Abstract

There are many advantages to using direct frequency modulation for OFDR based DAS. However, achieving sufficiently linear scan via direct frequency modulation is challenging and poses limits on the scan parameters. A novel method for analyzing sinusoidal frequency modulated light is presented and demonstrated for both static and dynamic sensing. SFS-OFDR projects the measured signal onto appropriate sinusoidal phase terms to obtain spatial information. Thus, by using SFS-OFDR on sinusoidal modulated light it is possible to make use of the many advantages offered by direct frequency modulation without the limitations posed by the linearity requirement.

© 2015 Optical Society of America

1. Introduction

Distributed Acoustic Sensing (DAS) has been attracting a considerable amount of attention in recent years for various applications including intrusion detection, railroad monitoring, pipeline protection, seismic profiling, oil and gas well monitoring and more [1–8]. All current implementations of DAS are based on fiber-optic reflectometry. Most DAS methods obtain the position information from the time delay of the backscattered signal. The spatial resolution in these methods is determined by the duration of the interrogating pulse: Δz=vgTp/2. Hence, as in Optical Time-Domain Reflectometry (OTDR) [9, 10], there is a fundamental tradeoff between the spatial resolution and the Signal to Noise Ratio (SNRPinTp). It was recently demonstrated that DAS can also be implemented via Optical Frequency Domain Reflectometry (OFDR) [11–13]. OFDR is a well-established method for measuring the reflection profile of an optical fiber [14–18]. The method is based on transmitting into the fiber light whose instantaneous frequency varies linearly with time during at least some fraction of the interrogation period. The backscattered light from the fiber is then mixed with a reference and detected. The detector output (the beat signal) is Fourier-transformed to yield spatial information. In contrast with time domain reflectometry, OFDR enables excellent spatial resolution alongside with high SNR. This is possible since in OFDR the resolution is determined solely by the frequency sweep range, ΔF, independent of the duration of the interrogation pulse: Δz=vg/(2ΔF). Thus, using longer and more energetic pulses, it is possible to increase the SNR without sacrificing spatial resolution [16–18]. Despite its clear advantages, the use of OFDR for implementation of DAS was rarely studied. As described below, one reason for this is the technical challenges which arise when attempting to generate light with highly linear frequency sweep at high repetition rates.

There are two principal approaches for generating linearly frequency-modulated light for OFDR. One approach makes use of an external electro-optic modulator [19–22]. The second imparts frequency variations onto the transmitted light by direct modulation of one of the laser's parameters (e.g. temperature, the central wavelength of its reflectors, an intra-cavity filter etc.) [23–25]. There is a fundamental difference between the two aforementioned modulation methods. In the case of the externally-modulated OFDR, the modulator must be driven by a signal generator whose RF frequency can be swept over a frequency range of at least the desired ΔF. On the other hand, in the case of the directly-modulated OFDR, the scanned frequency range depends on the modulation signal’s peak-to-peak amplitude rather than its bandwidth. Furthermore, an OFDR system has two other important design parameters: the scan repetition rate fr=1/Tr, and the sweep time TsTr. In DAS related applications high repetition rates are necessary in order to handle wide acoustic bandwidths. Naively it would seem that for a bandwidth of fmax setting the repetition rate to fr=2fmax should be sufficient. However, this requirement alone is not enough. Since OFDR assumes that the fiber is stationary within the sweep time, Ts, the sweep of the desired range, ΔF, must be completed during a time much shorter than Tr=(2fmax)1. In such cases the necessary RF-generator specifications for implementing externally-modulated OFDR can be rather challenging. In contrast, as demonstrated below, a directly-modulated OFDR system can be implemented with a simple every day RF generator

These trivial requirements from the RF generator, however, facilitated by the direct-modulation method, are not without their price. First, the implementation of directly-modulated OFDR requires the use of a fast-tuning tunable laser with efficient conversion from driving signal to frequency. This is, however, not a severe hurdle as many such lasers are currently readily available. The harsher problem is that in direct-frequency-modulation a highly linear sweep is difficult to achieve, since the tuning mechanism is often intricate and non-trivially depends on the driving signal. In many lasers, for example, the tuning mechanism is based on a PZT. In these cases the driving signal must change smoothly in time and the use of a sawtooth driving signal is undesired due to the long transient oscillations that follow a jump in the signal. Another way to describe this problem is if we regard the tuning mechanism as a linear system whose frequency response is highly non-flat. In such a case attempting to drive it with a broadband signal (such as sawtooth) consisting of more than one frequency will result in a severely corrupted modulation that will be significantly different than the driving signal. To deal with this issue it is natural to work with a sinusoidal driving signal [12,13]. Although this function is not linear on the whole, using a short enough time window, it can be approximated as linear. Nevertheless, this inherent non-linearity introduces many problems. First of all, since the linear approximation must hold for the backscatter from the end of the fiber, there is an inherent tradeoff between the fiber length and the interrogation period. Consequently, the spatial resolution and acoustic bandwidth are hindered as the fiber is lengthened. Second, since the linear approximation cannot hold with the same precision for different reflectors with different delays, the spatial resolution is not constant with respect to position along the fiber. Furthermore, due to the same reason, the conversion between frequency and position may depend on the position along the fiber as well. These problems, all caused by the non-linearity of the frequency sweep, can be corrected using a variety of recently introduced methods [21,26]. Yet, these methods require auxiliary interferometers or inline reflectors and make no use of the prior knowledge regarding the non-linearity, caused by the driving signal.

In this paper a novel processing method for directly-modulated sinusoidal modulation based OFDR system is introduced. The Sinusoidal Frequency Scan OFDR (SFS-OFDR) accurately corrects for the driving-signal’s non-linearity without the need for auxiliary or inline interferometers. Consequently, by using longer interrogation time windows SFS-OFDR allows higher spatial resolution and acoustic bandwidth compared to regular Fourier-transform based OFDR. Moreover, it is experimentally demonstrated that SFS-OFDR is capable of achieving Δz=0.66m static spatial resolution at a sweep repetition rate of fr=21KHz and interrogation time window of Ts12μs along a L1.48km fiber. Namely, it produces over 4.7107 resolution cells per second. Furthermore, it is also experimentally demonstrated that SFS-OFDR is capable of detecting and resolving two 1KHz perturbations 1.74m apart, as well as locate the fall of a paperclip with ~0.6m resolution. The paper is organized as follows: In sec. 2 we briefly describe the theory behind SFS-OFDR; Sec. 3 describes the experimental apparatus; The main results are shown in sec. 4, demonstrating SFS-OFDR’s superiority over regular OFDR when direct modulation is used; Also in sec. 4 we examine the limits of SFS-OFDR and present dynamic results; Finally in sec. 5 we discus some of the implications and open issues of SFS-OFDR.

2. Theory

Consider a fiber-optic system as described in Fig. 1. Modulated light from the laser source is launched into a sensing arm, and the backscattered beam is mixed with a reference and detected by an I/Q optical receiver. The frequency of the laser source is varied in a sinusoidal manner over a frequency range ΔF, such that the instantaneous frequency is given by:

finst(t)=f0+ΔF2sin(ωrt)
where f0 is the nominal laser frequency at t=0, and ωr=2πfr is the modulation angular frequency. The laser’s output is easily obtained by integration:
Ein(t)=E0exp[i2πtfinst(t')dt']=E0exp{i2π[f0tΔF2ωrcos(ωrt)]}
The sensing fiber can be considered as a distributed reflector with a z-dependent backscatter coefficient ρ(z). Consequently the backscatter field is obtained by summing all reflections:
EB(t)=0Lρ(z')Ein(t2z'vg)exp[iϕ(z')]dz'
where vg is the group velocity of the light in the fiber, and ϕ(z) is the accumulated round-trip phase of the field backscattered from position z. Hence, the output of the coherent I/Q receiver, V(t)=I(t)+iQ(t), is given by:
V(t)=A0Lρ˜(z')exp{iπΔFωr[cos(ωr(t2z'vg))cos(ωrt)]}dz'
where A is a constant describing the responsivity and gain of the receiver, and ρ˜(z) is the complex backscatter coefficient, henceforth referred to as the reflection profile, defined as:
ρ˜(z)=ρ˜(z)exp{i[ω02zvgϕ(z)]}
Notice that the instantaneous frequency in Eq. (4) can obtain negative values. Therefore, in order to make use of any information in these “negative beat frequencies”, it is necessary to use an I/Q optical receiver which can produce the complex backscatter signal: V(t)=I(t)+iQ(t) [27].

 figure: Fig. 1

Fig. 1 The experimental setup.

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An approximated expression for the reflection profile can be extracted from the detected signal V(t) by projecting it onto z-dependent phase factors corresponding to the expected phase of a backscatter from position z:

ρ˜^(z)=T2T2V(t)exp{iπΔFωr[cos(ωr(t2zvg))cos(ωrt)]}dt
where T is the interrogation time window, in which the signal is sampled. The relation between the estimated reflection profile ρ˜^(z) and the actual reflection profile ρ˜(z) can be written as:
ρ˜^(z)=0Lρ˜(z')g(z,z')dz'
Thus, the estimated reflection profile is a weighed sum of the actual reflection profile with a weight function given by g(z,z'). It can be shown that for any T,L,ωr, and ΔF, the real part of this function peaks for z=z' and rapidly decays (showing some oscillations) for increasing |zz'|, while the imaginary part is negligible in comparison. Some simulations and a few special cases with analytic solution for g(z,z') appear in the Appendix.

3. Experiment

An experimental OFDR system with an array of discrete reflectors was constructed (Fig. 1). Light from an ultra-coherent tunable laser source (NKT Koheras AdjustiK Benchtop) with a central wavelength of 1550nmwas split using a 50/50 PM splitter between a reference arm and a sensing arm. The reference arm was connected to the Local Oscillator (LO) port of a Dual Polarization 90° Optical Hybrid (Kylia), while the second output of the PM splitter was connected to the sensing arm using an optical circulator. Port 2 of the circulator was used to connect the sensing arm, and the output of the circulator (port 3) was fed into the Signal port of the optical hybrid, which had four pairs of output fibers. Each pair of fibers was connected to a balanced optical receiver, which produced four electronic signals representing the four degrees of freedom of the light returning from the sensing arm. Hence, the described setup was capable of a complete measurement of the returning field (four degrees of freedom: two quadratures of two polarization components). These were sampled and stored by a Digital Storage Oscilloscope (600MHZ, Agilent Infiniium MSO9064A). The laser's instantaneous frequency was controlled by applying electric signal to an internal piezoelectric actuator (PZT) with a conversion coefficient of: K(21KHz)=18.7MHz/V. The PZT was driven by a sinusoidal signal with an amplitude of 10V and a frequency of 21KHz, for a total frequency range (peak to peak) of ΔF373.5MHz.

First, the sensing arm was connected to an array of 10 FBGs at equal center wavelengths, and 10m spacing. The FBG fiber was terminated with an open PC connector and its total length was L814m. Data was collected from within a half modulation period time window, centered on the expected backscatter delay of the first FBG. The collected data from a 3.57μs time window (7.5% of the modulation period) was analyzed using SFS-OFDR (according to Eq. (6)), as well as using the regular OFDR (Fourier-transform), in order to compare the methods for an approximately linear frequency modulation. Furthermore, the collected data from a 10.71μs time window (22.5%of the modulation period) was analyzed to demonstrate SFS-OFDR’s ability to cope with the non-linear modulation. Second, the sensing arm was elongated by a 665m fiber to produce a total length of L1479m. Data was collected from a 12μs time window (25%of the modulation period), centered on the sine’s zero crossing, and analyzed using SFS-OFDR (according to Eq. (6)) to achieve 0.66m FWHM static spatial resolution. Centering the time window on the sine’s zero crossing is necessary in order to get the maximal scanned BW for the given time window. Then, to demonstrate the dynamical capability, the sensing arm was connected to a L780m fiber with two <0.5m segments, 1.74mapart, wrapped around PZT actuators. The first PZT was driven by a 1070Hz sinusoidal signal, while the second was driven by a 1030Hz sinusoidal signal. Data was collected from a 9.5μs time window (20% of modulation time period, and about 0.95% of perturbation time periods) over 5000 modulation periods (namely, a total time of ~238ms). This was done 50 times to yield statistical information. Lastly, a paperclip was dropped on the same L780m fiber, where the segment containing the PZT actuator was replaced by segment buried in sand. Data was collected from a 12μs time window (25% of modulation time period) over 5000 modulation periods (namely, a total time of ~238ms).

4. Results

A Fourier-transform was applied to the collected data from the 3.57μs, and 10.71μs time windows (7.5%, and 22.5% of the modulation period respectively). These time windows were chosen such that one is within the linear approximation and the other is not. The data sets were multiplied by a Blackman window prior to the application of the transform to suppress sidebands. The slope of the frequency modulation at the center of the time window was used to map the beat frequency axis into a distance axis. The resulting reflection profile magnitude is shown in Figs. 2(a)-2(d). The effects of the sinusoidal modulation can be clearly seen even within the small time window (Figs. 2(a) and 2(b)). First, the spatial resolution is degraded with increasing distance from the first FBG for which the time window is optimally linear. Second, the distance between the first and last FBG is incorrect, 85.05m instead of the expected 90m. Also, the end of the fiber appears at z=753.5m instead of the expected L814m. Furthermore, in the case of the longer time windows for which the linear approximation does not hold (Figs. 2(c) and 2(d)), it is clear that the non-linearity of the modulation not only engenders the aforementioned inaccuracies but also severely distorts the reflection profile.

 figure: Fig. 2

Fig. 2 Reflection profile magnitude obtained via OFDR on the data collected from (a) the 3.57μs time window, and (c) the 10.71μs time window. A zoom-in to the 10 FBGs for (b) the 3.57μs time window, and (d) the 10.71μs time window.

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On the other hand, the same data was analyzed with SFS-OFDR (according to Eq. (6) in the same time windows, again with a Blackman window. The resulting reflection profile magnitudes are plotted in Figs. 3(a)-3(d) superimposed on the Fourier-transform based OFDR results. The 10 FBGs are clearly better resolved for both time windows. Moreover, their width is independent of their distance from the first FBG, the total distance between the first and tenth FBG is 89.7m, and the end of the fiber appears at z=813.8m, all in much better accordance with the actual sensing fiber parameters, as well as within the resulting spatial resolution (as will be reported later). Furthermore, the reflection profile magnitude shows no signs of distortion for the larger time window, but rather a sharpened better resolved result.

 figure: Fig. 3

Fig. 3 Reflection profile magnitude obtained via SFS-OFDR on the data collected from (a) the 3.57μs time window, and (c) the 10.71μs time window. A zoom-in to the 10 FBGs for (b) the 3.57μs time window, and (d) the 10.71μs time window.

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To better evaluate the spatial resolution offered by SFS-OFDR, the collected data from various time windows was processed, again using a Blackman window. The resulting reflection profile magnitudes are shown in Fig. 4. The time windows are specified in terms of percentages out of the modulation period. Notice that in addition to the contracting width there appears to be a slight left-shift of the peak, as well as gradually growing side bands visible after passing the 15% time window. We attribute these effects to higher harmonics in the modulation process. These higher harmonics are further addressed in the discussion, and ways of coping with them are suggested. In practice these effects pose an effective limit on the width of the time window. Nevertheless, since the spatial resolution depends on the scanned bandwidth, most of the spatial resolution improvement is gained between the 5% and 15% time windows for which these effects are almost unobservable. It is noteworthy that in order for linear approximation to hold, and OFDR spectrum to be undistorted, a maximum time window of about 4% should be applied. For instance, the time window used to produce the spectrum shown in Fig. 2(b) was 7.5%, and the effects of the non-linearity are clearly visible.

 figure: Fig. 4

Fig. 4 (a) One of the FBGs’ peaks as obtained by various time windows specified as percentages out of the full modulation period. (b) Zoom in on the peaks up to the 3dB width.

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Figure 5 shows the FWHM as a function of the scanned bandwidth (top axis) and time window (as percentage out of the modulation period, bottom axis). The measured data was fit to the expected theoretical dependence up to a multiplication constant corresponding to an effective widening: Δz=Avg/(πΔF). The fit yielded a value of A=2.7. For reference, the figure also shows simulated results for OFDR and SFS-OFDR, both using a Blackman window, where the constant A was found to be: A=2.45 for OFDR, and A=2.55 for SFS-OFDR. Although the actual fit does not achieve the simulated value, it does not fall far behind. Moreover, the overall tendency is as expected from theory, and predicts a spatial resolution of <0.5m for a half modulation period time window, i.e. a full BW time window. It should be noted that the theoretical value of A, without a Blackman window is A=sinc1(1/2)1.9 for the case of OFDR, and A=J01(1/2)1.5 for the case of SFS-OFDR with a half modulation period time window (see Appendix for details). The theoretical spatial resolution stated above assumes negligible laser phase noise. In all our results, we have considered time windows of the order of ~10μs, which is far shorter than the coherence time of our ultra-coherent source (>1ms). Clearly, for a source with a broader linewidth (shorter coherence time) phase noise effects cannot be generally neglected.

 figure: Fig. 5

Fig. 5 FWHM of one of the FBGs as a function of the scanned BW and time window, as percentage from the modulation period, for the measured data and simulated results.

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Figure 6 below shows the results of applying SFS-OFDR to data collected within a 12μs time window (25% of the modulation period), corresponding to ΔF=0.264GHz from a L1479m long fiber. This time window was chosen since it is the longest for which the unwanted effects presented in Fig. 4 are still negligible. The average measured FWHM of the 10 FBGs was 0.66m, and an example can be seen in Fig. 6(c), alongside a simulated theoretical result for this scanned frequency range. The resulting FWHM is in uncanny agreement with the fit from Fig. 5 which predicts a FWHM of 0.67m, and also not far behind the theoretical limit of SFS-OFDR predicts a FWHM of 0.37m. It can clearly be seen that even though a Blackman window was used in the SFS-OFDR process, there are visible sidebands. As stated above, we attribute this to higher harmonics in the modulation process. Nevertheless, these effects are at least 10dB lower than the peak, and for sensing fibers without very high reflectors will be very low. Also visible is a considerable widening of the end of the fiber, contrary to the high reflector in the middle of the fiber. We attribute this to residual imbalance between the I/Q channels which affects the response in the presence of negative beat frequencies, although further research is needed to conclude this. It should be noted that the overall downslope of the reflection profile magnitude is due to the detector’s bandwidth, and not a side-effect of SFS-OFDR.

 figure: Fig. 6

Fig. 6 (a) Reflection profile magnitude obtained via SFS-OFDR on data collected from quarter modulation period time window, (b) a zoom-in on the 10 FBGs, and (c) one of the FBGs’ reflective magnitude as measure, as predicted from theory and as predicted from theory when using Blackman window. The dashed line marks the 3dB points.

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Finally, the dynamical sensing capabilities of SFS-OFDR were tested in two ways: 1. the ability to detect and resolve two closely spaced sinusoidal excitations at acoustical frequencies was tested; 2. the ability to detect and localize an impulse perturbation. For the first test, the excitations were applied to the sensing fiber via a pair of PZT cylinders. The lengths of the wrapped fiber segments was <0.5m and the length of the fiber between them was 1.74m. To demonstrate the spatial resolution of the method for dynamic measurements each of the PZT's was supplied with an AC voltage of a different frequency (1070Hz and 1030Hz) and the system output was recorded during 5000 consecutive scans (namely during a total time of ~238ms). For each scan a window of 9.5μs (20% of the modulation period) was processed (according to Eq. (6)) yielding a time dependent reflection profile. This time window was chosen so that it would provide sufficient resolution to resolve the separate perturbations while not being adversely affected by the presence of higher harmonics (see Sec. 5 below). The dynamical information was obtained from the phase of the reflection profile [12,28]. First the phases of the 5000 consecutive profiles where referenced to the first one. Then, for each of the 5000 profiles, each resolution cell was referenced to the preceding resolution cell, effectively resulting in a differential-phase reflection profile. Next, the time-dependent differential-phase was extracted and Fourier-transformed to yield an acoustic spectrum for each resolution cell along the fiber. The dynamic spatial resolution can be estimated by plotting the magnitudes of these spectra, at the excitation frequencies (1070Hz and 1030Hz), as a function of position (Fig. 7). Since the fiber was exposed to ambient acoustic noise, in addition to the applied excitations, each recording yielded a slightly different graph. Hence, the graphs in Fig. 7 were generated from averages over 50 different measurements and from the corresponding standard deviations.

 figure: Fig. 7

Fig. 7 (a) The magnitudes of the acoustical spectra at 1070Hz and 1030Hz as a function of position. Solid plots are averages over 50 measurements. Dashed plots are the averages plus and minus one standard deviation (b) Zoom-in on the location of the two perturbations.

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It is clearly seen in Fig. 7(a) that there are significant magnitudes at the excitation frequencies only at positions close to the perturbations. In Fig. 7(b) the two perturbations are clearly separated, even with respect to one standard deviation. The measured distance between the two peaks is 1.8m (with a 0.1m sample spacing), in good agreement with the actual spatial separation. At 20% of the modulation period the expected static spatial resolution is Δz0.81m. It should be noted that the two peaks cross one another at ~4dB, suggesting they could indeed be even closer and still be separated, although not as close as Δz0.81m. This difference between the spatial resolution measured in the dynamical and static cases is partially explained by noting that the dynamical data was collected while the system operated with a K(21KHz)=14.8MHz/V PZT conversion coefficient (rather than the 18.7MHz/V with which the static data was collected). Taking this into account we expect a static spatial resolution of Δz1m. Even so, it is clear that the dynamical spatial resolution does not achieve the static one, although it does not fall far behind. In fact, the dynamic spatial resolution is less than twice that of the static one, a major improvement on currently established methods [29]. For the second test, the fiber segment containing the PZT actuators was replaced by a 10msegment from which ~5cmwere buried underneath ~1cmof sand. A paperclip was dropped on the sand from a height of ~5cm. SFS-OFDR (25% processing window) was used to obtain the time-dependent reflection profile of the sensing fiber (can be seen in Fig. 8(a)). For each position along the fiber the variance of the reflection profile was calculated within a moving time window of a 100 modulation periods (a total time of ~4.76ms). This variance as a function of position and time is shown in Fig. 8(b). The inset clearly shows increased variance due to the impact of the paperclip. The width of the detected peak implies ~0.6m dynamic spatial resolution in this case. Figure 8(c) shows the time dependence of the reflection profile at the position of the perturbation (z671.5m). Again the paperclip impact is evident.

 figure: Fig. 8

Fig. 8 (a) Time-dependent reflection profile magnitude, (b) The variance of the reflection profile magnitude in a moving time window of 100 modulation periods with a zoom-in box on: z=655685m; t=0.120.14s, and (c) Time-dependent reflection magnitude at the position of the perturbation.

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5. Discussion

In OFDR there are always nonlinearities entering the scanning mechanism, the most fundamental of which is the laser’s phase noise. When these nonlinearities are not accounted for they severely degrade the spatial resolution. Correctly accounting for these nonlinearities can be rather challenging, and requires auxiliary interferometers to accurately estimate them. In directly-modulated OFDR there is another, more dominant, cause of nonlinearities, which is the scanning mechanism itself. In SFS-OFDR the scan is intentionally performed in a sinusoidal manner. As long as the amplitude of the scan is small enough, the scan mechanism can be approximated as a linear time-invariant system. In contrast to attempting a sawtooth sweep, a sinusoidal profile contains a single frequency, making it the most natural choice for such a system. The method introduced in this paper models only the linear response of the laser, and achieves significant results, which were presented above. However, throughout the paper we have limited ourselves to analyzing data from within a quarter of the modulation period, even though the theoretical analysis predicts better results for larger time ranges. The reason for this seemingly unnecessary limitation is an observed degradation in the results, when using larger time windows. We believe these negative effects to be the consequence of higher harmonics in the scanning mechanism, which are not accounted for by the presented model. Figure 9(a) below shows the phase of a single reflector collected from a full modulation period time window. Notice the clear sinusoidal profile. Figure 9(b) shows the remaining phase after subtracting the first harmonic, i.e. the estimated phase according to the presented model. Indeed the presence of higher harmonics are clearly visible in the reflector’s remaining phase.

 figure: Fig. 9

Fig. 9 (a) The phase of a single reflector, and (b) the remaining phase after subtracting the estimated phase according to SFS-OFDR.

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Figure 10 below shows the SFS-OFDR reflectivity-profile of this single reflector using data from half the modulation period superimposed on a simulated result of SFS-OFDR on a single reflector with second and third harmonics in its phase. The relative amplitude of these high harmonics in the simulation is a2=a3=3103. Although such a relative amplitude might seem negligible, it is actually not, and the effects can clearly be seen in the figure. This is due to the fact that these high harmonics enter in the phase in Eq. (4).

 figure: Fig. 10

Fig. 10 A comparison between the simulated effects of higher harmonics in the modulation process and the results obtained by SFS-OFDR on a half modulation period time window.

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We believe that it is possible to account for these high harmonics by generalizing the model, following the same steps as presented in the theory above.

On a different note, very little work has been done to quantify the bandwidth of OFDR based DAS, and also in this paper we have not addressed the issue in specifics. Nevertheless, as was already noted in the introduction, it is clear that in order to achieve a given bandwidth, using the Nyquist-imposed repetition rate is not enough. In this realization lies another advantage of SFS-OFDR. By using a sinusoidal internal modulation one fairly easily achieve very high repetition rates as well as short sweep times. It is also noteworthy that as far as SFS-OFDR is concerned working with very short sweep times need not impair the spatial resolution, since it is possible to keep the interrogation time constant and simply modulate with a higher frequency. For example, assuming that in order to have a bandwidth of fm=10KHz a sweep time of Ts=102(fm)1=106s is required, one can interrogate over 25% of a fr=250KHz modulation period, or even 50% of a fr=500KHz modulation period. These modulation frequencies are still fairly low and can easily be generated by everyday RF generators. It should be noted that the modulation frequency can reach values of ~250KHz with a 25% time window still two orders of magnitude larger than the equivalent (spatial resolution wise) OTDR pulse. However, as can be seen in the Appendix, the weight function g(z,z') is periodic with a period of vg/(2fr). This poses a limitation on the fiber length that becomes more severe as the repetition rate increases: L<vg/(2fr)108/fr. In practice, when attempting to reach this limit in the lab we have encountered a more severe limit which we believe is the result of the higher harmonics in the modulation process. Obviously the issue of bandwidth in OFDR and SFS-OFDR based DAS should be subject to further research.

6. Conclusion

In this work a novel method for implementing high spatial resolution DAS was studied. The method, Sinusoidal Frequency Scan OFDR (SFS-OFDR), has several significant advantages over competing methods for implementing DAS. First, as a variant of OFDR it offers superior SNR and spatial resolution in comparison with OTDR based methods. Second, in contrast with other OFDR systems, it can provide high spatial resolution alongside with high scan rates while maintaining trivial requirements from the needed RF generator and a simple design which does not require an auxiliary interferometer. The method experimentally achieved 0.66m static spatial resolution at a sweep repetition rate of 21KHz and interrogation time window of ~12μs along a fiber of L1479m, thus producing over 4.7107 resolution cells per second. Furthermore, the method experimentally achieved a 4dB separation between two 1KHz perturbations, 1.74m apart and located the fall of a paperclip with 0.6m resolution.

Appendix

By substituting Eq. (4) into Eq. (6) an integral form for g(z,z') is obtained:

g(z,z')=AT2T2exp{iπΔFωr[cos(ωr(t2z'vg))cos(ωr(t2zvg))]}dt
Via a few algebraic manipulations it can be expressed as:
g(z,z')=AT2T2exp{iH(zz')sin[ωrt+F(z+z')]}dt
where H(zz')=2πΔFωrsin[ωrvg(zz')], and F(z+z')=ωrvg(Lzz') are both independent of the integration variable.

First we may consider the special case where T is chosen such that it is equal to the full modulation period. In this case the phase shift F(z+z') is irrelevant (the integrand is periodic over the integration range) and the integral is readily solved to give:

g(z,z')=Aωrππexp[iH(zz')sin(x)]dx=2πAωrJ0[H(zz')]
where J0[x] is zeroth order Bessel function of the first kind. Using the definition of two points being resolved if one's peak coincides with the other's first zero, as customary for OFDR, we obtain a theoretical spatial resolution of:
Δz=vgωrsin1(β1frΔF)0.77vg2ΔF
where β12.4048 is the first zero of J0[x].

A more interesting case is when T is chosen such that it is equal to the half the modulation period. It is a model case since it is the shortest time range to achieves the full offered ΔF. In this case we consider the real and imaginary parts of g(z,z') separately. The real part of g(z,z') is actually periodic in half the modulation period. Thus, again the phase shift F(z,z') is irrelevant, and the integral is readily solved to give:

Re{g(z,z')}=Aωrπ2π2cos{H(zz')sin[x+F(z+z')]}dx=πAωrJ0[H(zz')]
As for the imaginary part of g(z,z'), via some algebraic manipulations it can be written as:
Im{g(z,z')}=2Aωr0F(z+z')sin[H(zz')sin(x)]dx
This integral is not easily solved. Figure 11 below shows some simulations of g(z,z') for the case of T=Tr/2 as well as other cases. It is easy to see from the simulations that the imaginary part of g(z,z') is negligible in comparison to its real part. This can be understood by considering F(z+z') and H(zz'). First we note that typical repetition rates are ωr104Hz, so ωr/vg104m1, and F(z+z')(Lzz')104. When |F(z+z')|1, namely (z+z')L, we can expand the integrand to first order and find:
Im{g(z,z')}2Aωr0F(z,z')sin[H(zz')x]dx=2A{1cos[H(zz')F(z+z')]}H(zz')ωr
Since H(zz') appears in the denominator, if it is very large the imaginary part is indeed negligible. If H(zz') is very small then the numerator vanishes and again we find the imaginary part to be negligible:
limH(zz')02{1cos[H(zz')F(z+z')]}H(zz')=0
When |F(z+z')|1, namely (z+z')0,2L and L104m, then either both z and z' are close to zero or both are close to L. In any case (zz')104 and we can expand H(zz') to first order and find:
H(zz')2πΔFvg(zz')
Usually ΔF109Hz, so ΔF/vg10m1, and H(zz')10(zz'). In this case we find:
Im{g(z,z')}2Aωr01sin[10(zz')sin(x)]dx
For (zz')>˜1m the integrand oscillates rapidly, and thus the result is negligible. For (zz')<˜101m the integral can be solved numerically to give Im{g(z,z')}~2A/ωr, which is not negligible in comparison to the real part. However, this is of no consequence, since for (zz')<˜101 we wish to obtain a large contribution to g(z,z').

 figure: Fig. 11

Fig. 11 Simulated form of the weight function g(z,z') for (a) the case of T=Tr/2 and ωr=2π20KHz, (b) the case of T=Tr/5 and ωr=2π20KHz, and (c) the case ofT=Tr/5 and ωr=2π50KHz.

Download Full Size | PPT Slide | PDF

Figure 11 depicts some simulations of g(z,z') with various parameters. For numerical reasons, in all the simulations we set ΔF=100MHz and L=5km. Figure 11(a) depicts the case of T=Tr/2 analyzed above and ωr=2π20KHz. Figures 10(b) and 11(c) were calculated with T=Tr/5, as was used for the presented dynamical results. In Fig. 11(b) ωr=2π20KHz, while in 10.d ωr=2π50KHz. Notice that for T=Tr/5 (this is actually true for any T<Tr/2), g(z,z') rises to plateaus according to the value of F(z+z'), and shows secondary maxima according to the value of H(zz'). However, these plateau and secondary maxima are still 2030dB below the primary peak, and will not affect the Rayleigh reflection profile.

Acknowledgment

This research was supported in part by the Ministry of Science, Technology & Space, Israel.

References and links

1. Z. Zhou and S. Zhuang, “Optical fiber distributed vibration sensing system using time-varying gain amplification method,” Opt. Eng. 53(8), 086107 (2014). [CrossRef]  

2. Z. Qin, L. Chen, and X. Bao, “Distributed vibration/acoustic sensing with high frequency response and spatial resolution based on time-division multiplexing,” Opt. Commun. 331, 287–290 (2014). [CrossRef]  

3. A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014). [CrossRef]  

4. A. Hartog, B. Frignet, D. Mackie, and M. Clark, “Vertical seismic optical profiling on wireline logging cable,” Geophys. Prospect. 62(4), 693–701 (2014). [CrossRef]  

5. Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013). [CrossRef]  

6. M. M. Molenaar, D. J. Hill, P. Webster, E. Fidan, and B. Birch, “First downhole application of distributed acoustic sensing for hydraulic-fracturing monitoring and diagnostics,” SPE Drill. Complet. 27(1), 32–38 (2012). [CrossRef]  

7. Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration vensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

8. F. Tanimola and D. Hill, “Distributed fibre optic sensors for pipeline protection,” J. Nat. Gas Sci. Eng. 1(4–5), 134–143 (2009). [CrossRef]  

9. M. K. Barnoski and S. M. Jensen, “Fiber waveguides: a novel technique for investigating attenuation characteristics,” Appl. Opt. 15(9), 2112–2115 (1976). [CrossRef]   [PubMed]  

10. M. Tateda and T. Horiguchi, “Advances in optical time-domain reflectometry,” J. Lightwave Technol. 7(8), 1217–1224 (1989). [CrossRef]  

11. D. P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express 20(12), 13138–13145 (2012). [CrossRef]   [PubMed]  

12. D. Arbel and A. Eyal, “Dynamic optical frequency domain reflectometry,” Opt. Express 22(8), 8823–8830 (2014). [CrossRef]   [PubMed]  

13. A. B. Am, D. Arbel, and A. Eyal, “OFDR with double interrogation for dynamic quasi-distributed sensing,” Opt. Express 22(3), 2299–2308 (2014). [CrossRef]   [PubMed]  

14. W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981). [CrossRef]  

15. B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” in Proceedings of IEEE Conference on Avionics Fiber-Optics and Photonics (IEEE, 2006), pp. 38–39. [CrossRef]  

16. H. Barfuss and E. Brinkmeyer, “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” J. Lightwave Technol. 7(1), 3–10 (1989). [CrossRef]  

17. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005). [CrossRef]   [PubMed]  

18. G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett. 32(10), 926–927 (1996). [CrossRef]  

19. K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator,” IEEE Photonic. Tech. L. 7(7), 804–806 (1995). [CrossRef]  

20. X. Fan, Y. Koshikiya, and F. Ito, “Centimeter-level spatial resolution over 40 km realized by bandwidth-division phase-noise-compensated OFDR,” Opt. Express 19(20), 19122–19128 (2011). [CrossRef]   [PubMed]  

21. X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett. 32(22), 3227–3229 (2007). [CrossRef]   [PubMed]  

22. F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol. 30(8), 1015–1024 (2012). [CrossRef]  

23. R. Passy, N. Gisin, J. P. von derWeid, and H. H. Gilgen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12(9), 1622–1630 (1994). [CrossRef]  

24. C. Jihong Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photonic. Tech. L. 17(9), 1827–1829 (2005). [CrossRef]  

25. C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013). [CrossRef]  

26. O. Y. Sagiv, D. Arbel, and A. Eyal, “Correcting for spatial-resolution degradation mechanisms in OFDR via inline auxiliary points,” Opt. Express 20(25), 27465–27472 (2012). [CrossRef]   [PubMed]  

27. H. Gabai, Y. Botsev, M. Hahami, and A. Eyal, “Optical frequency domain reflectometry at maximum update rate using I/Q detection,” Opt. Lett. 40(8), 1725–1728 (2015). [CrossRef]   [PubMed]  

28. A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013). [CrossRef]  

29. Z. Ding, X. S. Yao, T. Liu, Y. Du, K. Liu, Q. Han, Z. Meng, and H. Chen, “Long-range vibration sensor based on correlation analysis of optical frequency-domain reflectometry signals,” Opt. Express 20(27), 28319–28329 (2012). [CrossRef]   [PubMed]  

References

  • View by:

  1. Z. Zhou and S. Zhuang, “Optical fiber distributed vibration sensing system using time-varying gain amplification method,” Opt. Eng. 53(8), 086107 (2014).
    [Crossref]
  2. Z. Qin, L. Chen, and X. Bao, “Distributed vibration/acoustic sensing with high frequency response and spatial resolution based on time-division multiplexing,” Opt. Commun. 331, 287–290 (2014).
    [Crossref]
  3. A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
    [Crossref]
  4. A. Hartog, B. Frignet, D. Mackie, and M. Clark, “Vertical seismic optical profiling on wireline logging cable,” Geophys. Prospect. 62(4), 693–701 (2014).
    [Crossref]
  5. Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013).
    [Crossref]
  6. M. M. Molenaar, D. J. Hill, P. Webster, E. Fidan, and B. Birch, “First downhole application of distributed acoustic sensing for hydraulic-fracturing monitoring and diagnostics,” SPE Drill. Complet. 27(1), 32–38 (2012).
    [Crossref]
  7. Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration vensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).
  8. F. Tanimola and D. Hill, “Distributed fibre optic sensors for pipeline protection,” J. Nat. Gas Sci. Eng. 1(4–5), 134–143 (2009).
    [Crossref]
  9. M. K. Barnoski and S. M. Jensen, “Fiber waveguides: a novel technique for investigating attenuation characteristics,” Appl. Opt. 15(9), 2112–2115 (1976).
    [Crossref] [PubMed]
  10. M. Tateda and T. Horiguchi, “Advances in optical time-domain reflectometry,” J. Lightwave Technol. 7(8), 1217–1224 (1989).
    [Crossref]
  11. D. P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express 20(12), 13138–13145 (2012).
    [Crossref] [PubMed]
  12. D. Arbel and A. Eyal, “Dynamic optical frequency domain reflectometry,” Opt. Express 22(8), 8823–8830 (2014).
    [Crossref] [PubMed]
  13. A. B. Am, D. Arbel, and A. Eyal, “OFDR with double interrogation for dynamic quasi-distributed sensing,” Opt. Express 22(3), 2299–2308 (2014).
    [Crossref] [PubMed]
  14. W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
    [Crossref]
  15. B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” in Proceedings of IEEE Conference on Avionics Fiber-Optics and Photonics (IEEE, 2006), pp. 38–39.
    [Crossref]
  16. H. Barfuss and E. Brinkmeyer, “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” J. Lightwave Technol. 7(1), 3–10 (1989).
    [Crossref]
  17. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005).
    [Crossref] [PubMed]
  18. G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett. 32(10), 926–927 (1996).
    [Crossref]
  19. K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator,” IEEE Photonic. Tech. L. 7(7), 804–806 (1995).
    [Crossref]
  20. X. Fan, Y. Koshikiya, and F. Ito, “Centimeter-level spatial resolution over 40 km realized by bandwidth-division phase-noise-compensated OFDR,” Opt. Express 19(20), 19122–19128 (2011).
    [Crossref] [PubMed]
  21. X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett. 32(22), 3227–3229 (2007).
    [Crossref] [PubMed]
  22. F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol. 30(8), 1015–1024 (2012).
    [Crossref]
  23. R. Passy, N. Gisin, J. P. von derWeid, and H. H. Gilgen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12(9), 1622–1630 (1994).
    [Crossref]
  24. C. Jihong Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photonic. Tech. L. 17(9), 1827–1829 (2005).
    [Crossref]
  25. C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
    [Crossref]
  26. O. Y. Sagiv, D. Arbel, and A. Eyal, “Correcting for spatial-resolution degradation mechanisms in OFDR via inline auxiliary points,” Opt. Express 20(25), 27465–27472 (2012).
    [Crossref] [PubMed]
  27. H. Gabai, Y. Botsev, M. Hahami, and A. Eyal, “Optical frequency domain reflectometry at maximum update rate using I/Q detection,” Opt. Lett. 40(8), 1725–1728 (2015).
    [Crossref] [PubMed]
  28. A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
    [Crossref]
  29. Z. Ding, X. S. Yao, T. Liu, Y. Du, K. Liu, Q. Han, Z. Meng, and H. Chen, “Long-range vibration sensor based on correlation analysis of optical frequency-domain reflectometry signals,” Opt. Express 20(27), 28319–28329 (2012).
    [Crossref] [PubMed]

2015 (1)

2014 (6)

Z. Zhou and S. Zhuang, “Optical fiber distributed vibration sensing system using time-varying gain amplification method,” Opt. Eng. 53(8), 086107 (2014).
[Crossref]

Z. Qin, L. Chen, and X. Bao, “Distributed vibration/acoustic sensing with high frequency response and spatial resolution based on time-division multiplexing,” Opt. Commun. 331, 287–290 (2014).
[Crossref]

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

A. Hartog, B. Frignet, D. Mackie, and M. Clark, “Vertical seismic optical profiling on wireline logging cable,” Geophys. Prospect. 62(4), 693–701 (2014).
[Crossref]

D. Arbel and A. Eyal, “Dynamic optical frequency domain reflectometry,” Opt. Express 22(8), 8823–8830 (2014).
[Crossref] [PubMed]

A. B. Am, D. Arbel, and A. Eyal, “OFDR with double interrogation for dynamic quasi-distributed sensing,” Opt. Express 22(3), 2299–2308 (2014).
[Crossref] [PubMed]

2013 (3)

Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013).
[Crossref]

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

2012 (5)

2011 (1)

2010 (1)

2009 (1)

F. Tanimola and D. Hill, “Distributed fibre optic sensors for pipeline protection,” J. Nat. Gas Sci. Eng. 1(4–5), 134–143 (2009).
[Crossref]

2007 (1)

2005 (2)

B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005).
[Crossref] [PubMed]

C. Jihong Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photonic. Tech. L. 17(9), 1827–1829 (2005).
[Crossref]

1996 (1)

G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett. 32(10), 926–927 (1996).
[Crossref]

1995 (1)

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator,” IEEE Photonic. Tech. L. 7(7), 804–806 (1995).
[Crossref]

1994 (1)

R. Passy, N. Gisin, J. P. von derWeid, and H. H. Gilgen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12(9), 1622–1630 (1994).
[Crossref]

1989 (2)

H. Barfuss and E. Brinkmeyer, “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” J. Lightwave Technol. 7(1), 3–10 (1989).
[Crossref]

M. Tateda and T. Horiguchi, “Advances in optical time-domain reflectometry,” J. Lightwave Technol. 7(8), 1217–1224 (1989).
[Crossref]

1981 (1)

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

1976 (1)

Am, A. B.

Arbel, D.

Bao, X.

Z. Qin, L. Chen, and X. Bao, “Distributed vibration/acoustic sensing with high frequency response and spatial resolution based on time-division multiplexing,” Opt. Commun. 331, 287–290 (2014).
[Crossref]

Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013).
[Crossref]

D. P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express 20(12), 13138–13145 (2012).
[Crossref] [PubMed]

Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration vensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

Barfuss, H.

H. Barfuss and E. Brinkmeyer, “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” J. Lightwave Technol. 7(1), 3–10 (1989).
[Crossref]

Barnoski, M. K.

Belal, M.

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Berlang, W.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Birch, B.

M. M. Molenaar, D. J. Hill, P. Webster, E. Fidan, and B. Birch, “First downhole application of distributed acoustic sensing for hydraulic-fracturing monitoring and diagnostics,” SPE Drill. Complet. 27(1), 32–38 (2012).
[Crossref]

Botsev, Y.

Brinkmeyer, E.

H. Barfuss and E. Brinkmeyer, “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” J. Lightwave Technol. 7(1), 3–10 (1989).
[Crossref]

Chen, H.

Chen, L.

Clark, M.

A. Hartog, B. Frignet, D. Mackie, and M. Clark, “Vertical seismic optical profiling on wireline logging cable,” Geophys. Prospect. 62(4), 693–701 (2014).
[Crossref]

Cox, B.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Detomo, R.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Diao, D.

Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013).
[Crossref]

Ding, Z.

Du, Y.

Eickhoff, W.

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

Eyal, A.

Fan, X.

Feng, Z.

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

Fidan, E.

M. M. Molenaar, D. J. Hill, P. Webster, E. Fidan, and B. Birch, “First downhole application of distributed acoustic sensing for hydraulic-fracturing monitoring and diagnostics,” SPE Drill. Complet. 27(1), 32–38 (2012).
[Crossref]

Frignet, B.

A. Hartog, B. Frignet, D. Mackie, and M. Clark, “Vertical seismic optical profiling on wireline logging cable,” Geophys. Prospect. 62(4), 693–701 (2014).
[Crossref]

Froggatt, M.

B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005).
[Crossref] [PubMed]

B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” in Proceedings of IEEE Conference on Avionics Fiber-Optics and Photonics (IEEE, 2006), pp. 38–39.
[Crossref]

Gabai, H.

Gifford, D.

B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005).
[Crossref] [PubMed]

B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” in Proceedings of IEEE Conference on Avionics Fiber-Optics and Photonics (IEEE, 2006), pp. 38–39.
[Crossref]

Gilgen, H. H.

R. Passy, N. Gisin, J. P. von derWeid, and H. H. Gilgen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12(9), 1622–1630 (1994).
[Crossref]

Gisin, N.

G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett. 32(10), 926–927 (1996).
[Crossref]

R. Passy, N. Gisin, J. P. von derWeid, and H. H. Gilgen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12(9), 1622–1630 (1994).
[Crossref]

Grandi, S.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Hahami, M.

Han, Q.

Hartog, A.

A. Hartog, B. Frignet, D. Mackie, and M. Clark, “Vertical seismic optical profiling on wireline logging cable,” Geophys. Prospect. 62(4), 693–701 (2014).
[Crossref]

He, Q.

Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013).
[Crossref]

Hill, D.

F. Tanimola and D. Hill, “Distributed fibre optic sensors for pipeline protection,” J. Nat. Gas Sci. Eng. 1(4–5), 134–143 (2009).
[Crossref]

Hill, D. J.

M. M. Molenaar, D. J. Hill, P. Webster, E. Fidan, and B. Birch, “First downhole application of distributed acoustic sensing for hydraulic-fracturing monitoring and diagnostics,” SPE Drill. Complet. 27(1), 32–38 (2012).
[Crossref]

Horiguchi, T.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator,” IEEE Photonic. Tech. L. 7(7), 804–806 (1995).
[Crossref]

M. Tateda and T. Horiguchi, “Advances in optical time-domain reflectometry,” J. Lightwave Technol. 7(8), 1217–1224 (1989).
[Crossref]

Hornman, K.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Ito, F.

Jensen, S. M.

Jiang, S.

C. Jihong Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photonic. Tech. L. 17(9), 1827–1829 (2005).
[Crossref]

Jihong Geng, C.

C. Jihong Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photonic. Tech. L. 17(9), 1827–1829 (2005).
[Crossref]

Kiyashchenko, D.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Koshikiya, Y.

Koyamada, Y.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator,” IEEE Photonic. Tech. L. 7(7), 804–806 (1995).
[Crossref]

Kreger, S.

B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” in Proceedings of IEEE Conference on Avionics Fiber-Optics and Photonics (IEEE, 2006), pp. 38–39.
[Crossref]

Li, C.

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

Li, W.

Liu, K.

Liu, T.

Lopez, J.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Lu, Y.

Mackie, D.

A. Hartog, B. Frignet, D. Mackie, and M. Clark, “Vertical seismic optical profiling on wireline logging cable,” Geophys. Prospect. 62(4), 693–701 (2014).
[Crossref]

Masoudi, A.

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Mateeva, A.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Meng, Z.

Mestayer, J.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Mo, S.

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

Molenaar, M. M.

M. M. Molenaar, D. J. Hill, P. Webster, E. Fidan, and B. Birch, “First downhole application of distributed acoustic sensing for hydraulic-fracturing monitoring and diagnostics,” SPE Drill. Complet. 27(1), 32–38 (2012).
[Crossref]

Mussi, G.

G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett. 32(10), 926–927 (1996).
[Crossref]

Newson, T. P.

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Passy, R.

G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett. 32(10), 926–927 (1996).
[Crossref]

R. Passy, N. Gisin, J. P. von derWeid, and H. H. Gilgen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12(9), 1622–1630 (1994).
[Crossref]

Potters, H.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Qin, Z.

Z. Qin, L. Chen, and X. Bao, “Distributed vibration/acoustic sensing with high frequency response and spatial resolution based on time-division multiplexing,” Opt. Commun. 331, 287–290 (2014).
[Crossref]

D. P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express 20(12), 13138–13145 (2012).
[Crossref] [PubMed]

Sagiv, O. Y.

Shimizu, K.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator,” IEEE Photonic. Tech. L. 7(7), 804–806 (1995).
[Crossref]

Soller, B.

B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005).
[Crossref] [PubMed]

B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” in Proceedings of IEEE Conference on Avionics Fiber-Optics and Photonics (IEEE, 2006), pp. 38–39.
[Crossref]

Spiegelberg, C.

C. Jihong Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photonic. Tech. L. 17(9), 1827–1829 (2005).
[Crossref]

Tanimola, F.

F. Tanimola and D. Hill, “Distributed fibre optic sensors for pipeline protection,” J. Nat. Gas Sci. Eng. 1(4–5), 134–143 (2009).
[Crossref]

Tateda, M.

M. Tateda and T. Horiguchi, “Advances in optical time-domain reflectometry,” J. Lightwave Technol. 7(8), 1217–1224 (1989).
[Crossref]

Tsuji, K.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator,” IEEE Photonic. Tech. L. 7(7), 804–806 (1995).
[Crossref]

Ulrich, R.

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

von derWeid, J. P.

G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett. 32(10), 926–927 (1996).
[Crossref]

R. Passy, N. Gisin, J. P. von derWeid, and H. H. Gilgen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12(9), 1622–1630 (1994).
[Crossref]

Webster, P.

M. M. Molenaar, D. J. Hill, P. Webster, E. Fidan, and B. Birch, “First downhole application of distributed acoustic sensing for hydraulic-fracturing monitoring and diagnostics,” SPE Drill. Complet. 27(1), 32–38 (2012).
[Crossref]

Wills, P.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

Wolfe, M.

B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005).
[Crossref] [PubMed]

B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” in Proceedings of IEEE Conference on Avionics Fiber-Optics and Photonics (IEEE, 2006), pp. 38–39.
[Crossref]

Xiao, X.

Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013).
[Crossref]

Xu, S.

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

Yang, C.

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

Yang, Z.

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

Yao, X. S.

Zhan, B.

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

Zhang, B.

Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013).
[Crossref]

Zhang, W.

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

Zhou, D. P.

Zhou, Z.

Z. Zhou and S. Zhuang, “Optical fiber distributed vibration sensing system using time-varying gain amplification method,” Opt. Eng. 53(8), 086107 (2014).
[Crossref]

Zhu, T.

Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013).
[Crossref]

Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration vensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

Zhuang, S.

Z. Zhou and S. Zhuang, “Optical fiber distributed vibration sensing system using time-varying gain amplification method,” Opt. Eng. 53(8), 086107 (2014).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

Electron. Lett. (1)

G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett. 32(10), 926–927 (1996).
[Crossref]

Geophys. Prospect. (2)

A. Mateeva, J. Lopez, H. Potters, J. Mestayer, B. Cox, D. Kiyashchenko, P. Wills, S. Grandi, K. Hornman, W. Berlang, Z. Yang, and R. Detomo, “Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling,” Geophys. Prospect. 62(4), 679–692 (2014).
[Crossref]

A. Hartog, B. Frignet, D. Mackie, and M. Clark, “Vertical seismic optical profiling on wireline logging cable,” Geophys. Prospect. 62(4), 693–701 (2014).
[Crossref]

IEEE Photonic. Tech. L. (3)

Q. He, T. Zhu, X. Xiao, B. Zhang, D. Diao, and X. Bao, “All fiber distributed vibration sensing using modulated time-difference pulses,” IEEE Photonic. Tech. L. 25(20), 1955–1957 (2013).
[Crossref]

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator,” IEEE Photonic. Tech. L. 7(7), 804–806 (1995).
[Crossref]

C. Jihong Geng, C. Spiegelberg, and S. Jiang, “Narrow linewidth fiber laser for 100-km optical frequency domain reflectometry,” IEEE Photonic. Tech. L. 17(9), 1827–1829 (2005).
[Crossref]

J. Lightwave Technol. (5)

F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol. 30(8), 1015–1024 (2012).
[Crossref]

R. Passy, N. Gisin, J. P. von derWeid, and H. H. Gilgen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12(9), 1622–1630 (1994).
[Crossref]

Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration vensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

H. Barfuss and E. Brinkmeyer, “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” J. Lightwave Technol. 7(1), 3–10 (1989).
[Crossref]

M. Tateda and T. Horiguchi, “Advances in optical time-domain reflectometry,” J. Lightwave Technol. 7(8), 1217–1224 (1989).
[Crossref]

J. Nat. Gas Sci. Eng. (1)

F. Tanimola and D. Hill, “Distributed fibre optic sensors for pipeline protection,” J. Nat. Gas Sci. Eng. 1(4–5), 134–143 (2009).
[Crossref]

Laser Phys. Lett. (1)

C. Li, S. Xu, S. Mo, B. Zhan, W. Zhang, C. Yang, Z. Feng, and Z. Yang, “A linearly frequency modulated narrow linewidth single-frequency fiber laser,” Laser Phys. Lett. 10(7), 075106 (2013).
[Crossref]

Meas. Sci. Technol. (1)

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Opt. Commun. (1)

Z. Qin, L. Chen, and X. Bao, “Distributed vibration/acoustic sensing with high frequency response and spatial resolution based on time-division multiplexing,” Opt. Commun. 331, 287–290 (2014).
[Crossref]

Opt. Eng. (1)

Z. Zhou and S. Zhuang, “Optical fiber distributed vibration sensing system using time-varying gain amplification method,” Opt. Eng. 53(8), 086107 (2014).
[Crossref]

Opt. Express (7)

Opt. Lett. (2)

SPE Drill. Complet. (1)

M. M. Molenaar, D. J. Hill, P. Webster, E. Fidan, and B. Birch, “First downhole application of distributed acoustic sensing for hydraulic-fracturing monitoring and diagnostics,” SPE Drill. Complet. 27(1), 32–38 (2012).
[Crossref]

Other (1)

B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” in Proceedings of IEEE Conference on Avionics Fiber-Optics and Photonics (IEEE, 2006), pp. 38–39.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 The experimental setup.
Fig. 2
Fig. 2 Reflection profile magnitude obtained via OFDR on the data collected from (a) the 3.57μs time window, and (c) the 10.71μs time window. A zoom-in to the 10 FBGs for (b) the 3.57μs time window, and (d) the 10.71μs time window.
Fig. 3
Fig. 3 Reflection profile magnitude obtained via SFS-OFDR on the data collected from (a) the 3.57μs time window, and (c) the 10.71μs time window. A zoom-in to the 10 FBGs for (b) the 3.57μs time window, and (d) the 10.71μs time window.
Fig. 4
Fig. 4 (a) One of the FBGs’ peaks as obtained by various time windows specified as percentages out of the full modulation period. (b) Zoom in on the peaks up to the 3dB width.
Fig. 5
Fig. 5 FWHM of one of the FBGs as a function of the scanned BW and time window, as percentage from the modulation period, for the measured data and simulated results.
Fig. 6
Fig. 6 (a) Reflection profile magnitude obtained via SFS-OFDR on data collected from quarter modulation period time window, (b) a zoom-in on the 10 FBGs, and (c) one of the FBGs’ reflective magnitude as measure, as predicted from theory and as predicted from theory when using Blackman window. The dashed line marks the 3dB points.
Fig. 7
Fig. 7 (a) The magnitudes of the acoustical spectra at 1070Hz and 1030Hz as a function of position. Solid plots are averages over 50 measurements. Dashed plots are the averages plus and minus one standard deviation (b) Zoom-in on the location of the two perturbations.
Fig. 8
Fig. 8 (a) Time-dependent reflection profile magnitude, (b) The variance of the reflection profile magnitude in a moving time window of 100 modulation periods with a zoom-in box on: z=655685m ; t=0.120.14s , and (c) Time-dependent reflection magnitude at the position of the perturbation.
Fig. 9
Fig. 9 (a) The phase of a single reflector, and (b) the remaining phase after subtracting the estimated phase according to SFS-OFDR.
Fig. 10
Fig. 10 A comparison between the simulated effects of higher harmonics in the modulation process and the results obtained by SFS-OFDR on a half modulation period time window.
Fig. 11
Fig. 11 Simulated form of the weight function g( z,z' ) for (a) the case of T= T r /2 and ω r =2π20 KHz , (b) the case of T= T r /5 and ω r =2π20 KHz , and (c) the case of T= T r /5 and ω r =2π50 KHz .

Equations (17)

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f inst ( t )= f 0 + ΔF 2 sin( ω r t )
E in ( t )= E 0 exp[ i2π t f inst ( t' )dt' ]= E 0 exp{ i2π[ f 0 t ΔF 2 ω r cos( ω r t ) ] }
E B ( t )= 0 L ρ( z' ) E in ( t 2z' v g )exp[ iϕ( z' ) ]dz'
V( t )=A 0 L ρ ˜ ( z' )exp{ i πΔF ω r [ cos( ω r ( t 2z' v g ) )cos( ω r t ) ] }dz'
ρ ˜ ( z )= ρ ˜ ( z )exp{ i[ ω 0 2z v g ϕ( z ) ] }
ρ ˜ ^ ( z )= T 2 T 2 V( t )exp{ i πΔF ω r [ cos( ω r ( t 2z v g ) )cos( ω r t ) ] }dt
ρ ˜ ^ ( z )= 0 L ρ ˜ ( z' )g( z,z' )dz'
g( z,z' )=A T 2 T 2 exp{ i πΔF ω r [ cos( ω r ( t 2z' v g ) )cos( ω r ( t 2z v g ) ) ] }dt
g( z,z' )=A T 2 T 2 exp{ iH( zz' )sin[ ω r t+F( z+z' ) ] }dt
g( z,z' )= A ω r π π exp[ iH( zz' )sin( x ) ]dx = 2πA ω r J 0 [ H( zz' ) ]
Δz= v g ω r sin 1 ( β 1 f r ΔF )0.77 v g 2ΔF
Re{ g( z,z' ) }= A ω r π 2 π 2 cos{ H( zz' )sin[ x+F( z+z' ) ] }dx = πA ω r J 0 [ H( zz' ) ]
Im{ g( z,z' ) }= 2A ω r 0 F( z+z' ) sin[ H( zz' )sin( x ) ]dx
Im{ g( z,z' ) } 2A ω r 0 F( z,z' ) sin[ H( zz' )x ]dx= 2A{ 1cos[ H( zz' )F( z+z' ) ] } H( zz' ) ω r
li m H( zz' )0 2{ 1cos[ H( zz' )F( z+z' ) ] } H( zz' ) =0
H( zz' ) 2πΔF v g ( zz' )
Im{ g( z,z' ) } 2A ω r 0 1 sin[ 10( zz' )sin( x ) ]dx

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