Dynamic optical frequency domain reflectometry

Dror Arbel; Avishay Eyal

doi:10.1364/OE.22.008823

1. Introduction

Fiber optical reflectometry techniques for intrusion detection, distributed vibration sensing and distributed acoustical sensing are attracting a lot of attention in recent years. In many cases the system comprises a single single-mode or polarization maintaining sensing fiber and an interrogator which produces the interrogation signal and receives the returning signals from the sensing fiber [1–10]. Among the various reflectometry techniques phase-sensitive methods can obtain the highest sensitivity. In this family of methods some form of coherent mixing of waves is used to provide optical phase information. In Phase-Sensitive Optical Time Domain Reflectometry (ϕ-OTDR) temporal phase variations are transformed into measurable intensity fluctuations by using a source whose coherence length is longer than a spatial resolution cell and a direct detection receiver [1]. In this approach the unresolved backreflected components from a given resolution cell interfere coherently. This results in a spackle-like backscatter profile. The temporal variations of the backscatter profile are correlated with the external perturbations that affect the respective fiber position and can be used for extracting local mechanical information. The main advantage of this approach is its simplicity. The main disadvantage is the relatively low sensitivity of direct detection which may limit the range and refresh rate of the sensor. A more sensitive configuration is coherent-detection phase-sensitive OTDR [5]. In this technique the backscattered lightwaves are mixed with a reference and detected by a balanced receiver. OTDR-based methods have inherent tradeoff between spatial resolution and Signal to Noise Ratio (SNR) and dynamic range. This is because higher resolution requires shorter pulses. But for a given maximum peak power the pulse cannot be shortened without reducing the pulse energy and hence the SNR. In contrast, Optical Frequency Domain Reflectometry (OFDR) techniques can facilitate increased SNR without sacrificing spatial resolution or resorting to long averaging periods. The reason for that is that the spatial resolution in OFDR is determined only by the frequency scan range of the interrogating signal. Thus longer and more energetic interrogation pulses can be used while maintaining high resolution.

Despite its significant advantages in SNR, dynamic range and spatial resolution OFDR was rarely used for dynamic sensing. Zhou et. al. demonstrated dynamic strain sensing via time resolved OFDR in short segments of fibers (~17m) at low frequency (0-32Hz) [9]. Recently we described OFDR dynamical strain sensing in fibers with discrete reflectors [11]. Ding et. al. demonstrated detection of vibrations over 12km fiber with frequencies up to 2KHz by cross-correlating vibrated and un-vibrated sensor states [12]. While the method is long-range and dynamic the need for measurement of two states and for digital implementation of cross-correlation is a drawback in many real-time applications. One of the reasons for the relatively few demonstrations of long-range dynamic OFDR sensing may be the use of a trigger interferometer which is typically employed to overcome the laser tuning errors. Its use limits the length of the sensing fiber due to sampling rate considerations. Recent efforts to overcome this limitation required signal processing that limited real time monitoring [13–15]. In [14, 15] the effect of acoustic phase noise on OFDR measurement was analyzed and demonstrated but no attempt was made to use the measurement for acoustical sensing.

In this paper we describe a dynamic Optical Frequency Domain Reflectometry (OFDR) system which enables real time, long range, acoustic sensing at high sampling rate. The system is based on a fast scanning laser and coherent detection scheme. It is similar to the system we described in [14] but replacement of the data acquisition card and the function generator enabled 2 orders of magnitude increase in the sampling rate and frequency sweep rates. This facilitated dynamic measurements of the sensing fiber rather than its static characterization as was performed in ref [14]. Tuning correction is not implemented as the tuning range of the laser is set to few megahertz. This relatively short scan range limits the spatial resolution of system to few tens of meters but ensures that the scan will be sufficiently linear and enables real time operation. Moreover, as the system operates with a fast frequency sweep rate (~1012 Hz/s) the length of the time window recorded in every scan can be kept rather short (16μs) while achieving the targeted resolution. This ensures that acoustically induced phase variations during a single scan remain small. The induced changes in the phase can be observed from one scan to the next. This is in contrast with the works described in ref [11, 12] where the sweep rates were much slower. In ref [12], for example, the laser sweep rate was about 3 orders of magnitude smaller than in this work and the sweep duration was much longer. This means that it operated in a completely different regime. While in long-sweep methods vibrations appear as sidebands in the spatial response derived from a single scan, in the current short-sweep method there are no sidebands and vibrations are manifested as variations between spatial responses of consecutive scans. This is a fundamental difference since sidebands of two simultaneous closely located vibration events can interfere and prohibit accurate detection. The system was used to measure the Rayleigh scattering in conventional single mode fibers as a function of time. As common in OFDR the output of the coherent detector is Fourier transformed and the magnitude is displayed. Each spectral component in the transform corresponds to a different position along the sensing fiber. It is a result of the beating between the reflections of all the scatterers in a spatial resolution cell. As acoustic perturbations or vibrations disturb this fiber segment the mutual phases of the reflections vary, leading to amplitude fluctuations which are in correlation with the acoustical signal. The results are plotted as spectrograms which describe the magnitude variations as a function of position along the fiber and time. Using the system detection of minute impulses and oscillatory excitations in a 10km fiber at a rate of 1KHz was demonstrated.

2. Theory

Consider a fiber-optic system as described in Fig. 1. Light from a laser source is launched into a measurement arm and the back-reflected beam is mixed with a reference and detected by a coherent I/Q receiver. In OFDR the frequency of the laser is varied at a nominally constant rate, $γ$ , over a frequency range $Δ f$ . The laser output field can be expressed as:

E (t) = E_{0} \exp [j (ω_{0} t + π γ t^{2})] rect (\frac{t}{T})

where

ω_{0}

is the nominal radial frequency at

t = 0

and

T

is the duration of the excitation waveform. In the most general case the measurement fiber can be described as a distributed reflector with z-dependent reflectivity

r (z)

. Consider a single reflection in the fiber at position

z

. The back-reflected field from this point can be expressed as:

E_{S} (t) = r (z) E (t - \frac{2 z}{c})

where

c

is the speed of light in the fiber. The back-reflected field is detected by a coherent receiver whose reference is taken from the frequency scanned laser field. After combining the quadrature components at the output of the coherent receiver, the system response to a spatial impulse is obtained:

V (t) = a r (z) \exp {j [2 π γ \frac{2 z}{c} t + φ (z)]} rect (\frac{t - z / c}{T - 2 z / c})

where

φ (z)

is the phase acquired by the interrogation wave in the trip to point

z

and back. To obtain the response of a distributed sensing fiber we integrate (3) over the entire fiber:

V (t) = a \int_{0}^{L} r (z') \exp {j [2 π γ \frac{2 z'}{c} t + φ (z')]} rect (\frac{t - z' / c}{T - 2 z' / c}) d z'

To obtain spatial information it is common to take the Fourier transform of

V (t)

. Great simplification can be obtained if we assume that:

rect (\frac{t - z' / c}{T - 2 z' / c}) \approx rect (\frac{t}{T})

This is valid for situations where

2 z' / c < < T

. In this case the Fourier transform of

V (t)

gives:

\tilde{V} (ω) = \frac{a T}{\sqrt{2 π}} \tilde{r} (ω) * \sin c (\frac{ω T}{2 π}) = \frac{a T}{\sqrt{2 π}} \int_{}^{} \tilde{r} (ω') \sin c [\frac{(ω - ω^{'}) T}{2 π}] d ω^{'}

where:

\tilde{r} (ω) = {r (z) \exp [j φ (z)] |}_{z = ω c / 4 π γ}

It can be seen that the value of

\tilde{V} (ω)

at a given beat frequency is a weighted sum of phasors. The fiber points which contribute to the sum come mainly from the range

(f - 1 / T) c / 2 γ < z < (f + 1 / T) c / 2 γ

. In agreement with the well-known result the spatial resolution can be defined as the width of the sinc in Eq. (6). It is given by

Δ z = c / γ T = c / Δ f

where

Δ f

is the total scan range of the laser. When a given fiber segment is exposed to external perturbations such as acoustical field or vibrations the mutual phases of the phasors changes and so does their sum.

Fig. 1 The experimental setup.

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3. Experiment

The experimental setup is described in Fig. 1. Light from an ultra-coherent laser (Orbits Lightwave Ethernal) was split between a reference arm and a sensing arm. The laser wavelength was 1550.12nm and its linewidth ~400Hz. The laser instantaneous frequency was controlled by applying electric signal to internal piezoelectric actuators (PZT). To prevent undesired mechanical transients due to discontinuities in the driving signal the PZT was driven by a sinusoidal signal away from its resonant frequency. This resulted in a smooth variation of the lasers frequency. The period of the sinusoidal signal was 1ms. Out of the total period a sub-segment of 16μs, where the variation of the laser's frequency was close to linear, was sampled at a rate of 250MSamples/s and recorded in each cycle. This resulted in a frequency sweep rate of γ = 1043GHz/s. The reference light beam was transmitted through a variable optical attenuator (VOA) followed by a polarizer into the reference port of a Dual Polarization 90° Optical Hybrid (90°OH). The light in the sensing arm was transmitted through a differential delay module and directed to the input port of a circulator (port 1). The returning light from the sensing fiber exited port 3 of the circulator and entered the signal port of the 90°OH. The 90°OH had four pairs of output fibers. Each pair of fibers was connected to a balanced optical receiver. These produced four electronic signals which represented the four degrees of freedom of the light returning from the sensing network. Hence, the described setup was capable of a complete measurement of the returning field (four degrees of freedom: two quadratures of two polarization components). In this work, however, we focused on the signals produced by one polarization component. The polarization dependent attributes of the methods are the topic of a further study.

The outputs of the balanced receivers were sampled, analyzed and displayed by a Digital Storage Oscilloscope (600MHZ, Agilent Infiniium MSO9064A).

Several sensing networks were connected to the interrogation unit. One example is shown in Fig. 2. Five spools of communication-type single mode fiber were connected to the interrogator. The lengths of the fibers on each spool were approximately: 1.25km, 0.72km, 40m, 4.57km and 3.42km giving a total length of roughly 10km. The 0.72km fiber was enclosed inside a box. The other spools were isolated from the ground by an acoustically absorbing surface to prevent crosstalk between them.

Fig. 2 A 10km sensing fiber.

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To characterize the response of the system to an impulse the excitation of the sensing fiber was performed by tapping the spools gently one after the other with one finger. The time between one tap to the following tap was roughly 0.5sec. The scan rate was 1KHz which determined the acoustical bandwidth of the sensor to be ~500Hz. Another sensing network is described in Fig. 3. This configuration included a PZT-based fiber stretcher and was used for testing detection of sinusoidal excitations. The sensing fiber was wrapped around the same PZT at two different points: z = 1230 m and z = 5109 m. Following calibration the PZT enabled excitation at predetermined elongations and frequencies.

Fig. 3 Sinusoidal excitation with PZT.

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4. Results

As described above the main effect of acoustical excitation was to perturb the phase in the beating term in Eq. (7). This could be viewed in real time by setting the scope to display the magnitude of the FFT of the coherent receiver output. Any external perturbations of the sensing fiber at this state were visible on the scope as variations of the FFT magnitude at positions which corresponded to the spatial location of the excitation. The position of the excitation was obtained using the relation: $f_{b e a t} = γ 2 z / c$ . In order to extract the time varying phase the receiver output was recorded, during multiple scans, and processed in a PC. Each recording yielded a matrix ${V (t_{k}, t_{j}); k = 1 : K, j = 1 : J}$ where K is the number of samples in one scan and J is the number of scans. One dimensional Fourier transform yielded the complex OFDR response as a function of time: $\tilde{V} (ω_{k}, t_{j})$ . One simple manner to present the results was to plot ${| \tilde{V} (ω_{k}, t_{j}) |}^{2}$ . It was found, however, that another representation yielded better contrast between perturbed to idle instances. To explain the procedure we make the definition ${| \tilde{V} (ω_{k}, t_{j}) |}^{2} \equiv a_{k} (t_{j})$ . The first step is to Fourier transform $a_{k} (t_{j})$ to obtain ${\tilde{a}}_{k} (ω_{j})$ . Next, the negative components of ${\tilde{a}}_{k} (ω_{j})$ are omitted and the sequence is transformed back to the time domain. The complex signal which is obtained, ${\hat{a}}_{k} (t_{j})$ , is known as the analytic signal associated with $a_{k} (t_{j})$ [16]. Finally the phase difference between two consecutive scans, $Δ θ (t_{j}) = \arg [{\hat{a}}_{k} (t_{j})] - \arg [{\hat{a}}_{k} (t_{j - 1})]$ is obtained. This procedure was found to be useful in detecting rapid oscillations in the presence of noise and slowly varying phase drifts. Experimental examples for this phase at four different positions along the fiber are shown in Fig. 4. Plots a and b correspond to the phase at fiber sections in the first spool and plots c and d correspond to sections in the second spool. The responses to impulse excitations at different times are clearly seen in both spools. Different features of the responses can be observed. The responses corresponding to fiber positions inside the box showed resonating behavior due to reverberations. It can also be seen that different sections in the same spool showed markedly different responses. In addition, the responses were significantly noisier in some of the sections. This phenomenon is attributed to the acoustical coupling between the fiber to the spool and the position on the spool which was different for different fiber sections.

Fig. 4 Responses to impulses at four separated points.

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An example for the total response is shown in Fig. 5. Several features of the system can be observed from the data: The five taps (on the five spools) are clearly seen in the plot (the third tap is less visible since the third spool was much shorter than the other four spools), the system is highly sensitive along the entire length, the resolution is about 40m as the excitation of the shortest spool (III) is visible and oscillations at ~100Hz can be seen following the excitation. The second spool was isolated inside a box and its response to the tapping was 3 times longer than the other responses due to reverberations. Another representation of these results is given in the right panel of Fig. 5. This representation is in the form of a seismogram. To generate the plot the length of the sensing fiber was divided into sections of 20m and the normalized phase signal at each section is plotted as a function of time.

Fig. 5 (a) The total response to impulses (b) a seismogram representation of a subsection.

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It is interesting to concentrate on the third spool which is much shorter than the other spools. Figure 6(a) shows another example of excitation of the system with taps. The response at the location of the third spool and its close vicinity is plotted. The ten graphs in the figure correspond to ten equally spaced positions along the fiber. The separation between each two neighboring points is approximately 13m. The oscillations around $t \approx 1.5 s$ and $t \approx 3 s$ correspond to taps on the second and fourth spools respectively. The oscillations that start at $t \approx 2 s$ (enclosed with the red dashed line) result from the tap on the third spool. These oscillations appear over a length of roughly $l \approx 4 \times 13 m = 52m$ where for ideal resolution they should have been observed over 40m (the length of the third spool). The difference is the result of the finite spatial resolution of the system which can be safely stated to be not worse than 40m. To check if the resolution degrades with distance the short spool was connected at the end of the sensing fiber. A short fiber jumper was connected to it to reduce reflections from the fiber end. Figure 6(b) shows the measured impulse response in this case. No significant change in the spatial resolution was observed.

Fig. 6 (a) The response at the vicinity of the third spool. (b) Response of the short spool at the end of the sensing fiber.

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Figure 7 shows the response of the system to oscillatory excitation at two separated positions (at z = 1230 m and z = 5109 m). In the left panel (Fig. 7(a)) the response is mapped as a function of position and frequency. Figures 7(b)-7(c) show horizontal and vertical cross-sections of the total response. The fiber stretcher was fed by a sinusoidal signal with frequency of 40Hz. The resulting periodic elongation of the fiber was at amplitude of about 400nm. The 40Hz spectral peaks at the positions of the PZT are clearly seen. Significant responses can be seen also around 0Hz, 50Hz and 100Hz. The DC and low frequency content is attributed to thermal instabilities and 1/f noise. The response at 50Hz and 100Hz is due to acoustic noise at the laboratory from equipment, computers, fluorescent bulbs etc. Figure 7(b) can also be used to estimate the minimum fiber elongation that can be detected. Using the peaks as a reference it can be seen that the noise level near 5km is equivalent to ~40nm and to ~66nm near 9km. The increase in noise level as a function of distance is attributed to acoustic phase noise which accumulates along the fiber. Also observed are equally spaced peaks with frequency difference of 10Hz at the position of the excitation (see Fig. 7(c)). This is attributed to the non-linearity of the excitation method which led to beating between the strong 50Hz component and the 40Hz excitation. In order to test this hypothesis we synthetically generated the signal $exp {j [0.55 \sin (2 π 40 t) + \sin (2 π 50 t)]}$ which emulates phase modulation by two tones. Its spectrum, which is also plotted in Fig. 7(c), supports the hypothesis.

Fig. 7 40Hz sinusoidal excitation at z = 1230 m and z = 5109 m. (a) The total response in the space-frequency domain. (b) A horizontal cross-section of the response at 35Hz (green) and 40Hz (blue). (c) Vertical cross-section at 4700m (green), z = 5109 m (blue) and the spectrum of $exp {j [0.55 \sin (2 π 40 t) + \sin (2 π 50 t)]}$ (red).

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6. Discussion and conclusions

As in all OFDR techniques the resolution of the method is determined by the total frequency sweep range, $Δ F$ . The maximum frequency deviation in the laser that was used was 10GHz which can ideally facilitate centimeters resolution. In dynamic operation, however, there are several important considerations that significantly degrade the maximum resolution. First, to achieve good linearity and to avoid the need to supply the tuning PZT with a high voltage it was required to considerably reduce the frequency sweep range. Second, to prevent undesired transients by the tuning PZT we utilized sinusoidal frequency tuning and recorded the system response only during the linear portion of the sine wave. These factors led to the observed resolution of tens of meters. It is expected, however, that improvements in the frequency tuning driving electronics can significantly improve the spatial resolution.

The data produced by the method can be used as input to higher level processing algorithms which classifies the measurements and detects events and threats according to their acoustic signature. Simple example for such processing is to use spectral filtering for separating fast acoustically induced oscillations and slow thermally induced phase variations. Another example is monitoring the statistical characteristics of the signal from a particular position and detecting non-stationary events.

A dynamical OFDR technique for vibrational and acoustical sensing was proposed and experimentally tested. The method is based on a fast sinusoidal tuning of a fiber laser and a coherent receiver which facilitates real time dynamic OFDR measurement. The spectral components fluctuate due to acoustically-induced phase variations in the sensing fiber. The system was excited with impulses and sinusoidal stretching and successfully sensed and recorded the excitation along the entire length of a 10km sensing fiber.

References and links

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Dynamic optical frequency domain reflectometry

Abstract

1. Introduction

2. Theory

3. Experiment

4. Results

6. Discussion and conclusions

References and links

Cited By

Figures (7)

Equations (7)

Optics Express