A High-Performance DAS System Using Point-Backscattering-Enhanced Fiber and Study of Its Noise Characteristics

Distributed acoustic sensing (DAS) system with point-backscattering-enhanced fiber (PBSEF) has the capability of breaking the signal-to-noise ratio limit of traditional DAS; therefore, it would become one of the most powerful DAS technologies and expand the applications of DAS systems. To optimize the performance when designing DAS system with PBSEF, it is crucial to understand the relationship between the system noise and the reflectance enhancement, which is yet to be systematically studied. In this article, both experimental investigation and theoretical analysis of a typical $3\times3$ heterodyne DAS system with PBSEF were carried out. The relationship between system noise level and the reflectance enhancement was studied by both experiments and simulations, and the results, with good agreements between each other, show that the system noise level drops exponentially as the reflectance increases. With 29.7-dB reflectance enhancement, the system noise level decreased from 9.5 to 0.44 $\text{p}\varepsilon /\surd $ Hz. The influences of intensity noise and phase noise were also analyzed based on the theoretical model. The findings of the quantitative relationship and the noise influence can be used as a universal guidance for the design of PBSEF-based high performance DAS systems.


I. INTRODUCTION
D ISTRIBUTED acoustic sensing (DAS) is a technology that uses the in-fiber backscattered light to locate and measure the dynamic microstrain caused by sound applied to an optical fiber [1], [2], [3], [4].Due to its outstanding advantages, such as high sensitivity, long sensing range, lightweight, compatibility with telecom fibers, and excellent robustness in harsh environments [5], [6], [7], DAS has found applications in various areas, including oil and gas detection [8], perimeter intrusion detection [9], railway monitoring [10], and structural health monitoring [11].Recently, DAS has also been successfully demonstrated in seismic detection caused by earthquake, ocean wave propagation, and glacial activities [12], [13], [14].The applications of DAS technology have been extended beyond traditional areas, thus in turn requiring DAS systems with better performance to meet the challenging needs.
Traditional DAS systems use Rayleigh backscattering (RBS) to demodulate the strain induced by the acoustic signals, and the most studied RBS-based sensing modality is phase-sensitive optical time-domain reflectometry ( -OTDR).
-OTDR-based DAS systems have been studied extensively over the past 20 years and have been proven to be scientifically and commercially successful [15], [16], [17].Despite the aforementioned advantages, DAS still faces a big challenge, i.e., the sensitivity, which is largely dependent on the system noise level, of DAS is limited by the weak RBS light [18].To break this limitation, different interrogation techniques, such as chirped pulse -OTDR [19] and coded pulse sequence -OTDR [20], were proposed and generated promising results.However, the sensitivity enhancement was achieved at the expense of increasing the complexity of the system scheme and signal processing method.
An alternative approach to improve the sensitivity of DAS is to use backscattering-enhanced fiber, which can be adopted into relatively simple interrogation schemes [18], [21].The improved readiness of the technologies for inscribing large quantities of fiber Bragg gratings (FBGs) or reflecting points paved the way to realize ultrahigh-sensitivity and low-noise DAS systems [22].Zhu et al. proposed the first ultraweak FBG-based DAS system.By scanning the frequency of the probe light pulse, dynamic quantitative strain measurement was demonstrated by monitoring the interference signal between the pulses from adjacent FBGs, and strain deviation less than 6.2 nε was achieved [23].Recently, a DAS system with an optical fiber inscribed with UV-fabricated backscattering-enhanced points was reported with dynamic strain resolution of 97.5 pε/ √ Hz [24].Very recently, a lownoise DAS system using backscattering-enhanced fiber with a series of ultrafast laser-inscribed points was demonstrated by Redding et al. with an average phase noise floor of −90 dB (re rad 2 /Hz) and minimum detectable strain as low as 0.15 pε/ √ Hz at a frequency of about 2 kHz.Redding et al. [18] and Ogden et al. [25] also provided a measurement of noise level versus four different reflectance levels in their follow-up work.These studies proved that the RBS enhanced fiber can effectively reduce the noise level of DAS systems, but the relationship between the reflectance of pointbackscattering-enhanced fiber (PBSEF) and the noise level of the system remains to be investigated.This is crucial because the sensing range and the system performance of DAS with PBSEF are subject to power depletion and crosstalk [23], [26].Hence, to achieve higher sensitivity and maintain low crosstalk, the reflectance of the introduced point reflectors needs to be carefully optimized.Therefore, there is an essential demand to quantitatively investigate the relationship between the reflectance of PBSEF and system noise level.
In this work, the relationship between the system noise level and the reflectance was experimentally investigated.Meanwhile, simulation model was built and the influence of the reflectance enhancement on the system noise level was analyzed.Experimental and simulation results were in good agreement, and both showed that the noise level drops exponentially as the reflectance increases.Furthermore, the influence of phase noise under different reflectance enhancement was studied, showing that phase noise becomes more dominating when reflectance reaches relatively high level.

A. System
The diagram of the sensing system is illustrated in Fig. 1.For signal detection and demodulation, we use a symmetric 3 × 3 coupler in heterodyne detection to obtain a set of signals with 120 • phase shift, which can be directly used in phase calculations and can reliably identify the returned signal when PBSEF is used.
A narrow linewidth laser (NLL) was used in the system, and its output was split into two paths by a 90/10 fiber coupler, with 90% of the power acting as the probe light and 10% acting as the local oscillation.The probe light was modulated by an acousto-optical modulator (AOM), which introduced a frequency shift of 200 MHz while carving the light into pulses with a repetition rate of 20 kHz and full-width at half-maximum (FWHM) of 14.4 ns.The pulses from the AOM were then amplified by an Erbium doped fiber amplifier (EDFA) before being injected into the PBSEF, which is a section of specially designed PBSEF that produces a pulse train by partial reflection.The returned pulses were directed into one input of a symmetric 3 × 3 coupler, with the local oscillation directed into another input.The light from the three outputs of 3 × 3 coupler was detected and then acquired by an oscilloscope, which had a sampling interval of 0.32 ns and was triggered by a clock synchronized with the probe pulse.Due to the frequency difference between the returned light and the local oscillation, the three detected signals have a carrier frequency of 200 MHz and fixed phase shift of 120 • as follows: where superscript n indicates that the signals are generated by the nth injected probe pulse, S n 1 , S n 2 , and S n 3 are the signals detected by the three detectors, G 1 , G 2 , and G 3 quantify the comprehensive effect of the gain of the detectors, the loss of each channel, and the residual asymmetry of the coupler, I 0 is the intensity of the local oscillator, and the time varying factor I n s (t) is the intensity of the reflected pulses with the information of the pulse envelope.f AOM is the frequency shift introduced by the AOM, ϕ 0 is the initial phase difference between the reflected light and the local oscillator, and ϕ n (t) is the time-varying phase from the acoustic signal sensed by the fiber.The DC component from I 0 is not included here because the detector has a none-zero lower cutoff frequency.G 1 , G 2 , and G 3 can be estimated using the RMS of the AC component of each channel and then used to normalize the raw data.A bandpass filter can then be used to extract the component with a carrier frequency of f AOM from the normalized data.Using the well-established methods [27], the phase of each pulse can be calculated.Meanwhile, by adding the square of the three normalized data, the square of I n s (t) can be recovered and then used for locating the reflectors.By subtracting the demodulated phase of one pulse from the next, the dynamic phase change sensed by the fiber between two adjacent scattering enhancement points (SEPs) can be calculated and converted to strain.

B. Simulation Model
To thoroughly investigate the relationship between the reflectance enhancement and the system noise level, the sensing system was numerically modeled and simulated using MATLAB following the flowchart illustrated in Fig. 2.
The block FibGen represents the model that describes the PBSEF used in the simulation.The RBS is originated from the inhomogeneities of the fiber, and it simulated following the model in [28].The sensing fiber in the model consists of fiber segments with an equal length of D, and each segment has scattering points with random location and reflectance.The locations of the scattering points, L p , are described as follows: where p represents the pth scattering point, and its random location in the pth segment follows equal distribution.The reflectance of the scattering points r p follows the standard uniform distribution, which is given by the following expression: where r 0 is related to average reflectance of the scattering points and N is the total number of scattering points.
To simulate the SEPs, some additional reflecting points are added to the sensing fiber by setting the scattering points at certain positions to a desired reflectance R p .
The block NLL defines the parameters of the laser, with a center wavelength of 1550 nm and linewidth of 5 kHz.The function of the block probe pulse is to generate a second-order Gaussian pulse with an FWHM of 14.4 ns and a frequency shift of 200 MHz, which is a close estimation of the parameters used in the experiment.The simulated pulse is shown in Fig. 3(a).
The backscattered electric field E RBS is calculated in the block BefGen by modeling the interactions between the probe pulse and the scattering points in the fiber.E RBS is the superposition of the reflected pulses by all the scattering points, with delay and phase shift determined by the positions of the SEPs and amplitude determined by the reflectance.This process can be expressed by the following equation: where A 0 is the amplitude of the electrical field of the input pulse, c is the speed of light in vacuum, λ 0 is the wavelength of the NLL, and a(t, τ p ) is the envelope of the electric field of the pulse reflected by the pth scattering point, which can be expressed as where T p is the FWHM of the probe pulse, n o is the order of gaussian pulse, τ p = 2n e L p /c is the time delay of the light reflected by the pth scattering point, t is the time of the detection, and β is the propagation constant of the probe pulse, which can be expressed by where n e is the effective refractive index of the fundamental mode.Equation (4) shows that the amplitude of E RBS is mainly determined by the reflectance of the scattering points, while the phase differences among the reflected pulses are random due to the random locations.The interferences among the pulses result in characteristic RBS pattern, as the red curve in Fig. 3(b) shows.The black curve in Fig. 3(b) shows the intensity of the reflected light when there are six SEPs with 15 dB of reflectance enhancement and 5-m spacing.The pulses have different amplitudes due to their interferences with RBS.
The returned light and the local oscillation are mixed at the 3 × 3 coupler, and the electrical fields at an output of the 3 × 3 coupler are given by [28]  where E Local is the electrical field of the local oscillation and it is given by where A Local is the amplitude of the local oscillation electric field.The outputs of PD1, PD2, and PD3 are proportional to the square of the complex amplitude of the electrical fields, and each has a carrier frequency of f AOM , as Fig. 3(c) shows.
The inset in Fig. 3(c), which is the zoomed-in view of the interference pattern of the fourth SEP, shows the 120 • phase difference among the three interference fringes.Using the same method mentioned in Section II-A, the phase change between adjacent pulses can be calculated, system noise level can be evaluated, and the relationship between the system noise level and the reflectance of the SEPs can be obtained by changing the reflectance of the SEPs.
C. System Noise in the Simulation 1) Adding the Intensity and Phase Noise: Intensity noise in the system comes from four main sources: relative intensity noise (RIN) of the NLL, instability of the AOM, ASE noise of EDFA, and the photodetector noise.The first three types of noises should be included in the simulation before the block 3 × 3 heterodyne detection in Fig. 2 as the form of additive electric field, so their impacts on the interactions among the scattered light components by the scatter centers can be simulated.The noise of the detector can be added after the block 3 × 3 heterodyne detection.The following analysis assume that all the noises have normal distribution N (t).
The local oscillator contains only the noise from the NLL.Assuming its signal-to-noise ratio (SNR) is SNR 0 and the phase noise of the NLL is φ noise,NLL , then its electric field is given by For the probe pulse, its intensity noise originates from the NLL, the AOM, and the EDFA.The RIN and the noise from the AOM have the same frequency and phase as the signal, so they are coherent noise and could be amplified by their interference with the local oscillator, which is an ideal single frequency output from the NLL.The ASE noise is incoherent, so its intensity is only additive to the total intensity.Considering both types of noises, the total electric field of the pulse by the pth scattering point is given by in which E S is the electric field of the signal without intensity noise, λ is the wavelength of the light after frequency shift by AOM, and E I is the electric field of the incoherent noise, which is mainly the ASE noise.E C is the electric field of coherent noise, which the combined effect of the RIN of the NLL and the AOM driver instability.By ignoring the intensity of the coherent noise, which is considerably lower than the other terms, the total intensity can be expressed as in which the first term is the intensity of the signal, the second term is the intensity of the coherent noise, and the last term is the intensity of the incoherent noise.
At the output of the AOM, considering only the coherent noise, the SNR 1 is When adding the coherent noise, its amplitude can be estimated by It is worth noting that at the output of the AOM, the intensity noise is relative to the signal amplitude, so the electric field of the coherent noise is given by For the incoherent noise, assuming SNR 2 is given by the ratio between the signal and the intensity noise added by the EDFA, then it is expressed by Because the incoherent noise has much broader bandwidth than the NLL and totally random phase, it is only added to the total intensity, and there is no cross term left after its interference with the light from NLL.To simulate this process, noise needs to be integrated over the bandwidth of the BPF and it would be time-consuming.A more convenient way is to add a π /2 phase difference between the incoherent noise and the rest of the light, so the incoherent noise only adds to the total intensity without producing any cross term due to destructive interference.This way, the incoherent noise can be given by Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
Knowing E C and E I , the electric field of the reflected pulse by the pth scattering center expressed in (10) can be calculated, and then, (4) in Section II-B becomes 10 SNR 2 /20 • N (t) Until now, only the phase noise of the NLL is considered.The AOM driver could also introduce phase noise and it can be included by adding another term after φ noise,NLL .
By substituting E RBS and E Local expressed in ( 9) and ( 17) into (7) in Section II-B, the electric field detected by each photodetector is obtained, and the output signal of each detector could easily be calculated for it is proportional to the intensity of the light, with the photodetector noise included, the signals from the detector could be expressed as where G 1,2,3 is the gain for the detectors, and A PD1,2,3 is the standard deviation of the normally distributed detector noise.The ratio between the average RBS signal and the detector noise can be directly calculated from the data acquired by the oscilloscope, so A PD,1,2,3 can be derived and directly used in the simulation.
2) Evaluating the SNR in Detection: In the simulation, the intensity noise from different devices could be added in different stages of the simulation following the path of pulse propagation.However, it is difficult to make sure that the amount of noise added in the simulation is the same as that in the experiment at every stage.SNR 0 can be estimated from the measured RIN spectrum of the NLL.The ratio between the average RBS signal and the detector noise can be directly measured by the oscilloscope, so A PD,1,2,3 can be derived, but SNR 1 and SNR 2 cannot be accurately measured directly due to the limited resolution of the oscilloscope.To make sure the simulation data are as close as possible to the experiment data, the value of SNR 1 and SNR 2 in the simulation was properly set to make sure that the output signals of the PDs have the same final signal quality as that of the experimental data.
To quantify the quality of the detected signal, we defined the SNR at the PD as SNR PD = P S P NL + P NU (19) where P S is the total power of the signal in the frequency ranging from 150 to 250 MHz, and P NL and P NU are the total noise power in the frequency range of 100-150 MHz and 250-300 MHz.The power here is calculated from the power spectrum density (PSD) averaged over 5000 frames and three channels.Using the PSD of the simulated and measured signal from the section of fiber without reflectance enhancement, shown in Fig. 4, the SNRs are calculated and compared.Although both SNR 1 and SNR 2 can be changed in the simulation, SNR 1 is relatively high because intensity introduced by AOM is negligible compared to that from the EDFA.So, SNR 1 is set to a fixed value of 50 dB, and SNR 2

A. Reflectance Varying PBSEF
Since the aim of our work was to study the relationship between the system noise level and the reflectance enhancement, FBGs were used as the SEPs in the fiber for its less dependence on the state of polarization of the incident light compared with that of discrete defects inscribed by femtosecond laser.One PBSEF sample with 23 FBGs was specially fabricated for this purpose.The fiber has 100-m regular lead-in fiber, followed by 23 FBGs with a bandwidth of 0.5 nm, center wavelength of 1550 nm, and different reflectance.The FBGs were fabricated in seven groups.The spacing between adjacent FBGs in the same group was 5 m but larger between groups.Only the FBG pairs with 5-m spacing between them are considered sensors, so the seven groups of FBGs form 16 pairs, which are considered as 16 sensors.
When the reflected signal was interrogated using the system illustrated in Fig. 1, its envelope can be retrieved by adding the square of the filtered signals from the three channels.The retrieved signal envelope of 21 FBGs belong to group 1 to group 6 is plotted in Fig. 5(a).Group 0, which has two FBGs, is not plotted here for they are only used for testing the system response not the noise characteristics.
Upon locating the pulses, the reflectance enhancement of each SEP was calculated by comparing the amplitude of each pulse with the average RBS signal level in the region without reflectance enhancement.Meanwhile, by adding a reflector with known reflectance at the beginning of the sensing fiber, the absolute reflectance of each FBG can also be calculated by comparing the pulse amplitudes.Fig. 5(b) plots the reflectance enhancement and reflectance of the same 21 FBGs as Fig. 5(a).The measurement shows that the reflectance enhancement ranges from 1.2 to 33.4 dB, and the reflectance ranges from −69.8 to −37.6 dB.It should also be noted that the reflectance enhancement is about 71 dB higher than the reflectance, and this is valid for only this system setup, for broader interrogator pulse, and this value could be smaller because the RBS level will increase.Such a relatively large reflectance range supports the investigation on the relationship between system noise level and the amount of reflectance enhancement in such fiber.
It should also be noted that for weaker FBGs, the estimation of the reflectance enhancement is less accurate compared to that of the stronger FBGs due to the interference between light reflected by the FBGs and the RBS.However, the same method for estimating the reflectance enhancement is also used in the simulation to make sure the simulation results are comparable with the experimental results.
The ideal case is that the reflectances of the FBGs were similar in the same group but different among groups, but due to the instability of the fabrication system, it was difficult to control the reflectance precisely.Even though the fabrication was not perfect, the sensing fiber has gradually changing reflectance, which meets our requirement for the investigation carried out in this work.

B. Sensor Response and Linearity
With the DAS system described in Section II-A and the sensing fiber detailed in Section III-A, experiment was carried out to investigate the system performance.The normalized signals detected by the three photodetectors are plotted in Fig. 6(a).The zoomed-in view of the data from the FBGs in group 1 (dashed rectangle) is plotted in Fig. 6(b).It shows that after the normalization, the signals have the same  amplitude and envelope, which ensures the signal fidelity after demodulation.
To demonstrate the functionality of the sensing system, the 5-m-long fiber between the first two FBGs, which belong to group 0 and have average reflectance enhancement of 23.2 dB, was wrapped around a piezotransducer (PZT) tube driven by a sinusoidal signal, generating a strain signal with an amplitude of 5 nε.The measured signals, both in the time domain and in the frequency domain, are shown in Fig. 7.
The results show that the response is uniform, and no crosstalk was observed in the subsequent sensors.This is because even though the phase change in one section of fiber affects the phase in all the following sensors, the differential between adjacent SEPs can keep only the phase change in that certain section of fiber.Meanwhile, as shown in Fig. 5, the average reflectances of the SEPs gradually increased from group 2 to group 7, and the time-domain response in Fig. 7(a) also shows that for the sensors not affected by PZT, their noise levels drop as the sensor number (i.e., the average reflectance) increases, which means sensor formed by stronger SEPs has lower noise level as expected.This will be quantitively studied by both experiments and simulations in Section II-C.

C. System Noise Characteristics
To investigate the influence of the SEP reflectance to the noise level, the sensing fiber was placed on a vibration isolation platform and multiple measurements were carried out, and PSDs of the strain of all the sensors including the fiber without SEPs were calculated.Noise level of each sensor group was calculated by averaging the PSDs of the signals of all the sensors in that group from 250 Hz to 10 kHz over eight measurements to suppress the randomness from the measurements.Group 1 was not included because the section Meanwhile, the model described in Section II-B was used to analyze the system noise level for different SEP reflectances.In the simulation, the electrical noise of the detector, the RIN of the light source, and the amplified spontaneous emission noise from the EDFA were added to the signals as Gaussian random intensity noises.The amount of the noises was controlled to make sure the SNR of the signal from the detector is the same as that of the experiment.The types of added noise, the mechanism of their influence, and the way they were incorporated in the simulation are detailed in Section II-C.The definition of the SNR mentioned here is detailed in Section II-C.
During the simulation, a phase noise of 3 µrad/ √ Hz, which is the same as the average phase noise of the NLL in the frequency range of 250 Hz-10 kHz, was added to the light source in the simulation.In theory, the AOM driver could also introduce additional phase noise to the modulated pulse, and it could even be higher than that of the light source if the driver is not of high quality.Since we could not accurately measure the phase noise from the AOM, it is not considered in this stage of the simulation.The influence of this additional phase noise is simulated and discussed at the end of this section.Other noises such as the low frequency noise from the driving circuits and the environment were not considered in this simulation.The data processing procedure described in Section II-A was performed to obtain the strain and the system noise level from the simulated signal.By changing the reflectance of the SEP, the relationship between the noise level and the amount of reflectance enhancement was obtained and plotted in Fig. 9(b).
In Fig. 10, the reflectance enhancement of 0 dB represents the fiber without SEPs, while the rest of the data points are from measurements or simulation from the PBSEF.The plots show that the measured noise level drops from 9.5 to 0.44 pε/ √ Hz as the reflectance enhancement increases from 0 to 29.7 dB, while the noise level of the simulated data drops from 9.63 to 0.35 pε/ √ Hz.Both experimental and simulation results show that the system noise drops exponentially as the reflectance of the SEPs increases, proving that the reflectance has significant impact on the system performance of a DAS systems with PBSEF.On the other hand, increasing the reflectance cannot infinitely decrease the system noise level, which is also subject to other factors including the phase noise and RIN of light source, noise of the EDFA, electrical noise of the detectors, and the quantization noise from the digitization process.The simulated noise level is slightly lower than that of the experiment, and the discrepancy can be ascribed to the difference between the random noise added in the simulation and the real noise in the experiment such as the additional phase noise introduced by devices.
To further investigate the influence of the additional phase noise in the system, the same simulations were carried out with an additional phase noise ranging from 0 to 60 µrad/ √ Hz.System noise level was calculated and compared with the value when phase noise is 0 µrad/ √ Hz and the change of system noise level is plotted against the added phase noise in Fig. 10.According to the simulation results, for low reflectance enhancement, the phase noise has negligible impact on the system noise level, but as the reflectance increases, the impact of the phase noise becomes more dominating.For reflectance enhancement of 30 dB, when the phase noise increases from 0 to 60 µrad/ √ Hz, the corresponding system noise level changes from 0% to 16.51%, which is close to the experimental result.Therefore, it can be concluded from the simulation results that in the DAS system based on PBSEF, although low system noise level can be achieved by increasing the reflectance of SEPs, the additional phase noise from active devices other than the light could be influential, which needs to be considered to further improve the system performance.

D. Discussion of Large Sensing Arrays
As mentioned before, SEPs in the sensing fiber can provide higher signal level, but the system is also subject to power depletion and crosstalk when the reflectance is high and the number of SEPs is large.Power depletion occurs because each time the probe pulse passes a SEP, part of its power gets reflected and the propagating pulse becomes weaker, resulting in the amplitude drop in the reflected pulse train.The crosstalk is from the pulses reflected by more than one FBG and arrives at the detector at the same time as the signal pulse that is reflected only once by another FBG.Both power depletion and crosstalk have been quantitively analyzed in sensing systems using FBG arrays, in which direct detection is used, so the signal is proportional to the intensity of the light [26].However, in the system presented here, the signal used for demodulating the phase information in ( 1) is proportional to the square root of the intensity of the returned pulse.Assuming all the SEPs in the sensing fiber have an identical reflectance of R, then the pulse returned from the nth FBG will need to pass through the preceding n − 1 FBGs twice, experience the loss of the fiber between FBGs 2(n − 1) times, and reflected by the nth FBG once, so the returned power P n is given by • P 0 (20) in which P n is the returned power from the nth SEP, P 0 is the input power, and α is the fiber loss between adjacent SEPs.Because the system uses heterodyne detection, the interferometric term is dependent on the square root of the intensity of reflected light by the SEPs, so the power depletion, which is quantified by the ratio between the signal amplitudes from the nth and the first SEP, in the given system becomes The first-order crosstalk, which considers only the crosstalk from the pulse reflected two more times, has been provided in [26].Similar to the case of power depletion, the crosstalk in our system is also the square root of the that in a direct detection system and is given by in which C n is the power ratio between the pulses from multiple reflections and the pulse reflected only once.Equations ( 21) and (22) show that higher reflectance results in stronger crosstalk and more rapid power depletion, which is more directly shown in Fig. 11, plotted under the assumption that the spacing between SEPs is 5 m and the fiber loss is 0.2 dB/km.as the reflectance of SEP drops, and ultimately, the residual power depletion is only contributed by the fiber loss, but the crosstalk behaves differently, lower reflectance results in lower crosstalk, and the amount of crosstalk reduction is the same as the change of reflectance.For 2000 SEPs, the signal strength difference between the first and the last sensor will be 4.8 and 2.9 dB for reflectance of −35 and −40 dB, respectively, and the crosstalk is −3.5 and −8.5 dB, respectively.From this calculation, it could be concluded that the increase of reflectance could cause significant crosstalk, especially when long sensing range is required.Therefore, it is of importance to find out the relationship between the reflection of SEPs and the system noise level, for it provides a guidance for balancing the sensing range of the system and the performance.

IV. CONCLUSION
In this work, we carried out a quantitative analysis of the relationship between the system noise level and the reflection enhancement of a DAS system with PBSEF, and the results indicate that the noise level drops exponentially as the reflectance increases.Based on this finding, an ultralownoise DAS system with PBSEF is demonstrated with an average noise level of sub-pε/ √ Hz when the reflectance enhancement was > 23 dB while the noise level dropped to 0.44 pε/ √ Hz with 29.7-dB scattering enhancement.The studies also showed that the influence of phase noise becomes more dominating when the reflectance of SEPs reaches high level.In addition, for long-sensing range, our analysis suggested that the DAS system could suffer from power depletion and crosstalk as the reflectance becomes high.So, it is of great importance to balance the system noise level and sensing range.Based on the quantified relationship between the system noise level and the reflectance of PBSEF revealed by this work, high-performance DAS sensing systems could be designed with optimized PBSEF for various applications.

Fig. 3 .
Fig. 3. Simulation results.(a) Probe pulse used in simulation.(b) Intensity of backscattered signal from PBSEFs and RBS from regular fiber.(c) Outputs of PD1, PD2, and PD3 as a function of distance; inset: zoomed-in view of the signal from the fourth SEP.

Fig. 4 .
Fig. 4. Average PSDs of three measured and three simulated signals.

Fig. 5 .
Fig. 5. Reflectance and reflectance enhancement of PBSEFs of the 21 FBGs belonging to group 1-group 6.(a) Retrieved signal envelope.(b) Calculated reflectance enhancement and reflectance; left axis: reflectance enhancement of the FBGs compared with the RBS and right axis: absolute reflectance of the FBGs.

Fig. 6 .
Fig. 6.Raw data.(a) One frame of normalized data from the detectors, with data from PD1 and PD3 shifted up and down by 1.5 to avoid overlap.The data in the black dashed rectangle are from the two FBGs in group 1.(b) Zoomed-in view of the data in the black dashed rectangle in (a).

Fig. 7 .
Fig. 7. Time-and frequency-domain response of the sensing fiber when 100-Hz signal was applied to the first sensor.(a) Time-domain results.(b) Frequency-domain results.

Fig. 8 .
Fig. 8. Response curve and the PSD of the signal detected by the first sensor.(a) Measured 100-Hz signal.(b) PSD of the signal at frequencies of 100 Hz, 1 kHz, 5 kHz, and 8 kHz.

Fig. 8 (
a) plots the time-domain response of the 100-Hz signal and its fitted curve.Fig. 8(b) shows the PSD of this sensor with a signal of different frequencies applied to the PZT.The result shows an SNR over 30 dB at 100 Hz and an average noise level below 1 pε/ √ Hz in the frequency range over 60 Hz when this pair of SEPs have an average reflectance enhancement of 23.2 dB.The smaller peaks other than target signal may generated by high-frequency noises that folded back to the 0-10-kHz frequency range.

Fig. 9 .
Fig. 9. Noise characteristics.(a) PSDs and average noises of the sensor groups with 3.32-and 29.7-dB reflectance enhancement.(b) Averaged strain noise calculated from measured and simulated data as a function of the reflection of SEPs.

Fig. 10 .
Fig. 10.Averaged strain noise calculated from different phase noises as a function of the reflection of SEPs.

Fig. 11 plots
R n 1 and C n as a function of n with reflectance ranging from −71 to −35 dB, corresponding to reflectance enhancement ranging from 0 to 36 dB.The range was chosen to match the parameters the SEPs used in the experiment.Fig.11(a) shows that power depletion reduces

Fig. 11 .
Fig. 11.Power depletion and crosstalk of the system with sensing fiber of different reflectances.(a) Power depletion versus number of SEPs and reflectance; inset is the power depletion of 2000 SEPs for different reflectance.(b) Crosstalk versus number of SEPs and reflectance.