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Abstract
Phase-sensitive optical time domain reflectometry (φOTDR) is an excellent distributed fiber sensing technique and has been applied in various areas. Its noise is however never been comprehensively studied to the best of our knowledge. The different detection noise sources in such a sensing system are thoroughly investigated. The impacts of thermal noise, shot noise and the beat between signal and the amplified spontaneous emission from a pre-amplifier have been theoretically and experimentally demonstrated. Due to the random nature of the φOTDR signal, the detection noise demonstrates distinct features at different fiber positions in a single measurement. The theoretical analysis and the experimental result explicitly affirm most of the fiber sections, and the difference at some positions may be explained by ambient noise.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Phase-sensitive optical time domain reflectometry (φOTDR) is a popular distributed fiber sensing technique that acquires the coherent Rayleigh scattering in time domain. The φOTDR sensor relies on the interference of the light backscattered within the optical pulse length. The interference is a position dependent random process owing to the stochastic longitudinal distribution of the refractive index, so the obtained signal varies randomly along the fiber. The fiber property change induced by an external stimulus can modify the interference process, which finally varies the optical amplitude and causes an extra phase delay to the backscattered light. As a result, the environmental information can be retrieved from the change of optical amplitude and phase, named amplitude- and phase-method, respectively [1]. So far, the φOTDR has demonstrated high sensitivities for temperature, strain, pressure, birefringence and acoustic measurement [1–5] and it has been applied to many areas, such as structural health monitoring, oil and gas industry and homeland security. Recently, this technique turns out to be an effective tool to measure seismic and microseismic events in large scale [6–9].
The sensing performance of the φOTDR is governed by the SNR of the system, for example, a low SNR not only results in a large measurand error but also limits the sensing distance. The SNR is obviously determined by two factors: signal and noise. The signal in a φOTDR system is the Rayleigh backscattered light from the fiber, which is usually very weak. Therefore, current research focuses on the enhancement of the obtained signal to improve the SNR, particularly for long distance sensing. Different light amplification methods have been used to directly enhance the power of the backscattered light [10–12]. Pulse coding is another way to increase the SNR of the φOTDR measurement [13]. A Bragg grating inscribed continuously along the whole fiber can improve the backscatter coefficient and lead to a ∼ 15 dB increase of the optical power [14]. The fading issue has also been addressed. The random nature of the coherent Rayleigh light results in extremely low signal at many points along the fiber, where poor sensing performance can be expected. Currently, the fading can be suppressed or eliminated by using multi-frequency probes, rotated-vector-sum method and so on [15,16].
Despite of the great success in the signal enhancement, the other factor in the SNR, i.e. noise, attracted little attention. In the ideal case, the obtained trace should remain the same under a given condition (the optical frequency, temperature and strain remain unchanged). In practice, however, various noise sources exist in the φOTDR system, deteriorating the signal, so the trace shape varies over time even under the same environmental condition and the sensing performance is thus undermined. For example, the wavelength drift of the light source can cause a shift of the measurement result [17]. Insufficient extinction ratio of the optical pulses can increase the background noise level and the intra-band coherent noise [18,19]. Although such noise can be suppressed or eliminated by using high-performing equipment, the obtained signal is always accompanied with detection noise, that originates from the photodetector of which the detection noise is believed as the dominant factor in an optimized φOTDR system. However, this noise type has never been thoroughly studied to the best of our knowledge. Many investigations on the φOTDR sensing performance just assume the obtained trace is suffered from Gaussian noise and researchers usually take it for granted that the noise variance is constant over the distance [20–22]. Such an assumption has never been examined and proven, albeit it provides satisfactory estimation of the measurand error [21,23].
In this paper, the detection noise is theoretically and experimentally investigated in φOTDR systems. Thermal noise, shot noise, and the spontaneous emission from the pre-amplifier have been discussed and each of them plays a major role depending on the detection scheme. Our results show that although the detection noise can be considered as a Gaussian distributed variable, its variance is highly dependent on the local optical power and varies along the fiber in most cases. The φOTDR system can suffer from environmental fluctuations due to its high sensitivity, which may induce large signal variations and the resultant noise could deviate from Gaussian distribution. These findings not only boost the improvement of the sensing performance evaluation by theoretical and numerical methods, but also equally support the development of noise reduction methods, which can further enhance the sensing performance.
2. Theoretical analysis of detection noise
In a φOTDR system, an optical pulse from a highly coherent light source is sent into the fiber and scattered continuously at the inhomogeneities while it is travelling along the fiber. The backscattered light is acquired by a photodetector as a function of time, and the environmental information can be retrieved from the optical amplitude or phase. The refractive index of the fiber fluctuates in the longitudinal direction due to the random property of the inhomogeneity. The interference condition thereby varies along the fiber, so the obtained φOTDR trace exhibits a stochastic profile. The existence of various noise can cause a deviation of the detected signal from its actual value. Therefore, the signal should be sufficiently strong and/or the noise must be highly suppressed, i.e. high SNR, in order to guarantee the reliability of the measurement. The SNR or the trace quality governs the overall performance of the φOTDR system. For example, analysis has demonstrated the relationship between the SNR and the phase error [21,23]. In a φOTDR system, the power level of the backscattered light is determined by three factors: the peak power of the incident optical pulse, the pulse width and the Rayleigh backscatter coefficient. In practice, the peak power of the pulse is limited to around 20 dBm to avoid unexpected optical nonlinear effects [24], and the typical backscatter coefficient of a standard single mode fiber is about −80 dB for a 1 ns pulse. Thus, the received optical power is determined by a given pulse width and the pulse width needs to be narrow enough to achieve a high spatial resolution. Consequently, the optical power of backscattered light is limited and usually very weak. Enormous efforts have been invested to enhance the received power, however the noise part has since been given little attention.
Thermal and shot noises are the most common noise sources existing in all photodetectors and the standard deviation (SD) of the corresponding voltages can be expressed as [25,26]
where Beq is the equivalent bandwidth, it is defined as π/2·B with electrical bandwidth of the photodetector B, Ct is the input capacitance of the detector, e=1.6×10−19 C presents the electrical charge, gm is the FET transconductance, h=6.63×10−34 J·s is the Planck constant, Id is the dark current, k=1.38×10−23 J/K is the Boltzmann constant, Pin is the optical power incident into the photodetector, Rf is the transimpedance of the photodetector, T is the temperature, η is the quantum efficiency of the detector, and ν represents the optical frequency. Note that thermal noise is independent on the optical power, so the detected Rayleigh trace is supposed to exhibit a uniform detection noise along the fiber if the φOTDR system is thermal noise limited.Due to the weak backscattered light, different signal enhancement methods are necessary in practice and pre-amplification is probably the simplest way to effectively enhance the signal. A pre-amplifier is employed to boost the backscattered light before the photodetector. However, the amplified spontaneous emission (ASE) from the amplifier introduces noise to the system although most of the ASE can be blocked by a narrowband optical filter. A small portion of the ASE can travel with the amplified light and pass the filter and then it interferes with signal light at the photodetector. This interference introduces additional noise to the measurement, which is called sig-ASE noise and can be expressed as [25,26]
where F is the optical noise figure of the amplifier, G corresponds to the gain factor and Ps is the optical power of the backscattered light. With the pre-amplification, the shot noise becomes larger, and Pin in Eq. (2) should be modified as Pin=G·Ps. Under this condition, the total noise is the sum of the thermal, shot and sig-ASE noises. According to Eqs. (2) and (3), the shot noise and sig-ASE noise are proportional to the optical power, which exhibits a stochastic profile along the fiber. Thus the detection noise is supposed to vary along the fiber if pre-amplification is used in the φOTDR system.Note that there exist other methods to enhance the φOTDR signal, and the noise feature will change from case to case. For example, RIN from the pump must be considered when Raman inline amplification is used [12]. Focusing on the most general scenario, this paper considers only the fundamental noise sources as expressed by Eqs. (1)–(3).
To compare different kinds of noise in practice, the parameters in Eqs. (1)–(3) take their typical values as: Ct=8 pF, gm=5·10−3 S, Id=0.15 nA, T=296 K at room temperature, η=0.63 for a classical InGaAs detector, and ν=193.55 THz [26]. Considering the photodetector used in the experiment, Beq = 110 MHz and Rf = 14 kΩ. If a 100-ns pulse with 20 dBm peak power is used in the φOTDR system, the power level of the backscattered light can be estimated by the Rayleigh backscatter coefficient, so Ps is taken as −40 dBm in this case. The standard deviation of different noises are plotted as a function of the gain factor G or the corresponding optical power in Fig. 1. The thermal noise is obviously independent on the gain factor and it plays the main role when G is small. As the gain increases, the sig-ASE noise grows fast because it is proportional to the gain according to Eq. (3). And it overlaps with the total noise after ∼ 13 dB gain, thereby indicating the sig-ASE noise becomes the dominant role. Meanwhile, the signal becomes stronger and the shot noise finally surpasses the thermal noise. It is however much smaller compared with sig-ASE noise.
Fig. 1. Standard deviation of the different detection noise as a function of optical power and gain of the pre-amplification.
Although a similar result has been reported in [26] for Brillouin sensing, the situation is more complex in a φOTDR system. The stochastic fluctuation of the refractive index along the fiber leads to a random interference of the backscattered light within the pulse width. As a result, the optical amplitude and intensity obey Rayleigh and exponential distributions, respectively [27]. In addition, shot and sig-ASE noises are proportional to the local optical power as shown by Eqs. (2) and (3). Therefore, the noise originating from the photodetection is supposed to fluctuate randomly along the fiber in a φOTDR system, unlike other distributed fiber sensors. In the extreme case, the dominant noise can change along the fiber in a single measurement. For example, the thermal noise may play the dominating role at the fading position, the remaining signal from other part of the fiber is limited to shot noise or sig-ASE noise.
3. Experiment
A simple φOTDR system based on direct detection is built as shown in Fig. 2(a) beneath, in order to investigate the characteristic nature of its noise. The light source is a semiconductor laser working at 1550.1 nm with a linewidth of 2.9 kHz. The laser possesses an ultra-low phase noise <10 µrad/√Hz and a low RIN <−130 dB/Hz, so the noise from the light source has a negligible contribution to the overall noise. The continuous wave from the laser is converted into optical pulses with a high extinction ratio over 60 dB by a semiconductor optical amplifier (SOA). Then the generated pulses are amplified by an erbium-doped fiber amplifier (EDFA). The ASE from the EDFA is suppressed by a narrowband filter and the peak power is adjusted by an attenuator to be around 20 dBm before the pulses are launched into a 1380 m long standard single mode fiber. The whole fiber is immersed in water to minimize the environmental perturbations. The backscattered light is guided directly into a photodetector through a circulator for pure direct detection. A pre-amplification module can be used before the photodetector to enhance the light. The module consists of another EDFA and an optical filter with a narrow bandwidth of 25 GHz to suppress the ASE. The gain of the EDFA pre-amplifier can be adjusted by the driving current. The output of the photodetector is digitalized at a speed of 500 Ms/s and with a 14-bit resolution.
Fig. 2. Experimental setup to characterize the detection noise for a φOTDR based on (a) direct detection and (b) coherent detection.
The noise feature has also been experimentally investigated in a φOTDR system based on coherent detection as shown in Fig. 2(b). A splitter is used to divide the output of the laser into two parts, one is for pulse generation and the other serves as a local oscillator (LO). The optical pulses generated by the SOA pass through an acousto-optic modulator (AOM) and experience an optical frequency shift of 110 MHz. The backscattered light is mixed with the LO by a 50:50 coupler and a balanced photodetector is used to obtain the output of the coupler.
Three photodetectors are used here for different purposes and their key parameters are listed in Table 1. PD3 is a balanced photodetector used for coherent detection. It has to be pointed out that Eq. (1) usually fails to predict the thermal noise in practice, because most photodetectors employ a voltage amplifier after the transimpedance to further boost the output, which introduces additional noise [28]. The actual thermal noise of the detectors are measured to be ∼ 0.257 mV, ∼ 0.645 mV and ∼ 1.695 mV respectively, when no light entering the detector.
Table 1. Parameters of the used photodetectors.
The pulse repetition rate is 50 kHz and 10,000 traces are consecutively obtained to analyze the noise feature in the φOTDR system. Thus, the measurement time is only 0.2 s and such a short time guarantees a negligible optical frequency drift of the laser. As a result, it can be safely concluded that the whole system is mainly suffered from the detection noise. The trace averaged over the 10,000 measurements is considered as noise-free and represent the actual φOTDR signal.
3.1 Thermal noise
Due to the detection noise, the obtained signal at any position of the fiber should vary randomly during the measurement time. Based on the analysis in Section II, the φOTDR system is thermal noise limited in the case of pure direct detection, and the noise variance is supposed to be uniform along the fiber since it is independent on the optical power. However, the random nature of the φOTDR signal makes the situation complicated, the backscattered light can interfere constructively at some positions, so that shot noise is no longer negligible.
The pulse width used for the pure direct detection is 60 ns, corresponding to a spatial resolution of 6 m. PD1 is used in this case because of its low thermal noise and the small bandwidth (35 MHz) that is just large enough for this spatial resolution [29]. The standard deviation (SD) and the mean value of the signal obtained in 10,000 measurements are plotted along the fiber in Fig. 3(a). The red solid line represents the mean value at each position, which exhibits a stochastic profile due to the random nature of the φOTDR signal. Compared with the averaged signal, the corresponding SD remains almost as a constant with a very small variance, and it is irrelevant to the averaged signal for most part of the fiber. The SD averaged along the fiber is 0.268 mV, very close to the thermal noise measured without input light. Note that 1 sampling point equals 0.061 mV, so the difference between the averaged SD in Fig. 3(a) and the measured thermal noise is much smaller than 1 sampling point.
Fig. 3. Investigation result of the thermal noise in a φOTDR system with 6 spatial resolution. (a) the standard deviation (black line) and the averaged value (red line) of the obtained signal along the fiber, (b) and (c) are the probability density functions and its Gaussian fitting (red curve) of the signal at position 435.9 m and 666 m, respectively.
The statistics of the obtained signal is further analyzed at two representative positions:435.9 m and 666 m, corresponding to the locations of a very high and a very low average signal respectively. The temporal variation of the signal at the position is studied statistically and their probability density functions (PDFs) are shown in Fig. 3(b) and 3(c). The result is also fitted by a Gaussian distribution function, which is represented by the red curve. It is obvious that the signal obeys Gaussian distribution and the SD used for fitting is almost the same as the experimentally obtained value. It is worth pointing out that although the mean values of the fitting gaussian distribution (the position of the peak) are quite different in Fig. 3(b) and 3(c), their variances are very similar because the whole system is now governed by thermal noise. However, the variance shown in Fig. 3(b) is slightly larger than that in Fig. 3(c) probably due to the contribution of shot noise. This factor will be investigated in the next section.
3.2 Shot noise
As shown in Fig. 3, the signal variance becomes larger at the positions with strong signal due to shot noise. And it is dependent on the incident optical power Ps of the photodetector, as expressed in Eq. (2). The power distribution along the fiber can be calculated by the electrical signal as
where Vs is the detected signal and $\Re $ is the responsivity of the photodetector. The values of $\Re $ are listed in Table 1 for the used photodetectors. For example, the average of the calculated Pin along the fiber is –40.9 dBm based on the signal Vs obtained by pure direct detection. The peak power of the 100 ns incident pulse is ∼21.2 dBm, so the backscattered light is measured as –38.8 dBm. This value is very close to the calculated result, indicating Eq. (4) provides a good estimation of the optical power.In a φOTDR system based on pure direct detection, thermal noise plays the dominant role as discussed in the last section, and it is difficult to observe shot noise because the backscattered light is so small that the related shot noise can usually be neglected compared with the thermal noise. It is necessary to enhance the incident power Ps in order to observe the impact of shot noise. And the only method in such a basic system is to increase the optical energy launched into the fiber using wider pulses, because the peak power is limited by modulation instability. The pulse width is adjusted to 120 ns while its peak power is still at the threshold of modulation instability. In this way, the optical power Pin is enhanced, making the shot noise more obvious.
The measurement is repeated 10,000 times under the same environmental condition, the mean and standard deviation of the obtained signal are plotted in Fig. 4(a). Only a short fiber section from 1000 m to 1200 m is shown for a good illustration. The SD of the measurement signal turns out to vary along the fiber in this case, unlike the thermal noise dominated situation where the SD is almost the same along the fiber. According to the figure, the SD at fading points with extremely weak signal is very small and close to the measured thermal noise of ∼0.26 mV. However, strong signals can lead to large SDs over 0.34 mV; this value is obviously greater than the thermal noise, demonstrating the impact of shot noise. As a result, the measurement suffers from both thermal and shot noise. The system noise can therefore be estimated by summing up the shot noise calculated by Eq. (2) and the measured thermal noise. The theoretical results are compared with the experimental value in Fig. 4(b), and they reassert perfectly well when the SD is low. However, noticeable discrepancies can be observed at the positions with large SD values, and the theoretical analysis underestimates the deviation in this case. This difference is further analyzed in section 4.2, and the result implies that environmental perturbations may affect the measurement. The positions exhibiting constructive interference, i.e. peaks with high values, seem to suffer more from these issues. Consequently, large deviations can be observed at these positions, as shown in Fig. 4(b). This also explains the different profiles between the standard deviation and the averaged value shown in Fig. 4(a).
Fig. 4. The spatial profile of experimentally obtained detection noise in a φOTDR system with pure direct detection in comparison with (a) the averaged signal and (b) the theoretical result of the noise.
The analysis above reveals that shot noise is non-negligible in the φOTDR system based on pure direct detection if the backscattered light is large enough. The whole system suffers from both thermal and shot noise in this case. The two noise sources are independent and follow Gaussian and Poisson distributions, respectively. Hence, the signal obtained at a given position is supposed to demonstrate a distribution deviated from Gaussian profile. The PDF of strong signals at three positions are shown in Fig. 5, and they are fitted by Gaussian function. There exist small differences between the fitting curve and the experimental result as shown in Fig. 5(a) and 5(c). Such small deviation can be neglected, so the distribution can be approximated as Gaussian. However, the PDF shows a flat top in Fig. 5(b), which is an obvious deviation from the Gaussian distribution. This is probably due to the environmental perturbation and will be analyzed later.
Fig. 5. Probability density functions of φOTDR signals obtained by pure direct detection and the Gaussian fitting at (a) 1009.5 m, (b) 1044.5 m and (c) 1359 m. Red lines represent Gaussian fitting.
Shot noise is supposed to dominate a φOTDR measurement based on coherent detection, because a strong LO is used to beat with the weak Rayleigh backscattered light. The measurement is repeated 10,000 times using the setup shown in Fig. 2(b), the pulse width is 20 ns and the power of the LO is ‒13 dBm. The output of the balanced photodetector is a RF signal whose amplitude is proportional to the strength of the local backscattered light.
The φOTDR signal obtained by direct detection at a given position varies randomly during the measurement and its temporal variation is used in this paper to characterize the noise. However, coherent detection provides a RF signal that turns out to oscillate or fluctuate over time at a given position, an example is presented in Fig. 6(a). Such a behavior is totally different from that based on direct detection and it is impossible to characterize the noise by the temporal variation of the signal. To avoid this problem, the amplitude of this oscillating signal is analyzed, which is proportional to the detected signal and can be calculated based on the Hilbert transform of the temporal signal. The red line in Fig. 6(a) represents the calculated amplitude and it varies randomly over time due to the noise in the detected signal. The averaged value of the obtained amplitude and the corresponding standard deviation are compared in Fig. 6(b) and they exhibit almost the same profile along the fiber. The SD seems quite large compared with the amplitude, this may be explained by the error accumulated in the calculated process.
Fig. 6. Experimental results of the φOTDR measurement based on coherent detection. (a) Temporal evolution of the signal obtained at 167.6 m and its amplitude calculated by Hilbert transform. (b) Comparison of the standard deviation and the averaged result of the calculated amplitude within a fiber section.
The overlap of the two lines in Fig. 6(b) demonstrates that the noise in coherent detection is proportional to the detected signal level, indicating the measurement is dominated by shot noise as expected. This reveals one difference between direct and coherent detection based φOTDR systems: the dominant noise. Sig-ASE noise is the main noise source in direct detection since pre-amplification is necessary in practice and shot noise is supposed to dominate the coherent detection. Note that analysis on coherent detection is just a very preliminary study and the proof is indirect. The experiment and data analysis need to be further developed for a solid validation.
3.3 Sig-ASE beat noise
Since the Rayleigh backscattered light is very weak, it is very rare to use pure direct detection in practice. The signal is usually enhanced by a pre-amplifier in optical domain. The dominant noise changes as well according to the theoretical analysis. This section focuses on a φOTDR system with a pre-amplification scheme which contains an EDFA and a narrowband optical filter as shown in Fig. 2(a). The pre-amplifier can greatly enhance the light (> 30 dB) but it generates the ASE that travels with the amplified signal. Although the ASE is small compared to the amplified light, it mixes with the optical signal at the photodetector and their beat, so called the sig-ASE noise, can be a large value. According to Fig. 1, the sig-ASE noise overcomes thermal noise and starts to dominate the measurement when the amplification is larger than 10 dB. This signal gain can be easily realized by almost all commercial EDFAs, thus the φOTDR system is expected to be sig-ASE noise dominated as long as the pre-amplification is used.
It is interesting to point out that the sig-ASE noise is independent on the optical bandwidth of the signal entering the photodetector, according to Eq. (3). Thus, this type of noise cannot be suppressed by filtering the ASE from the pre-amplifier. However, a narrowband optical filter is still necessary to reduce the ASE-ASE noise and ASE-shot noise [25].
In order to make a fair comparison with the investigations in the former part of this paper, all the experimental settings of the pure direct detection remain unchanged for the pre-amplification, including the output voltage range of the A/D converter. Since the backscattered light is very weak, the range is set to the minimum in the pure direct detection, which is able to provide the finest details of the signal. By adjusting the driving current of the pre-amplifier, the light is enhanced by a factor of ∼19 dB. The working point of the gain is carefully chosen so that the sig-ASE noise is sufficiently large compared to thermal noise, as shown in Fig. 1; and it is small enough to ensure the amplified signal to fit in the voltage range used for pure direct detection. The detection noise in this case is therefore dominated by sig-ASE noise, which can be approximated as Gaussian distributed as the bandwidth of the optical filter (25 GHz) is much larger than the detection bandwidth (35 MHz) [30].
The spatial distribution of the obtained noise in this case is analyzed and compared with the averaged signal as shown in Fig. 7(a). At first glance, the noise over the whole fiber is much larger than the measured thermal noise because of the ASE from the pre-amplifier. And the noise varies with the signal as expected along the fiber, revealing again the impact of the sig-ASE noise. This kind of noise can be actually calculated using Eq. (3) based on the gain value and the optical power obtained by Eq. (4). As a result, it is possible to theoretically estimate the total noise by summing up the measured thermal noise and the calculated shot noise and sig-ASE noise. The calculated noise is compared with the experimental result in Fig. 7(b). The theoretical analysis demonstrates a good agreement with the experiment in most cases, but their difference becomes non-negligible when the noise is large. This difference has been observed in the previous section and will be partially explained in section 4.2.
Fig. 7. The spatial profile of experimentally obtained detection noise in a φOTDR system with pre-amplification in comparison with (a) the averaged signal and (b) the theoretical result of the noise.
The PDFs of the signals at four positions during the 10,000 measurements are plotted in Fig. 8 in order to investigate the statistical feature of the obtained noise for the φOTDR system with pre-amplification. They are shown in a single coordinate to facilitate the comparison. According to Fig. 8, the signals at these positions vary randomly and follow a Gaussian distribution, because the histogram matches very well the Gaussian fitting. And the signal from other fiber sections demonstrates the same statistical feature. It can therefore be concluded that the obtained noise in this case is a Gaussian variable. The total noise in this case is dependent on the signal strength, and it becomes larger at the positions with stronger signals because of the sig-ASE noise and this tendency can be observed clearly in Fig. 8. From the left-hand side to right-hand side of the figure, the PDF becomes broader as the signal becomes larger, meanwhile the probability peak decreases.
Fig. 8. Probability density function of signals obtained at four different positions and their Gaussian fitting.
4. Discussions
Per the findings in this paper, current theoretical and numerical models [21,27] can be further improved to approach the actual scenarios. The simulated noise, instead of being a constant, needs to be adjusted based on the local signal level. In this way, the simulation will be closer to the experiment. Also, the non-uniform distribution of the noise indicates that some SNR enhancement methods used in other distributed sensing systems cannot be simply applied to the φOTDR sensing system. For example, pulse coding is a popular method to improve the SNR in Raman and Brillouin sensors. It is therefore evident from the preceding analysis in this paper that when long series of pulses are launched into the fiber, it leads to strong backscattered light and this make the φOTDR sensing system prone to more noise which finally yields inaccuracies in the decoding process. Consequently, the sensing performance may not be improved as much as expected by using the long coding series. This section discusses the impact of the noise on the trace quality and the difference between the theoretical and experimental results as aforementioned.
4.1 Trace quality
Signal to noise ratio is an essential parameter for a φOTDR system because it determines the overall sensing performance and is a popular factor to evaluate the trace quality. The signal is determined by the optical power of the incident pulse, the backscattering coefficient of the optical fiber, the response of the photodetector and the detection method. The last factor also determines the noise of the system based on the analysis above. As a result, the SNR of a φOTDR system is defined in this paper as the ratio of the average of the signal acquired over a certain amount of continuous measurement under the same condition and the corresponding standard deviation.
The performance can only be described by the statistics of the SNR along the fiber owing to the random nature of the φOTDR signal. For direct detection, the intensity of the backscattered light is detected, which follows an exponential distribution. The noise feature is whereas highly dependent on the detection methods and needs to be analyzed case by case.
For pure direct detection, thermal noise usually dominates the measurement and shot noise may play a role if the backscattered light is strong enough. Since the peak power of the incident pulse is limited by modulation instability, the SNR can only be improved by using wider pulse or scattering enhanced fiber. The former method impairs the spatial resolution, while the latter is costly. This paper investigates the SNR of the φOTDR system with different pulse widths and the results are shown Fig. 9. We explicitly assume that the measurement is affected only by thermal noise for narrow pulses because shot noise is negligible in this case. Therefore, the noise is supposed to be constant along the fiber and the SNR responses to the exponential distribution just like the optical intensity. This tendency can be clearly observed in Fig. 9 and the obtained signal has a large probability to possess a very low SNR of ∼ 2 dB. As the pulse becomes wider, the probability peak shifts to a larger value, meaning that the general SNR gets enhanced. Meanwhile, the probability beyond 10 dB increases, indicating there are more sampling points with high SNR due to the strong backscattered light.
Fig. 9. Probability density function of the SNR obtained by a φOTDR system with different pulse widths based on pure direct detection.
The SNR for the φOTDR system with the pre-amplification module has also been studied statistically. A photodetector PD2 with a 3 dB bandwidth of 200 MHz is used in this case for a fine spatial resolution. 10 ns pulses are used for the measurement, corresponding to 1 m spatial resolution. And the backscattered light experiences different gain factors by tuning the driving current of the pre-amplifier.
The PDFs of the measured SNR along the tested fiber are plotted in Fig. 10. It confirms that the pre-amplification can enhance the SNR of the system as the probability peaks correspond to larger SNR value compare with Fig. 9, in spite of a much narrow pulse width. However, the SNR improvement is not significant as the gain factor increases. The positions of the probability peaks change only ∼ 1 dB while the gain increases almost 5 dB. Sig-ASE noise dominates the measurement as discussed above and it is proportional to the gain factor, shown by Eq. (3). Meanwhile the measured signal is proportional to the gain. Consequently, the SNR becomes independent on the amplification gain because the gain factor exists in both numerator and denominator and they are canceled out. The gain factor therefore has little impact on the obtained SNR. However, a high gain is particularly necessary for long distance sensing. Fiber attenuation makes the light backscattered from the far end extremely weak and even below the threshold of the photodetector. The light needs to be intensively amplified to provide meaningful information.
Fig. 10. Probability density function of the SNR obtained by a φOTDR system with different pre-amplification gains for a 10 ns pulse width.
Figure 10 reveals the impact of the noise on the trace quality. The dominant noise increases while the signal is amplified, resulting in a barely improved SNR. The noise reduction is therefore needed to further enhance the SNR. However, it is difficult to reduce the noise by hardware modification based on the analysis above. The noise originating from the photodetection is determined by the measurement requirement. For example, all the three types of noise are dependent on the detection bandwidth, which needs to be large enough to guarantee the spatial resolution. Thermal noise can be reduced if the detector works at a low temperature, but the noise reduction is negligible since thermal noise is very small compared with other noise sources. Consequently, post-processing is currently the main method to reduce the noise and improve the SNR. Wavelet transform and empirical mode decomposition are popular denoising methods, as summarized in [31].
The wavelet denoising method is employed here to suppress the sig-ASE noise. At each fiber position, the noisy signal acquired during the measurement is at first processed by discrete-time wavelet transform and the wavelet coefficients are obtained. Then, a threshold is set to adjust the coefficients. Finally, the new signal is reconstructed based on the adjusted coefficients through the invert wavelet transform. The denoised result is compared with the noisy data in Fig. 11. It is obvious that the PDF peak of the denoised data shifts to the right-hand side, meaning most of the data exhibits a higher SNR than the raw one. Such a simple denoising method improved the SNR by ∼ 2 dB when the pre-amplification is about 29 dB, the SNR improvement is better than the situation of 34.85 dB gain. This paper presents a deep understanding of the noise source in different φOTDR systems, which can help develop novel denoising algorithm to further improve the SNR.
Fig. 11. Improvement of the SNR by wavelet transform for a φOTDR system with different pre-amplification gains with a 10 ns pulse width. Solid lines represent the noisy data and dotted lines correspond to the data denoised by wavelet transform.
4.2 Deviations between theory and experiment
The detection of the noise sources, i.e. thermal, shot, and sig-ASE, have been theoretically analyzed in a basic φOTDR system. Since the latter two noise sources are signal intensity dependent, the obtained noise is supposed to vary along the fiber. The experimental results validate the theoretical analysis, and the obtained noise agrees perfectly with the theoretical estimation for most part of the fiber. However, clear difference between theoretical and experimental results can be observed at positions mainly with large signals, as shown in Fig. 4(b) and 7(b).
The signals at four positions shown in Fig. 7(b) are chosen as an example to investigate noise underestimation in the theoretical analysis. The temporal variations of the signal are presented in Fig. 12. The obtained signal should be constant over time in the ideal case, whereas all the signals exhibit a certain temporal variation in Fig. 12, which are caused by noise. The red line possesses the highest average value and is comparatively stable. The standard deviation corresponds to the noise peak between 1100 m and 1125 m as shown in Fig. 7(b) and agrees very well with the theoretical estimation. It is therefore convincing to conclude that the sig-ASE noise is responsible for causing the temporal variations as indicated in the red line. On the contrary, the blue, green and pumpkin curves show obvious temporal fluctuations starting at ∼ 40 ms. The frequency of the oscillation is high from 50 ms to 100 ms and becomes low afterwards. Due to such large variations, three noise peaks exist between 1075 m and 1100 m and the experimental result is much higher than the theoretically calculated noise as shown by Fig. 7(b). The large variations occurred at many locations along the fiber of which the signal demonstrates temporal oscillations that cannot be explained by the detection of the noise. Note that such fluctuation has a totally different origin as the one obtained by coherent detection, as shown in Fig. 6(a).
Fig. 12. Temporal variations of the pre-amplified φOTDR signal obtained at four different fiber positions within a short time of 200 ms.
An extreme case is shown in Fig. 13(a) where the detected signal at a distance of 1240.6 m tends to increase continuously over time. This behavior can only be explained by the change of the local signal which may be caused by environmental perturbations, albeit the fiber spool is isolated in a water tank. Fiber movement, strain release in the spool and thermal turbulence are possible explanations. The increasing trend makes the signal obtained within the measurement time no longer follow Gaussian distribution, its PDF consequently shows a clear difference from the Gaussian fitting according to Fig. 13(b). This tendency can be simply removed by a linear detrending method, and the result demonstrates significant affirmation with Gaussian fitting as shown in Fig. 13(c). The standard deviation used for the fitting is 1.467 mV which is very close to the theoretical estimation of 1.244 mV. The good match implies that the signal is dominated by the sig-ASE noise when the environmental perturbation is removed. In practice, this kind of ambient noise is inevitable due to the high sensitivity of the φOTDR system [32,33]. However, detailed analysis on such noise is beyond the scope of this paper and needs to be studied in the future.
Fig. 13. Analysis of the pre-amplified φOTDR signal obtained at 1240.6 m. (a) Temporal variations of the signal over 200 ms, (b) probability density of the signal and (c) probability density of the linearly detrended signal. Red lines represent Gaussian fitting.
5. Conclusion
In this paper, thermal, shot and sig-ASE noise have been studied in a φOTDR sensing system for the first time to the best of our knowledge and their impacts on the quality of obtained traces have been investigated. The analysis shows that the noise is usually dependent on the level of the local signal. Thus, the noise feature can vary randomly along the fiber even in a single measurement. More importantly, this dependence eventually limits the improvement of the quality of the trace by just enhancing the signal. In addition, the high sensitivity of the φOTDR sensing system make it vulnerable to ambient noise. Based on the results, noise reduction methods should be used to further improve the quality of the trace. This paper also analyzes the noise in a coherent detection based φOTDR system and the preliminary result implies that the shot noise dominates the measurement as expected.
Funding
Zentrale Innovationsprogramm Mittelstand (ZF4044230RH9).
Acknowledgements
The research project was carried out in the framework of the Zentrale Innovationsprogramm Mittelstand (ZF4044230RH9, project acronym “FoLO”). It was supported by the Federal Ministry for Economic Affairs and Energy (BMWi) on the basis of a decision by the German Bundestag. The authors thank Marcus Schukar and Sven Münzenberger at BAM for their technical support and all the partners in the FoLO project for helpful discussion.
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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