2.1.

Principle of Heterodyne Detection Rayleigh BOTDA System

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 $v_{\mathrm{R}}$ is down-shifted from the pump light frequency $v_{\mathrm{P}}$ by $v_{\mathrm{m}}$ that is tunable in the vicinity of Brillouin frequency shift (BFS) $v_{\mathrm{B}}$ 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.

Fig. 1

Schematic diagram of heterodyne detection Rayleigh BOTDA system.

If the difference between the local light frequency $v_{\mathrm{L}}$ and probe light frequency $v_{\mathrm{R}}$ is $v_{\mathrm{f}}$, then the probe light carrying the SBS information and local light can be represented as

For local heterodyne detection, the ac component of the photocurrent from the PD in the heterodyne detection Rayleigh BOTDA system can be expressed as

Equation (3) shows that after heterodyne detection, the probe light is amplified by a factor of $\surd P_{\mathrm{L}}$ and the heterodyne signal frequency is decided only by $v_{\mathrm{f}}$. Therefore, the amplitude and frequency stability of the achieved signal can be improved by selecting a local light with suitably higher power and a $v_{\mathrm{f}}$ signal generator with high-frequency stability.

2.2.

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 $F_0+F$, 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

Furthermore, assuming that $N$, $\mathrm{\Delta }z/l_{\min }$, is the number of correlative scatter elements within the spatial resolution range $\mathrm{\Delta }z$ without scanning the laser wavelength; $M$, $1+\mathrm{\Delta }z/l_{\text{cycle}}$, 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

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 as¹⁰

Thus, the relative amplitude fluctuation of the detected probe light is given as

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 $⟨I^2⟩-{⟨I⟩}^2$ can be replaced by $(M/N){⟨I⟩}^2$.⁹ Upon substituting the variance of intensity $I$ into Eq. (9), the amplitude fluctuation is given as

Equation (10) shows that the amplitude fluctuation can be reduced by increasing the frequency scanning range and scanning number. More specifically, when $\mathrm{\Delta }zF$ 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, $V_{\mathrm{g}}=2\times {10}^8\mathrm{m}/\mathrm{s}$, $\mathrm{\Delta }z=13\mathrm{m}$, and $F=20\mathrm{GHz}$, 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 $\mathrm{\Delta }z$, and therefore, the amplitude fluctuation becomes stable.

Fig. 2

Amplitude fluctuation versus number of wavelength scans.

4.1.

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.

Fig. 4

3-D amplitude spectrum distribution in heterodyne detection Rayleigh BOTDA system (a) with single wavelength and (b) with 17 wavelength scans-based averaging.

Fig. 5

Normalized Brillouin amplitude distribution along the sensing fiber in heterodyne detection Rayleigh BOTDA system with different numbers of wavelength scans.

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 $n$ $(n=1,\dots ,17)$ 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 scans-based averaging and single wavelength are 0.001834 and 0.004804, respectively. According to the SNR formula $R_{\mathrm{SN}}=V^2/{\sigma }^2$ in which $V$ is the signal voltage and $\sigma$ 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.

Fig. 6

Amplitude fluctuation versus number of wavelength scans $n$.

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.

Fig. 7

Comparison of (a) single wavelength with 17 measurements-based averaging and (b) 17 wavelength scans-based averaging.

4.2.

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.

Fig. 8

BFS distribution along the sensing fiber in heterodyne detection Rayleigh BOTDA system under (a) single wavelength, (b) single wavelength with 17 measurements-based averaging, and (c) 17 wavelength scans-based averaging.