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The distributed vibration or dynamic strain information can be obtained using time-resolved optical frequency-domain reflectometry. Time-domain information is resolved by measuring Rayleigh backscatter spectrum in different wavelength ranges which fall in successive time sequence due to the linear wavelength sweep of the tunable laser source with a constant sweeping rate. The local Rayleigh backscatter spectrum shift of the vibrated state with respect to that of the non-vibrated state in time sequence can be used to determine dynamic strain information at a specific position along the fiber length. Standard single-mode fibers can be used as sensing head, while the measurable frequency range of 0–32 Hz with the spatial resolution of 10 cm can be achieved up to the total length of 17 m.
© 2012 Optical Society of America
1. Introduction
Optical fiber sensors (OFSs) have been attracting intensive research all over the world for several decades. They have already shown a superior advantage over their conventional electrical counterparts, which attributes to the distributed capability. A fully distributed OFS is usually operated by measuring the surrounding environment change along the length of the sensing fiber, which is very useful for the health monitoring of civil structures and small mechanical structures. The vibration frequency information is a useful parameter in such kind of the measurement, since the intrinsic frequency can be used to evaluate the structural condition and to identify the internal damages at an early stage. Many efforts have been made to fulfill the distributed vibration sensing, such as using polarization-optical time-domain reflectometry (OTDR) [1, 2], phase-sensitive OTDR [3–7], Sagnac or Mach-Zehnder interferometer [8–10], etc. OTDR technique requires injecting light pulses into one end of a fiber, and then detecting Rayleigh backscattered light returned from the fiber; pulse duration determines the spatial resolution of the measurement. For interferometric methods, special processing treatment is needed to locate the position of the vibration events. All the reported methods have limited spatial resolution on the order of meters, which might not be enough for aerospace type of applications which require centimeter spatial resolution.
On the other hand, strain or temperature measurement based on optical frequency-domain reflectometry (OFDR) technique has found its way to practical applications due to its high spatial resolution and simple configuration [11–15]. Rayleigh backscatter in optical fiber is caused by random fluctuations in the index profile along the fiber length; the scatter amplitude can be modeled as a long, weak fiber Bragg grating (FBG) with a random period. The surrounding environmental variations could cause the local spectrum shift of the Rayleigh backscatter in a distributed manner, which could be calibrated and then used to realize the distributed temperature or strain measurement. Note that over 600 m measurable range with fine spatial resolution has been reported [15], while very high spatial resolution could be achieved (∼mm range) with relative shorter measurable length (tens of meters) [13]. However, so far, all the reports based on OFDR system are only focusing on stationary measurement. If dynamic measurement capability could also be provided, OFDR technique can become a powerful tool for distributed sensing, both stationary and dynamic, to meet many kinds of practical applications, especially when high spatial resolution is a major concern with cost-effective configuration and short measurement time.
In this paper, we investigate the feasibility of the distributed dynamic sensing with time-resolved OFDR. The Rayleigh backscatter spectrum from the entire fiber can be obtained after the tunable laser source (TLS) completing one sweep; then the Rayleigh backscatter pattern as a function of fiber length is obtained by Fourier transform. Part of the spectrum could also be used to achieve this same purpose with a poorer spatial resolution. Since the TLS has a constant sweeping rate during the measurement, any part of the spectrum can be related to a specific time slot in which the spectrum was taken. By determining this spectrum shift, time-domain surrounding environmental variations can be resolved. This local Rayleigh backscatter spectrum shift of the vibrated state with respect to that of the non-vibrated state in time sequence could be used to determine strain information at a specific position along the fiber length. Standard single-mode fibers (SMFs) can be used as sensing fiber, while the measurable frequency range of 0–32 Hz with the spatial resolution of 10 cm can be achieved up to the total length of 17 m. All these parameters could in principle be improved, provided that tuning range and sweeping speed of the TLS, the delay length in the trigger interferometer, and the specifications of the data acquisition card could be properly adjusted.
2. Experiment setup and operation principle
The experiment setup is shown in Fig. 1. The OFDR configuration consists of a TLS (Agilent 81980A) with a continuous sweep mode and a ∼100 KHz linewidth working in 1550 nm range.
Fig. 1 Experiment Setup. TLS: tunable laser source; DAQ: data acquisition; OC: optical coupler; PC: polarization controller; PD: photodetector; PBS: polarization beam splitter; FUT: fiber under test; PZT: Lead zirconade titanate.
The trigger interferometer is an auxiliary Mach-Zehnder interferometer which is commonly used in OFDR systems to remove laser tuning errors from the data [11–15]. The maximum length of the fiber under test (FUT), Lmax is determined by the differential delay in the trigger interferometer using the Nyquist sampling criteria by [12]
where c is the velocity of light in vacuum; ng is the group index of FUT; τg is the group delay introduced by the trigger interferometer. Since the polarization state of the scattered signal is arbitrary, we adopt the polarization diversity detection technique. Polarization controller 1 (PC1) is required in polarization diversity measurement to adjust the polarization of the local path to have the same power for “s” and “p” components, respectively. PC2 is used to adjust the polarization of the input light to the FUT for optimization of the measurement. When the laser is tuned, the interference signals obtained from the combination of the Rayleigh scattering signal and the local laser beam is split by a polarization beam splitter (PBS); The resultant “s” and “p” components are then received and digitized as a function of the TLS frequency by a two-channel acquisition. Fourier transform is then used to convert these frequency data into time-domain data which could be scaled to the length of FUT; after performing a vector sum of the transformed “s” and “p” components [12], the Rayleigh backscatter pattern versus the length of the FUT could be obtained. Since the data acquisition and processing are performed in a discrete manner, the Rayleigh backscatter data has a step size, ΔL, which is determined by the scan range of the TLS, ΔλTLS, in the measurement, where λ is the central operating wavelength. From Eq. (2), the wider the spectrum swept, the more points one can obtain within certain length of the fiber.2.1. Stationary measurement
The distributed stationary strain information could be obtained by calculating the cross-correlation of the Rayleigh backscatter spectrum for a certain fiber section in the strain varied states with unchanged states. The length of this section determines the spatial resolution of the OFDR for strain measurement. Normally, there is a trade-off between strain resolution and the spatial resolution [11]. The signal-to-noise ratio of the cross-correlation could be improved if a longer fiber section is chosen which results in poorer spatial resolution but a better strain resolution. This spatial resolution should be properly chosen according to the system’s performance as well as the practical requirements. The strain sensitivity is first calibrated by measuring the Rayleigh backscatter spectrum shift with respect to strains under stationary condition. It has a value of ∼1 με/pm in standard SMF which is similar to that of an FBG in the 1550 nm wavelength range.
2.2. Dynamic measurement
Figure 2 shows the flow chart of the vibration measurement procedure using OFDR. The system runs two times taking the two sets of frequency-domain data; one is with the non-vibrated state and the other one is with the vibrated state. Evenly divided each set of data to N portions in time sequence which determines the sampling frequency for the dynamic signal applied on the FUT. For example, if the total laser sweeping time is T s, the sampling frequency could be N/T Hz which would give the maximum measurable frequency of N/(2T) Hz as indicated by Nyquist sampling theorem. The resultant each portion of data is Fourier transformed (using fast Fourier transform algorithm) into time domain and then scaled to the length along the fiber. A small part of Fourier transformed data, which corresponds to a fiber section determining the spatial resolution of the vibration measurement, is chosen from the first time slot T/N of the data under the vibrated state. The local spectrum is obtained through inverse Fourier transform. After performing cross-correlation calculation with the spectrum chosen from the same time slot data of the non-vibrated state, the spectrum shift of the Rayleigh backscatter indicating the strain change at that time slot could be obtained. This procedure is repeated by N times to obtain the strain variation information at the chosen fiber section for the total T s at a sampling frequency of N/T Hz. Fourier transform of this time-domain signal will provide the frequency information of the dynamic strain. Next, all the other fiber sections’ information could be obtained in the similar way realizing the distributed dynamic strain measurement.
Fig. 2 Flow chart of the dynamic strain measurement with optical frequency-domain reflectometry. TLS: tunable laser source; FFT: fast Fourier transform.
3. Experimental results and discussion
The length of path difference in the trigger interferometer in the experiment setup is 70 m which determines a maximum measurable range of ∼17 m determined by Eq. (1). The FUT used in the experiment is a standard SMF with a length of 10.8 m. A small circle is made at the end of the FUT to decrease the Fresnel reflection. A lead zirconate titanate (PTZ) tube with a diameter of 3 cm is used to provide dynamic strain on the fiber by wrapping a 20 cm fiber section on it. The input power to the FUT is 2 mW. The sweeping rate and range of the TLS are 40 nm/s and 50 nm respectively, corresponding to T=1.25 s for a complete scan with a length of 0.016 mm between the two successive data points. Figure 3(a) shows the Rayleigh backscatter as a function of fiber length after vector summing from the “s” and “p” components. In order to obtain Fig. 3(b), the frequency-domain data is evenly divided by N=80 portions in time sequence, only the first part (first time slot) of the data (0.625 nm sweeping range) corresponding to the length of 1.28 mm between the two successive data points is used to perform Fourier transform and then scaled to the fiber length. Both the curves are averaged with an effective length of 3.8 mm in order to provide a better view for Rayleigh backscatter level along the fiber. There is a relatively large fluctuation in Fig. 3(b) due to the limited data points within 3.8 mm length. In the following consideration, filtering is unnecessary for the Rayleigh backscatter spectrum shift calculation.
Fig. 3 Rayleigh backscatter as a function of fiber length with the TLS sweeping range of (a) 50 nm and (b) 0.625 nm. Both the curves are vector summed from the “s” and “p” components and a 3.8 mm filter is used for both cases.
Next, as an illustration, the Rayleigh backscatter spectrum shift at the vibration position of the fiber (4.26 m) at several different times is shown in Fig. 4 when a 5 Hz sinusoidal voltage is applied to the PZT tube. Two different fiber lengths corresponding to two different spatial resolutions are considered for comparison. The better the spatial resolution is, the worse the signal-to-noise ratio becomes as indicated in Fig. 4(b) [11]. For higher spatial resolution, less data points have to be chosen for the inverse Fourier transform and cross-correlation calculation; therefore, noise level will increase accordingly. After locating the peak position of the spectrum shift obtained by quadratic least square fitting at all the time slots at a particular fiber position, time-domain spectrum shift or time varied applied strain (∼1 με/pm) could be obtained as shown in Fig. 5. Two different positions are indicated when a 5 Hz vibration is applied to the PZT tube. At the vibrated position of 4.26 m, a sinusoidal varied spectrum shift (applied strain) could be clearly seen in Figs. 5(a) and 5(b) for both the 20 cm and 10 cm spatial resolution. At the non-vibrated position of 4.48 m, no significant variation could be observed as shown in Figs. 5(c) and 5(d). Repeated experiment confirms that 10 cm resolution is readily achievable for vibration measurement. Even a 8 cm resolution could also be achieved but with a poor single-to-noise ratio. In the following illustration, we choose 10 cm resolution for the measurement. Figure 6 shows the time-domain Rayleigh backscatter spectrum shift at vibrated position of 4.26 m with 10 cm resolution when a (a) 10 Hz and (b) 20 Hz sinusoidal voltage is applied to the PZT tube. The signal appeared in Fig. 6(b) is not as good as those of 5 Hz and 10 Hz, because the sampling rate is relatively slower; however, it is still enough to find the frequency information of such signal by fast Fourier transform. Finally, we investigate the distributed vibration measurement as shown in Fig. 7 with different vibration frequencies applied to the PZT tube. The figures are contour plots of power spectrum (log unit) of the time-domain strain signal along the fiber length with a 10 cm spatial resolution. Clearly, both the frequency and position information could be resolved. The vibration length is 20 cm consistent with the fiber length wound on the PZT tube.
Fig. 4 Examples of Rayleigh backscatter spectrum shift at different times with (a) 20 cm and (b) 10 cm spatial resolution at the vibrated position of 4.26 m when a 5 Hz sinusoidal voltage is applied to the PZT tube.
Fig. 5 Time-domain Rayleigh backscatter spectrum shift (applied strain) at vibrated position of 4.26 m with (a) 20 cm (b) 10 cm spatial resolution; non-vibrated position of 4.48 m with (c) 20 cm (d) 10 cm spatial resolution when a 5 Hz sinusoidal voltage is applied to the PZT tube.
Fig. 6 Time-domain Rayleigh backscatter spectrum shift (applied strain) at vibrated position of 4.26 m with 10 cm spatial resolution when a (a) 10 Hz and (b) 20 Hz sinusoidal voltage is applied to the PZT tube.
Fig. 7 Contour plot of the power spectrum (log unit) of the time-domain strain signal along the fiber length for vibration frequency of (a) 5 Hz, (b) 10 Hz, and (c) 20 Hz, respectively.
4. Conclusion
A distributed optical fiber sensor which could measure vibration has been demonstrated. The measurement is achieved through time-resolved OFDR. By determining the spectrum shift of the Rayleigh backscatter distributed along the fiber length of the vibrated state with respect to that of the non-vibrated state, dynamic strain information could be obtained. 10 cm spatial resolution of 17 m sensing length can be achieved. The measurable frequency range is 0–32 Hz. The frequency range, spatial resolution, and the sensing length could be improved with larger sweeping range, faster sweeping speed of the TLS with proper delay length in the trigger interferometer. The reported approach makes the OFDR system a powerful tool for both the stationary and dynamic strain measurement with one simple setup and only two repeated measurements.
Acknowledgments
The authors would like to thank Natural Science and Engineering Research Council of Canada (NSERC) Discovery Grants and Canada Research Chair Program for the financial support. D. P. Zhou would like to acknowledge the Province of Ontario Ministry of Research and Innovation and the University of Ottawa for the financial support of the Vision 2020 Postdoctoral Fellowship.
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