The few-mode fiber (FMF) based Brillouin sensing operated in quasi-single mode (QSM) has been reported to achieve the distributed curvature measurement by monitoring the bend-induced strain variation. However, its practicality is limited by the inherent temperature-strain cross-sensitivity of Brillouin sensors. Here we proposed and experimentally demonstrated an approach for simultaneously distributed curvature and temperature sensing, which exploits a hybrid QSM operated Raman-Brillouin system in FMFs. Thanks to the larger spot size of the fundamental mode in the FMF, the Brillouin frequency shift change of the FMF is used for curvature estimation while the temperature variation is alleviated through Raman signals with the enhanced signal-to-noise ratio (SNR). Within 2 minutes measuring time, a 1.5 m spatial resolution is achieved along a 2 km FMF. The worst resolution of the square of fiber curvature is 0.333 cm−2 while the temperature resolution is 1.301 °C at the end of fiber.
© 2017 Optical Society of America
The curvature is an essential parameter in many fields of manufacture and construction industry such as the mechanical arm, microelectronic system, and structural health monitoring. The optical fiber based curvature sensors have been extensively studied due to their unique advantages like easy to bend, high sensitivity, quick response and suitable for remote measurement. Various types of fiber curvature sensors have been realized utilizing long-period fiber gratings , tilted fiber Bragg gratings , gratings written in particular fibers [3–5], and inline interferometers [6–8]. However, all these configurations are point sensors, which cannot provide the continuous curvature information along the fiber link.
Recently, we have proposed and experimentally realized distributed curvature sensors based on few-mode fibers (FMFs) , and multi-core fibers (MCFs) . Different from single mode fiber (SMF) , the strain of the FMF and the outer cores of MCF are much more sensitive to curvature. Therefore, the curvature has been obtained by monitoring the strain variation using distributed Brillouin sensing technique . However, Brillouin based fiber sensors intrinsically suffer from the temperature-strain cross-sensitivity issue, which degrades the reliability of distributed curvature sensors in practical applications.
Various solutions have been proposed to overcome this limitation by sensing strain and temperature simultaneously, such as discrimination from multi-peak Brillouin gain spectrum (BGS) , simultaneous monitoring of both Brillouin frequency shift (BFS) and Brillouin intensity [14–16], hybrid Raman-Brillouin system , hybrid Rayleigh-Brillouin system , and spatial-division multiplexing (SDM) techniques [19–21]. Although these methods have the ability to distinguish between strain and temperature, several defects limit their practicality.
In particular, in a hybrid Raman-Brillouin system that is based on Raman optical time-domain reflectometry (ROTDR), the main uncertainty is the low signal-to-noise ratio (SNR) of the anti-Stokes spontaneous Raman scattering (SpRS) signal. Because the pump power of the hybrid system is constrained by the stimulated Brillouin threshold power, which is much lower than the input power of ROTDR . Besides, the narrow linewidth laser used for Brillouin sensing is not efficient for ROTDR . To enhance the SNR of the hybrid Raman-Brillouin system, Fabry-Perot laser containing multiple narrowband longitudinal modes [24,25], optical pulse coding technique [23,25,26], and SDM technique have been proposed . However, these solutions need hardware modifications thus adding complexity and instability.
In this paper, we propose and experimentally demonstrate an approach for simultaneously distributed curvature and temperature sensing based on FMFs. A hybrid ROTDR and Brillouin optical time-domain analysis (BOTDA) system is implemented, inspired by our previous works in distributed FMF Raman  and Brillouin sensing . The SNR of the SpRS is improved thanks to the larger nonlinearities threshold of FMFs [27,28], and wavelet transform (WT) based signal-processing technique [27,29]. By central-alignment splicing the FMF and SMF with a fusion taper , the FMF is quasi-single mode (QSM) operated with efficient fundamental mode excitement, which makes the FMF compatible with conventional SMF based ROTDR and BOTDA hardware. The distributed temperature profile is obtained through SpRS signal while the fiber curvature is estimated by measuring the BFS variation.
When light travels in an optical fiber, spontaneous Brillouin scattering is generated through the acoustic phonons excited by electrostriction mechanism. The backscattered Brillouin Stokes light suffers a Doppler shift, which is called Brillouin frequency shift (BFS). The BFS is linear with the fiber strain and temperature :31].
By measuring the variation of BFS, the distributed fiber curvature can be estimated. When a fiber is curved, the optical beam suffers a lateral displacement , which leads to strain at the bending position . The bending-induced BFS change of the fiber fundamental mode is given by [9,11]:32]:
Therefore, the Eq. (2) can be reduced to:9]. Although multi-mode fiber (MMF) has a larger spot size than FMF, mode coupling is very prone to occur in MMF resulting in measurement errors, especially when bending happens . FMF, however, supports only a few controllable modes , and the coupling between the fundamental mode and higher order modes can be suppressed by increasing the effective index differences , which makes FMF suitable for distributed curvature sensing through QSM operation.
When the temperature is constant, the curvature along the FMF can be obtained by measuring the distributed BFS. However, ambient temperature cannot stay the same, especially in long distance applications. The BFS of the FMF-based BOTDA system with simultaneous temperature and curvature variations can be expressed as follows:
In order to solve this cross-sensitivity issue, ROTDR technique is employed. When pump pulses propagate along the FMF, spontaneous Raman scattering (SpRS) will arise from the interactions of the pump pulses and lattice vibration modes. The anti-Stokes SpRS signal depends strongly on the fiber temperature at the scattering point, while the Stokes SpRS signal is practically insensitive to temperature variation. The temperature information is extracted from the ratio of these two SpRS components :Eq. (5) is determined, and fiber curvature can be then derived.
Unfortunately, the SNR of the SpRS is very low, and degrades as the sensing range increases. Moreover, the pump power of the hybrid ROTDR-BOTDA system is limited by the stimulated Brillouin threshold power, which is much lower than the threshold power of ROTDR . Besides, the stimulated Brillouin threshold power decreases with longer fiber. Therefore, the performance of the hybrid system is ultimately determined by the SNR of SpRS.
To enhance the system performance, the SpRS traces are denoised based on WT. Wavelets are irregular, of limited duration, and non-symmetrical, thus they are suitable for describing anomalies, pulses, and other events . During WT based denoising process, the raw data is firstly decomposed into various frequency bands based on one wavelet. The frequency bands constitute a wavelet coefficients vector, where the mid-frequency range represents the valuable part of Raman signals while the high-frequency components are considered noise. Then the noise elements are reduced or removed through soft thresholding approach . Finally, the denoised Raman signal is obtained through inverse WT.
In the following, we experimentally demonstrate the hybrid ROTDR-BOTDA system in QSM operated FMF with the WT denoising process, which provides simultaneously distributed curvature and temperature sensing.
3. Fiber parameters and experimental setup
The FMF is designed and fabricated with a step-index profile. The fiber has a doped core with a diameter of 20.6 μm, a pure SiO2 cladding with a diameter of 125 μm and a 250 μm diameter coating. The numerical aperture of the FMF is about 0.13, which means that four linear polarization modes can be supported at 1550 nm wavelength. Moreover, the effective index difference of the fiber is optimized to ensure the QSM transmission. The transmission attenuation coefficient of the fundamental mode is 0.246 dB/km at 1550 nm and 0.434 dB/km at 1450 nm (that is, anti-Stokes SpRS wavelength). The specific properties of each linear polarization mode are shown in Table 1.
To perform simultaneously distributed curvature and temperature sensing along this FMF, our proposed hybrid ROTDR-BOTDA system is implemented as shown in Fig. 1. A narrow linewidth (< 1 kHz) fiber laser (NKT Koheras-BasiK-E15) operating at 1550 nm is used in this system. It is split into two distinct branches through a 3 dB coupler to generate both pump and probe light.
In the probe wave branch (that is, the upper path), the light is double-sideband intensity modulated with a high-extinction-ratio (> 30 dB) electro-optic modulator (EOM), operating in carrier-suppression mode and driven by a microwave synthesizer (MS, Rohde-Schwarz SMF100A). The MS signal is swept from 10.6 GHz to 10.9 GHz with steps of 2 MHz to obtain the BGS. Then the CW probe is launched into the FMF through a variable optical attenuator (VOA) with an average power of −6 dBm.
In the pump branch (that is, the lower path), a semiconductor optical amplifier (SOA) is exploited to generate high on-off ratio (> 50 dB) pulses. The SOA is driven by an arbitrary function generator (AFG, Tektronix AFG3252C) with a 15 ns width and 40 μs period pulsed signal, allowing for 1.5 m spatial resolution and maximum 4 km measuring range. The pulse width is optimized by taking into account the spatial resolution, the incident threshold power, the system SNR and the implemented hardware limitation. The optical pulses are then boosted by an erbium-doped fiber amplifier (EDFA), and followed by an optical band-pass filter (BPF) to filter out the amplified spontaneous emission (ASE) noise. Subsequently, the boosted optical pulses pass through a polarization switch (PS, General Photonics PSW-002-15-90) to mitigate the polarization effects of the hybrid ROTDR-BOTDA systems . Then the pump pulses are launched into the other end of the FMF through an optical circulator with an average optical power of 0.4 dBm.
At the receiver side, the Stokes and anti-Stokes SpRS are extracted by a Raman filter (> 35 dB isolation degree), while the Brillouin-amplified probe wave is obtained through a bandwidth-variable tunable filter (BVTF, Alnair Labs BVF-300CL). The Raman and Brillouin optical signals are detected by two 125 MHz avalanche photodetectors and one 125 MHz pin photodetector, respectively. The electrical signals of the photodetectors are sampled by an oscilloscope with a 250 MHz sampling frequency, corresponding to a sampling interval of 0.4 m per point. For BFS measurement, 256 averages are taken at each orthogonal polarization state and scanning frequency. At the same time, SpRS signals are averaged 76800 times. Each result requires 2 minutes acquisition time, which is limited by the response time of the laboratory equipment.
To demonstrate the ability of this hybrid system to measure distributed curvature and temperature simultaneously, the 20 m end of a 2 km long and coiled FMF is placed in a temperature-controlled chamber (TCC). The curvatures are applied at four 4 m FMF sections (1980-1996 m) using a pile of four cylinders with different radii (that are, 0.9, 1.1, 1.6 and 2.7 cm), while the last 4 m fiber (1996-2000 m) keeps stress free. The winding process is carried out carefully to avoid axial stress, distortion or bending the fiber in other axes. We wrap the fiber along the wall of the cylinder. The bending radius of the fiber is stick to the cylinder. During the winding process, the fiber is kept loosely without longitudinal stretching. Moreover, the fiber twist is monitored and corrected. To ensure the compatibility of the FMF and SMF based hardware, both ends of the FMF are central-aligned spliced with SMF to excite only the fundamental mode in the FMF. In addition, a fusion taper process is employed to reduce the splicing loss due to core diameter mismatch, as depicted in the inset of Fig. 1. The total end-to-end splicing loss is 3.2 dB.
4. Results and discussion
First, curvature and temperature sensitivities of BFS are calibrated. Figure 2(a) shows the three-dimensional map of BGS measured along the FMF at room temperature (20 °C), where red represents higher Brillouin gain. The Brillouin peak gain frequency changes obviously at the end of the FMF where the bending happens.
The BFS along the FMF is then estimated by the quadratic least-square fitting process on the BGS of each fiber position, as depicted in Fig. 2(b). The variation of the BFS along the coiled fiber is due to the stress during the coiling process. In fact, the parameter of the coiling process should be optimized and different from SMF considering the curvature sensitivity of FMF. As a reference, the BFS trace is measured when the last 20 m FMF is kept loosely and stress-free. Figure 2(c) shows the respective BFS trace of the last 40 m FMF when the fiber is under stress-free and bending conditions. The change of BFS is evident at the curved section and varies with the bending radius. Figure 2(d) shows the measured BGS of point A (before the bending position), B (at the bending position) and C (after the bending position) in Fig. 2(c). The Lorentzian fitting of each BGS is also plotted with solid curves in the figure. The full width at half maximum (FWHM) of the BGS stays around 90 MHz, which corresponds to the pulse width applied. Moreover, no relevant distortion of the BGS traces has been observed, which confirms the reliability of the measured results when the fiber is curved.
The curvature sensitivity of BFS is estimated by calculating the average BFS change of different bending radii. Taking into account the 250 μm thickness of the optical fiber coating, the actual bending radii are 0.9125, 1.1125, 1.6125 and 2.7125 cm. The bend-induced BFS changes are plotted in Fig. 3(a), where the fitting curve indicates that the curvature coefficient C is 16.654 MHz/cm−2.
In order to obtain the temperature coefficient A, the BFS is measured when the TCC is set at 20 °C, 30 °C, 40 °C and 50 °C, while the rest of the fiber is kept at the room temperature. As shown in Fig. 3(b), the BFS of the fiber in the TCC changes significantly at different temperatures. The measured BFS of each temperature in Fig. 3(c) is calculated using the data of the last 4 m stress-free fiber. The temperature sensitivity of BFS is 1.048 MHz/°C, which is estimated with a linear fitting. In addition, the uncertainty in the determination of BFS is calculated as the standard deviation of the difference between two consecutive measurements at room temperature. The standard deviation is attained from a window of 4 m, which contains 10 points of data at close positions. The calculated uncertainty is then fitted by a quadratic function as shown in Fig. 3(d). The worst BFS resolution is 1.046 MHz at the end of the fiber.
As the curvature and temperature dependences of BFS have been calibrated, ROTDR is employed to solve the cross-sensitivity issue of Eq. (5) by measuring the temperature simultaneously. Figure 4(a) shows the temperature profiles obtained through 76800 times averaged SpRS signals when the TCC is set at different temperatures. The temperature resolution is estimated by calculating the standard deviation of the retrieved 20 °C temperature profile along a window of 4 m, as shown in Fig. 4(b). The worst temperature resolution at the fiber end is 4.875 °C. However, the worst temperature resolution of our Brillouin system is only ~1.096 °C, which is calculated by multiplying the estimated BFS resolution by the temperature coefficient. As aforementioned, the measurement resolution of this hybrid system mainly depends on the performance of ROTDR system.
In order to enhance the system capabilities, the averaged SpRS signals are processed with a WT based denoising. The averaged signals are decomposed into three scales based on Daubechies 3 wavelet (db3), and denoised using soft threshold. Figure 5(a) compares the raw anti-Stokes Raman trace and the one obtained after denoising. The quality of the Raman trace is improved significantly and about 10 dB SNR enhancement is achieved. The temperature profiles estimated using the WT based denoised SpRS signals are plotted in Fig. 5(b), while the enlarged graphics of the last 40 m fiber is shown in Fig. 5(c). Moreover, the temperature resolution along the fiber is shown in Fig. 5(d). The worst temperature resolution at the fiber end is improved to 1.301 °C that is comparable to the Brillouin measurement.
Once the temperature information is retrieved from SpRS signals, the curvature can be derived with the measured BFS. Combining results in Figs. 3(b) and 5(c), the distributed curvature radius profiles when the TCC is set at different temperatures are obtained, as shown in Fig. 6(a). Distinct from the general optical fiber curvature sensors, the change of BFS in FMF is proportional to 1/R2 (the square of the fiber curvature). This feature means a high-precision measurement when the bending radius is small. The measured 1/R2 profiles and the actual value are demonstrated in Fig. 6(b). It is important to mention that no loss of spatial resolution arises during the measurement, which implies that the proposed hybrid system is feasible for the simultaneously distributed sensing of curvature and temperature at each point of interests.
The measurement errors of 1/R2 result from the combination of the measurement uncertainties of the Raman and Brillouin system. Considering that these two kinds of noise are not correlated, the resolution of 1/R2 can be estimated by calculating the propagation of uncertainty, as shown in Fig. 7. The worst measurement resolution is calculated to be about 0.333 cm−2 at the end of the FMF.
In conclusion, we proposed and experimentally demonstrated a simultaneously distributed curvature and temperature sensor using FMF based hybrid ROTDR-BOTDA system. Thanks to a larger spot size than SMF, the BFS change of the QSM operated FMF is employed for curvature estimation while the temperature variation is alleviated through SpRS signals. Only one narrow linewidth laser is used in this system to secure the simultaneous measurement and same spatial resolution. The Raman and Brillouin signals are separated through a Raman filter and detected simultaneously. The Raman signals are denoised based on WT to overcome the incompatible pump power issue of the hybrid system. Within 2 minutes measuring time, a 1.5 m spatial resolution is achieved along a 2 km FMF. The worst 1/R2 and temperature resolutions are about 0.333 cm−2 and 1.301 °C, respectively. Moreover, the measurement accuracy and range can be improved by optimizing the fiber structure, for instance, to enhance the curvature sensitivity with a larger fiber core. In addition, the proposed system is established using conventional ROTDR and BOTDA hardware. Therefore, distributed Raman amplification , optical pulse coding , advanced signal processing methods , or a proper combination of these techniques can be exploited to further enhance the system performance .
National Natural Science Foundation of China (NSFC) (61331010); the 863 High Technology Plan of China (2013AA013402); the Program for New Century Excellent Talents in University (NCET-13-0235); Fundamental Research Funds for the Central Universities (2016YXZD038); Major Program of the Technical Innovation of Hubei Province of China (2016AAA014).
We would like to express our gratitude to Jiajia Zhao for her contribution to the calculation of fiber properties.
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