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Abstract
In this paper, a novel distributed twist sensor based on frequency-scanning phase-sensitive optical time-domain reflectometry (φ-OTDR) in a spun fiber is proposed and demonstrated. Owing to the unique helical structure of the stress rods in the spun fiber, fiber twist gives rise to the variation of the effective refractive index of the transmitting light, which can be quantitatively retrieved through frequency shift using frequency-scanning φ-OTDR. The feasibility of distributed twist sensing has been verified by both simulation and experiment. For proof of concept, distributed twist sensing over a 136 m spun fiber with a 1 m spatial resolution is demonstrated, and the measured frequency shift shows a quadratic fitting dependence on the twist angle. In addition, the responses of both clockwise and counterclockwise twist directions have also been explored and the experiment result indicates that the twist direction can be discriminated since the frequency shift directions are opposite in the correlation spectrum. The proposed twist sensor possesses some outstanding advantages, including high sensitivity, distributed twist measurement and twist direction recognition capability, etc., which is very promising for specific applications in industry, e.g., structural health monitoring, bionic robots, etc.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Twist sensing has drawn significant interest in various applications, including structural health monitoring [1], 3-D shape sensing [2] and bionic robots [3], etc. For instance, the reconstruction of the 3D shape of medical catheters and surgical instruments in minimally invasive surgery requires distributed twist information [4]. However, due to the large size and complicated manufacture, the applications of conventional twist sensors based on electromagnetic and electric methods are severely restricted [5]. Recently, fiber-optic sensors have attracted much attention as a result of many advantages, such as small size, lightweight, corrosion resistance and insensitivity to electromagnetic interference, etc. Therefore, fiber optic twist sensors turn out to be another attractive solution for these applications. So far, various optical fiber twist sensors have been reported, which can be mainly categorized into two types, including the fiber gating-based twist sensors [6–9], and the optical fiber interferometer-based twist sensors [10–12]. The fiber grating-based twist sensors have been developed by using different fiber gratings, such as long period gratings (LPGs) [6], fiber Bragg gratings (FBGs) [7], titled FBGs (TFBGs) [8], and polarization-maintaining chirped FBG (PM-CFBG) [9], etc. In addition, as for the optical fiber interferometer-based twist sensors, they are normally fabricated by various fiber interferometers, including the Sagnac interferometers (SIs) [10], multi-modes interferometers (MMIs) [11], and Mach-Zehnder interferometers (MZIs) [12], etc. However, these two types of twist sensors just be able to measure twist at a single spot, but not manage to achieve long range and distributed twist measurement, which severely restricts their applicability in many applications.
On the other hand, distributed fiber optical sensors (DOFS) are able to monitor every point along the fiber link with a single sensing fiber, which have been widely used for distributed sensing applications, including the distributed measurement of temperature, strain and vibration, etc. Among various distributed fiber optical sensors, the frequency-scanning φ-OTDR is well-known for its outstanding performance of ultra-high sensitivity and measurement resolution [13,14]. The technology has been widely used for distributed temperature and strain sensing with ultra-high resolution using normal single mode fibers (SMFs). However, due to the restriction of fiber geometry, the conventional SMFs based frequency-scanning φ-OTDR sensors are generally only sensitive to temperature and strain, but might not to other parameters. In recent years, the special optical fibers-based frequency-scanning φ-OTDR sensors have been explored, which makes the monitoring parameters of the sensing system more diversified, such as gas sensing [15], humidity sensing [16] and salinity sensing [17]. Gas sensing is achieved by utilizing the hollow-core photonic bandgap fiber, where phase modulation takes place when periodically modulated pump light is absorbed by gas molecules. Humidity sensing and salinity sensing are realized by using the polyimide coated fibers as the polyimide is a hygroscopic material that swells or shrinks by absorbing or losing water when the external humidity or salinity changes. Even though the unique frequency-scanning φ-OTDR sensors with ultra-high sensitivity and measurement resolution have shown excellent performance in a variety of applications, distributed twist sensing based on this technology has not been reported yet, while the recent studies have shown that the special optical fiber-based interrogation system turns out to be a promising solution to enable this specific application.
In this work, a novel distributed twist sensor utilizing frequency-scanning φ-OTDR in a spun fiber is developed. The spun fiber exhibits significant twist sensitivity due to the helical structure of the stress regions, in which the effective refractive index of the transmitted light changes as the fiber twist takes place, and the frequency-scanning φ-OTDR has been used to measure the fiber twist effect by retrieving the fiber twist induced frequency shift in the correlation spectrum between two measurements. Both simulation and experiment have been performed to validate the feasibility of the proposed distributed twist sensing technique. For concept validation, distributed twist sensing with 1 m spatial resolution over 136 m sensing range is demonstrated, and the measured frequency shift indicates a quadratic fitting dependence on the twist angle. Furthermore, discrimination between the clockwise and counterclockwise twist direction is also demonstrated, as the two cases give rise to opposite frequency shift directions in the correlation spectrum. The proposed novel sensor provides a very promising approach to enable high-sensitivity distributed twist measurement, which will find a lot of important applications in the future.
2. Operation principle and simulation
The working principle of frequency-scanning φ-OTDR technology is illustrated in Fig. 1. As shown in Fig. 1(a), pump pulses with different frequencies are launched into the sensing fiber in sequence, and the Rayleigh backscattering signal of each optical frequency is acquired, respectively. Due to the non-uniform distribution of the refractive index caused by the jitter of the medium density throughout the fiber, the obtained time-domain trace shows jagged intensity distribution, which is resulted from the interference of Rayleigh scattering within the pulse width, as shown in Fig. 1(b). A 3D optical spectrum showing the optical intensity distribution as a function of optical frequency and fiber length can be constructed by replotting the jagged intensity traces of all frequencies into one figure, as shown in Fig. 1(c). External disturbance, such as stress or temperature change applied to the sensing fiber will results in a variation in the effective refractive index of the transmitted light, and the phase differences between the scattering points in the sensing fiber vary accordingly, which leads to a change at the disturbed region in the 3D optical spectrum. A laser frequency shift can be utilized to compensate for this phase difference since it is related to both the frequency of the optic pulse and the effective refractive index in the fiber. The retrieval of frequency shift is done by calculating the cross-correlation between two measurements using the 3D optical spectrum data. Eventually, the disturbance can be retrieved from the frequency shift of the corresponding Rayleigh scattering spectrum with respect to the reference spectrum without external disturbance, as shown in Fig. 1(d).
Fig. 1. (a) Principle of frequency-scanning φ-OTDR; (b) Rayleigh backscattering time domain trace; (c) 3D Rayleigh backscattering optical intensity distribution as a function of optical frequency and fiber length; (d) correlation spectrum between two measurements.
Figure 2(a) shows the schematic diagram of the spun fiber. This fiber has a central core and two periodic helical stress rods at eccentric positions, which makes it to possess the circular polarization-maintaining characteristic. The spun fiber has a core diameter of 6.5 um, two stress regions diameter of 25 um, a cladding diameter of 125 um, and a helical period of 800 um, respectively. And the images of cross section and side view of the spun fiber are shown in Fig. 2(b) and Fig. 2(c), respectively. Due to the helical structure of the stress region of the spun fiber, fiber twist will give rise to deformation of the fiber geometry from its initial circular cross section to an elliptical one, as a result the strain induced by fiber twist will cause a significant change in the effective refractive index of light. The impact of fiber twist induced deformation on the property of the transmitting light has been investigated by simulation using finite element method. The stress region may be twisted into a distorted ellipse with bending rather than straight long and short axes since it is at an eccentric position. However, considering that the applied twist is very tiny compared with the pitch of the stress region, so the stress region after deformation can be assumed as a normal ellipse. Therefore, in order to simplify the structure, a circle stress region and deformed elliptical stress regions with different eccentricities have been used for simulation, which refers to the cases without and with twist applied, respectively. The eccentricity is defined as:
where a is the length of the long axe of the ellipse, and b is the length of the short axe of the ellipse. Note that different eccentricities of the elliptical stress region correspond to different twist levels in the simulation. The simulated effective refractive indexes of the fundamental mode with different eccentricities are shown in Table 1. The result reveals that the deformation of fiber geometry induced by fiber twist will cause noteworthy variation of effective refractive index of the transmitting light. As an example, Fig. 3 shows the simulated mode field distribution for a normal circle stress region without deformation and a deformed elliptical stress region with an eccentricity of 0.5 (e = 0.5), respectively. The result indicates that the transmitting light still remains single-mode property, however the effective refractive index is changed from 1.446959 to 1.446976 with an order of 10−5. This indicates that fiber twist will cause the variation of local optical property in the spun fiber, and this disturbance can be measured using frequency-scanning φ-OTDR.Fig. 2. (a) Schematic diagram of the helical structure of the spun fiber; (b) optical microscope image of cross section of the spun fiber; (c) optical microscope image of the side view of the spun fiber.
Fig. 3. The structure of the fiber cross sections without and with twist applied and the simulated mode field distribution without and with twist applied.
Table 1. Simulation results with different twist levels
The adopted algorithm to measure the frequency shift of Rayleigh backscattering spectrum is the correlation peak detection method, which can be expressed as:
If no environmental perturbation occurs between the two measurements, which indicates no change in the effective refractive index, the peak of the cross-correlation will be at f = 0, otherwise the correlation peak will appear at f =$\Delta \nu $, and $\Delta \nu $ is the frequency shift of the Rayleigh backscattering spectrum required to be measured. In addition, assuming tiny refractive index changes $\Delta n$($\Delta n \ll n$), the frequency shift $\Delta \nu $ to compensate for the given $\Delta n$ can be expressed as:
where n is the initial effective refractive index of the fiber and ${\nu _0}$ is the central frequency of the optic pulse.3. Experimental setup
The experimental setup of the proposed distributed twist sensor is shown in Fig. 4. A frequency-stabilized coherent laser with a narrow linewidth of 100 Hz operating at 1550 nm is used as the light source. The continuous light output from the light source firstly passes through an electro-optic modulator (EOM) with a bandwidth of 20 GHz, where the modulator is controlled by a microwave signal source to generate carrier-suppressed double-sideband modulation and then one of the sidebands is filtered out by a fiber grating filter with a bandwidth of 6 GHz. In order to maximize the carrier suppression, a polarization controller is employed at the input of the EOM since it is polarization dependent. In the meantime, considering the wide bandwidth of the grating filter, in order to filter out the carrier and another sideband, the modulation frequency of the microwave source is set to be higher than 10 GHz. Then the filtered sideband is chopped into optical pulses through a semiconductor optical amplifier (SOA) with high extinction ratio, which is modulated by an electrical pulse signal generated by the AWG. The pulse width used in the experiment is 10 ns, corresponding to a spatial resolution of 1 m. The optical probe pulses are then amplified by an erbium-doped fiber amplifier (EDFA), which is followed by a band-pass filter (BPF) to remove the amplified spontaneous emission (ASE) noise. Finally, the pump pulses are launched into the fiber under test (FUT) with a length of 136 m through a circulator. At the receiver side, a photodetector with a bandwidth of 500 MHz is used to convert the optical signal into an electrical signal, which is then collected by an oscilloscope with a sampling rate of 1GS/s.
Fig. 4. Experimental setup of the proposed system. EOM: electric-optic modulator; SOA: semiconductor optical amplifier; AWG: arbitrary waveform generator; EDFA: erbium-doped fiber amplifier; BPF: band-pass filter; PD: photodetector; FUT: fiber under test.
In our experiment, the frequency of laser is scanned by changing the output frequency of the microwave generator from 10 GHz to 13 GHz with a step of 20 MHz, thereby generating 151 frequencies in total. The fiber segment between 132 m and 133 m of the FUT is clamped utilizing two fiber rotators, as illustrated in Fig. 4. Then twists with different levels are applied to the clamped fiber segment with one end fixed, while the other end is rotated clockwise to different angles, and the Rayleigh backscattering spectrums are acquired, respectively. In order to improve the signal-to-noise ratio of measurements, the optical time-domain trace at each frequency is averaged by 512 times. Afterwards, in order to investigate the feasibility of twist direction recognition, counterclockwise twist with different levels have also been applied to the clamped fiber segment, and the data are collected in the same way, respectively.
4. Experimental results and discussion
4.1 Twist measurement results
In order to calibrate the response of the proposed system, calculations of cross-correlation between different measurements have been implemented, where the collected Rayleigh backscattering traces of different frequencies with clockwise twist applied are used to calculate the cross-correlation with the reference spectrum traces without twist applied, respectively. Figure 5(a) shows a typical measured spectra of Rayleigh backscattering without and with a 5° twist at the location of 132 m. It turns out that the spectrum waveforms are quite similar, but just with a frequency shift. The frequency shift is determined by the cross-correlation of the two spectra, of which the value is 120 MHz, as shown in Fig. 5(b).
Fig. 5. (a) Frequency spectra with and without twist at the location of 132 m; (b) cross-correlation curve between the two spectra traces.
Then the cross-correlation spectrum is obtained by calculating the cross-correlation along the fiber, as shown in Fig. 6(a). It is observed that an apparent frequency shift appears in the cross-correlation spectrum at the location where fiber twist takes place, while the correlation peak of the rest fiber segments remains at f = 0 where there is no fiber twist and the environment is stable. Figure 6(b) shows the enlarged view of the cross-correlation spectrum around the position with twist applied, where a frequency shift segment with a length of 1 m is observed, which is consistent with the set condition.
Fig. 6. (a) Cross-correlation spectrum along the fiber distance; (b) enlarged view of the cross-correlation spectrum around the location with twist applied.
In the experiment, in order to investigate the dependence of the frequency shift on the twist angle, different twist angles from 0° to 25° in turn with an interval of 5° have been applied to the sensing fiber. Since the proposed system is also sensitive to temperature, the twist measurement result might be affected by slight environmental temperature change during the measurement, therefore the average value of the frequency shift caused by temperature fluctuation within the untwisted fiber segment are used to compensate for the frequency shifts at the twisted segment, and the measured frequency shift after compensation under different twist angles are shown in Fig. 7(a). In addition, a dashed line which is the mean value of each frequency shift trace between 132 m and 133 m of the fiber segment has also been plotted in Fig. 7(a) for reference. It is worth noting that a threshold value of cross-correlation peak is set to isolate the invalid results where the correlation peak is very low, and the final mean values of the measured frequency shifts are obtained with those available results. It can be seen that the frequency shift increases with the increment of twist angle. The average values of the frequency shifts in Fig. 7(a) as a function of the twist angle are plotted in Fig. 7(b). Apparently, the frequency shift exhibits a nonlinear dependence on the twist angle, therefore the experiment data is fitted with a quadratic function. The fitting curve has a R-square coefficient of 0.9883 and a RMSE of 70.06 MHz. It is observed that the slope of the fitting curve increases as the twist angle enlarges, which indicates that the proposed sensor has higher sensitivity for larger twist angle. The error bars of each frequency shift are also plotted in Fig. 7(b) to characterize the uncertainty of the measurement results. It is important to note that the measurement dynamic range of the system can be improved by expanding the frequency scanning range of the modulated pulses. As can be seen in the dotted circle in Fig. 7(a), the frequency shifts around the front and the rear of the twisted fiber segment are also changed, rather than stable. This might be caused by the twist of both ends of the twist region brought by the applied twist. In addition, it is observed that the frequency shift traces within the 1 m fiber twisted segment are not flat, but showing fluctuation, which might result from not only the nonuniform twist level along the twisted segment but also incorrect fitting of the correlation spectrum caused by the insufficient signal intensity at the corresponding positions.
Fig. 7. (a) Measured frequency shifts at different twist angles; (b) frequency shift as a function of twist angles.
4.2 Twist direction recognition
As can be seen in Fig. 7, the clockwise fiber twists with different angles give rise to positive frequency shifts in the cross-correlation spectrum, which indicates the increments of the effective refractive index according to Eq. (3). This makes sense because the two stress regions of the fiber have the same clockwise helical directions and the clockwise twist will aggravate the helical structure, thus leading to an increase in the effective refractive index of light. On the contrary, the helical structure will be released with counterclockwise twist applied, which will cause a decrease in the effective refractive index of light. As a result, the response of system may be different in comparison with the case of clockwise fiber twist.
In order to investigate the characteristic of cross-correlation spectrum of counterclockwise twist, a typical 5° counterclockwise twist is applied to the fiber and the corresponding frequency shift is interrogated, as shown in Fig. 8. Figure 8(b) shows the enlarged view of the cross-correlation spectrum around the location with counterclockwise twist applied. Obviously, a negative frequency shift is obtained, which has opposite frequency shift direction with respect to the case of clockwise twist. It turns out that the unique feature can be utilized to achieve twist direction recognition by identifying the frequency shift direction in the cross-correlation spectrum. In addition, it is worth mentioning that a different frequency shift mean value of -153 MHz compared to the case of clockwise twist with the same 5° twist is obtained. This could be due to the different changes in the helical structure brought by the opposite twists. For the sake of adequate verification of the twist direction recognition, more experiments have been performed to investigate the dependence of the frequency shifts on the counterclockwise twists. Different counterclockwise twist angles from 0° to 25° in turn with an interval of 5° have been applied to the sensing fiber, and the measured frequency shifts after compensation under different angles are shown in Fig. 9(a). It can be observed that the increase of the frequency shift with twist angle exhibits a similar trend compared with the clockwise condition. Likewise, the average values of the frequency shifts in Fig. 9(a) as a function of the twist angle and the error bars of the corresponding frequency shifts are plotted in Fig. 9(b). The fitting curve has a R-square coefficient of 0.9901 and a RMSE of 65.83 MHz, and the fitting function is different from the clockwise condition. This might result from the fact that the twists with the same angle but opposite directions can lead to different change levels in the helical structure, since the clockwise and counterclockwise fiber twist gives rise to aggravation and releasing on the helical structure, respectively.
Fig. 8. (a) Cross-correlation spectrum along the fiber distance; (b) enlarged view of the cross-correlation spectrum around the location with counterclockwise twist applied.
Fig. 9. (a) Measured frequency shifts at different counterclockwise twist angles; (b) frequency shift as a function of counterclockwise twist angles.
4.3 Discussion
In this experiment, the laser frequency is scanned with 151 frequencies in total, and the Rayleigh time-domain traces of each frequency need to be averaged, so that it takes 1-2 minutes to finish single measurement, thus the measurement speed is slow. Since this work has validated the feasibility of the proposed distributed twist sensing using spun fiber, in the future fast dynamic twist sensing can be achieved using the fast frequency-scanning technology [18,19] and the chirp-pulse technology [20]. In addition, it is worth mentioning that although the sensing range in our experiment is only 136 m, it can be much extended. Finally, it can be observed from Fig. 7 and Fig. 9 that the range of deviation and fluctuation from the correct spectral offset is larger as the twist increases, which mainly results from the fitting error in the cross-correlation. It can be improved by broadening the frequency scanning range to obtain adequate frequency information, meanwhile optimizing the cross-correlation and fitting algorithm to decrease the fitting error, e.g., by performing the least mean squares method [21], the phase cross-correlation [22] and the sinc interpolation fitting algorithm [23]. While, reducing the spatial resolution might not be an effective method to solve this problem because it requires to shorten the pulse width, which degrades dramatically the SNR of the Rayleigh backscattering light, leading to an increase in the fitting error of the cross-correlation.
5. Conclusions
In summary, we propose a novel high-sensitivity distributed twist sensor utilizing frequency-scanning φ-OTDR in a spun fiber in this paper. Thanks to the unique helical stress region of the spun fiber, a change occurs in the effective refractive index of the transmitting light when external twist is applied. This change gives rise to a frequency shift in the cross-correlation spectrum of the frequency-scanning φ-OTDR system, thereby distributed twist measurement can be achieved by retrieving the frequency shift. In our experiment, 136 m distributed twist sensing with a spatial resolution of 1 m is demonstrated and the measured frequency shift reveals a quadratic fitting dependence on the twist angle, which suggests a higher sensitivity with the increment of the twist angle. Additionally, the response of the proposed system to both clockwise and counterclockwise twist has been further explored. The experiment results confirm that the twist direction can be discriminated since the direction of the frequency shifts are opposite in the correlation spectrum. It is believed that the proposed novel high-sensitivity distributed twist sensing system with the capability of twist direction recognition will find great potential and application prospects for torsion measurement in a wide variety of applications.
Funding
National Key Research and Development Program of China (2021YFB2800902); National Natural Science Foundation of China (61931010, 62105111); Hubei Province Key Research and Development Program (2021BAA008); Fundamental Research Funds for the Central Universities (HUST: 2021XXJS026); Natural Science Foundation of Hubei Province (2021CFB049).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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