultaneously. Experimental results verified that the false crosstalk was only affected by the sensor position and not related to the FBG itself.

This paper is arranged as follows. Section 2 is about the model and numerical simulation of the false crosstalk. Section 3 presents the experimental results with various leading fiber lengths in the interferometric FBG sensor array and the crosstalk probability distribution. Finally, a summary is given in Section 4.

2. Origin of the false crosstalk: modeling and simulation

2.1 Effectively discriminating Rayleigh backscattering

The principle of interferometric FBG sensor arrays has been described in [12–14]. Figure 1 depicts a sensing end structure of a 2WDM${\times}$ 4TDM interferometric FBG sensor system, where the eight-TDM channels are called CH1–CH8, and the two-WDM channels are called WDM1 and WDM2, respectively.

 

Fig. 1. Sensing end structure of a 2WDM${\times}$ 4TDM interferometric FBG sensor array

Download Full Size | PDF

As illustrated in Fig. 1, the FBGs are distributed serially along the fiber, and the pulse interval ${\tau _s}$ is equal to the light roundtrip between adjacent FBGs. The 1^st pulse of the input pulse pair reflected by FBG1 and the 2^nd pulse of that reflected by FBG0 will exactly overlap and interfere at FBG0, and this interference pulse which include the phase information of CH1 is just the 1^st pulse in the returned pulse train. Similarly, the next interference pulse including the phase information of CH2 will occur at FBG1, which is the 2^nd pulse in the returned pulse train. The optical pulses with two different wavelengths are separated in time sequence after passing through a delay optical fiber with a length of ${d_0}$, and the returned optical pulse train will be detected by a photoelectric detector. The interrogation light transmitted in the direction of the interferometer is called the downstream light, whereas the light returned by the interferometer is called the upstream light.

Ideally, the output pulse received by the photodetector at one time is only formed by the interference of two pulses reflected by two adjacent gratings, which are called the main pulses. In fact, due to the dual reflection and transmission characteristics of the FBG, the main pulse will contain the crosstalk caused by the superposition interference of multiple reflected lights. As a result, the output pulses will mix with the crosstalk coherence components and additional noise. According to Ref. [12], the crosstalk was related to the FBG reflectivity, and the crosstalk of a 2TDM structure could be reduced to −60 dB when the reflectivity was 0.1%. Thus, the crosstalk could be effectively suppressed in the low-reflectivity FBG sensing system. Our recent study found that when the length of the front leading fiber was changed, crosstalk was generated and changed in the experiment. Based on the dynamic discontinuous RB model, we deduced that such crosstalk was caused by the parasitic interference in the leading fiber.

In the inline FBG sensor system, the downstream interrogation light and upstream light share the same leading fiber. If the fiber is sufficiently long or the interrogation frequency is sufficiently high, the returned pulse train will meet post-order interrogation pulses at a point in the fiber, which is defined as the collision point. The RB light generated by post-order interrogation pulses near the collision points and the upstream returned pulses are in the same wave train from a highly coherent light source, thus, they will have high coherence and interfere in time and space. Meanwhile, the noise interference term induced by RB noise is presented as the inter-channel crosstalk in the demodulation results. We define the crosstalk caused by the aforementioned phenomenon of parasitic interference as false crosstalk.

Figure 2 takes a 2TDM optical structure as an example to analyze the influence of RB noise on crosstalk in the sensing system. The two channels are defined as CH1 and CH2 and a 1-kHz strain signal ${\varphi _C}$ is applied on CH1. In Fig. 2, ${E_{11}}$ and ${E_{12}}$ represent the 1^st and 2^nd pre-order interrogation pulses, while ${E_{21}}$ and ${E_{22}}$ represent the 1^st and 2^nd post-order interrogation pulses. ${E_1}$ and ${E_2}$ are the 1^st and 2^nd main interferometric pulses in the returned pulse train, corresponding to CH1 and CH2 signals, respectively.

 

Fig. 2. Optical pulses propagation in the 2TDM system

Download Full Size | PDF

Here, ${v_g} = c/{n_{eff}}$ is the group speed of light, ${n_{eff}}$ is the effective refractive index of the fiber, T is the pulse width, ${\tau _s}$ is the pulse interval, L is the leading fiber length, ${T_i} = 1/{f_{AOM}}$ is the interrogation period, ${f_{AOM}}$ is the interrogation frequency, and $\frac{1}{2}{\tau _s}{v_g}$ is the interval between two adjacent FBGs.

Here, A is defined as the collision point of ${E_2}$, where ${E_2}$ and the RB light of ${E_{21}}$ completely overlap in time and space and interfere with each other. The length d from A to the first sensor FBG0 at the sensing end is $({{{{T_i}} / 2} - {\tau_s} - {T / 2}} ){v_g}$. So, the q^th collision point away from FBG0 is

Here, the relationship between the number of collision points and the leading fiber length can be obtained as

In Eq. (2), $\lfloor\cdot \rfloor$ denotes the downward rounding operation. It is shown that the number of collision points is positively correlated with L and ${f_{AOM}}$. When ${n_{eff}}$ is 1.481, T is 190ns, ${\tau _s}$ is 244ns and ${f_{AOM}}$ is 400 kHz, the relationship between the number of collision points and the leading fiber length is shown in Fig. 3.

 

Fig. 3. Relationship between the number of collision points and the leading fiber length

Download Full Size | PDF

Figure 3 shows that with the increase of the leading fiber length, the number of collision points of the CH2 signal increases stepwise. Similarly, it can be concluded that the properties of the collision points of the other channels and the performance of RB noise at those positions are consistent with the previous findings.

Extending the conclusions above to a 2WDM${\times}$ 4TDM sensor system as depicted in Fig. 1, we can obtain the sensor positions where the collision points of CH2–CH8 signals occur, which are written as

In the TDM/WDM interferometric FBG sensor system, the collision points of CH8–CH2 signals appear sequentially on the leading fiber, as the leading fiber length increases. The RB noise at the collision point interferes parasitically with the returned pulses and results in an increase of the crosstalk in the final demodulation result. In a word, the false crosstalk is caused by the optical position of the sensor in the FBG hydrophone multiplexing array system.

2.2 Discriminating Rayleigh backscattering induced false crosstalk

Section 2.1 analyzes the distribution of collision points where the false crosstalk is generated in the leading fiber and gives the relevant conditions of the sensor positions. To quantitatively describe the mechanism, a false crosstalk model is established as follows by taking an example of the optical structure shown in Fig. 2.

Here, the expressions of the pre-order interrogation pulses ${E_{11}}$ and ${E_{12}}$ are written as

In the 2TDM structure of Fig. 2, the output optical pulse train contains two main interference pulses, ${E_1}$ and ${E_2}$.${E_1}$ is included by the returned light ${E_{o,1}}$ of ${E_{11}}$ reflected by FBG1 and the returned light ${E_{o,2}}$ of ${E_{12}}$ reflected by FBG0. The expressions of ${E_{o,1}}$ and ${E_{o,2}}$ are written as

Here, r is the FBG reflectivity, ${\varphi _C}$ is the sinusoidal signal loaded on CH1, ${\varphi _{d - 0}}$ is the phase delay from FBG0 to point A, ${\varphi _{s0}}$ is the inherent phase delay of the sensing fiber between FBG0 and FBG1.

Then, the intensity ${I_1}$ of ${E_1}$ can be expressed as

Since CH2 is on the back end of CH1, its signal will pass through the front end of CH1 during transmission and carry all the phase information of CH1, including the applied signal ${\varphi _C}$.

If the effect of the RB light is not considered, the returned signal ${E_2}$ only includes the returned light ${E_{o,11}}$ of ${E_{11}}$ reflected by FBG2 and the returned light ${E_{o,22}}$ of ${E_{12}}$ reflected by FBG1, which are presented as

Here, ${\varphi _{l - 0}}$ is the phase delay from FBG1 to point A. The intensity ${I_{02}}$ of ${E_2}$ is

Here, the phase of ${I_{02}}$ does not include ${\varphi _C}$, which means the loaded signal on CH1 does not transmit to CH2 and has no effect on the result of CH2.

When considering the RB noise in Fig. 2, ${E_{21}}$ and ${E_2}$ interfere with each other. Under this circumstance, the RB light ${E_{rb}}$ of ${E_{21}}$ is expressed as

Here, ${\varphi _{0 - A}}$ is the phase delay from the beginning of the leading fiber to point A, and $rr$ is the RB rate. Thus, the intensity ${I_2}$ of ${E_2}$ is written as

The first three terms in Eq. (10) are the DC terms without the phase information, and the 4^th is the main interference term that does not contain ${\varphi _C}$ in phase. The 5^th and 6^th terms are the crosstalk coherence terms where ${E_{rb}}$ interferes with ${E_{o,11}}$ and ${E_{o,22}}$, respectively, and both of their phase information contain the signal carrier term ${\varphi _C}$. This indicates that part of the signal on CH1 in the front will appear on CH2, and when a signal appears anywhere in front of the sensor, the output will always carry that signal. In other words, there will be false crosstalk between channels induced by the RB noise in the linking fiber when compared with Eq. (8).

For the last sensing unit in the minimum space division structure, the fibers including all the sensing cavities before can be regarded as the common-mode leading fiber. Thus, for CH2 in Fig. 2, if there are other FBG hydrophones in front of FBG1, all the sensors in the front end are equivalent to the leading fiber of this sensor, whose phase information exists in ${\varphi _{l - 0}} - {\varphi _{0 - A}}$. When a signal is applied to these sensors, it will be passed to the following ones through the crosstalk coherence terms in Eq. (10). Therefore, for any sensor in the TDM/WDM interferometric FBG sensor array, when the RB noise near collision points exists, the signal from the front end transmitted to the rear end will universally affect the output, whether the front end is a fiber or a hydrophone in any multiplexing form.

In practical systems, the magnitude of crosstalk is usually defined by the crosstalk between channels. Specifically, when a b-V signal is applied to only one channel, the amplitude of the crosstalk signal measured in the other channel is d V, then the crosstalk magnitude $Cr$ (in decibels) of the two channels is defined as

Combined with Eqs. (6) and (10), we can obtain the crosstalk magnitude with and without RB noise as

Equation (12) indicates that the magnitude of the false crosstalk is related to the grating reflectivity r and the RB rate $rr$. In theory, the RB noise intensity is related to the RB rate $rr$, the leading fiber length L, and the pulse width T. The increase of $rr$ and T directly leads to the increase in intensity, while the growth of L results in a step increase in the number of collision points, which indirectly causes an increase in intensity. In the model, it is related to the increase of ${E_{rb}}(t)$ in Eq. (10), which leads to an increase in the value of the crosstalk coherence term and ultimately raises the false crosstalk magnitude. Briefly, the false crosstalk magnitude increases with the decrease in grating reflectivity r and the increase in RB intensity.

As mentioned above, the false crosstalk is caused by the RB noise at collision points due to the increasing length of the leading fiber. Meanwhile, the crosstalk increases gradually with the increase in RB noise intensity. Unlike traditional crosstalk caused by optical devices, this crosstalk changes with the length of the leading fiber in the front end.

2.3 Numerical simulation

Numerical simulation is implemented to analyze the output signals and crosstalk probability distribution of sensing channels to further investigate the influence of RB noise on the false crosstalk. According to the model in Section 2.2, the simulation parameters are given in Table 1. To simplify the model, the laser frequency ${\upsilon _0}$ is set to 0, and phase ${\varphi _0}$ is the original phase of light pulse with an approximate value of $3/\pi$, where $\omega$ used to generate the probability distribution is a random variable obeying an average distribution in the interval of [0,1]. ${\varphi _D} = C\cos (2\pi {f_{PGC}}t)$ is a PGC modulated signal introduced on ${E_{11}}$ with an amplitude C of 2.37 V and a frequency ${f_{PGC}}$ of 15.625 kHz. ${\varphi _C}(t) = {C_0}\cos (2\pi {f_0}t)$ is the signal loaded on CH1 with an amplitude ${C_0}$ of 1 V and a frequency ${f_0}$ of 1 kHz. The magnitude ${E_0}$ is 1 V, and the RB rate $rr$ is ${10^{ - 4}}$.

Table 1. Simulation parameters of the analog optical signal

View Table

The frequency domain characteristics of the simulated CH1 and CH2 signals with and without the influence of RB noise are shown in Fig. 4. The level of background noise is kept around $- 100rad/\sqrt {Hz}$. When there is a −45-dB signal response of CH1 signal at 1 kHz, the response of CH2 about −75dB only appears with the RB noise, which results from the changes in the leading fiber length. Based on these results, we can conclude that when the leading fiber length is larger than a certain threshold, a collision point will occur and the RB noise near that location will lead to the signal crosstalk between channels.

 

Fig. 4. Demodulation results of simulated (a) CH1 signal, and CH2 signals (b) with RB noise and (c) without RB noise

Download Full Size | PDF

It is generally required that the background noise of the fiber optic hydrophone multiplexing system is equivalent to the phase noise in the deep-sea environment at zero-level sea state, and the crosstalk is less than −40 dB in practical applications [15]. Therefore, to specifically describe the system performance and crosstalk magnitude, we define a parameter called the crosstalk distribution probability and propose requirements for it: the sampled crosstalk measurements being ≤ −40 dB should account for more than 90% of the time, that is, the crosstalk distribution probability must be ≥ 90%. This parameter intuitively reflects the crosstalk magnitude.

To further demonstrate the influence of RB noise on the false crosstalk, the crosstalk distribution probability of CH2 signal with and without RB noise is investigated by setting the parameter $rr$ 0 or ${10^{ - 4}}$ after multiple measurements, where the leading fiber length is set as 0 m or 250 m. With these two different lengths, we can simulate the state with or without interference induced by RB light, which can reveal the physical image and relevant features. The modulation result is shown in Fig. 5.

 

Fig. 5. Crosstalk probability distribution of CH2 with and without RB noise

Download Full Size | PDF

In Fig. 5, the probability for the crosstalk to be ≤ −40 dB in CH2 without the RB noise remains above 90%, which means no crosstalk exists in the system. In contrast, the probability of crosstalk being ≤ −40 dB with RB noise is below 90%, not satisfying the probability requirements. The simulation indicates that RB noise is a vital factor influencing the false crosstalk.

The model in Section 2.2 shows that the false crosstalk magnitude depends on the grating reflectivity and RB noise intensity. To prove the validity of this conclusion, the following simulation is conducted.

Firstly, the relationship between the false crosstalk and grating reflectivity is studied by changing the grating reflectivity r, which was set to 0.1%, 0.6%, 1%, 1.5%, 2%, and 2.5%, respectively. $rr$ is maintained at ${10^{ - 4}}$, and the values for the other parameters are given in Table 1. Figure 6 depicts the variations of crosstalk distribution probability of CH2 with the grating reflectivity in a 2TDM system.

 

Fig. 6. Crosstalk probability distribution of CH2 with various FBG reflectivity

Download Full Size | PDF

As the grating reflectivity increases, the probability of CH2 crosstalk being ≤ −40 dB gradually increases, which indicates that the crosstalk magnitude gradually decreases. This result shows that the false crosstalk magnitude is inversely correlated with the grating reflectivity and tends to decrease as the grating reflectivity increases.

Next, the variations of crosstalk under various RB noise intensities are simulated. Since the RB noise intensity is proportional to the rate $rr$, the change of the intensity is achieved by changing $rr$. Figure 7 illustrates the variations of crosstalk distribution probability of CH2 versus $rr$.

 

Fig. 7. Crosstalk probability distribution of CH2 with various RB coefficients (intensities)

Download Full Size | PDF

It is found that the false crosstalk increases with the intensity of RB noise, and there is a positive correlation between them. These simulation results are consistent with the conclusions based on the theoretical model in Section 2.2. Based on the above results, it is concluded that in the TDM/WDM interferometric FBG sensor system, the false crosstalk is induced by the parasitic interference in the leading fiber, which affects the TDM and WDM structures simultaneously.

3. Experimental results and discussion

3.1 System setup

The schematic diagram of the 2WDM${\times}$ 4TDM interferometric FBG sensor system is shown in Fig. 8.

 

Fig. 8. Schematic diagram of a path-matching interferometric FBG-FP hydrophone system

Download Full Size | PDF

Two narrow-linewidth low-noise fiber lasers with a central wavelength of 1539.77 nm (ITU-C47) and 1533.47 nm (ITU-C55) were used as the light sources. The continuous laser sources were pulsed by an acousto-optic modulator (AOM) with a modulation frequency of 400 kHz, and the pulse width was 190 ns. The AOM output pulse was then converted to two cloned interrogation pulses through a compensation interferometer (CIF) with imbalanced arms. The CIF arm difference (49.65 m) determined that the pulse interval ${\tau _s}$ was 244 ns, which was twice the interval between adjacent FBGs in the array for path matching.

Ten FBGs were imprinted in the sensing end. The wavelengths of the first five and the last five FBGs were 1539.77 and 1533.47 nm, belonging to WDM1 and WDM2, respectively. The reflectivity r of all FBGs was 0.6%. The delayed fiber length ${d_0}$ between WDM1 and WDM2 was 20 m, and the space between any two adjacent FBGs was 24.825 m. The eight TDMs were defined as CH1–CH8.

We selected G625D fibers with various lengths for specific operations and applied a sinusoidal excitation ${\varphi _C}(t) = {C_0}\cos (2\pi {f_0}t)$ by a PZT wounded on the CH1 or CH5 sensing channel, which had an amplitude of 1 V and a frequency of 1 kHz. Meanwhile, the remaining sensing segments were acoustically shielded and vibration isolated, and the crosstalk would be calculated based on the amplitude of the demodulation signal at the corresponding frequency point. Thus, we could compare the variations of crosstalk under different leading fiber lengths by using the crosstalk probability distribution.

3.2 Discussion

A basic test was first performed to ensure the array reliability of the system crosstalk performance, where the leading fiber length L was as short as 1.5 m and a sinusoidal excitation of 1 kHz was imposed on CH1 or CH5. The demodulation result of each channel signal is shown in Fig. 9 and the crosstalk distribution probability of each channel signal is shown in Fig. 10. Due to the use of a 0.6% ultra-low reflectivity grating design, whether the signal was loaded on CH1 or CH5, the probability of crosstalk being ≤ −40 dB in each channel was maintained above 90%. The results demonstrated no crosstalk between channels was present in the system, indicative of good performance and suitability for following experiments.

 

Fig. 9. DDiagram of demodulation results when L = 1.5m with (a), (b) signals loaded on CH1 and (c), (d) signals loaded on CH5.

Download Full Size | PDF

 

Fig. 10. Diagram of crosstalk probability distribution when $L = 1.5\textrm{m}$ with (a), (b) signals loaded on CH1 and (c), (d) signals loaded on CH5

Download Full Size | PDF

Then, to analyze the influence of leading fiber length on crosstalk in the TDM structure, the length of the leading fiber varied from 21, 34, 40.5, 53.5, 100, 133.8, 146.8, 153.3, 166.3, 172.8, 179.3, 185.8, to 192.3 m. The two ends of the fibers were connected with patch cords. The crosstalk probability for each channel of WDM1 is depicted in Fig. 11 when a 1-kHz signal was imposed on CH1.

 

Fig. 11. Diagram of crosstalk probability distribution with different lengths for (a) CH2, (b) CH3, and (c) CH4

Download Full Size | PDF

As shown in Fig. 11, the crosstalk increased with the increase in leading fiber length L. Furthermore, when L was larger than a certain value, the probability of crosstalk being ≤ −40 dB for one certain channel would always be less than 90% and remained constant. For example, when L was greater than 133.8 m, the probability of crosstalk being ≤ −40 dB for CH4 signals was always less than 90%. Meanwhile, when L was larger than 146.8 or 179.3 m, the probability of crosstalk being ≤ −40 dB for CH3 or CH2 signals was always below 90% as well.

To further analyze the effect of false crosstalk on WDM structures, the crosstalk between different WDMs was investigated. In this case, a 1-kHz signal was implied on CH1, and the leading fiber lengths L were set as 21, 40.5, 47, 53.5, 60, 73, 87, 93.5, and 100 m, respectively. Figure 12 illustrates the crosstalk of channels in WDM2 resulting from variations in the leading fiber length.

 

Fig. 12. Diagram of crosstalk probability distribution with different lengths for (a) CH5, (b) CH6, (c) CH7, and (d) CH8

Download Full Size | PDF

It could be found that the variations of the leading fiber length led to the occurrence of crosstalk between WDMs. In Fig. 12, when L was larger than 21, 47, 73, and 93.5 m, respectively, the crosstalk between WDMs appeared on CH8, CH7, CH6, and CH5 signals with a stable probability of crosstalk ≤ −40 dB being less than 90%, and all the probability requirements were not satisfied. Thus, the false crosstalk would affect TDM and WDM simultaneously.

Substituting the experimental values into Eq. (3), we could obtain the theoretical positions of the collision points corresponding to CH2–CH8. Combined with the fiber length interval where the crosstalk probability of each channel failed to meet the requirements for the first time in Figs. 11 and 12, the fitting diagram of the sensor positions and fiber lengths is plotted in Fig. 13. It could be seen that when the crosstalk probability of each channel did not pass for the first time, there was always a collision point of the corresponding channel on the linking fiber under the specific leading fiber length. According to the theoretical model in Section 2.2, the RB noise at the collision point of the corresponding channel caused by the increasing leading fiber length was the key factor in producing the false crosstalk in the hybrid multiplexing array. This showed that the changes in the optical position of the sensor would alter the crosstalk. The experimental conclusions were consistent with the theoretical model.

 

Fig. 13. Fitting diagram of sensor positions and crosstalk-generating leading fiber lengths

Download Full Size | PDF

Finally, to confirm that the false crosstalk was only related to the sensor position and not to the grating itself, the WDMs structures were processed reversely, i.e., WDM2 was in the front instead, and a 1-kHz signal was implied on CH1 of WDM1. When L was 100 m, the crosstalk probability distributions of the previous and reversed WDM structures are shown in Fig. 14. In Figs. 14(a) and (b), the implied signal transmitted from WDM1 to WDM2 and caused crosstalk phenomenon with a stable probability of crosstalk ≤ −40 dB being less than 90% in each channel of WDM2, while the probability of crosstalk ≤ −40 dB is more than 90% in each channel of WDM1, which means no crosstalk phenomenon occurs in WDM1.Compared with Figs. 14(c) and (d), when a 1-kHz signal was implied on CH1 of WDM1 in the back, the signal did not transmit to the front WDM2 but still appeared on the remaining channels of WDM1, which were at the same positions as WDM2 in Fig. 14(b). The results indicated that the crosstalk could only transmit from the former WDM to the latter and the latter would not affect the signals of the former. Therefore, it could be inferred that the resulting false crosstalk only depended on the sensor position and was not related to the grating itself.

 

Fig. 14. Diagram of crosstalk probability distribution (a), (b) in order and (c), (d) in reverse order

Download Full Size | PDF

The above experimental results revealed that the false crosstalk in the TDM/WDM interferometric FBG sensor array could only propagate from front to back, which was related to the position of the sensors and not to the performance of the grating itself. Also, the leading fiber length was a vital factor affecting the crosstalk; When it was greater than a certain threshold, the crosstalk occurred, whose size increased gradually with the fiber length. That is, in the time-division and wavelength-division hybrid multiplexing structure, the change of sensor position would lead to the generation and change of the false crosstalk.

4. Conclusions

This paper focused on a newly discovered false crosstalk problem in the TDM/WDM interferometric FBG sensor array and analyzed its causes by constructing a theoretical model and conducting simulation tests. Both theory and experimental results showed that the false crosstalk was induced by the RB noise in the leading fiber, which was related to the position of the sensor, but not to the performance of the grating itself. For a 2TDM structure, the front end of the sensor could accommodate a leading fiber at most 172.8 m long due to the existence of the false crosstalk. This research provides key technical support for optimizing the overall structure design of fiber grating hydrophones, improving the basic system performance, and expanding the large-scale multiplexing capacity.