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Resolving the range ambiguity in OFDR using digital signal processing
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Measurement Science and Technology Meas. Sci. Technol. 25 (2014) 125102 (6pp)
doi:10.1088/0957-0233/25/12/125102
Resolving the range ambiguity in OFDR using digital signal processing Nicolas Riesen, Timothy T-Y Lam and Jong H Chow Department of Quantum Science, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 0200, Australia E-mail:
[email protected] Received 17 January 2014, revised 26 August 2014 Accepted for publication 9 September 2014 Published 20 October 2014 Abstract
A digitally range-gated variant of optical frequency domain reflectometry is demonstrated which overcomes the beat note ambiguity when sensing beyond a single frequency sweep. The range-gating is achieved using a spread spectrum technique involving time-stamping of the optical signal using high-frequency pseudorandom phase modulation. The reflections from different sections of fiber can then be isolated in the time domain by digitally inverting the phase modulation using appropriately-delayed copies of the pseudorandom noise code. Since the technique overcomes the range ambiguity in OFDR, it permits high sweep repetition rates without sacrificing range, thus allowing for high-bandwidth sensing over long lengths of fiber. This is demonstrated for the case of quasi-distributed sensing. Keywords: fiber sensing, FMCW, metrology, optical frequency domain reflectometry, range ambiguity (Some figures may appear in colour only in the online journal)
1. Introduction
the disturbances. In order for OFDR to rival the range and bandwidth of the more commonplace technique of optical time domain reflectometry (OTDR) [4], whilst providing much improved spatial resolution, a hybrid, time-resolved variant of OFDR is needed. Such a technique has recently been reported [10] and here it is shown that it could potentially meet the goals of high-bandwidth and high resolution distributed sensing over long lengths of fiber. The technique, which is known as Digitally Enhanced OFDR, merges digital interferometry (DI) and standard OFDR. The time-resolved nature of DI-OFDR has previously been exploited to allow for reductions in the required sampling rate of OFDR [10]. In the present context, however, the technique’s advantage over traditional OFDR stems from its ability to solve the range ambiguity when sensing beyond a single frequency sweep.
Coherent optical frequency domain reflectometry (OFDR), also known as frequency modulated continuous wave reflectometry (FMCW), is a high resolution optical fiber sensing technique commonly used for network maintenance and diagnostics of short to intermediate lengths of fiber [1]. Significant interest however exists for extending such techniques to long range [2, 3] and also high measurement bandwidth [3]. High measurement bandwidth permits the detection of high-frequency (e.g. acoustic) perturbations, as is desired for applications pertaining to infrastructure health monitoring and perimeter security. High-bandwidth distributed sensing can be used for the monitoring of bridges, railways and pipelines; for cracks, failures or third-party intrusion [4]. Measurement bandwidths as high as tens of kilohertz can, for instance, allow for the successful identification of various failure modes in buried onshore and subsea oil and gas pipelines [5–7]. Other applications for distributed acoustic fiber sensing that are gaining interest include seismic activity assessment and intrusion detection along borders [4, 8–9]. OFDR is of particular interest for such applications due to its high resolution, which permits accurate identification of the nature and location of 0957-0233/14/125102+6$33.00
2. The beat note/range ambiguity In traditional OFDR a single linear sweep of the lightwave frequency is typically used, which gives rise to beating between reflection events along a test fiber and a local oscillator. When continuously interrogating a fiber in real time, successive 1
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Figure 2. A single sweep of triangular frequency modulation.
permitted, whilst still realizing the best possible spatial resolution Δxmin for the given frequency excursion Fs [11], is equal to the sweep repetition rate frep. Thus, if high resolution and high measurement bandwidth are both desired, high sweep repetition rates are necessary if the frequency scan range cannot be increased indefinitely1. In this regime the limiting factor on range will not be the source coherence length, but rather the period of a single frequency sweep. Therefore very high measurement bandwidth and high resolution may come at the expense of range. Moreover, for Rayleigh backscatter based sensing [12, 13], the measurement bandwidth fBW is precisely equal to the sweep repetition rate frep and cannot be improved by simply increasing the acquisition rate [13]. Therefore the range/ beat note ambiguity is particularly detrimental in the case of Rayleigh backscatter based high-frequency sensing. Range ambiguity ultimately limits such high-bandwidth techniques to very short range. The application of digital range-gating [14, 15] to OFDR however, overcomes any imposed range constraint, and this is demonstrated for quasi-distributed sensing.
Figure 1. The beat note ambiguity in OFDR (b) occurring for reflections with delays τ + (N – 1)Ts, of different frequency sweeps (a). Here τ is a given delay relative to the local oscillator, Ts is the triangular frequency modulation period and N is an integer.
linear sweeps are required, which is equivalent to using triangular or sawtooth frequency modulation. Nonetheless, the sensing range is still restricted by the duration of a single sweep [11]. This is because in traditional OFDR there is no way of discerning between reflections from different sweep periods, as is shown in figure 1. This is known as the beat note/range ambiguity of OFDR [11]. In order to avoid this, the sweep repetition rate, frep = 2/Ts, is usually kept quite low, in which case the source coherence length Lc typically limits the range. This occurs when vg L c Ts/2. From equations (2) and (3), it can be inferred that the maximum measurement bandwidth
1
Note that if the frequency excursion can be increased indefinitely, the measurement bandwidth in quasi-distributed OFDR sensing could be improved by increasing the acquisition rate. 2
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Figure 3. Resolving the beat note fb ambiguity of OFDR when sensing beyond a single frequency sweep by applying DI. In traditional OFDR, the beat notes of signals reflected from different frequency sweeps are indistinguishable (a), (b). However, by using digital rangegating (c), it is possible to isolate the beat notes based on their time delays (d). The pseudorandom noise (PRN) chips here represent individual elements of the PRN code and they are associated with individual range-gated sections of the fiber. In other words, the return signal(s) from each of these sections of fiber have unique shifts in the PRN code sequence and hence can be isolated accordingly.
and π phase shifts [14–16]. The phase shifts are determined by a time-varying pseudorandom noise (PRN) code, c(t – τ0), which has individual chip values of ±1 and a frequency of fPRN. This is equivalent to directly multiplying the probe beam signal by the PRN code and it effectively time stamps the signal. τ0 represents the time at which PRN phase modulation commences. The light reflected from the test fiber is then combined with the local oscillator and the resulting interferometric signal is measured using the photodetector. Each PRN chip has a time interval of ΔT = 1/fPRN, which corresponds to a fiber section (see figure 3(c)) of length ΔL = vgΔT/2, where vg is the carrier group velocity. Therefore, reflections occurring within ΔL lengths of fiber (i.e. delay intervals of ΔT) can be isolated or despread when decoding with the matched-delay code sequence, c(t – τj). This is due to the autocorrelation properties of the PRN code. In this paper, maximal length based PRN codes [17] are used, for which c(t – τj)c(t – τj) = 1 whilst c(t – τj)c(t – τk ≠ j) remains a random code [17]. Thus, signals within different ΔT delay intervals can each be isolated in DI-OFDR, with the residual signals remaining spread by the high-frequency PRN phase modulation. The beat spectrum from each isolated delay interval can then be analyzed as a normal heterodyne signal. As mentioned, each delay interval can be made less than or equal to the duration of a single frequency sweep (or half the period of the triangular frequency modulation). In this way, signals from different frequency sweeps can be separated. This means that, whilst the signals may have the same beat notes (see figure 3(b)), they are distinguishable in the time domain by demodulation with the appropriately delayed PRN code sequence (figure 3(d)). For the present implementation of DI, the level of suppression (i.e. isolation) of the residual signals outside of a given isolated PRN chip is given by [10]
permits sensing over essentially arbitrary lengths of fiber, irrespective of sweep period. The application of DI to OFDR represents the merging of the realms of time domain and frequency domain fiber sensing. The solution to the range ambiguity of OFDR when applying DI is shown in figure 3. Here, triangular frequency modulation is assumed and degeneracy of the beat notes (a), (b) is shown to occur for reflections with delays τ + (N – 1)Ts, where τ is a given delay relative to the local oscillator and N is an integer. With the application of DI to OFDR, signals can be isolated based on their relative delays. This can be thought of as a partitioning of the fiber into equal-length segments (each associated with an integer shift in the PRN code sequence), as shown in figure 3(c). Provided the corresponding time delay intervals are smaller than, or equal to, a single frequency sweep period, the signals of different sweeps can be isolated and distinguished2. Therefore, the beat note/range ambiguity of OFDR can be resolved (see figure 3(d)). 4. Experimental demonstration A schematic of the experiment is shown in figure 4. Here a coupler splits the frequency modulated lightwave into a local oscillator (LO) and a probe beam. An electro-optic modulator (EOM) is then used to phase modulate the probe beam with 0 2
Note in the previous work [10], the DI-OFDR technique was shown to allow for a reduction in the required sampling rate of standard OFDR. The maximum level of undersampling permitted occurred when fPRN = fs = γ1/2. This was demonstrated for a single frequency sweep. Conversely, this paper considers multiple frequency sweeps, in which case the PRN phase modulation is simply designed to satisfy fPRN = fs ≥ frep, so that the return signals from different frequency sweeps can be distinguished. Although the sampling rate chosen here is sufficiently high such that the first advantage is not realized, it is worth emphasizing that the two benefits could be realized simultaneously.
3
S ≅ 2 / ts fPRN ,
ts ≤ (2n − 1) / fPRN
(4)
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Figure 4. Digitally enhanced homodyne OFDR using SSB-SC external frequency modulation. Shown here are three reflectors in three uniquely time-stamped sections of the test fiber. Each fiber section here represents a different frequency sweep. The signals can be distinguished by decoding with the appropriately-delayed PRN code sequence, c(t – τj).
where ts is the measurement time and 2n – 1 is the PRN code length. This result assumes that ts fPRN >> 1 and that the sampling frequency fs ≥ fPRN. Therefore, increasing the measurement time or the PRN frequency improves the level of residual signal suppression. The noise floor of each isolated delay interval equals the level of suppression multiplied by the residual signal power [10]. Since decreasing the measurement time increases the residual signal noise floor (for a given PRN frequency), its permitted value ultimately sets the limit on the achievable measurement bandwidth. Nonetheless, this could still entail acoustic-level bandwidths, even for moderate PRN frequencies and low noise floors. The experimental setup shown in figure 4 used a 400 Hz linewidth fiber laser (Orbits Lightwave EthernalTM). Single sideband suppressed carrier (SSB-SC) external frequency modulation was implemented using a Dual Mach Zehnder modulator (Photline MXIQ-LN-40). External frequency modulation allowed for fast and highly linear frequency sweeps, whilst still permitting the use of a highly coherent fiber laser with slow tuning speed. SSB-SC frequency modulation was used instead of double sideband suppressed carrier modulation (DSB-SC), because it avoids fluctuations in the beat note intensities (at micron-scale intervals) along the fiber length [18]. The RF inputs to the Dual Mach Zehnder modulator were generated using an amplified voltage-controlled oscillator (VCO), whose output was split using a π/2 hybrid coupler. The VCO was driven using a triangular waveform from a standard function generator. The single sideband was scanned over Fs ≈ 50 MHz. This amounts to an optimal theoretical OFDR spatial resolution of Δxmin = vg/2Fs ≈ 2.1 m. We note that it is possible to improve the spatial resolution by simply using a larger frequency scan Fs, in addition to nonlinear sweep compensation [19]. Figure 5 verifies the solution to the range ambiguity in OFDR when applying DI. The test fiber consisted of an angledflat connector at 0.31 km, followed by a Faraday mirror at 3.68 km. The two discrete reflections had approximately equal
power at the photodetector. Triangular frequency modulation with f = 1/Ts = 27.3 kHz (i.e. γ = frep Fs = 2.73 THz s−1) was used. This means that, for traditional OFDR, the sensing range is limited to just 1.895 km. The beat notes of the two discrete reflections occurred at fb1 = γτ1 = 8.217 MHz (which aliases down to 1.783 MHz when sampling at fs = fPRN = 10 MHz) and fb2 = 2.839 MHz. Thus the beat notes are nearly identical, despite the second reflection occurring at almost 12 times the distance of the first. Clearly the beat note of the second reflection is not proportional to its distance along the fiber (i.e. fb2 ≠ γτ2). This is a result of the reflection occurring in a different frequency sweep. Whilst the two reflections cannot be distinguished in traditional OFDR, the application of DI to OFDR removes the range constraints associated with a finite sweep duration, allowing for the two reflections to be distinguished in the time domain. The solution to the beat note/range ambiguity is demonstrated in figures 5(a)–(c) for a measurement bandwidth of 5 kHz (i.e. ts = 0.2 ms and 2000 data samples taken). Figure 5(a) shows the original OFDR beat spectrum of the two reflections. As previously mentioned, the beat notes are nearly identical because the reflections occur in different frequency sweeps. However, the application of DI to OFDR allows for the two reflections to be isolated, as shown in figure 5(b) for the first reflection and figure 5(c) for the second reflection. This confirms that reflections in different frequency sweeps can be distinguished, allowing for the range ambiguity of OFDR to be solved. In this case, the level of residual signal suppression is ~13 dB compared with the theoretical of 2/(tsfPRN)1/2 ≈ 13.5 dB. Moreover, figures 5(d)–(f) show a second set of results, this time with a reduced measurement bandwidth of 133 Hz (i.e. ts = 7.5 ms and 75 000 data samples). The decrease in measurement bandwidth is due to an increase in measurement time, which is necessary to improve the theoretical level of residual signal suppression from 13.5 dB to 21.4 dB (for the given PRN frequency). The standard OFDR beat spectrum of 4
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Figure 5. DI-OFDR with beat note ambiguity resolved when sensing beyond a single frequency sweep. The standard OFDR beat spectrum of the two reflections of different frequency sweeps is shown in (a), for 5 kHz and (d), 133 Hz measurement bandwidths. In either case, the beat notes nearly overlap, with isolation of the two reflections possible in the time domain when using DI. This is shown for both the 5 kHz (b), (c) and 133 Hz (e), (f) measurement bandwidth examples. Note that harmonics appear in the spectra as expected when the measurement occurs over several sweeps.
signal suppression can however be increased simply by using a higher PRN frequency.
the two reflections is again shown in figure 5(d). As before, the use of DI allows for the two reflections to be isolated (see figures 5(e), (f)). Therefore, the beat note ambiguity of reflections occurring in different frequency sweeps can be resolved when using this technique. The slight discrepancy between the theoretical and measured suppression is attributed to high background noise and imperfect PRN phase modulation [10]. The imperfect phase modulation results from constraints, such as the finite bandwidth of the analog electronics used. It also accounts for a slight reduction in the power of the recovered return signals compared with standard OFDR. For both results, the spatial resolution achieved was 3 m ± 1 m, with the best resolution measured being identical to theoretical predictions. The results of figure 5 therefore demonstrate the solution to the beat note ambiguity when sensing beyond a single frequency sweep in DI-OFDR. Therefore, when using DI-OFDR, the sensing range is not constrained by the frequency sweep period, but is instead limited only by the coherence length of the source and the signal-to-noise ratio. The signal-to-noise ratio is in part determined by the residual signal suppression which is a function of the measurement time. For this reason, a trade-off exists between the measurement bandwidth and the level of residual signal suppression. The level of residual
5. Concluding remarks In conclusion, the application of digitally enhanced interferometry to OFDR has been demonstrated. DI-OFDR overcomes the beat note/range ambiguity of OFDR. The technique therefore permits high sweep repetition rates without sacrificing range, which facilitates high-bandwidth sensing over long lengths of fiber. By overcoming the beat note ambiguity, DI-OFDR can also help reduce the effect of environmental perturbations on spatial resolution, since the technique accommodates an increase in tuning rate for a given frequency excursion without penalizing the sensing range [20]. Increasing the sweep repetition rate without degrading the range is also of particular importance in Rayleigh backscatter based sensing, in which the measurement bandwidth is strictly limited by the sweep repetition rate [13]. The measurement bandwidth cannot be improved by simply increasing the acquisition rate whilst increasing the frequency scan range. 5
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We note that the principles of DI-OFDR could also be applied to FMCW radar to solve the Range × Doppler ambiguity which limits the maximum unambiguously measurable velocity of a target to the range-limiting sweep repetition rate [21–24]. In other words, the technique could overcome the trade-off between measurable velocity and range in FMCW radar. In addition, the technique could also provide an elegant solution to the multi-target detection problem [25] commonly faced in FMCW radar, since nearby targets could be distinguished in the time domain. However, as mentioned, the most promising application for this novel technique undoubtedly lies in long-haul distributed fiber sensing with high resolution spatial localization of acoustic signals. References [1] Soller B, Gifford D, Wolfe M and Froggatt M 2005 High resolution optical frequency domain reflectometry for characterization of components and assemblies Opt. Express 13 666–74 [2] Ding Z, Yao X, Liu T, Du Y, Liu K, Han Q, Meng Z, Jiang J and Chen H 2013 Long measurement range OFDR beyond laser coherence length IEEE Photon. Technol. Lett. 25 202–5 [3] Williams J 2012 Distributed acoustic sensing for pipeline monitoring Pipeline Gas J. 239 (7) [4] Owen A, Duckworth G and Worsley J 2012 OptaSense: fibre optic distributed acoustic sensing for border monitoring Proc. EISIC (Odense, Denmark) pp 362–4 [5] Jaaskelainen M 2009 Fiber optic distributed sensing applications in defense, security and energy Proc. SPIE 7316 731606 [6] Frings J and Walk T 2011 Distributed fiber optic sensing enhances pipeline safety and security Oil Gas Eur. Mag. 37 132–5 [7] Rajeev P, Kodikara J, Chiu W and Kuen T 2013 Distributed optical fibre sensors and their applications in pipelines monitoring Key Eng. Mater. 558 424–34 [8] Bao X and Chen L 2012 Recent progress in distributed fiber optics sensors Sensors 12 8601–39 [9] Wild G and Hinckley S 2008 Acousto-ultrasonic optical fiber sensors: overview and state-of-the-art IEEE Sensors J. 8 1184–93
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