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Long-range C-OFDR measurement of fiber Rayleigh scatter signature is described. The Rayleigh scatter signature, which is an interference pattern of backscatters from the random refractive indices in fibers, is known to be applicable to fiber identification and temperature or strain sensing by measuring its repeatability and its spectral shift. However, these applications have not been realized at ranges beyond the laser coherence length since laser phase noise degrades its repeatability. This paper proposes and demonstrates a method for analyzing the optical power spectrum of local Rayleigh backscatter to overcome the limitation imposed by laser phase noise. The measurable range and spatial performance are also investigated experimentally with respect to the remaining phase noise and noise reduction by signal averaging with the proposed method. The feasibility of Rayleigh scatter signature measurement for long-range applications is confirmed.
© 2016 Optical Society of America
1. Introduction
Rayleigh scattering measurements performed using an optical reflectometer have been widely used for fault detection and evaluation in optical fiber networks and optical components [1–3]. Recently, some attractive applications of Rayleigh scattering measurement including a fiber identification [4], highly sensitive temperature or strain sensing [4–6], and 3D shape sensing [7] have been proposed. In these applications, a randomly jagged scatter amplitude waveform which is measured by employing optical reflectometry with coherent detection is used as a “signature” for identification or sensing. The origin of the jagged appearance is interference between Rayleigh backscatters caused by random refractive indices generated when fiber is manufactured [8]. The measured waveforms are thus identical and unique for individual fibers and for fiber segments when the fiber and measurement conditions are the same. In the applications mentioned above, the signature must be measured with high repeatability.
Certain methods have been proposed for measuring the Rayleigh scatter signature. Reference [5] proposed a highly-sensitive temperature measurement using coherent optical time domain reflectometry (C-OTDR) with a gas-stabilized distributed feedback laser whose frequency was precisely controlled. This approach makes it possible to perform measurements on long fibers (over tens of kilometers) with a temperature resolution of 0.01 °C and a spatial resolution of one meter. However, the C-OTDR setup is complex, especially as regards frequency stabilization and control when the aim is to achieve measurements with high repeatability. Moreover, it requires a lot of time to undertake many measurements at different laser frequencies. In contrast, an approach using coherent optical frequency domain reflectometry (C-OFDR) is very attractive because Rayleigh backscatter responses in both the time and spectral domains are easily and quickly obtained by sweeping the optical frequency of the laser. For this reason, C-OFDR is now the most common approach for scatter signature applications [4,6,7]. However, the use of C-OFDR for scatter signature applications is limited to short measurement ranges (up to several hundred meters) since scatter signature repeatability is not maintained for long fibers beyond the laser coherence length due to laser phase noise. The expansion of the scatter signature measurement range with C-OFDR would be useful as it would mean the possibility of using the approach for identification or sensing in, for example, telecommunication-scale fiber networks.
In this paper, we present a way to realize scatter signature measurements with C-OFDR for the range beyond the laser coherence length. The laser phase noise limitation is overcome by introducing the optical power spectrum of local Rayleigh backscatter as the signature. We also investigate the influence of the remaining phase noise on the repeatability of the proposed method with various measurement ranges and spatial resolutions. In addition, we employ signal averaging for the proposed method to enhance the repeatability degraded by the detector noise for long-range measurement and discuss the effect of signal averaging on the proposed method. With this method, we demonstrate distributed temperature sensing over a 100-km measurement range with a temperature resolution of better than 0.01 °C and confirm the potential for long-scale applications.
This paper is organized as follows. Section II reviews the theoretical background to the scatter signature measurements with C-OFDR using the conventional and proposed methods. Section III describes the C-OFDR configuration we used in the experiment. Section IV includes our experimental results and discussion, and Section V provides the conclusion.
2. Measurement principles
2.1 Complex scatter spectrum with conventional method
In this section, we review the principle of the conventional method used to obtain the scatter signature with C-OFDR.
Figure 1 shows an example of a C-OFDR setup. A continuous light wave whose frequency is swept with respect to time is divided by the coupler and used as probe and local lights, and the backscattered lights are mixed and then detected by a coherent receiver. Then, the beat signal I(t) produced by the interference between the local and backscattered lights can be written as [9,10]
where M is the number of scatterers in the fiber, ai is the ith scatter amplitude, zi is the position of the ith scatterer, ν0 is the initial frequency of the probe light, γ is the frequency sweep rate, n is the effective refractive index of the fiber, c is the speed of light in a vacuum, and θ(t) and θ(t-2nzi/c) are the laser phase noises of the local and backscattered lights, respectively. Here, we define a one-dimensional scatter model [5,8], in which discrete scatterers are distributed along the fiber as shown in Fig. 2. Since the beat frequency of I(t) is proportional to zi, we can obtain the complex amplitude of the scatter as a function of distance by Fourier transforming I(t). After the Fourier transform, a complex optical spectrum of the Rayleigh backscatter for a local segment of the fiber can be obtained by performing an inverse Fourier transform on windowed distance domain data (a segment of OTDR-like traces) [6], and it is used as a fiber signature in the conventional method. Since the optical frequency of the probe light is swept, the inverse Fourier transformed data can be translated to the optical frequency domain. If the segment size is much larger than the spatial resolution of C-OFDR, the complex scatter spectrum for the segment za<z<zb, σab(t), can be represented byHere the complex scatter spectrum is written as a function of t since the probe light frequency is swept with respect to time. It is noteworthy that the difference between the phase noises of the local and backscattered light, θ(t)-θ(t-2nzi/c) depend on the scattering position. Thus the phase component of σab(t) is perturbed randomly at every measurement if the scattering position is far beyond the laser coherence length. This leads directly to the degradation of the scatter signature repeatability. Therefore, the maximum measurable range with the conventional method is limited by the laser coherence length.2.2 Scatter power spectrum in proposed method
To obtain the scatter signature with high repeatability for long distances beyond the laser coherence length, we introduce the square of the absolute value of the complex scatter spectrum, which we call the scatter power spectrum. The scatter power spectrum |σab(t)|2 can be written as [11]
where the first term shows the summation of the optical power of the scatters in za<z<zb, and the second term stands for the interference between the backscattered lights from different scatterers in the segment. It is noteworthy that the phase noise of the local light is cancelled out in the second term, which indicates that the influence of the laser phase noise in |σab(t)|2 does not depend on the scattering position, whereas the difference between the phase noises of the scatter remains in the segment, θ(t-2nzj/c)- θ(t-2nzi/c). Therefore, the repeatability of the scatter power spectrum is not limited by the measurement range. In contrast, the segment size determines the influence of the laser phase noise. The scatter power spectrum is expected to be given precisely when the segment size is enough small compared with the laser coherence length. Although the scatter power spectrum does not contain the phase components of the Rayleigh backscatter, it can be handled by the signature for individual fibers as well as the complex spectrum because its waveform is randomly jagged due to random refractive index fluctuations in the fiber. The scatter power spectrum can be considered as a reflected power spectrum from a weak and random period grating, thus a spectral shift in the scatter power spectrum also occurs when the temperature or strain is changed as in the reflection spectrum of fiber Bragg gratings [12].3. Experimental setup
Figure 3 shows our experimental setup. We prepared two lasers with different coherence lengths, namely Lasers 1 and 2, to investigate the influence of the laser phase noise. The coherence lengths of Lasers 1 and 2 were about 10 km and 500 m respectively, which were estimated in [13]. The optical frequencies were swept with a single side band (SSB) modulator [14], and the sweep range and rate were controlled by changing the modulation signal generated by an RF synthesizer. In this study, the sweep range was set at 2 GHz, which corresponds to the ideal spatial resolution of 5 cm if the laser phase noise is not taken into account. We changed only the sweep rate in the experiment. A 100-km long single mode fiber (SMF) was used as the fiber under test (FUT), and placed in a soundproof box to reduce acoustic noise. To investigate the temperature response, we placed a relevant fiber section in a temperature-controlled water bath whose temperature was accurate to 0.01°C. A polarization diversity scheme was employed in the interferometer to eliminate polarization-dependent effects due to such factors as birefringence. The Rayleigh backscatter of the P- and S-polarization states were individually detected by two balanced photodetectors, and acquired by a two-channel A/D converter. A Fourier-transform and an inverse Fourier-transform were performed on these two sets of polarization data individually, and a vector sum was calculated to generate a polarization-independent spectrum. The repeatability of the scatter signature was evaluated by calculating the cross-correlation between the two sets of measurement results.
4. Experimental results and discussion
4.1 Rayleigh scatter signatures beyond laser coherence length
Figure 4 (a) and 4(b) show the cross-correlation of the complex scatter spectrum and the scatter power spectrum at each segment position of the FUT. The optical frequency sweep rate and the segment size were 100 GHz/s and 100 m, respectively. The time interval of the measurements was 0.1 sec during which the fiber conditions were expected to remain stable. The complex scatter spectrum was not maintained at positions beyond the coherence length. On the other hand, the scatter power spectrum was identified over a long range. The repeatability degradation of the scatter power spectrum in the region beyond 70 km seemed to be affected by the detector noise whose power relative to the signal was increased by the attenuation of the FUT.
Fig. 4 Cross-correlations of (a) complex scatter spectrum, (b) scatter power spectrum at each segment position. The segment size was 100 m.
Figure 5 (a) and 5(b) show the scatter power spectra and cross-correlation measured at temperatures of 35.00 and 35.02 °C, respectively. We changed the temperature of a fiber section at around 40 km, and carried out the measurement with Laser 1. The scatter power spectrum was shifted after the temperature change, resulting in a correlation peak shift. Figure 6 shows the temperature dependence of the spectral shift of the scatter power spectrum. Applying a linear least squares fit to the plot, we estimated the sensitivity of the scatter power spectrum to the temperature change at −1.28 GHz/°C, which is similar to the result obtained with the conventional method [6].
Fig. 5 (a) Scatter power spectra, (b) cross-correlation of the scatter power spectra at 40 km measured at 35.00 and 35.02 °C. In the cross-correlation, the spectrum at 35.00°C was used as reference data. The segment size was 25 m. Laser 1 with Lc = 10 km was used.
Fig. 6 Temperature dependence of spectral shift of the scatter power spectrum measured at 40 km. The solid line is a linear least square fit. The segment size was 25 m.
4.2 Segment size and frequency sweep rate dependence
Figure 7 shows the segment size dependence of the repeatability of the scatter power spectrum at 20 km. The correlation decreased due to the phase noise difference among the scatters in the segment when the segment size was longer than the coherence length, as mentioned in Section II. On the other hand, we found that the repeatability of the scatter power spectrum was also decreased when the segment size was small. This is due to the broadening of the spatial resolution of the C-OFDR measurement. If the beat frequency of C-OFDR corresponding to segment position is randomly fluctuated for each measurement, the scatter power spectra will become less correlated. At the scattering position z, which is at a distance greater than the coherence length Lc, the power spectrum of the beat signal of C-OFDR can be given by a Lorentz function whose spectral width Δfb is twice the laser linewidth Δf [10]. In that case, the broadened spatial resolution Δzmax can be estimated with
where we assume z = (c/2nγ)fb for the relationship between the beat frequency fb and z, Δf = c/πLc for the relationship between the laser linewidth and the coherence length Lc. Equation (4) indicates that the influence of the spatial resolution broadening can be suppressed by increasing the frequency sweep rate of the probe light.Figure 8 shows the sweep rate dependence of the cross-correlation of the scatter power spectrum measured with Laser 2. As the sweep rate increased, the scatter power spectra for a small segment size become more correlated. Since the segment size indicates the spatial resolution for identification or sensing, the use of a higher sweep rate is an effective way to achieve applications that require high resolution. The spatial resolution could be further improved by combining a technique that compensates for beat frequency fluctuations such as a resampling method based on concatenated phase signals for the region beyond the coherence length as our group has reported in [15,16].
Fig. 8 Frequency sweep rate dependence of the cross-correlation of the scatter power spectrum at 20 km.
4.3 Signal averaging for enhanced measurable range
With a complex scatter spectrum, the laser phase noise perturbs the scatter interference pattern itself when the position is at a distance greater than the coherence length. Signal averaging the complex scatter spectrum is thus not effective for long-range measurement. In contrast, for the scatter power spectrum in the proposed method, the influence of the laser phase noise is suppressed and does not depend on the scattering position. The measurable range can thus be further improved by employing signal averaging to reduce the detector noise such as thermal noise or shot noise.
Figure 9 shows the cross-correlation of the scatter power spectrum after signal averaging. We used a frequency sweep rate of 400 GHz/s, a time interval of 0.1 s, and a segment size of 50 m. The repeatability of the scatter power spectrum for long distances was improved by signal averaging regardless of laser type. We also found that the repeatability for Laser 2 significantly increased by signal averaging at around 50 km. For Laser 2, it is expected that an uncertainty of the scatter power spectrum due to the fluctuation of the segment position by the spatial resolution broadening of C-OFDR is reduced to a certain level by signal averaging. To prove this assumption, we observed the average scatter power spectra and Fresnel reflection peaks using a 50-km long SMF and Laser 2, where we used a segment size of 50 m and an averaging number of 10. Figure 10 shows the repeatability of the averaged scatter power spectra when the relative segment positions were changed. Figure 11 shows the observed Fresnel reflection intensity. The 3dB spatial resolutions of C-OFDR at 50 km were 80, 40, and 20 m for sweep rates of 100, 200 and 400 GHz/s, respectively, as shown in Fig. 11. These results agreed with the broadening of the correlated relative positions compared with the used segment size of 50 m shown in Fig. 10. Therefore, an effective segment size after signal averaging that contributes to cross-correlation becomes large due to the spatial resolution broadening of C-OFDR, which results in increased repeatability for the measurement with Laser 2. In other words, the effective spatial resolution for signature applications is degraded, which should be taken into account particularly when the segment size is insufficiently large with the actual spatial resolution of C-OFDR.
Fig. 9 Averaging number dependence of the cross-correlation of the averaged scatter spectra measured with (a) Laser 1, (b) Laser 2.
4.4 Demonstration of long-range distributed temperature sensing
In this section, we report the demonstration of distributed, highly-sensitive temperature sensing beyond the laser coherence length. Figure 12 shows the configuration of the sensing fiber we used. We prepared three fiber sections at the end of a 100-km long SMF, and placed each section in different temperature-controlled water baths. We set stable temperatures for Sections A and C, and carried out the C-OFDR measurements while changing the temperature of Section B. Laser 1 was used as a light source, and the frequency sweep rate was 400 GHz/s. The averaging number and measurement interval were 200 and 0.1 sec, respectively. The segment size was set at 25 m, which was much larger than the spatial resolution of 2 m obtained from the Fresnel reflection observed at the end of the FUT.
Figure 13 shows the spectral shift of the averaged scatter spectrum along the FUT at each temperature. Linear spectral shifts caused by temperature changes were observed in Section B. The temperature resolution in this demonstration was estimated to be 0.003 °C by converting the full-width at half-maximum of the correlation peaks to the temperature. The measurable temperature range was estimated to be 1.4 °C, which would be expanded by using tunable laser sources with a wide frequency sweep range for a C-OFDR system.
Fig. 13 Spectral shift distribution of averaged scatter spectrum at each temperature in Section B. The spectrum at 30.5°C was used as reference data in the cross-correlation.
5. Conclusion
We proposed a technique for the long-range C-OFDR measurement of a Rayleigh scatter signature beyond the laser coherence length by analyzing the optical power spectrum of the scatter in a local fiber segment. We confirmed experimentally that the influence of the laser phase noise did not depend on the measurement range and could be controlled by changing the signature size and the frequency sweep rate of the C-OFDR used in the proposed method. Moreover, signal averaging in proposed method was effective in reducing the detector noise resulting in further improvement of the measurable range. We also demonstrated distributed temperature sensing with a measurement range of 100 km, a spatial resolution of less than 30 m, a measurable temperature range of 1.4 °C, and a temperature resolution of 0.003 °C. We believe that our proposed method can extend the scalability of scatter signature applications to a long range.
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