We demonstrate interrogation of a large-capacity sensor array with nearly identical weak fiber Bragg gratings (FBGs) based on frequency-shifted interferometry (FSI). In contrast to time-division multiplexing, FSI uses continuous-wave light and therefore requires no pulse modulation or high-speed detection/acquisition. FSI utilizes a frequency shifter in the Sagnac interferometer to encode sensor location information into the relative phase between the clock-wise and counter-clockwise propagating lightwaves. Sixty-five weak FBGs with reflectivities in the range of −31 ~-34 dB and with near identical peak reflection wavelengths around 1555 nm at room temperature were interrogated simultaneously. Temperature sensing was conducted and the average measurement accuracy of the peak wavelengths was ± 3.9 pm, corresponding to a temperature resolution of ± 0.4 °C. Our theoretical analysis taking into account of detector noise, fiber loss, and sensor cross-talk noise shows that there exists an optimal reflectivity that maximizes multiplexing capacity. The multiplexing capacity can reach 3000 with the corresponding sensing range of 30 km, when the peak reflectivity of each grating is −40 dB, the sensor separation 10 m and the source power 14 mW. Experimental results and theoretical analysis reveal that FSI has distinct cost and speed advantages in multiplexing large-scale FBG networks.
© 2015 Optical Society of America
As a mainstream optical sensing technology, fiber Bragg gratings (FBGs) have been extensively applied in structural health monitoring [1–3 ], force monitoring in biomedical devices , temperature and stress monitoring in harsh environments [5, 6 ]. Their major advantages are small size, long term stability and robustness in hazardous environments, immunity of electromagnetic interference, and the ability to be multiplexed in large numbers. The latter is particularly useful in large civil engineering structures and in oil and gas exploration and distribution systems. In order to reduce the system cost and multiplex a large number of FBGs for multipoint measurements, many multiplexing schemes have been developed, including optical time-domain reflector (OTDR) , optical frequency-domain reflector (OFDR) , space-division multiplexing (SDM) , wavelength-division multiplexing (WDM) time-division multiplexing (TDM) and combinations thereof [10, 11 ]. However, except for a recent few demonstrations [12–14 ], FBG multiplexing usually has capacities limited to a few or tens of gratings. The reasons are many. For example, for WDM, the multiplexing capability is limited by the available bandwidth and the dynamic range requirements of the sensors. For SDM, it is the signal-to-noise ratio. But there is also a common problem associated with the FBG sensors that limit the multiplexing capability. The conventional FBGs involve a complex and costly fabrication process, where for each grating, the fiber buffer layer has to be stripped at the intended location, the fiber portion has to be placed in the set up and aligned precisely for FBG writing, it then has to be recoated after writing, etc. Such a manual process is clearly not scalable to thousands of FBGs along a single fiber.
New in-line FBG fabrication during fiber draw [13, 15 ] greatly reduces the fabrication steps and the cost of large-scale FBG sensor arrays, as well as enhances the reliability and longevity of the product. However, it also imposes constraints on sensor multiplexing and interrogation techniques. Traditional WDM schemes cannot be used because of the near identical reflection wavelength of in-line fabricated FBGs, and TDM has been the only method demonstrated so far for large-scale multiplexing of in-line FBGs. In-line FBGs also have weak reflections, which on one hand alleviates the spectral shadowing effect and the cross-talk noise due to multiple reflections between sensors, but on the other hand creates a challenge for maintaining high SNR, with reduced wavelength accuracy as a consequence. So far two successful techniques based on TDM have been reported [13, 14 ]. The advantages of using TDM are: (1) not limited by source coherence; (2) large measurement range, limited only by signal-to-noise ratio (SNR). However, they do suffer some drawbacks: (1) They require pulse modulation (nanoseconds) and fast detection/data acquisition; For example, in , the CW light from a tunable laser was modulated into nanosecond pulses by an electro-optic modulator (EOM), the reflected pulse from each FBGs was detected by a1.8 GHz photo detector, and the serial data from the photo detector was collected by a 40GS/s oscilloscope. (2) Because of the poor temporal utilization of the source (i.e., low duty cycle), high power amplifiers are required. For example, three EDFAs in , two SOAs and one EDFA in  were used; (3) In most realizations of TDM interrogation techniques, the FBGs are interrogated individually one-by-one instead of simultaneously, causing the measurement time to increase linearly with the number of sensors.
In this paper we adopt the frequency-shifted interferometry (FSI) to interrogate the in-line near identical weak FBG arrays. FSI retains the advantages of TDM mentioned above, while requiring only a continuous-wave light source, without pulse modulation, fast detection/acquisition, or optical amplification. It also has the advantage of interrogating all sensors simultaneously; therefore the measurement time is independent of the number of sensors. Sixty-five gratings over 3 km of fiber were interrogated experimentally. The wavelength measurement stability for all gratings were under ± 15.2 pm with an average stability of ± 3.9 pm. Theoretical analysis indicates multiplexing nearly 3000 FBGs over 30 km of range is possible with FSI. It is the first time FSI is used to interrogate large near identical weak FBG arrays, and the results of this work show a promising, cost-effective alternative to TDM multiplexing of large FBG sensor arrays.
2. Operation principle
Our FBG interrogation system based on the FSI scheme is illustrated in Fig. 1 . The sensing arm contains an array of weak FBGs with nearly identical reflection wavelengths. The interrogation unit consists of a folded Mach-Zehnder interferometer with an acousto-opticmodulator (AOM) in one arm, serving as a frequency shifter. Its operation is equivalent to that of a Sagnac interferometer with an asymmetrically located frequency shifter in the Sagnac loop . Two counter-propagating lightwaves going through path A and path B as shown in Fig. 1 will interfere back at the coupler C1, after being reflected from each FBG. The differential interference intensity at the balanced detector (BD) can be expressed as [17, 18 ]:Fig. 1. I i (λ) represents the power arriving at the BD reflected from the ith FBG at wavelength λ, and can be described as:16, 17 ]. I0 (λ) is the constant independent of the FBG reflectivity Ri(λ) [16, 17 ]:18] in dB, and Ps is the output power of TLS.
From Eqs. (1)-(2) one can easily see that the grating location information is in the phase of the expression, whereas the grating spectral information is in the amplitude. To obtain both the amplitude and the phase information for all FBGs at each wavelength, one can linearly sweep the frequency shift f over a range Δf (taken to be 90-110 MHz in our experiment) over time, and then Fast Fourier Transform (FFT) the time-domain signal ΔI (t) to obtain ΔI (Li), Li being the distance along the sensing arm. Details are described in . In this work, we modified the conventional FSI demodulation algorithm [18, 19 ] and obtained the peak wavelength and location of each FBG by the following three steps:
- (1) First fix the laser wavelength, obtain the location-resolved Fourier spectrum, ΔI (Li), by sweeping the AOM frequency and performing FFT on the time-domain signal. Then, scan the source wavelength to acquire a three-dimensional (3D) matrix data ΔI (λ, Li).
- (2) Using an appropriate threshold value to reject noise, find the peak reflection location (Li) and the raw reflection spectrum for each FBG from the 3D matrix data ΔI (λ, Li).
- (3) For each FBG, perform cubic spline interpolation to its raw reflection spectrum obtained from ΔI (λ, Li), in order to determine the peak wavelength (λi) of each FBG reflection.
By monitoring the peak wavelength variation of an FBG according to the above algorithm, we can further infer the ambient measurands such as temperature, strain and so on [2, 20 ].
We would like to note that FSI is a fundamentally different approach than OFDR, which was also used for FBG sensor array multiplexing . OFDR varies the frequency modulation on the source so as to create a one-to-one correspondence between frequency difference and time delay (or location separation), such that the latter can be deduced from the beat frequency between the delayed test signal and the reference signal. FSI relies on interference between two lightwaves that traverses exactly the same path for it uses a Sagnac interferometer. The two lightwaves are frequency shifted by the same amount at different times, resulting in a phase difference that corresponds to the time delay. Therefore, OFDR requires a separate reference signal (either RF or optical), while FSI is always self-referenced, and therefore FSI can also be performed using an incoherent light source.
3. Experiments and results
Our experimental system is depicted in Fig. 1. An FBG sensor array was written directly on the fiber during the fiber draw process. It contains 65 FBGs with peak reflectivity ranging from −31 to −34 dB and an average peak wavelength of 1555.033 nm. Except for the separation between the 60th and the 61st FBG, which is about 183 m, all other grating separations are about 43 m. The interrogation system consists of a tunable semiconductor laser (TSL) (Santec TSL-510C) set to an output power of 4 mW with a scanning wavelength increment of 0.03 nm, and an AOM (Brimrose AMM-100-20-25-1550-2FP) set to sweep linearly from 90 to 110 MHz at a step size of 0.0165 MHz. The interference signals at both ports of C1 are sent to the balanced detector (BD) (New Focus Model 2117) and its output is connected to a data acquisition board (NI USB-6361) with100 KHz sampling rate, and synchronized with the AOM scanning cycle. The gain of the BD is set to 104, with a corresponding bandwidth of 250 KHz.The measured transmission coefficients k1 and k2 of path A and path B are 0.98 and 0.4, respectively, and the sum of all other insertion losses αc is ~0.8 dB.
A sample time-domain interference signal at 1555.02 nm obtained by the DAQ is shown in Fig. 2(a) , while its FFT, after conversion into the spatial domain is shown in Fig. 2(b). Here only fifty-nine Fourier peaks are obtained from the 65-FBG sensor array, because the FBGs have slightly different peak wavelengths, due to slight variations in the in-line fabrication process (such as tension, draw speed etc.). The measured distances between the Fourier peaks corresponding to adjacent FBGs are all about 43 m, except for the distance between the two peaks corresponding to the 60th and the 61st FBG, which is measured to be 184 m. These measured distances are in good agreement with the distances estimated from the FBG fabrication process. As we can also see from Fig. 2(b), the FFT spectrum has a high frequency-domain SNR  of 20 dB, and the gap between the 60th and the 61st FBG shows there is no significant crosstalk.
By wavelength scanning, all of the FFT spectra at different wavelengths, i.e. ΔI (λ, Li) mentioned in Section 2, were obtained, and their 3D projection is shown in Fig. 3 . Sixty-five bright reflection spectra exactly corresponding to 65 FBGs in the sensor array are clearly visible, demonstrating that the peak wavelengths are not identical, though all are within a 0.30 nm range as shown in Fig. 4(b) . It further proved that the FSI scheme can interrogate every weak FBGs from a serial sensor array despite the severe spectral overlap. More detailed spectral plots obtained from FSI can be seen in Fig. 4(a), where variations in reflection spectra, in terms of peak wavelength, reflectivity and spectral width are clearly visible. Note that even the smaller side peaks of the weak FBG reflection spectra are visible, demonstrating the high SNR obtained by this technique.
The system was tested for temperature sensing. The last five FBGs in the sensor array were placed in a high-low temperature test chamber (SIDA CTP2005), whereas the rest of the FBGs were kept outside the chamber at room temperature, about 26 °C. The chamber has a temperature stability of 0.1 °C. Initially, all FBGs were exposed in the ambient environment (with the chamber off and the door open). Three measurements were taken as a reference. Then the chamber is activated and its temperature was set to cover the range of 0 °C to 80 °C, at an increment of 5 °C. Each temperature was first kept for half an hour to ensure a steady temperature distribution inside the chamber and then 3 repeated measurements were taken. The results are shown in Fig. 5 . The peak wavelengths of the last five FBGs increase as the temperature increases, whereas for the first sixty FBGs outside the chamber no noticeable wavelength shift was observed. Figure 6 illustrates the peak wavelength of one of the last five FBGs at different temperatures. By linear fitting, the temperature sensitivities of the last five FBGs are found to range from 11.0 to 11.2 pm/°C, with an average value of 11.1 pm/°C, which is slightly larger than that of regular FBGs reported in the literature . We attribute this slight deviation to the slightly thicker coating of the fabricated weak FBGs.
Currently, one round of interrogation is completed within 80 seconds, mostly limited by the software control speed of the AOM frequency scan and the slow wavelength tuning. The software implementation of FFT is also quite slow. Even so, the current measurement time is on the same order as those reported by TDM interrogation methods [14, 20 ], which range from about 20 seconds to 90 seconds. Our measurement speed can be greatly improved by (1) implementing hardware control of AOM frequency scan, which can reduce from the current 1.2 sec/scan to milliseconds per scan; (2) using a faster wavelength tuning mechanism such as a scanning Fabry-Perot filter with an ASE source which can reduce from the current 1.5 sec/scan to 50 ms/scan ; (3) implementing hardware FFT algorithm. Overall we expect the measurement time to be reduced to < 1 second with the proposed implementations. Note that unlike TDM where interrogation time increases linearly with number of sensors, FSI interrogates all the FBGs simultaneously, which not only can provide fast dynamic data correlations between different sensors, but also results in measurement time independent of the number of sensors, as long as the frequency scan step size (which affects the measurement distance) is unchanged. Therefore, the same amount of time will be used whether there are 65 sensors or thousands of sensors on the fiber.
Finally, to test the system stability, the measurement was repeated 40 times under the same condition, and the obtained one standard deviation of each peak wavelength is shown in Fig. 7 . The measurement error ranged from ± 0.9 to ± 15.2 pm with a mean value of ± 3.9 pm. The difference in the measurement errors is mainly caused by the different peak reflectivities and hence different SNRs of the weak FBGs . According to the obtained temperature sensitivity, the resolution of the FSI system for temperature measurement was ± 0.4°C, which was superior to the TDM system reported in literature .
4. Crosstalk and performance analysis
4.1 Crosstalk simulation
In general, FBG sensor arrays suffer from two types of cross-talk: spectral shadowing and multi-path interference (MPI). Spectral distortion caused by shadowing, as mentioned in Section 2, can be completely removed in the FSI system [16, 17 ]. However, spectral shadowing does result in reduced signal return, particularly for FBGs far downstream. If MPI is neglected, the real reflected power from the ith (i = 1,2,…,N) FBG at wavelength λ is precisely Ii (λ) as shown in Eq. (2). Using the experimental parameters in Section 3 (unless stated otherwise, all simulation parameters used in this section are kept the same as the experimental parameters in Section 3), we estimate the return power from each grating assuming the worst case – that all FBGs have the identical peak wavelength. Shown in Fig. 8 , return power variations from the 1st to the 65th FBG are plotted for various grating reflectivity. For FBGs having the reflectivity in the range of −31 ~-34 dB (see Section 3) the difference between the returned power from the 65th FBG and the 1st FBG is less than 1.5 dB. Thus, spectral shadowing does not pose a problem on the FSI interrogation scheme for the present sensor array.
MPI refers to the fact that the reflected light by upstream FBGs can undergo multiple reflections and may arrive at the detector at the same time as the real reflected signal from a downstream FBG, and therefore make the latter indistinguishable. This problem exists in both TDM [13, 23 ] and FSI interrogation systems . Generally, only the first-order crosstalkwhich undergoes three reflections needs to be considered, as higher-order MPI crosstalks undergoing five or more reflections are much weaker due to the weak FBGs and therefore negligible. Again, considering the worst case when all FBGs have the identical peak wavelength, and assuming all FBGs have the same reflectivity R (λ), the first-order crosstalk power affecting the ith FBG can be approximated as Fig. 9 . For our weak FBGs having reflectivity in the range of −31 to −34 dB, the worst-case first-order crosstalk power, which affects the 65th FBG, is at least 29 dB weaker than the reflected signal power as shown in Fig. 8.
Taken together both Fig. 8 and Fig. 9, the SNR reduction induced by both the spectral shadowing and the first-order crosstalk in the 65-FBG sensor array with −31 to −34 dB reflectivity range is negligible, and the reflected signals have worst-case SNRs in excess of 29 dB considering both crosstalk effects.
4.2 Performance analysis for large-scale multiplexing
The multiplexing capacity and the sensing range are two key parameters for an FBG sensing network. In this section, we calculate the ultimate capacity and sensing range that can be handled by our FSI system. In order to make sure all FBG sensors can be measured in the presence of crosstalk and noise, the reflected signal power Ii must be much larger than the sum of the first-order crosstalk power Ci and the minimum power Pmin specified for the balanced detector (BD), i.e.
For the convenience of discussion, we define SNR as the ratio of the real reflected power from the ith FBG to the sum of its first-order crosstalk power and the BD sensitivity, i.e.,Fig. 10 , when the sensor separation and the number of multiplexed FBGs remain unchanged, and when the source power is 14 mW, the variations of SNRs under different sensor separations all experience a first-up-then-down trend as the FBG reflectivity increases. Therefore, the multiplexing capacity is expected to have a similar tendency. That is to say, there is an optimal reflectivity for maximizing the multiplexing capacity, which corresponds to the abscissa value of the highest point on the SNR curve. As expected, Fig. 11 confirms that the multiplexing capacity indeed varies as a function of reflectivity for various sensor separations, and an optimal reflectivity for maximum capacity exists, and is fairly consistent with the reflectivity that corresponds to the maximum SNR. In addition, as we can also see in Fig. 11, for FBG reflectivity less than −30 dB, the multiplexing capacity increases with decreasing sensor separation due to the decrease of the fiber transmission loss with the reduced sensor separation and hence resulting in the increased SNR as shown in Fig. 10. For FBG reflectivity equal to or more than −30 dB, the multiplexing capacity remains independent of the sensor separation, because high reflectivity means that the SNR is dominated by cross-talk and little affected by fiber loss, as demonstrated in Fig. 10. The optimal condition under 14 mW input power is found when the reflectivity of each FBG is −40 dB, and the sensor separation is 10 m, yielding a multiplexing capacity of 3068, and the corresponding sensing range of 30.68 km.
In the case of constant sensor separation (e.g. 10 m), the impact of the source power and the FBG reflectivity on the multiplexing capacity was simulated, which is shown in Fig. 12 . As can be seen, when the reflectivity is less than −30 dB, the multiplexing capacity is increased with the source power since the ascending source power increases the SNR. However, when the reflectivity is more than or equal to −30 dB, the multiplexing capacity does not change with the source power, which is again due to SNR being cross-talk limited, independent of source power. In addition, the optimal reflectivity also exists for the maximum multiplexing capacity under different source powers. It is respectively −40 dB and −45 dB when the source power is lower than 20 mW and equaling to 20 mW. The maximum multiplexing capacity corresponding to the best reflectivity is increased by the rising source power. However, further source power increase beyond 14 mW resulted in little gain of capacity. In summary, the current FSI system with moderate source power (14 mW) is capable of multiplexing 3000 weak FBGs at 10 m separation with a minimum SNR of 10 dB.
We presented and demonstrated the experimental and theoretical study of a weak FBG sensor network consisting of nearly identical FBGs, interrogated by the FSI scheme. Sixty-five near-identical weak FBGs written in-line during fiber draw were experimentally multiplexed and a temperature sensing experiment was conducted. The location and reflection spectrum of each FBG was obtained and was found to be consistent with the expected parameters. The average measurement error of peak wavelengths is ± 3.9 pm, which is corresponding to a temperature resolution of ± 0.4 °C. Moreover, by theoretical analysis, it was found that an optimal reflectivity for the maximum multiplexing capacity exists for a given sensor separation distance, and the multiplexing capacity increases with the decrease of sensor separation and with the increase of source power. When we set the peak reflectivity is −40 dB, the sensor separation at 10 m and the source power at 14 mW, 3068 identical weak FBG sensors can be multiplexed in a single fiber array. In conclusion, the experiment and simulation results indicate that the FSI-based multiplexing scheme for identical weak FBG sensors suits for large-scale sensor networks, and can find potential applications in multipoint detecting and distributed measurements.
This research is supported in part by the National Natural Science Foundation of China (NSFC) (Grant No.61290311, 61377091, 61475044, and 61505152), National Key Technology Research and Development Program of China (2014BAG07B01), Key Technology Research and Development Program of Hubei Province (2014BAA085) and the Fundamental Research Funds for the Central Universities (WUT: 2013-II-023).
References and links
2. D. Kinet, P. Mégret, K. W. Goossen, L. Qiu, D. Heider, and C. Caucheteur, “Fiber Bragg grating sensors toward structural health monitoring in composite materials: challenges and solutions,” Sensors (Basel) 14(4), 7394–7419 (2014). [CrossRef] [PubMed]
3. M. H. Yau, T. H. Chan, D. P. Thambiratnam, and H. Tam, “Static vertical displacement measurement of bridges using fiber Bragg grating (FBG) sensors,” Adv. Struct. Eng. 16(1), 165–176 (2013). [CrossRef]
4. M. S. Milczewski, J. C. da Silva, C. Martelli, L. Grabarski, I. Abe, and H. J. Kalinowski, “Force monitoring in a maxilla model and dentition using optical fiber Bragg gratings,” Sensors (Basel) 12(12), 11957–11965 (2012). [CrossRef] [PubMed]
6. G. Laffont, R. Cotillard, and P. Ferdinand, “Multiplexed regenerated fiber Bragg gratings for high-temperature measurement,” Meas. Sci. Technol. 24(9), 094010 (2013). [CrossRef]
7. Yu. N. Kulchin, O. B. Vitrik, A. V. Dyshlyuk, A. M. Shalagin, S. A. Babin, and I. N. Nemov, “Differential multiplexing of fiber Bragg gratings by means of optical time domain refractometry,” Meas. Tech. 54(2), 170–174 (2011). [CrossRef]
8. K. Yuksel, P. Megret, and M. Wuilpart, “A quasi-distributed temperature sensor interrogated by optical frequency-domain reflectometer,” Meas. Sci. Technol. 22(11), 115204 (2011). [CrossRef]
9. K. Stępień, M. Slowikowski, T. Tenderenda, M. Murawski, M. Szymanski, L. Szostkiewicz, M. Becker, M. Rothhardt, H. Bartelt, P. Mergo, L. R. Jaroszewicz, and T. Nasilowski, “Fiber Bragg gratings in hole-assisted multicore fiber for space division multiplexing,” Opt. Lett. 39(12), 3571–3574 (2014). [CrossRef] [PubMed]
10. K. de Morais Sousa, W. Probst, F. Bortolotti, C. Martelli, and J. C. da Silva, “Fiber Bragg grating temperature sensors in a 6.5-MW generator exciter bridge and the development and simulation of its thermal model,” Sensors (Basel) 14(9), 16651–16663 (2014). [CrossRef] [PubMed]
11. Y. B. Dai, P. Li, Y. J. Liu, A. Anand, and J. S. Leng, “Integrated real-time monitoring system for strain temperature distribution based on simultaneous wavelength and time division multiplexing technique,” Opt. Lasers Eng. 59, 19–24 (2014). [CrossRef]
12. L. Ricchiuti, J. Hervás, D. Barrera, S. Sales, and J. Capmany, “Microwave photonics filtering technique for interrogating a very-weak fiber Bragg grating cascade sensor,” IEEE Photonics J. 6(6), 5501410 (2014). [CrossRef]
13. Y. M. Wang, J. M. Gong, B. Dong, D. Y. Wang, T. J. Shillig, and A. Wang, “A large serial time-division multiplexed fiber Bragg grating sensor network,” J. Lightwave Technol. 30(17), 2751–2756 (2012). [CrossRef]
14. Z. Luo, H. Wen, H. Guo, and M. Yang, “A time- and wavelength-division multiplexing sensor network with ultra-weak fiber Bragg gratings,” Opt. Express 21(19), 22799–22807 (2013). [CrossRef] [PubMed]
15. H. Y. Guo, J. G. Tang, X. F. Li, Y. Zheng, and H. F. Yu, “On-line writing weak fiber Bragg gratings array,” Chin. Opt. Lett. 11(3), 030602 (2013). [CrossRef]
16. L. Qian, “Sagnac Loop Sensors,” in Fiber Optic Sensing and Imaging, J.U. Kang and Springer, eds. (Academic, 2013), pp. 119–146.
17. F. Ye, L. Qian, and B. Qi, “Multipoint chemical gas sensing using frequency-shifted interferometry,” J. Lightwave Technol. 2009 27(23), 5356–5364 (2011).
18. Y. Ou, C. Zhou, A. Zheng, C. Cheng, D. Fan, J. Yin, H. Tian, M. Li, and Y. Lu, “Method of hybrid multiplexing for fiber-optic Fabry-Perot sensors utilizing frequency-shifted interferometry,” Appl. Opt. 53(35), 8358–8365 (2014). [CrossRef] [PubMed]
19. F. Ye, L. Qian, Y. Liu, and B. Qi, “Using frequency-shifted interferometry for multiplexing a fiber Bragg grating array,” IEEE Photonics Technol. Lett. 20(17), 1488–1490 (2008). [CrossRef]
20. Y. M. Wang, J. M. Gong, D. Y. Wang, B. Dong, W. H. Bi, and A. Wang, “A quasi-distributed sensing network with time-division-multiplexed fiber Bragg gratings,” IEEE Photon. Technol. Lett. 23(2), 70–72 (2011). [CrossRef]
21. M. Froggatt, B. Childers, J. Moore, and T. Erdogan, “High density strain sensing using optical frequency domain reflectometry,” Proc. SPIE 4185, 249–255 (2000).
22. F. Ye, “Frequency-shifted interferometry for fiber-optic sensing,” PhD Thesis, University of Toronto, (2013).
23. C. C. Chan, W. Jin, D. J. Wang, and M. S. Demokan, “Intrinsic crosstalk analysis of a serial TDM FBG sensor array by using a tunable laser,” Proc. LEOS36, 2–4 (2000).