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Abstract
The polarization switching and phase generated carrier (PS-PGC) hybrid method is typically adopted to control signal fading induced by fiber birefringence and to precisely demodulate signals in interferometric fiber Bragg grating (FBG) sensor arrays. Unlike simple PGC demodulation, the real-time phase delay between the detected interference and the PGC carrier in the hybrid method has more adverse effects as both demodulation accuracy and background noise can be deteriorated, which may invalidate the polarization switching (PS) method. Aiming at this issue, the real-time phase delay and its compensation method were analyzed in detail in this paper. The features of the real-time phase delay in the PS-PGC hybrid method were summarized and the differences among polarization channels were investigated. Theoretical analysis indicated that the real-time phase delay mainly affected the interference complex synthesis (ICS) procedure, ultimately bringing about errors in the PS-PGC algorithm. The method for demodulating the real-time phase delay from sampled interference was presented, which provided the key compensation parameter. Experimental results showed that the compensation method could greatly improve the stability of the demodulated signal and suppress the sensor background phase noise. The amplitude of the demodulated signal was stabilized with a fluctuation less than ± 0.75dB and a noise suppression of 5dB. The acceptable compensation error was also analyzed.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The inline interferometric fiber Bragg grating (FBG) sensor array has been widely used in ultra-weak signal sensing applications, such as acoustic detection [1], seismic sensing [2–4]. The inherently integrated sensor array structure has only FBGs written inline, providing benefits of simple and compact structure, potential low cost and high reliability [5–6], making it especially attractive for applications in harsh environments. The interferometric interrogation method is of high sensitivity in its physical nature, providing an excellent foundation for ultra-weak signal sensing [7].
Compared to conventional fiber interferometers, it is more difficult for the inline FBG interferometer to obtain stable demodulation and low background noise, as no optical fiber devices can be added in the array to eliminate disturbances from the interrogation system, the leading fiber and even the sensor itself. The most prominent obstacle for the inline FBG interferometer is the polarization-induced signal fading [8], which is mainly caused by random fiber birefringence fluctuations and is usually solved using a pair of Faraday rotator mirrors in the Michelson interferometer [9–10]. The PS method is one solution that mainly modulates interrogation pulses [11–12]. Besides the unique problem for the FBG structure, common problems in fiber interferometers should also be addressed, such as random sensor sensitivity fluctuations [13] mainly caused by environment-induced sensor phase drifting. Fortunately, those common problems have been well studied with lots of solutions proposed, such as the PGC method [14]. Considering both unique and common problems, it can be known that the interrogation design and the demodulation algorithm are the essence of an excellent inline interferometric FBG sensor system. Therefore, ingenious and precise demodulation parameters are of great significant, even determining whether the sensor can be used in practical applications. The polarization switching and phase generated carrier (PS-PGC) hybrid method was proposed under this background and has been proved useful by a series of experiments [7–12].
This paper focused on performance promotion for the interferometric FBG sensor array using the PS-PGC hybrid method, considering the real-time phase delay between the detected interference and the PGC carrier as a key demodulation parameter. In a simple PGC system, the real-time phase delay has been noticed and its compensation method has attracted much attention recently [15–22]. Early methods tried to control the initial phase of PGC carrier from the perspective of hardware [15]. However, the real-time phase delay is related to every part of the demodulation system, difficult to be controlled accurately. Later, some researches tried to pre-estimate the real-time phase delay and compensate it in the demodulation algorithm [16–22], whose focus was still the pre-estimated result of the real-time phase delay. Compared to simple PGC demodulation, the real-time phase delay in the PS-PGC hybrid method has more sophisticated effects. We have fully demonstrated the PS-PGC method in Ref. [7] and Ref. [12], showing that the PGC carrier existed in all of four polarization channels. Therefore, both the suppression of polarization-induced signal fading and the picking-up of the sensor phase were highly related to the real-time phase delay. In this paper, the real-time phase delay and its compensation method in the PS-FGC hybrid method were analyzed in detail. The principles of how the real-time phase delay affects the PS-PGC hybrid processing procedure and corresponding results were investigated. Real-time phase delays of all polarization channels were analyzed. A compensation method was proposed, which was experimentally demonstrated to be effective in promoting sensing performance.
This paper is arranged as follows. Section 2 is about theoretical demonstrations of the real-time phase delay in the PS-PGC system and its compensation method. Section 3 is on experimental results with the measured real-time phase delay in the PS-PGC system and the evaluated compensation effects. In Section 4 a brief summarization is presented.
2. Theory
2.1 Basic principle of interferometric FBG sensor array
A typical structure of an interferometric FBG sensor array is shown in Fig. 1. Three FBGs are written inline in a single fiber with absolutely uniform reflection centers. If interrogated using a pair of laser pulses, interference occurs when the second pulse reflected by the ith FBG overlaps with the first pulse reflected by the (i + 1)th FBG(i = 0, 1), as shown in Fig. 1. Two-time division multiplexed sensor elements named S1 and S2 can thus be formed, each containing two adjacent FBGs and a length of fiber between the two FBGs.
The two reflected pulses for S1 and S2 can be written as
2.2 Brief review of PS-PGC hybrid processing method
We have demonstrated the PS- PGC hybrid processing method in previous reports [7–12]. In order to analyze the influence of real-time phase delay, a brief review is given here. The sensor impulse is defined as
In a practical experimental system, the key device to obtain ${\Re _n}$ is a PS module. The laser input to the PS module is typically linearly polarized, and this polarization state is called the X polarization. If a half-wave voltage is acted upon the PS module, the output laser can be modulated to its orthogonal polarization state, i.e., the Y polarization. Thus, we can control the polarization of two interfering laser pulses. If the polarization states of two laser pulses are modulated into XX, XY, YY and YX successively, as shown in Fig. 2, the interferences of four polarization channels for each sensing unit can be obtained, named as IXX, IXY, IYY and IYX, respectively.
The Jones matrix of the laser pulse pair in the XX polarization channel can be expressed as in Eq. (6) given that the laser intensity is normalized to be 1.
Then, the ICS can be completed as
2.3 Real-time phase delay in PS-PGC hybrid processing method
As demonstrated in Eq. (7) and Eq. (9), a phase modulation of $C\cos (2\pi {f_0}t)$ is expected for the four polarization channels. Although the signal generator can provide an exact signal of $C\cos (2\pi {f_0}t)$, there is a time delay when the carrier signal is acted on ${E_{in1}}$ and detected by the photo-detector. This delay can be caused by the optical path, the circuit transmission, the optical detection process, etc. [15–16]. Considering a time delay of $\Delta t$, the real carrier signal is $C\cos [2\pi {f_0}(t\textrm{ + }\Delta t)]$ and thus an original phase delay of $\theta = 2\pi {f_0}\Delta t$ exist in Eq. (7) and Eq. (9), which can be written as
The analysis above indicates that the real-time phase delay mainly affects the ICS procedure and ultimately adds error to the demodulation. In order to compensate for the real-time phase delay, the complex synthesis can be revised as
3. Experimental results and discussion
3.1 System setup
The schematic diagram of the experimental system is shown in Fig. 4. Three FBGs were written in a single-mode fiber. The center wavelength was all 1539.8nm ± 0.01nm with a 3dB bandwidth of approximately 0.36nm, and their relativities were carefully controlled to be 0.6%. The spacing between any two adjacent FGBs was 39.75m.
A narrow line-width fiber ring laser was used whose relative intensity noise was −120dB/√Hz @ 1 kHz. The laser wavelength was 1539.8nm, in accordance with the FBG reflection center. The laser output was modulated into pulses by an acoustic-optical modulator (AOM) from GOOCH&HOUSEG with an interrogation frequency of 320kHz. A Mach-Zehnder (M-Z) fiber interferometer was used as the compensation interferometer (CIF), providing a pair of interrogating laser pulses with a time delay determined by optical path imbalance (OPI). The time interval of the interrogating laser pulse pair should be exactly in accordance with the laser round trip time between two adjacent FBGs, as demonstrated in Fig. 1, thus the latter was measured firstly to provide CIF designing instruction. The laser pulse outputted by the AOM was directly injected to the FBGs array and the reflected light pulse train was recorded by the detector and the sampling module shown in Fig. 4. Then an oscilloscope from Tektronix was used to display the recorded results, as shown Fig. 5, and the laser round trip time between two adjacent FBGs was measured to be 392ns. Afterwards, CIF fiber lengths of the two arms were carefully adjusted to generate a laser pulse pair with a time interval of exactly 392ns and the final measured fiber length imbalance was 79.5m. Therefore, a fiber refractive index of 1.479 could be calculated given a light speed in vacuum of 3×108m/s. Part of the short arm of the CIF was wounded on a PZT to introduce the modulation signal for PGC demodulation. The PGC modulation amplitude and frequency were set to be 2.37 and 10kHz, respectively. The pulse pairs were then injected to a PS module from Photline, where the polarization of each pulse can be modulated individually with a PS modulation frequency of 80kHz. All parameters in the experimental system are shown in Table 1 and Table 2.
Table 1. Parameters of FBG sensors array
Table 2. Parameters of interrogation system
We applied a sinusoidal signal of 1kHz to S1, and the sampled interferences for S1 and S2 are shown in Fig. 6. For both S1 and S2, four polarization channels were obtained. Figure 6(a) shows the interference of S1 in the frequency domain while Fig. 6(b) shows the interference of S2 in the frequency domain. It can be seen that for S1 the 1kHz signal was carried on the PGC modulation frequency at 10kHz and its harmonics above while the PGC modulation frequency was also10kHz and no obvious signal at 1kHz was carried on for S2, indicating a small crosstalk.
3.1 Measurement of real-time phase delay
The real-time phase delays of S1 and S2 were obtained as demonstrated in Section 2.3. We sampled the interferences for 87 times, and the demodulated real-time phase delays of the four polarization channels are shown in Fig. 7 for S1 and S2, respectively. If a certain polarization channel is considered, the real-time phase delays were the same for S1 and S2, as the interrogation pulse pair was the same one though reflected by different FBGs. As shown, the phase delay for the four polarization channels showed a fixed difference of about 0.2rad, mainly determined by the time delay of interrogation pluses. As shown in Fig. 2, the time delay of interrogation pulses between two adjacent polarization channels is the reciprocal of the AOM frequency, which was 3.125µs in our experiment. Therefore, the theoretical phase delay was 0.1963rad given a PGC frequency of 10kHz, in agreement with the experimental results. Furthermore, the PS modulation frequency is generally 8 times of the PGC frequency for full period sampling, and the AOM frequency is 4 times of the PS modulation frequency, as indicated in Fig. 2. As a result, the fixed phase delay difference for the four polarization channels is $2\pi {f_{PGC}}/(32{f_{PGC}})$, where ${f_{PGC}}$ refers to the PGC frequency, which is a constant number of 0.1963rad. This discussion indicates that when the PGC frequency is changed, the measure real-time phase delay remains unchanged.
As mentioned above, the real-time phase delay is mainly caused by the optical path, the circuit transmission and the photo-detection process, which is a fixed parameter once the system starts working. Figure 7(a) indicates that for the four polarization channels, the real-time phase delays were −1.19rad, −1rad, −0.6rad and −0.8rad, respectively. Slight fluctuations were observed which may be caused by the phase delay demodulation method. As shown in Eq. (17), the real-time phase delay is obtained by the division of $X_{_{2MNn}}^{\prime\prime}$ and $X_{_{1MNn}}^{\prime\prime}$, which eliminates a common factor of $\sin ({\varphi _{sn}} + U{a_{MNn}})$. When ${\varphi _{sn}} + U{a_{MNn}}$ is close to zero, $\sin ({\varphi _{sn}} + U{a_{MNn}})$ is also a small number close to zero. Therefore, the result of Eq. (17) is not stable since that a small number close to zero is divided. The PGC-DCM method was used to demodulate the corresponding phase in each polarization channel and the result of the real-time phase delay of S1 versus the demodulated signal phase is shown in Fig. 8.
Figure 8 clearly shows that when the phase $({\varphi _{sn}} + U{a_{MNn}})$ is smaller than 0.2rad, the real-time phase delay is not stable. Therefore, when the demodulated phase is near, $\pi \,/\,2$, the corresponding real-time phase delay can be used as the compensation parameter. Figure 8 also indicates that the demodulated sensor phases are not equal for the four polarization channels as $U{a_{MNn}}$ is related to fiber birefringence. The fluctuations of the real-time delays for the four polarization channels were not identical, showing relatively smaller fluctuations for the YX and YY channels in our experiments.
3.2 Compensation of real-time phase delay
We used the demodulated real-time phase delay of −1.19rad, −1rad, −0.6rad and −0.8rad as the compensation parameters for the XX, XY, YX, YY polarization channels, respectively. Figure 9(a) shows the demodulated results without any compensation. The four-polarization channels were demodulated using the PGC-DCM algorithm directly and the results are colored in red, blue, yellow and green, respectively. The results from the PS method are colored in black. Each polarization channel contains a factor related to fiber birefringence, as indicated in Eq. (10), thus the demodulated results of the four polarization channels differed from each other with their demodulated amplitudes at 1kHz being −18.35dB, −26.6dB, −30.11dB and −41.43dB (0dB re 1rad/ Hz1/2), respectively. The PS-PGC method delivered a signal amplitude of −32.16dB. Figure 9(b) shows the demodulated results when the real-time phase delays were completely compensated. Significant improvements can be seen, showing more consistent demodulated signal amplitudes, which were −24.35dB, −24.74 dB, −24.8 dB and −24.87dB (0dB re 1rad/ Hz1/2), respectively. The PS-PGC hybrid method obtained a signal amplitude of −24.75dB in this case.
Fig. 9. Demodulated signal at 1kHz (a) with no compensation and (b)with completely compensated phase delay.
As indicated in Eq. (14), the fiber birefringence factor ${U_{MNn}}$ cannot be eliminated completely when there are real-time phase delays in the four polarization channels. As a result, the demodulated signal amplitude will fluctuate with environmental disturbances, i.e., polarization induced signal fading. We sampled the interferences of S1 for 87 times, and the demodulated signal amplitudes at 1kHz with and without real-time phase delay compensation are shown in Fig. 10. Without compensation, the demodulated signal amplitude fluctuates from −32dB to −17dB with the PS-PGC hybrid method, indicating that the PS method was invalid. When the real-time phase delays were completely compensated, the demodulated signal amplitude was −24.75dB with a fluctuation less than ± 0.75dB. The fiber disturbance-induced polarization did not affect signal demodulation and the PS-PGC hybrid method can reduce the effect of the polarization-induced signal fading well.
Fig. 10. Demodulated signal amplitude fluctuations with and without real-time phase delay compensation.
Here the real-time phase delays were compensated using fixed parameters demodulated from the sampled interference, and Fig. 7 indicates that there was fluctuation when tested for a long period. For one single frame data, the compensation parameter may deviate from the true value. To evaluate the case when the real-time phase delay is not compensated completely, the demodulation results were tested when the compensation parameter deviated from the true value, as shown in Fig. 11. The x-axis shows the deviation percentage from the true value, and the y-axis is the amplitude fluctuation of the corresponding demodulation signal. Figure 11 indicates that the PS-PGC hybrid method can deliver an acceptable signal amplitude fluctuation less than ± 1.5dB when the compensation value deviation is less than 20%. It should be noted that if the signal amplitude fluctuation is larger than ± 1.5dB, the sensor cannot be used in practical environments.
Figure 12 shows the results of S2 with and without real-time phase delays. As the signal at 1kHz was applied only to S1 and the FBG reflectivities were controlled to be less than 1%, there was no obvious signal and the crosstalk was lower than 40dB. Figure 12(a) shows the demodulated results of S2 for a certain frame data with and without real-time phase delay compensation, colored in black and red, respectively. It can be found that if there was no compensation, the background noise was higher than that with complete compensation. As the phase background usually fluctuates with environmental disturbances, the result from a certain single frame data may not be convincing. Therefore, we demodulated S2 for 87times and the average results are shown in Fig. 12(b). It is clear that with the real-time phase delay compensation, the background noise level can be lowered by about 5dB than that without compensation. However, the difference was not obvious at frequency bands lower than 300Hz, which can be explained by the fact that the noise induced by environmental disturbances is much greater than by fiber-birefringence-induced polarization fading.
Fig. 12. Demodulated noise background of S2 for (a) single frame data and (b) average results accumulated for 87 times.
4. Conclusions
This paper focused on performance promotion of interferometric FBG sensor arrays in which the real-time phase delay was analyzed in detail. As the PS-PGC hybrid processing method was used for sensor demodulation, the real-time phase delay must be compensated as both the demodulation accuracy and background noise could be deteriorated. The method to obtain the real-time phase delay was presented and experimental results of all polarization channels were obtained. For most of the time, the demodulated real-time phase delay remained a fixed value but fluctuations existed when the corresponding sensor phases were close to zero. There was a fixed difference between two adjacent polarization channels which was mainly caused by the interrogation time delay. As indicated by theoretical derivation, the real-time phase delay mainly affects the ICS and introduces error to the PS-PGC algorithm. The compensation method was thus presented. Experimental results showed that the compensation method could greatly improve the stability of the demodulated signal and suppress the sensor background phase noise. The demodulated signal amplitude was stabilized with a fluctuation less than ± 0.75dB and a 5dB noise suppression was observed. An acceptable compensation error of 20% was also derived by evaluating the demodulated signal amplitude. Research on real-time phase delay can facilitate more stable sensor performance to interferometric FBG sensor arrays and thus greatly promote their applications in harsh environments in practice.
Funding
National Natural Science Foundation of China (61901488).
Disclosures
The authors declare no conflicts of interest.
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