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Abstract
We proposed a method based on the Brillouin optical time domain analysis (BOTDA) system to demodulate the length changes of the heating region using the intensity of probe light, under the premise that the temperature in the heating region does not change and the Brillouin frequency shift (BFS) of the heating region is known. This method can realize the recognition of small length under the condition of wide pulse width. The theoretical analysis shows that the different lengths of the heating region will lead to different gains when the spatial resolution corresponding to the pulse width of the pulsed light is larger than the length of the heating region. And through theoretical derivation and simulation, it is concluded that the relationship between the intensity of probe light and the length of the heating region satisfies the exponential growth. Further experiments verify that the exponential growth is approximately linear in the range of small length changes. The length of the heating region can be inversely deduced by using the linear relationship by detecting the intensity of probe light. When the length of sensing fiber is 100 m and the heating region changes from 2 cm to 8 cm, 1 cm heating region changes can be identified.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Brillouin optical time domain analysis (BOTDA) [1,2] has advantages of high received signal strength, high spatial resolution, long sensing-distance and high-precision measurement. It is widely used to monitor the health of large-scale buildings, such as bridges, oil pipelines, tunnels, etc. in real time. BOTDA is based on the stimulated Brillouin scattering (SBS) effect in optical fiber, in which the pump light and probe light propagate in opposite directions, and the linear relationship between BFS and temperature and strain is used to achieve distributed sensing [3–5]. In the BOTDA system [6–9], spatial resolution, measurement accuracy, and sensing distance have always been the research hotspots of many researchers. These indicators interact with each other, and improving one indicator always comes at the expense of one or more other indicators [10–25]. The spatial resolution of the traditional BOTDA system depends on the pulse width of the pulsed light, and a higher spatial resolution can be achieved as the pulse width of the pulsed light decreases. Due to the influence of the phonon lifetime, the pulse width of the pulsed light cannot be less than 10 ns, which makes it difficult for the spatial resolution of the system to reach below 1 m. In the case of narrow pulses, the Brillouin gain spectrum (BGS) is broadened, which greatly affects the accuracy of the BFS. The above situation shows that high spatial resolution and high precision measurement cannot be achieved simultaneously in the BOTDA system. Researchers have proposed many methods to improve the spatial resolution. In 2004, Seok-Beom Cho et al. [26] proposed to use the double-pulse technique to double the resolution of two adjacent events at a sensing distance of 2.1 km without reducing the dynamic range. In 2008, Che-Hien Li et al. [27] achieved a spatial resolution of 2 cm using pulse pre-pumping technology, and it is expected to achieve a sensing distance of 100 m. Anthon W. Brown et al. [28] proposed a Brillouin loss-type BOTDA based on dark pulse pumping, and achieved a spatial resolution of 50 mm at a sensing distance of 100 m. The differential pulse technology proposed by Xiaoyi Bao et al. [29,30] used the time trace obtained by two pulsed lights with different pulse widths to perform subtraction, which can significantly improve the spatial resolution of the system, and achieve a spatial resolution of 18 cm on a 1 km sensing fiber. In 2021, the rising edge demodulation algorithm [31] proposed by Yongkang Dong et al. combined with the differential pulse technology experimentally achieved a spatial resolution of 8 mm on a polarization-maintaining fiber with a sensing distance of 11 m. Most of the above technologies shorten the pulse width of pulsed light by various methods, break through the limitation of phonon lifetime, and achieve high spatial resolution. In this paper, a method is proposed to achieve high spatial resolution without reducing the pulse width of pulsed light. The length of heating region is characterized by the intensity of probe light.
We proposed a method for demodulating the length of the heating region using the intensity of probe light. The method realizes the demodulation of the length of the heating region under the premise of the known BFS of the heating region, and focuses on improving the spatial resolution of the BOTDA system. The traditional BOTDA system determines the length of the heating region by the number of sampling points of the heating region on the time trace. The method proposed in this paper realizes the identification of the length of the heating region by using the amplitude of the time trace of the heating region obtained by the wide pulse whose spatial resolution is larger than the length of the heating region. Using this method, it is easy to monitor the length change of the heating region on the order of cm. This paper theoretically analyzes the time trace obtained in two cases when the spatial resolution corresponding to the pulse width of the pulsed light is smaller than the length of the heating region and larger than the length of the heating region. The reason why the latter does not reflect the heating region in the three-dimensional BGS is explained in detail. The theoretical analysis process of this study can provide a new idea for improving the spatial resolution of the BOTDA system.
2. Principle
2.1 Analysis
This section firstly analyzes the limitations of wide pulsed light in distributed detection, and further theoretically proves the feasibility of using the intensity of probe light to demodulate the length of the heating region. In the BOTDA system, the pump light and the probe light traveling in opposite directions will produce SBS effect in the fiber. In the gain-type BOTDA system, the energy of the pump light is transferred to the probe light. When the frequency difference is exactly the BFS of the fiber, the SBS effect is the most obvious, the gain obtained by the probe light is the largest, and the amplitude of time trace is increased. The sensing is realized by using the linear relationship between BFS and temperature and strain. In the BOTDA system, the frequency of probe light is swept to obtain the three-dimensional BGS along the fiber. Based on the acquired gain spectrum, the position of the heating region, the length of the heating region, and the BFS of the heating region are determined. The above is the practice when the spatial resolution of the pulse width of the pulsed light is smaller than the length of the heating region, and it is also the demodulation principle of the heating region of the traditional BOTDA system. When the spatial resolution of the pulse width is larger than the length of the heating region, the three-dimensional BGS obtained by sweeping the frequency of probe light is shown in Fig. 1.
Fig. 1. Top view of the three-dimensional BGS, the pulse width is 50 ns, the length of heating region is 50 cm.
Figure 1 shows a top view of the three-dimensional BGS. In the figure, the 100 m-long sensing fiber has a 50 cm heating region near the end, and the heating temperature is 70°C, room temperature is 25°C. Pulsed light with a pulse width of 50 ns is used for detection with a spatial resolution of 5 m. The BFS of the fiber obtained in the figure is 10.627 GHz. The heating region is close to the end of the fiber, and the position of the heating region can be determined from the figure, but the length of the heating region and the BFS of the heating region cannot be obtained intuitively. That is often said that the use of wide pulses cannot detect the tiny lengths, and the spatial resolution of the pulse width cannot meet the requirements of detecting the length of the heating region. There are two reasons why we cannot see the heating region above the three-dimensional BGS. First, because the pulsed light with a wide pulse width is used for detection in the experiment, any heating region is always approximately equal to the length of the spatial resolution corresponding to the pulse width of the pulsed light. Second, the length of the heating region is much shorter than the spatial resolution corresponding to the width of the pulsed light, which leads to a small gain obtained by the probe light when the frequency of the probe light sweeps to the BFS of the heating region. The above two reasons lead to the inability to determine the length of the heating region and the BFS of the heating region on the three-dimensional BGS.
The BGS of the room temperature region and the heating region are respectively taken on the 100 m long fiber, as shown in Fig. 2. The BFS of the sensing fiber is 10.627 GHz, and the amplitude at the peak of the BGS is 132.4 mV. Figure 2(b) shows the BGS at the heating region of the sensing fiber near the end. From the figure, it can be read that the BFS corresponding to the maximum amplitude is 10.627 GHz. The gain spectrum at this position does not show the gain spectrum we expect to characterize the information of heating region. The reason for this is that the pulse width of the 50 ns pulse light used in the experiment is too wide, and the length of the fiber in the room temperature region covered by the pulse light with the 50 ns pulse width in the duration is much longer than the length of the heating region. As a result, when the scanning frequency of the probe light is the BFS in the room temperature region of the optical fiber, the gain obtained is still very large. Similarly, when the scanning frequency of the probe light is the BFS of the heating region, the gain obtained is very small. Because the length of the heating region is too short, the BFS at the highest amplitude in the gain spectrum is still the BFS corresponding to the room temperature region, and the BGS in the room temperature region is still present. Of course, the difference between the two figures is still obvious. In Fig. 2(a), the amplitude at the peak of the BGS in the room temperature region is greater than that at the peak of the BGS at the position of the heating region in Fig. 2(b). At the same time, there is a small bump on the right side of the gain spectrum in Fig. 2(b), which represents the BFS in the heating region. From the Fig. 2(b), the BFS in the heating region can be read as 10.674 GHz. The above situation shows that when the spatial resolution of the pulse width of the pulsed light is larger than the length of the heating region, we cannot determine the length of the heating region and the BFS of the heating region through the three-dimensional BGS. However, compared with the BGS in the room temperature region of the fiber, there will be a change in amplitude. This provides us with an idea to identify the length of the heating region by finding the relationship between the detected intensity of probe light and the length of the heating region in the case of a wide pulse width.
2.2 Theory
When the frequency difference between the probe light and the pump light is the BFS in the heating region. With the increase of the length of the heating region, the time trace under the conditions that the spatial resolution of the pulse width is smaller than the length of the heating region and the spatial resolution of the pulse width is larger than the length of the heating region as shown in Fig. 3. Figure 3(a) is the measured time trace with the increase of the length of the heating region when the spatial resolution of the pulse width of the pulsed light is smaller than the length of the heating region. Without considering the pump consumption, the measured time trace of the heating region only broadening with the increase of the length of the heating region, and the intensity does not change. Figure 3(b), the spatial resolution of the pulse width of the pulsed light is much larger than the length of the heating region. As the length of the heating region increases, in addition to the broadening phenomenon in the time trace, the intensity of probe light of the heating region continues to increase. This is because in the duration of a pulse, the longer the heating region, the longer the gain time obtained by the probe light in this period, thus showing an increase in intensity in time trace.
Fig. 3. Schematic diagram of the intensity of probe light demodulating the length of the heating region. (a) The spatial resolution corresponding to the pulse width of the pulsed light is smaller than the length of the heating region; (b) the spatial resolution corresponding to the pulse width of the pulsed light is larger than the length of the heating region.
The SBS process in an optical fiber is described by the following coupling equation:
Here ${I_S}$ and ${I_P}$ represent the intensities of the probe light and the pump light, respectively, ${g_B}$ represents the Brillouin gain coefficients, $\alpha $ represents the loss coefficients of the probe light and the pump light in the fiber. Without considering the pump consumption, the distribution of the intensity of pump light can be expressed using Eq. (3), as follows: where ${I_P}(z)$ is the intensity of pump light at any position of the fiber, and ${I_P}(0)$ is the intensity of pump light at the beginning of the fiber. Substituting Eq. (3) into Eq. (1) for integration, the distribution of the intensity of probe light along the fiber can be expressed using Eq. (4), as follows:Transforming Eq. (8) as follows:
2.3 Simulation result
Figure 4 shows the results of the simulation experiment. The length of the sensing fiber is 100 m, the pulse width of the pulsed light is 200 ns, and the corresponding spatial resolution is 20 m. There is a heating region near the middle part of the entire sensing fiber. The length of heating region varies from 2 m to 10 m in steps of 1 m. With the increase of the length of the heating region, the measured time trace of probe light under the length of each heating region are shown in Fig. 4(a). The horizontal axis represents the sensing distance, and the vertical axis represents the intensity of probe light. It can be clearly seen from the curve that the time trace of the heating region broadened as the length of the heating region increase, and the intensity of the probe light also increased with the increase of the length of the heating region. It is fully explained that the gain provided to the probe light is different for different lengths of heating region. There is a positive correlation between them. Each point in Fig. 4(b) is the average of the time trace under each simulated heating region in Fig. 4(a). The horizontal axis represents the length of the heating region corresponding to each time trace of probe light, and the vertical axis represents the corresponding intensity of probe light at the length of heating region. An exponential fitting is performed on the scatter plot, as shown by the red curve in the Fig. 4(b). The fitting expression is shown in Fig. 4(b), which is consistent with that described in Eq. (10). The simulation results show that in the case of wide pulsed light, the intensity of the probe light and the length of the heating region satisfy an exponential growth.
Fig. 4. Simulation results show that the spatial resolution corresponding to the pulse width of the pulsed light is larger than the length of the heating region. (a) The change of the intensity of probe light corresponding to the heating region changing from 2 m to 10 m in steps of 1 m. (b) Exponential fitting of the intensity of probe light corresponding to the length of each heating region.
At the same time, the case where the spatial resolution of the pulse width of the pulsed light is smaller than the length of the heating region is also explored. Figure 5 shows the simulation results.
Fig. 5. Simulation results show that the spatial resolution corresponding to the pulse width of the pulsed light is smaller than the length of the heating region. The change of the intensity of probe light corresponding to the heating region changing from 2 m to 10 m in steps of 1 m.
The length of the sensing fiber is still 100 m, the pulse width of the pulsed light is 20 ns, the corresponding spatial resolution is 2 m, and the length of the heating region changes from 2 m to 10 m in steps of 1 m. The horizontal axis represents the sensing distance, and the vertical axis represents the intensity of probe light. Ignoring the consumption of pump light, it can be seen from the Fig. 5 that with the increase of the length of the heating region, when the spatial resolution of the pulse width of the pulsed light is smaller than the length of the heating region, the gain time obtained by the probe light at each position in the heating region is the same. It shows that the intensity of probe light does not increase with the increase of the length of the heating region, only with the increase of the length of the heating region, the time trace of probe light of the heating region is broadened.
The length of the heating region was further reduced, and the heating region was changed from 10 cm to 50 cm in steps of 10 cm. As shown in Fig. 6(a), it is the time trace corresponding to each heating region, and Fig. 6(b) shows the intensity of the probe light and the length of the heating region satisfy a linear increase, the fitting expression is also in the figure.
Fig. 6. (a) The change of the intensity of probe light corresponding to the heating region changing from 10 cm to 50 cm in steps of 10 cm. (b) Linear fitting of the intensity of probe light corresponding to the length of each heating region.
3. Experimental results
Figure 7 is an experimental setup of the BOTDA system. The light emitted by a narrow linewidth laser (DFB-LD) with a wavelength of 1550 nm and the linewidth of 3 kHz is divided into two beams by a polarization-maintaining coupler (PM coupler). The upper branch is the probe light and the lower branch is the pump light. The upper branch uses an electro-optical intensity modulator (EOM) and a bias control board for double-sideband carrier suppression, and uses a microwave signal generator (MWG) to sweep the frequency of probe light. The light from the EOM is divided into two paths by a 99:1 coupler, and 1% of the light is fed back to the bias control board to stabilize the working point of the EOM, 99% of the light is amplified by an erbium-doped fiber amplifier (EDFA), and then enters the sensing fiber through a polarization scrambler (PS) and an isolator. The light in the lower branch first passes through the variable optical attenuator (VOA) and enters the semiconductor optical amplifier (SOA) for pulse modulation, then enters the pulsed optical amplifier for amplification, and enters the sensing fiber through the optical circulator (OC). The Brillouin signal is filtered by a tunable fiber Bragg grating (FBG) to filter out the low-order sidebands of the probe light, and the Brillouin signal is detected by a 300 M photodetector (PD), and the signal is collected and stored by an industrial personal computer (IPC). In the experiment, a heating plate was used to heat the fiber near the end of the 100 m-long single-mode fiber, and the heating temperature was kept at 72°C. The BFS of the fiber at room temperature 25°C is 10.627 GHz, and the BFS in the heating region is 10.674 GHz. The length of the heating region is varied from 10 cm to 50 cm in steps of 5 cm. The length of the heating region increases away from the direction of the pump light. In the experiment, pulsed light with a pulse width of 50 ns is used for detection. The repetition frequency of pulse light is 200 kHz, and the input power of the pump light and the probe light are 1.2 mW and 0.7 mW, respectively. The frequency shift of the probe light is 10.674 GHz. The sampling rate of the acquisition card is 2 GS/s, the number of average times is 5000, and the number of sampling points is 3000.
As shown in Fig. 8, Fig. 8(a) is the time trace of the probe light obtained under different lengths of heating region, the horizontal axis is the sensing distance, and the vertical axis is the amplitude of the probe light detected by the photodetector. The position of heating region is where the time trace begins to rise. Under the condition that the parameters of the entire BOTDA system are kept unchanged, such as the injected optical power, the frequency shift of the probe light, the pulse width of the pump light, the repetition frequency of the pump light, and the sampling rate of the acquisition card, the average times, and the number of sampling points are all constant value. Only changing the length of the heating region, the amplitude of time trace at the position of the heating region increased with the increase of the length of the heating region, which is consistent with the experimental theory and simulation results. A change in length of 5 cm in the heating region can be recognized. Each point in Fig. 8(b) is the value obtained by accumulating and averaging over the entire pulse duration according to the time trace of different lengths of heating region in Fig. 8(a). The horizontal axis represents each length of the heating region, and the vertical axis represents the corresponding amplitude at the length of the heating region. The blue line in the Fig. 8(b) is the result of exponentially fitting, the fitting expression is shown in Fig. 8(b), which is consistent with the form of Eq. (10), and the curve fitting is close to 0.99. It is proved that when the resolution of pulse width is larger than the length of the heating region, the gain obtained by the probe light satisfies the exponential growth with the increase of the length of the heating region. The difference between Fig. 8(c) and Fig. 8(b) is that each point in Fig. 8(c) is linearly fitted, the fitting expression is shown in Fig. 8(c), and the curve fitting is also close to 0.99. In the case of a small range of length variation, the curve conforming to exponential growth is close to linearly growth. This provides convenience for the subsequent demodulation of the length of the heating region by detecting the intensity of probe light.
Fig. 8. Experimental results. (a) The change of the amplitude of probe light corresponding to the change of the length of heating region from 10 cm to 50 cm in steps of 5 cm; (b) the exponential fitting of the amplitude of probe light corresponding to the length of each heating region; (c) the linear fitting of the amplitude of probe light corresponding to the length of each heating region.
The length of the heating region was further reduced as shown in Fig. 9, and the length of the heating region was changed from 2 cm to 8 cm in steps of 1 cm. Parameter settings of the system remain unchanged. Figure 9(a) is the time trace of the probe light at each length of heating region, the horizontal axis is the sensing distance, and the vertical axis is the amplitude of the probe light detected by the photodetector. Each point in Fig. 9(b) is the value obtained by accumulating and averaging over the entire pulse duration according to the time trace of different lengths of heating region in Fig. 9(a). The horizontal axis represents each length of the heating region, and the vertical axis represents the corresponding amplitude at the length of the heating region. The red line is the result of linearly fitting, the fitting expression is shown in Fig. 9(b), the curve fitting is close to 0.99. It shows that when the length of the heating region with a small variation range, the amplitude of the time trace in the heating region and the length of the heating region satisfy a linear relationship.
Fig. 9. Experimental results. (a) The change of the amplitude of probe light corresponding to the change of the length of heating region from 2 cm to 8 cm in steps of 1 cm; (b) the linear fitting of the amplitude of probe light corresponding to the length of each heating region.
As shown in Table 1, pulse light with pulse widths of 50 ns, 70 ns, and 90 ns was used to detect the heating region from 20 cm to 50 cm in steps of 5 cm. The power of probe light is the constant of 0.705 mW. The measurement was repeated 3 times under each pulse width. The experimental results show that with different pulse widths, the fitting slopes obtained are different. The pulse width remains unchanged, and the test is repeated three times, and the slope between the amplitude of probe light and the length of the heating region is basically unchanged. In Table 2, the pulse width of the pulsed light is 50 ns, and the length of the heating region changes from 10 cm to 50 cm in steps of 5 cm. Three sets of experimental data were obtained when the power of probe light was 0.738 mW, 0.977 mW, and 1.172 mW, respectively. Under the condition that the pulse width of the pulsed light remains unchanged, the slope values obtained under different power of probe light are different, but the three sets of slope values obtained under the same power of probe light basically remain unchanged. This also proves that when the pulse width of the pulsed light is constant, the power of the probe light is constant, and the length of the fiber is constant, the amplitude of the probe light and the length of the heating region always satisfy a specific growth rate. This provides a basis for inverting the length of the heating region by using the intensity of the probe light through a linear fitting relationship.
Table 1. Slopes for three experiments at three pulse widths
Table 2. Slopes for three experiments at three power of probe light
4. Conclusion
In this paper, we displayed when the spatial resolution of the pulse width is larger than the length of the heating region, the reason why the length of the heating region and the BFS of the heating region cannot be distinguished on the three-dimensional BGS. The first one is that when we use pulsed light with a wide pulse width for detection, and the length of the heating region obtained on the three-dimensional gain spectrum is always approximately equal to the length of the spatial resolution corresponding to the pulse width of the pulsed light. Second, the length of the heating region is too short to provide sufficiently gain for the probe light, and the intensity of the probe light is too weak, so the size of the BFS in the heating region cannot be distinguished. Then a method to demodulate the length of the heating region by the intensity of the probe light is proposed. This method utilizes a pulsed light whose spatial resolution of the pulse width is much larger than the length of the heating region under the premise of the known BFS of the heating region. The intensity of the probe light increased with the length of the heating region. The relationship between the intensity of the probe light and the length of the heating region satisfies exponential growth through simulation, which is verified in experiments. At the same time, with a small range of length variation, the exponential growth can be approximately considered as a linear growth, which greatly simplifies the calculation process of using the intensity of probe light to infer the length of the heating region. The length change of the heating region of 1 cm was successfully discriminated through experiments. The relationship between the slope of the linear fitting and the pulse width of the pulsed light and the power of the probe light was further studied. The experimental results show that the slope changes with the pulse width and the power of probe light. Under the same pulse width or the same power of probe light, the slope of repeated experiments remains basically unchanged. The reliability of demodulating the length of the heating region according to the intensity of the probe light with a satisfied linear relationship is demonstrated. The demodulation of the length of heating region based on the intensity of probe light proposed in this paper provides a new idea for researchers to improve the spatial resolution of the BOTDA system.
Funding
National Natural Science Foundation of China (61527819, 61875146, 62075151, 62075153); Patent Promotion and Exploitation Program of Shanxi Province (20200734); Transformation of Scientific and Technological Achievements Programs of Higher Education Institutions in Shanxi; Fund for Shanxi “1331 Project” Key Innovative Research Team; Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering.
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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