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Abstract
A random coding method for a Brillouin optical time domain reflectometer (BOTDR) fiber sensor is proposed. In this method, a series of pulses modulated by random code are injected into the optical fiber to enhance the signal-to-noise ratio (SNR) and further improve the measurement accuracy. Random coding method allows the sensing range to be extended to several tens of kilometers while maintaining meter-scale spatial resolution and lower detection peak power, without modifying the conventional configuration of BOTDR. The decoding principle and the coding gain of random coding method are analyzed and simulated. We experimentally implement the method and evaluate its influence on the performance optimization of BOTDR. Compared with the single pulse with peak power of 10 mW, the measured BFS uncertainty over 4.93 km sensing fiber is reduced from 5.34 MHz to 0.38 MHz when 512-bit random coding pulses with the same peak power are utilized. The experimental results show that the coding gain of 11.93 dB is obtained by 512-bit random coding. Benefitting from the SNR enhancement, the sensing range is extended from 4.93 km to 64.76 km within a root-mean-square error (RMSE) of 3 MHz, when the pulse peak power is only 10 mW and the spatial resolution is 2 m.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Brillouin optical time domain reflectometer (BOTDR) has attracted a lot of attention owing to the unique ability of long sensing range and anti-electromagnetic interference [1,2]. BOTDR can perform fully distributed monitoring of temperature and strain disturbances, so it has broad application prospects in industrial applications [3]. However, there is a trade-off between the spatial resolution and the measurement distance for BOTDR [4]. Since the weak power of spontaneous Brillouin scattering signal and the inherent loss of optical fiber, the signal-to-noise ratio (SNR) is a dominant factor that affects the performance of BOTDR [5]. The pulse energy is positively related to the SNR, so the width or peak power of detection pulse can be increased to enhance the SNR. However, the wide probe pulse deteriorates the spatial resolution, and the pulse peak power is limited by non-linear effect [6,7].
To further enhance the optimized performance of Brillouin distributed fiber sensors, several advanced methods are proposed, such as distributed Brillouin pump amplification [8], Raman amplification [9,10], image processing [11,12], optical pulse coding (OPC) [13–23], and combination of these methods [14,15]. Benefitting from the advantages of efficiency and economy, OPC methods have been further developed. OPC method transmits a series of coding optical pulse sequences to the sensing fiber to increase the pump energy of the probe signal. The peak power of each pulse is limited below the non-linear effect threshold, and the spatial resolution is not impaired as determined by the width of each detected pulse in the coding sequence [16–18]. Among the OPC approaches of Brillouin sensing, although the cyclic coding [19,20] effectively reduced the average time, the measurement accuracy may be affected due to the imperfect sidelobe. The aperiodic coding that consists of multiple sequences is used, including linear combination coding and correlation coding. The most widely used linear combination coding is Simplex coding, which relies on a linear matrix to achieve encoding and decoding [14]. The coding gain obtained by Simplex coding is $(L\textrm{ + }1)/2\sqrt L$ [21] (L is the length of coding sequence). Correlation coding is mainly based on correlation operation, such as complementary Golay coding [4,22], which exhibits lower sidelobe noise after decoding. The coding gain obtained by Golay coding is $\sqrt L /2$ [24]. The researches prove that the coding method can improve SNR obviously while maintaining spatial resolution. Therefore, exploring new coding methods with higher coding gain is an effective way to further enhance SNR.
In this paper, we propose a random coding method in BOTDR to further improve SNR. Through applying random coding pulse, the SNR improvement of $\sqrt {2L} /2$ can be attained compared with single pulse method, which is larger than that of the conventional Golay coding and Simplex coding. Compared with single pulse method, the random coding method can obtain higher SNR with lower peak power, and random coding method is adopted to allow the use of low-power lasers and reduce user hazards. Meanwhile, the spatial resolution can be maintained as determined by the width of each coding pulse. The basic decoding principle, numerical simulation, and performance evaluation experiment are presented to prove that the proposed method can enhance the SNR to ensure high accuracy while keeping spatial resolution of BOTDR sensors.
2. Measurement mechanism and model
2.1 Characteristics of the random coding sequence
The key of random coding method decoding is to recover the response of a single pulse through the decoding algorithm. The decoding process relies on the self-correlation properties of random coding sequence.
Random coding sequence with non-return-to-zero (NRZ) pulses is “0, 1” random distribution coding sequence in time series. The time domain characteristics of random coding show a distribution balance, which means that when the sequence has enough bits, the number of “1” and “0” is roughly equal. Sufficient research on the generation and characteristic analysis of random numbers has done by researchers in our laboratory [25,26]. Figure 1(a) shows a partial random optical pulse coding sequence.
Fig. 1. Random coding sequence and its time-domain characteristics (a) A partially random optical pulse coding sequence (b) Self-correlation result of single group random coding (c) The averaging results of multiple groups coding self-correlation.
The self-correlation property of random coding sequence can be represented based on the delta-like function η(t) obtained by Eq. (1).
According to the characteristics of random coding, short coding segment cannot reflect the randomness, so the sidelobe noise of self-correlation curve is large. Low sidelobe of self-correlation curve can be obtained when code segment is long. The number of groups M and the sequence length L affect coding gain, as discussed in section 2.3. In the application of BOTDR random coding method, the trade-off between measuring speed and coding gain should be considered. This paper takes M = 30 and L = 512 as an example to demonstrate the performance of random coding method. Figure 1(b) shows the self-correlation result of single group random coding when L = 512. Due to the small number of bits in a single random coding, the self-correlation curve has large sidelobe noise. However, the sidelobe noise can be reduced by averaging multiple groups of random coding. Figure 1(c) gives the normalized η(t) curve when M = 30 and L = 512. It can be seen that the sidelobe noise is low, and the curve is approximate to the impulse function.
The self-correlation characteristic of low-sidelobe δ(t)-like function is an important basis for decoding process of random coding method in BOTDR sensors.
2.2 Decoding principle of the random coding method
The random coding pulses can provide more detection energy than single pulse. The signal decoding process is realized by cross-correlation between the backscattered light and the detection coding sequence. The basic idea of cross-correlation decoding is to spread the signal in the time domain, and reconstruct the impulse response by cross-correlating the detected signal with the probe. The random coding method can avoid the nonlinear effect and improve the SNR.
BOTDR sensor is a linear time-invariant system. When the single pulse detection light σ(t) is injected into the BOTDR system, the response is unit impulse h(t). The time-domain signal f(t) of Brillouin backscattering in optical fiber can be expressed as the convolution of detection optical signal p(t) and unit impulse response h(t), given by Eq. (3).
where * represents the convolution operation.Figure 2 shows the decoding principle of random coding method in BOTDR sensor. In the random coding method, a series of delayed pulses modulated by random coding are injected into the optical fiber. When the random coding sequence pi(t) with coding length L is injected into the optical fiber, the backscattering signal fi(t) can be expressed as Eq. (4). As is shown in Fig. 2(a).
The backscattering time domain curve is essentially the result of delayed superposition of single impulse response as Eq. (4). Si(t) can be obtained by cross-correlation operation between the Brillouin backscattering signal fi(t) and its corresponding detection random pulse sequence pi(t), as Eq. (5). As is shown in Fig. 2(b).
Through accumulating and averaging the obtained Si(t), the response of the single pulse system h(t) can be calculated as Eq. (6). As is shown in Fig. 2(c).
2.3 Coding gain of the random coding method
In BOTDR sensor, if the introduced noise amplitude is constant, the signal noise of the system will improve with the increase of detecting light power. The SNR depends on the mean square error (MSE) of decoding process results by random coding method. Compared with M-times average single pulse detection, the coding gain of random coding method is $\sqrt {2L} /2$, which is studied as follows.
The noise introduced during measurement is defined as ei(t). The system response fi(t) generated by the random coding sequence pi(t) can be expressed as:
The estimated value $\widehat h(t )$ of the unit impulse response obtained by decoding is
The MSE obtained by M-times averaging of the system signal is MSEave = σ2/M. Therefore, the coding gain of the random coding method is shown in Eq. (10) compared with the M-times average single pulse method.
Compared with the conventional Simplex coding and Golay coding, coding gain with different bits is shown in Fig. 3. The coding gain obtained by Simplex and Golay coding is $(L\textrm{ + }1)/2\sqrt L$ [21] and $\sqrt L /2$ [24] respectively. The gain of random coding is larger than that of Simplex and Golay coding.
2.4 Numerical simulation of the random coding method
To verify the decoding principle of the proposed random coding method, single power trace of center frequency is simulated numerically. Figure 4 shows the simulated response curves of 25 km fiber injected with single pulse and random coding pulse. The simulated disturbance position occurs at 20 km∼20.1 km.
Fig. 4. Simulation results of single power trace response curve (a) Single pulse response curve (b) Random coding response curve (c) The cross-correlation curve (d) Decoding process results of random coding method.
Single pulse response curve and random coding response curve are shown in Fig. 4(a) and Fig. 4(b) respectively. The results of cross-correlation between coded response and corresponding coded pulse sequence are depicted in Fig. 4(c). We take cross-correlation result curves of three groups random coding as examples. Where, M1, M2, and M3 respectively represent the cross-correlation results of three groups random coding and corresponding coding responses. It can be seen that different encoding results in different cross-correlation curves. Whereas, the decoding process results can be well restored to single pulse response curve by averaging the cross-correlation of multiple groups of coding, as Fig. 4(d) shows.
In Fig. 5, -20 dB intensity of noise is added to the simulation system. The relatively large noise makes the single impulse response almost covered by noise, as Fig. 5(a). Whereas the noise is obviously suppressed by decoding of random coding method, and the decoding results are basically consistent with the single impulse response, as is shown in Fig. 5(b).
Fig. 5. Simulation of single frequency demodulation results with -20 dB noise (a) Single pulse response curve (b) Decoding results of random optical pulse coding method.
Based on the demodulation results of a single power trace, frequency scanning (FS) simulation with -20 dB intensity of noise is carried out, as shown in Fig. 6. Three-dimensional Brillouin coding gain spectrum (3D-BGS) obtained by single probe pulse and random coding pulses is figured out in Fig. 6(a) and Fig. 6(b), respectively. It can be seen from the measured 3D-BGS that the results obtained by the single pulse FS-BOTDR system are basically covered by noise. However, the random coding BOTDR method can still distinguish the BFS position caused by disturbance. The BGS comparison at Brillouin shift disturbance position obtained by single pulse method and random coding method is shown in Fig. 6(c). In contrast, the scanning points have been unable to fit well with single pulse detection. From Fig. 6(d), we can see that the BFS of random coding method keeps smooth over 25 km, whereas incorrect measurement data sharply increases for single pulse. Under the same noise intensity, the SNR measured by random coding method is obviously better than that of single pulse detection.
Fig. 6. Frequency scanning simulation (a) Single probe pulse (b) Random coding pulses (c) The comparison of BGS curve (d) The comparison of BFS curve.
3. Experimental results and discussion
3.1 Experimental setup
The experimental setup is shown in Fig. 7. The continuous wave fiber laser (CW-Laser) with a wavelength of 1550 nm is employed as a coherent light source with an output power of 10 mW and a linewidth of 50 kHz. The lightwave from the laser is divided into probe and reference branches by an 80:20 coupler. The probe branch is modulated by Semiconductor optical amplifier (SOA) and field-programmable gate array (FPGA) to produce random coding sequence pulse light. The peak power of the probe pulse is approximately 10 mW, and the width of each bit coding is 20 ns. Then, the probe pulse light is injected into the fiber under test (FUT) through an optical circulator. Reference branch passing through a polarization scrambler to erbium-doped fiber amplifier (EDFA). The amplified backscattered light and the reference light are beaten in the photodetector, and the beat signal is converted into electronic signal. Then the output electronic signal is down-converted by a frequency mixer with a tunable electric local oscillator (ELO). Finally, the signal is collected by a data acquisition card (DAQ) and sent to a computer to process the data.
Fig. 7. The measurement system structure of FS-BOTDR with coherent detection: CW-Laser = Continuous Wave fiber Laser; SOA = Semiconductor Optical Amplifier; FPGA = Field-Programmable Gate Array; EDFA = Erbium Doped Fiber Amplifier; FUT = Fiber Under Test; PS = Polarization Scrambler; PD = Photodetector; ELO = Electric Local Oscillator; DAQ = Data Acquisition Card.
3.2 Characteristics of the actual random coding probe sequence
In the experiment, 512-bit random sequence is used to encode the optical pulse. The pulse width of every single coding is 20 ns, and the peak power injected into the sensing fiber is about 10 mW. The averaging random coding group number M is 30. The averaging number of random coding method and single pulse is 256 and 7680 respectively, which can ensure that the averaging number of these two methods is consistent in the comparison experiments.
The FUT is composed of single-mode optical fibers of fiber1 (24.024 km), fiber2 (3 m), and fiber3 (1.153 km), the whole length is 25.18 km, as illustrated in Fig. 8.
The random coding probe sequence is measured and its self-correlation characteristic is tested. Figure 9(a)∼(c) shows the time domain signal of random coding sequence, self-correlation results of single group coding, and average results of 30 group coding self-correlation. It can be seen that through averaging the self-correlation results of multiple coding groups, the sidelobe drops to a very low level, as shown in Fig. 9(c).
Fig. 9. Experimental results of self-correlation characteristics for random coding (a) Time domain signal of random coding sequence (b) Self-correlation results of single group random coding (c) The averaging results of 30 groups coding self-correlation.
Figure 10(a) shows the backscattering power trace of random coding sequence pulse at the center frequency of BGS. It can be seen that the backscattering power trace is equivalent to the delay superposition of the single pulse response, which is determined by the distribution of “0” and “1” in the injected pulse sequence. Figure 10(b) shows the power trace of single pulse at the same peak power.
Fig. 10. Characteristics of random coding sequence pulse and single pulse (a) Backscattering power trace of random coding sequence pulse (b) Backscattering power trace of single pulse (c) Backscattering power trace of single pulse with different peak power (d) The SNRE of different peak power for backscattering power trace of single pulse (e) Backscattering spectrum of random coding sequence pulse (f) Transmission spectrum of randomly coding sequence pulse
The ratio of PSignal to PNoise is defined as the signal-to-noise ratio at the end of optical fiber (SNRE) [27], as Eq. (11).
In Fig. 10(a) and Fig. 10(b), we can see that the SNRE is about 11.84 dB and 0.17 dB, respectively. Thus, compared with single pulse at the same peak power, the SNR of the random coding method is obviously improved.
In single pulse measurement experiment under the same conditions, SNRE can be improved by increasing the peak power of single pulse. However, when the peak power exceeds the threshold, it will produce non-linear effect in optical fiber, resulting in the decrease of SNRE. The power traces are tested when the single pulse peak power ranges from 200 mW to 400 mW, as Fig. 10(c) presented. It can be seen that SNRE increases with the increase of pulse peak power between 200 mW and 300 mW. Whereas the power traces decay rapidly at a certain optical fiber location in 350 mW and 400 mW. The reason is that the excessive incident light power causes the non-linear effect in fiber, and other non-Brillouin frequency components appear, leading to the rapid energy attenuation of the backscattering power trace. Figure 10(d) shows that when the single pulse peak power is 300 mW, the maximum SNRE (SNRE ≈1.89 dB) can be obtained. Under the experimental conditions, 300 mW is the optimal peak power of single pulse method. Compared with the optimal peak power (300 mW) single pulse, the SNR improvement of random coding method has an obvious advantage.
In Fig. 10(e) and Fig. 10(f), we can see that the backscattering spectrum is not distorted, and there is no sidelobe in the transmission spectrum. When the power of the detected signal exceeds the threshold of nonlinear effect, modulation instability, self-phase modulation, stimulated Brillouin scattering or other nonlinear effects will occur. The random coding sequence pulses injection into optical fiber does not cause non-linear effect, indicating that the peak power of coding pulses is properly selected.
3.3 Feasibility evaluation of the random coding method
To verify the random coding method is capable of measuring the BFS change, the result curves and evaluations are shown in this part. In the experiment, 30 groups of 512-bit random coding pulses are injected into the FUT in sequence, and cross-correlation decoding process is carried out. Decoding result of measured single frequency curve is shown in Fig. 11(a). The 3D-BGS diagram based on FS-BOTDR method is shown in Fig. 11(b). In the position where strain disturbance occurs, the curve shows obvious abrupt change.
The BFS curve is obtained by fitting the measured scanning frequency 3D-BGS. The single pulse method is compared with random coding method at the same peak power of 10 mW to visually demonstrate the performance improvement, as depicted in Fig. 12. Noticeably, the BFS for the random coding method keeps smooth along the tested fiber, whereas noise disturbance sharply increases versus the sensing distance after ∼5 km for the conventional single pulse method. It can be seen from the experimental results that the SNR improvement effect is close to the simulation results. Moreover, the single pulse method with optimal peak power (300 mW) is added for comparison in Fig. 12, as the detection power has proved to be the maximum for single pulse SNRE in Fig. 10(c)-(d).
Fig. 12. The comparison of BFS for random coding method with peak power of 10 mW, and single pulse with peak power of 10 mW and 300 mW, respectively.
The spatial resolution of the random coding method is compared with that of conventional single pulse method (300 mW peak power). It can be seen in Fig. 13 that the random coding method is capable of measuring the BFS change. The BFS variation amplitude of 70 MHz and rising-edge position of 24024 m are highly consistent with those obtained by the conventional single pulse method. The spatial resolution is approximately 2 m corresponding to every single pulse width of 20 ns.
Fig. 13. The comparison of spatial resolution for random coding method with peak power of 10 mW, and single pulse method with peak power of 300 mW.
Linearity is assessed by applying different tensile stresses to the measured sensing fiber, as 200 µε, 600 µε, 1000 µε, 1400 µε. The BFS distributions measured by random coding method are shown in Fig. 14. The BFSs under different strains are 10.109 MHz, 30.022 MHz, 50.338 MHz, and 70.542 MHz, respectively. The linear coefficient between BFS and strain is 0.0504 MHz/µε, neatly coinciding with the typical value [28]. The adjusted R-square is 0.99997, which indicates a strong linear relationship. The experimental results prove that the random coding method is capable of measuring the change of BFS.
3.4 Evaluation of SNR enhancement
The sensing range of the proposed random coding method is tested on 70.2 km-long optical fiber with the same parameters as the above experiment (30 groups of 512-bit random coding pulses with the width of 20 ns and peak power of 10 mW). Meanwhile, the single pulse method with the same peak power (10 mW) and optimal peak power (300 mW) is added for comparison, as shown in Fig. 15.
Fig. 15. BFS for random coding method with peak power of 10 mW and single pulse with peak power of 10 mW and 300 mW are compared on 70.2 km-long optical fiber.
The BFS distribution at every ten sampling points in Fig. 15 is taken as a statistical unit, and the root-mean-square error (RMSE) of each unit of data is calculated to determine the precision variation trend with the sensing fiber distance, as shown in Fig. 16. As can be seen from Fig. 16, RMSE abrupt change points are concentrated around 3 MHz. For the convenience of description, the distance from the starting point of sensing fiber to the RMSE abrupt change point is defined as the effective sensing range of BOTDR in this paper. Therefore, the effective sensing range of random coding method with peak power of 10 mW and single pulse with peak power of 10 mW and 300 mW are 64.76 km, 4.93 km, 28.01 km respectively within RMSE of 3 MHz. It can be seen that random coding method can obviously improve the effective sensing range than the pulse amplification method.
Fig. 16. RMSE distribution comparison of random coding method with peak power of 10 mW and single pulse with peak power of 10 mW and 300 mW on 70.2 km sensing fiber.
Comparing the effective sensing range of the same peak power (10 mW), the random coding method is 59.83 km longer than the single pulse method. The transmission loss of 1550 nm light wave in single-mode fiber is about 0.2 dB/km. It can be seen that the SNR of random coding method is about 11.97 dB higher than that of single pulse method.
To further estimate the coding gain of random coding method according to Eq. (10), MSE is compared with the single pulse method of 10 mW peak power in Fig. 17. As can be seen from the blue curve in Fig. 15 and Fig. 16, the measurement data after 4.93 km has been distorted due to the low power of single detection pulse. Therefore, we select the data of the 4.93 km at the beginning segment of fiber for precision comparison. The MSE measured by single pulse method is 2.013, whereas it is only 0.129 by random coding method. Compared with single pulse, the coding gain of random coding method is approximately 11.93 dB, which is highly consistent with the simulation result in Fig. 3.
Fig. 17. The comparison of MSE for random coding method and single pulse method with the same peak power of 10 mW.
The absolute uncertainty is evaluated to demonstrate the frequency resolution of the measurement results. Uncertainty refers to absolute uncertainty in this paper. yi = (${\bar{y}_\textrm{i}}$ ± absolute uncertainty). Where yi is the measurement value, ${\bar{y}_\textrm{i}}$ is the true value.
From the inset of Fig. 17, the uncertainty for random coding method and single pulse method is 0.38 MHz and 5.34 MHz, respectively. The uncertainty for random coding method 0.38 MHz corresponds to ∼7.6 µε strain resolution or ∼0.38 °C temperature resolution. It is confirmed that the accuracy of the measurement results is improved obviously by using the random coding method.
4. Conclusion
We propose a random coding method for SNR enhancement in BOTDR sensors. With the proposed method, SNR improvement of $\sqrt {2L} /2$ (L is the length of coding sequence) can be attained compared with conventional single pulse method, and further improve the accuracy of measurement results. The spatial resolution is maintained as determined by the width of each coding pulse. The feasibility of decoding theory is analyzed and verified by numerical simulation. Then, we implement random coding method and evaluate the performance, including its spatial resolution, accuracy, and sensing range. The experimental results show that 11.93 dB coding gain is obtained by 512-bit random coding. Compared with single pulse method, frequency resolution over 4.93 km optical fiber is reduced from 5.34 MHz to 0.38 MHz by random coding method. The sensing range at the same peak power of detection is increased from 4.93 km to 64.76 km within RMSE of 3 MHz when the detection peak power is only 10 mW while keeping the spatial resolution as 2 m. Hence, it is confirmed that the random coding method can enhance the SNR of BOTDR.
Funding
National Natural Science Foundation of China (61975142, 62005190); Natural Science Foundation of Shanxi Province (201901D211072); China Postdoctoral Science Foundation (2021M691989).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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