Rayleigh Brillouin optical time-domain analysis system using heterodyne detection and wavelength scanning

Abstract. This study proposes the use of heterodyne detection and wavelength scanning techniques to solve the problems of small signal and large noise in a Rayleigh Brillouin optical time-domain analysis (BOTDA) system and thereby improve the system performance. Based on an analysis of the Rayleigh BOTDA system, heterodyne detection is used to enhance the signal intensity and wavelength scanning is used to reduce the fading noise. Experimental results obtained using the proposed techniques show that the amplitude fluctuation and signal-to-noise ratio in a 50-m-long fiber near the fiber end with 17 wavelength scans-based averaging are, respectively, reduced by 0.91 dB and increased by 4.19 dB compared to those with a single wavelength. Furthermore, the Brillouin frequency shift in a 70-m-long fiber heated to 50°C and inserted at the center of the sensing fiber can be measured accurately with a maximum fluctuation of 0.19 MHz; this is equivalent to a temperature measurement accuracy of 0.19°C. These results indicate that the proposed techniques can realize high-accuracy measurement, and therefore, they show great potential in the field of long-distance and high-accuracy sensing.


Introduction
Distributed fiber optic sensors based on Brillouin optical time-domain analysis (BOTDA) have been used widely for structural health monitoring (SHM) of large-scale civil infrastructure because they enable the distributed monitoring of temperature or strain in kilometer-long fibers with submeter resolution. [1][2] In a traditional BOTDA system, a pump wave and a probe wave propagate in opposite directions along the optical fiber. When the probe wave lies within the Brillouin spectrum of the pump wave, stimulated Brillouin scattering (SBS) interaction occurs, and the probe wave experiences an amplification or attenuation depending on whether its frequency is lower or higher than that of the pump wave. Although traditional BOTDA systems afford advantages such as high signal-to-noise ratio (SNR) and long sensing distance, the requirement of a two-ended structure makes them inconvenient for large-scale SHM applications, such as monitoring the operating condition of a power cable with very long transmission distance, or applications in which the signal will become unavailable if the fiber is broken.
To improve the applicability of BOTDA systems, in 1996, Nikles et al. 3 proposed a single-ended structure that uses the Fresnel reflection of the sensing fiber end as a probe wave. Subsequently, some similar configurations were proposed and demonstrated experimentally to enhance the performance of Fresnel-reflection-based single-ended BOTDA systems. [4][5][6] However, Fresnel reflection at the fiber end is directly related to the condition of the fiber end face, for example, how clean it is or whether it has a connector; the condition strongly influences the measurement. Therefore, a single-ended BOTDA system that uses Fresnel reflection of the fiber end can only achieve limited performance.
In 2011, Cui et al. 7 demonstrated a single-ended directdetection BOTDA temperature sensing system in which Rayleigh backscattering in the fiber is used as the probe light. A Rayleigh BOTDA system can be operated even if the sensing fiber is broken and is not affected by the condition of the fiber end face; therefore, it affords unique advantages such as nondestructive measurement, single light source, and single-ended operation. However, a Rayleigh BOTDA system has a much smaller probe light than a traditional BOTDA system; this leads to a small signal and low SNR in the system. Among various system noises, coherent fading noise is dominant; it is generated by the phase correlation between Rayleigh backscattered lights. Therefore, it is essentially a signal-induced noise and cannot be effectively reduced by the commonly used signal averaging approach. As a result, it causes nonegligible amplitude fluctuations in the backscattered trace. On the other hand, as the wavelength scanning of a laser source can change the relative phase relations between the Rayleigh backscattered lights, if numerous independent backscattered signals measured at different frequencies are averaged, then the phase correlations between Rayleigh backscattered lights and thus the coherent fading noise can be reduced greatly. Although wavelengthscanning-based signal averaging techniques have been successfully used in coherent optical time-domain reflectometry and coherent optical frequency-domain reflectometry [8][9][10][11][12] for characterization and fault location in an optical fiber transmission system, few studies have focused on Brillouin distributed sensing. 13 In this paper, we propose a Rayleigh BOTDA system with improved SNR in which heterodyne detection and wavelength scanning techniques are used to enhance the signal intensity and to reduce the coherent fading noise, respectively. The principle analysis of signal intensity enhancement and amplitude fluctuation reduction in the proposed system is conducted theoretically, and an experimental setup is constructed to realize Rayleigh-BOTDA-based temperature sensing using the proposed techniques. Finally, the performances of the Rayleigh BOTDA temperature sensing system with single wavelength and 17 wavelength scans-based averaging are discussed based on a comparison of the experimental results.  Figure 1 shows a schematic of the heterodyne detection Rayleigh BOTDA system. Synthetic light composed of a continuous Stokes light and a pulsed light enters the sensing fiber. Then, the Rayleigh backscattering produced by continuous Stokes light acts as a probe light, and the pulsed light acts as a pump light for SBS interaction with the probe light. The probe light frequency v R is down-shifted from the pump light frequency v P by v m that is tunable in the vicinity of Brillouin frequency shift (BFS) v B of the fiber. When the probe light falls into the Brillouin gain spectrum of the pump light, SBS interaction occurs, and therefore, the probe light experiences an SBS gain in the sensing fiber. The SBS interaction becomes the maximum when the optical frequency difference between the probe light and the pump light is equal to the BFS. Heterodyne detection for measuring the Brillouin gain spectrum can be realized by introducing a coherent local light that is mixed up with the backscattered probe light on a photodetector (PD) at the input end. If the difference between the local light frequency v L and probe light frequency v R is v f , then the probe light carrying the SBS information and local light can be represented as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 6 3 ; 3 1 2 E R ðtÞ ¼ E R cos½2πv R t þ φ R ðtÞH SBS ðν; zÞ; (1) E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 6 3 ; where E R , v R , and φ R ðtÞ are, respectively, the probe light's optical field intensity, frequency, and phase at time t; H SBS ðv; zÞ is the SBS transfer function; and E L , v L ¼ v R − v f , and φ L ðtÞ are the local light's optical field intensity, frequency, and phase, respectively. For local heterodyne detection, the ac component of the photocurrent from the PD in the heterodyne detection Rayleigh BOTDA system can be expressed as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 3 2 6 ; 6 6 4 where R is the responsivity of the PD,is the conjugate, θðtÞ is the relative polarization angle between the probe light and the local light, and P R and P L are the powers of the probe light and local light, respectively. Equation (3) shows that after heterodyne detection, the probe light is amplified by a factor of p P L and the heterodyne signal frequency is decided only by v f . Therefore, the amplitude and frequency stability of the achieved signal can be improved by selecting a local light with suitably higher power and a v f signal generator with high-frequency stability.

Method for Reducing Fading Noise
In a heterodyne detection Rayleigh BOTDA system, amplitude fluctuations of the detected heterodyne signal are mostly caused by the coherent fading noises resulting from the interference between the Rayleigh backscattered lights in the fiber, variation of the relative phase, and polarization angle between the Rayleigh backscattered signal and the local light in the PD, as given in Eq. (3). The amplitude fluctuations generated by the polarization variation in the Rayleigh backscattered signal and local light can be reduced by carefully controlling the polarization of the continuous Stokes light and pulsed pump light using polarization controllers (PCs) and adequately scrambling the polarizations of the Rayleigh backscattered signal and local light using polarization scramblers (PSs); as a result, the influence of polarization variation in the Rayleigh BOTDA system can be neglected. Coherent Rayleigh noise (CRN) results from the interference among numerous lightwaves backscattered at different locations in the fiber through phase-intensity conversion, and it manifests as temporal amplitude fluctuations in the Rayleigh backscattered signal trace. 10 Because the CRN is signal-induced, it is amplified together with the probe light when SBS gain occurs, and thus, CRN becomes more severe in a Rayleigh BOTDA system. This reduces the SNR of the system and imposes a serious limitation on the achievable measurement accuracy. On the other hand, from the property of CRN, it can be known that if the wavelength of the laser source and physical state of the sensing fiber remain constant during the measurement time of Rayleigh BOTDA system, then the CRN-induced amplitude fluctuations in the Rayleigh signal should remain invariant. Furthermore, if the wavelength of the laser source is changed, then the relative phase relations of the Rayleigh backscattered lights also change, indicating that the phase correlation between the Rayleigh backscattered lights can be reduced effectively by wavelength scanning. As a result, by averaging the measured independent backscattered signals at different frequencies with changed relative phase relations and reduced phase correlations after wavelength scanning, the CRN-induced amplitude fluctuation can be reduced greatly.
Assuming that the frequency of the laser source is changed from F 0 to F 0 þ F, where F 0 is the laser frequency without wavelength scanning and F is the frequency scanning range, the frequency interval of wavelength scanning is given as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 6 3 ; 4 5 5 ΔF ¼ F∕n; where n is the number of wavelength scans. The correlative range in which strong correlation is maintained and the correlative period are, respectively, expressed as 9 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 6 3 ; 3 9 1 l min ¼ V g ∕4F; E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 6 3 ; 3 5 9 l cycle ¼ where V g is the group velocity of light in the fiber. Furthermore, assuming that N, Δz∕l min , is the number of correlative scatter elements within the spatial resolution range Δz without scanning the laser wavelength; M, 1 þ Δz∕l cycle , is the number of scatter elements among which strong phase correlations still remain after wavelength scanning; and the number of phase correlative scatter elements is reduced from N to M by wavelength scanning, the reduction of correlative scatter elements through wavelength scanning can be given by the ratio E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 7 ; 6 3 ; 2 2 2 The square root of the variance of the Rayleigh backscattering intensity can be considered as the amplitude fluctuation with respect to its mean value due to coherent fading noise. Therefore, the relative amplitude fluctuation of the detected probe light in units of dB is given as 10 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 8 ; 6 3 ; 1 2 1 Δ ¼ 5 logðhIi þ σÞ − 5 logðhIiÞ ¼ 5 log½1 þ σ∕hIi; where hIi is the mean value of the detected probe light intensity I, and σ is the square root of the variance of I.
Thus, the relative amplitude fluctuation of the detected probe light is given as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 9 ; 3 2 6 ; 5 4 8 Because the number of phase correlative scatter elements is reduced from N to M after wavelength scanning, the variance of the detected probe light intensity hI 2 i − hIi 2 can be replaced by ðM∕NÞhIi 2 . 9 Upon substituting the variance of intensity I into Eq. (9), the amplitude fluctuation is given as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 0 ; 3 2 6 ; 4 6 1 Equation (10) shows that the amplitude fluctuation can be reduced by increasing the frequency scanning range and scanning number. More specifically, when ΔzF is kept constant, with an increase in the wavelength scanning number, the amplitude fluctuation first decreases rapidly and then decreases slowly to a stable value, as is shown in Fig. 2. As show in Fig. 2, the simulation parameters, V g ¼ 2 × 10 8 m∕s, Δz ¼ 13 m, and F ¼ 20 GHz, have been used. Similarly, according to Eq. (10), when n is kept constant, the amplitude fluctuation shows a similar trend with an increase in the frequency scanning range. Furthermore, the characteristics of CRN-induced amplitude fluctuation shown in Eq. (10) can be well understood as follows: when the period of correlation becomes larger than the spatial resolution owing to a much larger number of scans in a specific frequency range, there will be no correlation scatter elements over Δz, and therefore, the amplitude fluctuation becomes stable. Figure 3 shows the experimental setup for a heterodyne detection Rayleigh BOTDA sensing system using wavelength scanning. A tunable laser with a linewidth of ∼100 Hz and an output power of 16 dBm operates in the wavelength range of 1549.66 to 1549.82 nm. The laser output is divided into two branches by a 20:80 polarization-maintaining coupler (PMC). The upper branch with 20% output is modulated into the pulsed pump light using electrooptic modulator 1 (EOM1) with a high extinction ratio of 40 dB; EOM1 is driven by a pulse generator. After being amplified by Erbium-doped fiber amplifier 1 (EDFA1), the pump pulses In the experiment, the FUT is a standard single-mode communication fiber (SMF), G.652D, with a total length of ∼1.97 km, and a knot is tied at the end of the fiber to minimize the impact of Fresnel reflection. Thereinto, the FUT is spliced into three sections with different lengths of 1 km, 70 m, and 900 m, respectively. The 70-m-long section is placed in a thermostatic water bath maintained at 50°C. At room temperature of 37.2°C, the BFSs of the three sections are measured to be ∼10.850 GHz. The pulsed pump light has a width of 130 ns and a power of 23 dBm, and the powers of the continuous Stokes light and local light are set to be 6 and −10 dBm, respectively. The frequency of the microwave generator is changed from 10.800 to 10.910 GHz with a step of 5-MHz to cover the Brillouin spectrum of the FUT, and the sampled backscattered probe lights are averaged 5000 times to improve the SNR of the measurement.

Results and Discussions
In the experiment, the wavelength of the laser source is 1549.66 to 1549.82 nm, and it is adjusted in a step of 0.01 nm to obtain 17 backscattered signals at different wavelengths. To illustrate the performance improvement of the proposed system, the amplitude fluctuation reduction and temperature measurement accuracy enhancement are analyzed as follows.

Amplitude Fluctuation Reduction
As noted in Sec. 2.2, amplitude fluctuations are mostly caused by the coherent fading noise, including the amplitude fluctuation induced by the polarization variation of Rayleigh backscattering in the fiber and CRN-induced amplitude fluctuation. The obtained three-dimensional (3-D) amplitude spectrum with single wavelength and 17 wavelength scans in the heterodyne detection Rayleigh BOTDA system are shown in Fig. 4. It should be noted that for obtaining the 3-D amplitude spectrum with 17 wavelength scans, the detected 3-D amplitude spectra at different wavelengths are averaged. Figure 4 clearly shows that the amplitude fluctuation with single wavelength is much larger than that with 17 wavelength scans-based averaging. To further illustrate the decrease in amplitude fluctuation and increase in SNR upon performing wavelength scanning, the normalized amplitude distribution of the measured Brillouin time domain signals at the microwave generator frequency of 10.850 GHz with different numbers of wavelength scans is shown in Fig. 5.
From Fig. 5, it can be seen clearly that the amplitude fluctuation with single wavelength is obviously large, indicating that the CRN has a serious impact on the normalized Brillouin amplitude distribution. However, with an increase in the number of wavelength scans, the amplitude fluctuations gradually decreased, which demonstrates that the wavelength scanning can reduce the CRN effectively. And when the number of wavelength scans is smaller than some value, say 5, the amplitude fluctuation reduction is significant, but when the number of wavelength scans is larger than this value, the reduction of amplitude fluctuation is no longer obvious.
To quantitatively clarify the relationship between the amplitude fluctuation and the number of wavelength scans, the amplitude fluctuation of the measured Brillouin time domain signals at different wavelength is obtained by the linear fitting of the measurements at the frequency of 10.850 GHz to their mean value for the 50-m-long fiber near the fiber end. Figure 6 shows the amplitude fluctuation under n ðn ¼ 1; : : : ; 17Þ wavelength scans-based averaging. This figure clearly shows that the amplitude fluctuation first decreases rapidly with an increase in the number of wavelength scans and then becomes stable for more than 8 wavelength scans; this is in good agreement with Eq. (10) and Fig. 2. Furthermore, calculations show that the maximum amplitude fluctuation with 17 wavelength scans is 0.913 dB smaller than that with single wavelength, and the root mean square errors with 17 wavelength scansbased averaging and single wavelength are 0.001834 and 0.004804, respectively. According to the SNR formula R SN ¼ V 2 ∕σ 2 in which V is the signal voltage and σ is the standard deviation of noise, the SNR with 17 wavelength scans-based averaging is 4.19 dB higher than that with single wavelength, indicating that the sensing distance of the system can be increased using wavelength scanning.
To further demonstrate the effect of wavelength scanning in reducing the coherent fading noise, the amplitude fluctuation comparison between single wavelength with 17 measurements-based averaging, conducted in 17 h, and 17 wavelength scans-based averaging is given in Fig. 7. Through linear fitting of the measurements to their mean value in the 50-m-long fiber near the fiber end, the maximum Brillouin amplitude fluctuation under 17 wavelength    scans-based averaging and single wavelength with 17 measurements-based averaging are obtained to be 0.205 and 0.274 dB, respectively, which indicates that the wavelength scanning technique can reduce the coherent fading noise more effectively.

Temperature Measurement Accuracy Improvement
To estimate the temperature measurement accuracy of the proposed sensing system experimentally, the BFS distributions along the entire sensing fiber under single wavelength, single wavelength with 17 measurements-based averaging, and 17 wavelength scans-based averaging are acquired by fitting the measured spectra with Lorentzian curve, as shown in Fig. 8. From Fig. 8(a), it is clearly seen that the BFS shows an unmeasurable fluctuation near the fiber end in the single wavelength system and has a similar character even if the frequency fluctuation has been obviously reduced through 17 measurements-based averaging. By contrast, Fig. 8(c) shows that the BFS can be measured accurately with 17 wavelength scans-based averaging. Taking the maximum fluctuation of the BFS in the heated section as the temperature measurement accuracy, the temperature measurement accuracies under single wavelength, single wavelength with 17 measurements-based averaging, and 17 wavelength scans-based averaging are evaluated to be 4.17°C, 0.44°C, and 0.19°C because the frequency fluctuations in the 50-m-long fiber of the heated section are 4.17, 0.44, and 0.19 MHz, respectively.

Conclusions
A Rayleigh BOTDA sensing system using heterodyne detection and wavelength scanning for enhancing the signal intensity and reducing the fading noise has been proposed and demonstrated theoretically and experimentally. We analyzed and compared the Brillouin amplitude and BFS distribution along the sensing fiber under different numbers of wavelength scans. The results show that the amplitude fluctuation and SNR for 17 wavelength scans-based averaging is reduced by 0.913 dB and enhanced by 4.19 dB, respectively, compared with those in a single wavelength system, and the BFS distribution along the sensing fiber can be measured accurately with 17 wavelength scans-based averaging. The analysis of the BFS fluctuation in the 50-m-long fiber of the heated section at the center of the 1.97-km-long sensing fiber shows that a temperature measurement accuracy of 0.19°C can be achieved with 17 wavelength scans-based averaging. These results indicate that the proposed techniques can effectively reduce the amplitude fluctuation and improve the SNR and temperature measurement accuracy in the Rayleigh BOTDA system. Therefore, the performance of single-ended distributed sensors can be improved, and new applications may be enabled.