Performance Improvement of Raman Distributed Temperature System by Using Noise Suppression

: In Raman distributed temperature system, the key factor for performance improvement is noise suppression, which seriously affects the sensing distance and temperature accuracy. Therefore, we propose and experimentally demonstrate dynamic noise difference algorithm and wavelet transform modulus maximum (WTMM) to de-noising Raman anti-Stokes signal. Experimental results show that the sensing distance can increase from 3 km to 11.5 km and the temperature accuracy increases to 1.58 ℃ at the sensing distance of 10.4 km.


Introduction
Since temperature was demodulated successfully by Raman backscattering over an optical fiber in 1985 [1], the Raman distributed temperature system (RDTS) has attracted interest for decades. And the system has been widely used in the online monitoring system of underground gas pipes [2], fault diagnosis of smart grid [3], and large nuclear infrastructures [4]. There are three demodulation methods in RDTS at present: (1) Rayleigh scattering demodulates Raman anti-Stokes scattering [5], (2) Raman Stokes scattering demodulates Raman anti-Stokes scattering [6][7], and (3) Raman anti-Stokes scattering demodulates itself [8]. In the method based on Rayleigh scattering demodulating Raman anti-Stokes scattering, the ratio of the intensity of Rayleigh scattering and Raman anti-Stokes scattering is used to demodulate the temperature. Another, the ratio of the intensity of Raman Stokes scattering and Raman anti-Stokes scattering is used to demodulate the temperature in the method of Raman Stokes scattering demodulating Raman anti-Stokes scattering. The two demodulation ways are called as dual-demodulation method, and both need two avalanche photodiodes (APD) and two amplifiers, which means higher cost and larger measurement error caused by the modal dispersion between the two different backscattering lights. Although a method by correcting the speed of the two scattering lights has been proposed to eliminate the measurement error [9], the speed of the two scattering lights is hard to measure. Raman anti-Stokes scattering self-demodulation method uses anti-Stokes scattering to demodulate anti-Stokes scattering, which averts the effect of the modal dispersion between the two backscatterings in principle and just needs one APD and one amplifier. In addition, self-demodulation avoids a way of noise compared with the dual-demodulation and improves the signal to noise ratio, so the method attracts lots of attention. This auto-correction method utilizes reflected anti-Stokes Raman scattering [10] and a double-ended distributed temperature sensor [11].
The wavelet transform modulus maximum (WTMM) method inherits the advantages of wavelet transform, which not only can interpret signals in both time and frequency domains simultaneously [12][13], but also can save the measurement time [14][15][16]. Moreover, it is available to capture singular points of signal when the signal has low signal to noise ratio (SNR) and has been demonstrated in dual-demodulation RDTS based on Raman Stokes scattering demodulating Raman anti-Stokes scattering [17].
In this paper, we introduce the WTMM method to self-demodulation RDTS to suppress the noise. Furthermore, we propose a dynamic noise difference algorithm to suppress the ground noise of optical receiver, which utilizes the average value of dark current noise floor behind Fresnel reflection to calculate the dynamic ground noise. By combining the dynamic noise difference algorithm with the WTMM method in self-demodulation RDTS, not only the influence of modal dispersion for temperature accuracy is eliminated, but also the sensing distance and temperature accuracy are improved in the experiment. In addition, it will not affect the system measurement time.

Self-demodulation method
The intensity of anti-Stokes light can be expressed as where C is a constant value determined by central wavelength of anti-Stokes light, M is the amplification factor of optical receiver, I 0 is the input intensity, h is Planck's constant, ∆ν is the Raman frequency shift, k is Boltzmann's constant, T is the measurement temperature where back scattering is happened,  and a  are the attenuation coefficient of input light and anti-Stokes light, respectively, and L is the position where back scattering happens.
In self-demodulation RDTS, temperature is measured by the intensity ratio [R(T)], between anti-Stokes signal [I(T 0 )] of the reference and the measured anti-Stokes [I(T)], which is expressed as where T is the measurement temperature, and T 0 is the temperature along the fiber under test (FUT) and set as reference temperature. Actually, the power of the input source and the amplification factor of the amplifier change as the time goes by. And they will influence the measurement results. So, a changed power factor ∆I and a changed amplification factor ∆M are introduced to R(T) , which is shown as follows: In order to eliminate the influence of the change of amplification factor and the input power on temperature measurement, an invariable length optical fiber whose temperature is maintained at a fixed value is introduced as correction fiber. The correction fiber is in front of fiber under test (FUT), so the amplification factor and the input power of the correction are the same with the FUT both in measured and reference intensities. Thus (3) can be modified as where T c and T c0 stand for the measured and reference temperatures of correction fiber, respectively. And the value of T c is equal to the value of T c0 . Using (4), the temperature can be demodulated accurately. The influence of the changes of input power and amplification factor on temperature demodulation resolution also can be eliminated effectively.

Dynamic difference noise algorithm
In RDTS, the Raman signal is submerged in noise which is caused by the optical receiver and data acquisition card. The optical receiver based on APD plays the most important role in the RDTS noise source.
The optical receiver consists of the APD and amplifier. The noise of amplifier is mainly caused by white noise and 1 f noise, the white noise is influenced by temperature, and the 1 f noise is related to frequency. And the ground noise current (I N ) of APD consists of the dark current (I DB ), surface leakage current (I DS ) of APD, and thermal noise current (I T ) of photo detector, which can be expressed as where q is the electronic charge, I D and I L are the dark current and surface leakage current without amplification, respectively, M is the multiplication factor, F(M) is the noise figure which is determined by the characteristics of random noise when avalanche happens, B e is the bandwidth of optical receiver, k is Boltzmann's constant, T r is the operating temperature of receiver, and R L is the load resistance.
As shown in (5), the value of ground noise current of APD is determined by multiplication factor, noise figure, and operating temperature. Actually, the change in noise figure can be neglected, and the multiplication factor is affected by operating temperature and bias voltage. And the noise of amplifier is also influenced by temperature. So the ground noise changes as the operating temperature and bias voltage change. Usually, researchers consider the operating temperature and voltage are stationary, but actually the temperature and voltage are changing, which limits the sensing distance because of the weak Raman anti-Stokes signal. So a dynamic noise difference algorithm using the average value of dark current noise floor behind Fresnel reflection as dynamic ground noise is proposed. Figure 1 explains this method.  Figure 1 shows the Raman anti-Stokes backscattering intensity after 10 000-time averages, which includes Raman anti-Stokes signal in the front of Fresnel reflection and noise floor behind Fresnel reflection. The average value of noise floor is used as dynamic ground noise, where the dynamic ground noise will change in different measurement times, and the value just uses one time to calculate the actual intensity of anti-stokes light of this measurement time. The dynamic noise difference algorithm is used to obtain the actual intensity of Raman anti-Stokes backscattering, and the value of the actual intensity of Raman anti-Stokes backscattering is calculated by subtracting dynamic ground noise from Raman anti-Stokes signal.

Wavelet transform and modulus maximum de-noising
The wavelet function families are generated from a single base wavelet function [φ(t)] dilated and translated by a scale factor a and a location factor b. A continuous signal f(t)'s wavelet transform can be express as follows: And when the Fourier transform () of single base wavelet φ(t) conforms to the allowable condition can be expressed as follows: Then the wavelet function families are discretized, meaning Based on (7), a method of multi-resolution analysis (MRA) is proposed by Mallet; the method unifies the construction of base wavelet, and puts forward a fast wavelet decomposition and reconstruction method which is widely used recently. The core of this method is decomposing the signal into detailed high frequency coefficients and approximate low-frequency coefficients, and reconstructing the signal by a filter which is orthogonal with the decomposition filter.
The WTMM is one of the fast wavelet decomposition and reconstruction methods. According to the relationship between Lipschitz exponents L and the scale factor j, the noise is reduced in RDTS. The theory [17] can be written as where c 1 is a constant, and j is the decomposition scale. For the signal, L > 0, which means the value of the WTMM will increase with an increase in j; for the white noise, L < 0, which will cause the value of the WTMM decrease along with an increase in j.
According to the characteristics of the signal and noise, WTMM can distinguish the signal and noise effectively.
In our work, the orthogonal wavelet function "sym6" is used because of the characteristics of least asymmetry, regularity, and similarity to signal. The least asymmetry means the method can avoid phase distortion, regularity indicates the de-noised signal can be smoother, and similarity to signal represents signal can be extracted more effectively. The scale of wavelet transform is "5" when the SNR of reconstructed detailed coefficient [18] and the results whether the reconstructed signal is distorted are considered. The process of WTMM in our work is shown as follows: (1) Decompose the original signal by the function "wavedec"; (2) Obtain the reconstructed detailed coefficient and approximate coefficient by the function "wrcoef"; (3) Utilize different threshold values to eliminate the modulus maximum of reconstructed detailed coefficient at different scales, respectively. If the value of modulus maximum is less than threshold, the modulus maximum changes into zero, else reserved; (4) If the symbol of the value stays the same at each decomposition scale, the rest modulus maximum remains unchanged, else set the value into zero; (5) Reconstruct the signal based on the reconstructed approximate coefficient and the detailed coefficient after Steps (3) and (4) by the function "waverec".  In the experiment, a pulsed laser with 10-ns pulse width at 1550 nm is used as the optical source. The pulse is injected into a WDM, then coupled into an 11.5-km multimode sensing fiber. Then the Raman anti-Stokes backscattering (AS) is filtered by the WDM and detected and amplified by the APD & AMP module. The intensity of the electrical signal is sampled by the data acquisition card (DAC), then the temperature is demodulated by the personal computer (PC). It is worth noting that the repeat frequency of input light is 8 kHz which means that the sensing distance can reach 12.5 km, but actually the fiber is 11.5 km, so the last 1-km sensing distance is used to get the noise floor, then the dynamic ground noise is calculated.

Experimental setup
In Fig. 2, the FUT includes three test zones. In

Sensing distance lengthened by using dynamic noise difference algorithm
In the experiment, the three test zones are set in the same TCC (Shanghai Bilon: GDH-3030), the temperature fluctuation is 0.005 ℃ 0.02 ℃, and the temperature is measured by Agilent E2308A whose accuracy is ± 0.2 ℃.
The fluctuation of ground noise of the optical receiver and the influence on measured result are analyzed. The fluctuation of ground noise is shown in Fig. 5. In Fig. 5, the values of the first 57 times are dynamic ground noise, and the last one is calculated by constant noise floor when the measurement is finished and there is no light input. As shown in Fig. 5, the ground noise fluctuates between -42.18 mV and -48.81 mV. The fluctuation is caused by the changes in operating temperature and bias voltage according to (5). In order to prove that the noise difference algorithm can enlarge sensing distance, constant ground noise and dynamic ground noise are used to demodulate temperature when the actual temperature is 40.02 , respectively. And the result ℃ is shown in Fig. 5. In Fig. 5, the ground noise after measurement whose value is -42.45 mV is used as constant ground noise; the reference dynamic ground noise is -44.86 mV, and the measurement dynamic ground noise is -47.19 mV.
(a) (b) Fig. 6 Measurement results by using dynamic ground noise and constant ground noise: (a) overall-distribution alone the fiber and (b) at Test 3. Figure 6(a) shows the measured temperature along the entire fiber, and Fig. 6(b) shows the measured result at Test 3. As shown in Fig. 6(a), the temperature error happens from 3 km and is enlarging as the sensing distance increases when the constant ground noise is used. In Fig. 6(b), the temperature accuracy optimizes from 6.62 to ℃ 1.15 by using dynamic ground noise at ℃ Test 3. In the experiment, it can be considered that the measurement intensity is weaker than actual intensity when constant ground noise is used, so the demodulate temperature is less than the actual value, and the demodulate temperature decreases as the intensity of useful signal decreases.

Temperature fluctuation decreased by WTMM de-noising
In the precondition of using the dynamic noise difference algorithm, the comparison between temperature demodulated by original signal and that by the signal after wavelet is shown in Fig. 7. The original signal is averaged 10 000 times, the input pulse power is 14.6 W, the decomposition scale of wavelet is "5", and the wavelet function is "sym6". As shown in Fig. 7, the de-noising effect is more and more effective as the sensing distance increases. Especially, in the end of sensing fiber, the temperature fluctuation changes from 5.98 to ℃ 1.23 by using ℃ the WTMM method. The phenomenon above is caused by the signal that is attenuated as the distance increases. In Test 1, the average value of amplitude of signal is 230.5 mV, and changes to 60.8 mV in Test 3, and then 40 mV at the end of the sensing fiber. Besides, the peak-topeak amplitude of noise changes from 1 mV to 0.1 mV after the WTMM method is used over the sensing fiber. Acording to (4), the intensity ratio of correction optical fiber almost keeps the same, but the ratio of FUT in different distances will be influenced by the noise. So, when the same value of noise is de-noised, the weaker signal results in a higher influence on temperature fluctuation.  Figure 8 shows the self-demodulation method measurement results, the temperature accuracy and uncertainty in three different test zones in self-demodulation method by combining dynamic noise difference algorithm with the WTMM method when the average room temperature is 22.82 ℃, the TCC is adjusted from 35 ℃ to 65 ℃ and the spacing is about 5 ℃. The decomposition scale of wavelet is "5" and the wavelet function is "sym6". Figures 8(a), 8(b), and 8(c) stand for the result of Tests 1, 2, and 3, respectively. In Figs. 8(a1), 8(b1), and 8(c1), it is obvious that the maximum temperature fluctuation of the three test zones is increasing with the sensing distance increasing. The highest fluctuation appears at Test 3 when the actual temperature is 65.02 ℃ . This phenomenon is caused by the average amplitude of Raman signal attenuating from 275 mV to 40 mV. However, the peak-to-peak of the noise stays the same after cumulative average and WTMM de-noising. The noise remains unchanged, and yet the Raman signal decreases, which must result in the higher temperature fluctuation. The error bar stands for uncertainty of the system which is shown in Figs. 8(a2), 8(b2), and 8(c2). As figures show, the uncertainty is enlarging as the sensing distance increases, which is also caused by the attenuated signal.

Measurement results
The measurement accuracy is also shown in Figs. 8(a2), 8(b2), and 8(c2). In the figures, the temperature accuracy is deteriorating as the sensing distance increases. The worst accuracies are 0.52 ℃, -1.00 ℃ , and -1.58 ℃ at Tests 1, 2, and 3, respectively. The reason is that WTMM method not only contributes to the signal de-noising, but also filters some Raman backscattering signals [14]. According to (4), in the front of the fiber, although some Raman backscattering signals are filtered, the influence on the measurement result does not take into consideration because of the high intensity of the Raman backscattering signals. But at the end of the fiber, the WTMM filters the same useful signal, while the average amplitude of signal attenuates almost 4 dB, so the temperature accuracy is lower than that of the front-end fiber obviously.
The repeatability of the system shown in Table 1 is also analyzed. Three test zones are set in the TCC and the temperature is controlled at 34.87 ℃. Then take measurement every 60 minutes. The average values of the five times measurement at three test zones are 35.058 ℃ , 34.116 ℃ , and 33.786 ℃ , respectively. The temperature fluctuation of the system at three test zones is 0.90 ℃, 0.42 ℃, and 1.02 ℃. This means the repeat ability of the system is well. Then we analyze the spatial resolution of the system, and the result is shown in Fig. 9, where the spatial resolution was defined in [19] (10%-90% response distance to a temperature step). Figures 9(a), 9(b), and 9(c) show the spatial resolution of Tests 1, 2, and 3, respectively, and the relevant spatial resolutions are 1.3 m, 1.6 m, and 2.1 m. As shown in Fig. 9, it is obvious that the spatial resolution is deteriorating as the sensing distance increases. This is mainly caused by the degraded SNR and the effect of optical Chromatic dispersion.

Conclusions
In this paper, dynamic noise difference algorithm and wavelet transform modulus maximum method are proposed to suppress the noise for self-demodulation Raman distributed temperature system. The system only uses one APD and one amplifier to demodulate the temperature, which eliminates the mode dispersion and saves the cost. In experiment, it is demonstrated that the modulus maximum de-noising method can reduce temperature fluctuation, and dynamic noise difference algorithm can enlarge the sensing distance in experiment. As a result, temperature fluctuation of ± 0.88 ℃ and spatial resolution of 2.1 m are achieved over an 11.5 km sensing fiber.