Polarization maintaining (PM) fibers can be used for distributed force/pressure sensing in which the birefringence axis of the PM fiber should preferably be oriented 45° from the direction of the force/pressure for the maximum sensitivity. However, it is a challenge to achieve such 45° axis orientation for a long length of PM fiber in practice. In this paper, we report the development of what we believe the first equipment and process for making PM fiber based sensing tapes, capable of automatically adjusting the fiber axis orientation 45° with respect to the tape surface. In particular, we develop a machine vision system with the ability of continuously determining fiber axis orientation in real time as the fiber passes by and feeding back the orientation information to a fiber rotation apparatus to automatically adjust its orientation before fixing the fiber on a transparent PET tape with UV epoxy. We show the results of a successfully fabricated 70-m-long PM fiber sensing tape achieving an axis orientation accuracy of 45 ± 3° throughout the whole length of the tape, which is further validated with a distributed polarization crosstalk analyzer (DPXA). Finally, we demonstrate distributed transversal load sensing with 14 force applying weights randomly distributed along the sensing tape using the DPXA, with a polarization crosstalk measurement uniformity of 0.62 dB (standard deviation) using the same applied weight of 100 grams. The same sensing tape can also be used for pressure sensing with properly designed fixtures.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Distributed and quasi-distributed fiber optic sensing systems, such as those based on Brillouin scattering and fiber Bragg gratings (FBG), generally measure axial strain and temperature, but cannot directly measure transversal stress, pressure, or force, often required in many applications [1–3]. For example, in down-hole oil drilling applications, hot vapor is often forced into a drilled down hole to reduce oil viscosity and help the oil hidden in the rocks to release [4,5]. Therefore, it is often necessary to measure the pressure and temperature as a function of depth inside the down hole . It is possible to convert the axial strain sensing into transversal pressure/force sensing with some clever mechanical fixtures, however, it will inevitably increase the complexity and cost, while sacrificing the measurement accuracy . Therefore, distributed fiber sensing for directly measure the transversal pressure/force as a function of location is important.
The coupling of the powers between two orthogonal polarization modes in a polarization-maintaining (PM) fiber is known as polarization crosstalk. It can be shown that a transversal force or load can induce such a polarization crosstalk and a distributed polarization crosstalk analyzer (DPXA) based on white light interferometry [7,8] can be used to measure the magnitudes of different polarization crosstalk peaks induced at different locations [9–13]. Because a pressure can be converted to a transversal load or force  with a properly designed fixture, distributed pressure sensing may also be accomplished by analyzing the polarization crosstalk peaks in a PM fiber with a DPXA, although its feasibility is still an open issue requiring further investigation. In addition, we found in our previous studies that the position of the crosstalk peaks changes with temperature due to the temperature dependence of the birefringence in the PM fiber [15–17]. Consequently, the distributed polarization crosstalk analysis can also be used to measure distance resolved temperature variations. Since different transversal stresses cause crosstalk peaks of different heights in the vertical axis, while the temperature changes cause the locations of a polarization crosstalk peak to change in the horizontal axis, the pressure (or force) and temperature induced polarization crosstalk changes are independent from each other. Consequently, they can be sensed simultaneously without affecting each other’s measurement accuracy, a clear advantage over the systems based on Brillouin scattering and FBGs [18–20] in which the strain and temperature measurements are not independent in general and special measures must be taken to overcome such a cross-dependence . Alternative techniques for the distributed sensing of transversal load, force, or pressure include polarization sensitive optical frequency domain reflectometer (P-OFDR) and polarization analyzing OFDR (PA-OFDR) [22,23]. However, their practicalities for the application need to be further explored.
We have demonstrated distributed pressure sensing using a PM fiber based distributed polarization analysis system for measuring hydrostatic pressures as a function of depth in a water tank . To achieve the best pressure sensitivity in such a system, the pressure or force exerting on the PM fiber should be 45° from the birefringence axis of the PM fiber [13,14,24], although a scheme of twisting the PM fiber to remove the angular dependence was proposed  with increased system complexity. It can be shown later that such a 45° fiber orientation with respect to the direction of the pressure/force also makes the polarization crosstalk least sensitive to the fiber axis misalignment [7,13], an important characteristic in practice.
It is difficult to determine the birefringence axis of a PM fiber in the field, not to mention keeping it 45° from the direction of the pressure/force to be sensed in practice. In order to achieve the 45° fiber orientation for practical applications, we propose to first lay the PM fiber on a tape-like strip made with thin metal or synthetic material with its birefringence axis pre-aligned 45° from the strip surface to form a sensing tape, as shown in Fig. 1, which can be rolled in to a spool for easy transportation if necessary. The sensing tape can then be fixed onto a surface to sense the force or pressure against the surface, assuring 45° orientations for optimizing measurement sensitivity.
In this paper, we describe the development of such PM fiber based sensing tape, focusing on the technology for automatically adjusting the orientation of fiber’s birefringence axis 45° to the tape surface. Specifically, we develop a machine vision system which adopts the Polarization Observation by Lens Effect (POL) method originally developed for PM fiber fusion machines  for analyzing the fiber side images to determine fiber birefringence axis orientation. Such a vision system is mounted on the sensing tape fabrication equipment we developed to continuously obtain fiber axis orientation information in real time as the fiber passes through an imaging window and feedback the information to a fiber rotation apparatus on the equipment to automatically adjusts fiber axis orientation before fixing the fiber on a transparent PET tape with UV epoxy. We utilize a distributed polarization crosstalk analyzer (DPXA) [8,26] modified for distributed sensing applications to validate the PM fiber axis orientation of the resulting sensing tape and show the results of a successfully fabricated 70-m-long PM fiber sensing tape, which achieved an axis orientation accuracy of 45 ± 3° throughout the whole length of the tape. Finally, we demonstrate distributed transversal load sensing with 7 different pressure applying weights and 14 identical weights randomly located along the sensing tape using a DPXA, with a measurement uniformity of 0.62 dB (standard deviation) using the same applied weight of 100 grams. We believe this is the first report of the equipment and process capable of making the PM fiber based sensing tapes with automatic 45° birefringence axis orientation adjustment, which achieved the longest such sensing tape for distributed load sensing applications. With a proper mechanism or suitable fixtures to convert pressure into transversal force, the same tape may also be used for distributed pressure sensing, subject to further validation. Note that the sensing tapes can be pre-made in a factory or laboratory and then be taken to the field to be installed with the sensing fixtures transferring the external force or pressure perpendicularly onto the tape surface, which automatically guaranties the direction of the force or pressure to be sensed 45° with respect to the PM fiber axis.
2. Theoretical background
As mentioned in the introduction, when a section of PM fiber is subject to a transversal force, as shown in Fig. 1(a), optical power originally propagating in the slow axis will couple to the fast axis, and vice versa. The coupling ratio or polarization crosstalk h, which is defined as the ratio between the coupled power and the original power, can be expressed as [13,24]:
The relationships between the crosstalk and the external line force f can be obtained numerically using Eqs. (1) and (3) and plotted in log scale shown in Fig. 1(b). It can be observed that 1) the highest crosstalk is obtained when the force angle α is at 45°, and 2) the crosstalk is least sensitive to the force angle variations around 45°. The relationship described by Eq. (1) will be verified experimentally in the next section.
Therefore, in order to achieve the highest sensitivity for sensing the force/pressure using polarization crosstalk analysis, the PM optical fiber should be laid on the sensing tape with its birefringence axis oriented 45° with respect to the tape surface while the force/pressure to be sensed is applied perpendicular to the tape surface.
3. Equipment and process
3.1 Sensing tape
We select a transparent PET film with a thickness of 0.3 mm and a width of 10 mm as the base material for the sensing tape. The film is waterproof with a smooth surface and having good anti-aging, anti-sticky, and anti-UV properties. A length of PANDA PM fiber  is bonded on the PET film using an ultraviolet (UV) curing adhesive at periodical locations, as shown in Fig. 2. As will be discussed in the next section, the birefringence axis of the PM fiber will be aligned 45° against the surface of the PET film with a specially designed machine.
We notice in the experiments that curing induced shrinkage of UV adhesives generally produces stresses, which in turn may induce residual polarization crosstalk in the PM fiber. This will generate an elevated polarization crosstalk background and reduce the detection sensitivity. Therefore, a proper UV adhesive with low curing stress must be identified and selected experimentally.
Three different types of adhesives [28–30] were studied. In particular, a proper amount adhesive of each type was applied onto a small section of PM fiber of the same batch and the corresponding residual crosstalk data were then obtained using a DPXA after the adhesives was cured, as shown in Fig. 3. It is evident that all adhesives induced residual polarization cross-talks. However, of the three adhesives studied, Norland Optical Adhesive 65 (“NOA65”) was most flexible and induced the least crosstalk, while Master Bond UV15 with lower shrinkage (1-2%) and much higher temperature resistance than other UV adhesives induced somewhat higher residual polarization-crosstalk. Finally, DSM950-200 from Focenter produced worst polarization crosstalk. Consequently, we select NOA65 UV as the adhesive for bonding the PM fiber to the PET film.
The spacing between the UV adhesive bonding points is also an important factor to consider for the fabrication of the sensor tape. Small spacing will result in a large number of bonding points along the tape and hence more adhesive shrinkage induced residual polarization crosstalk peaks in the fiber to worsen the detection sensitivity. In addition, in applications the sensing points should be between the bonding points to avoid the adhesive induced anomalies, requiring the spacing to be sufficient large to minimize the adhesive influences. On the other hand, too large a spacing between the bonding points may compromise the bonding strength of the fiber on the PET film. Therefore, the bonding spacing must be optimized in practice. In our fabricated sensing tapes, the spacing between bonding points is 2 cm, which still need to be optimized in the future for the best results.
3.3 Fabrication equipment and machine vision system
Figure 4 shows the equipment we designed and produced to fabricate the PM fiber based sensing tape described above. As illustrated in Fig. 4(a), the equipment consists of two synchronized wheels on the right-hand side, one is for supplying the PET film and the other for the PM fiber. The fiber supplying wheel is mounted on a fiber axis rotation apparatus such that it can be rotated back and forth for adjusting the birefringence axis angle of the PM with respect to the PET film surface. The PET film and the PM fiber are moved together passing through a side-image observation window where a machine vision system made of a light source for illuminating the fiber, a CCD camera with a lens system for projecting the fiber side images onto the CCD sensor array. The transparency of the PET film allows for the illumination to pass through and refractive index matching liquid is used between the fiber and PET film to eliminate the influence of the air gap in order to ensure satisfactory image sharpness.
The fiber side-images are analyzed in real time by the machine vision system as the fiber passes through the imaging window to determine the orientation of fiber’s birefringence axis, which is then feedback to the fiber rotation apparatus to adjust the fiber axis orientation. After the fiber section with the axis orientation determined passes through the side-image observation window, a UV adhesive drop is applied to the fiber in a preset spacing with a computer controlled adhesive disperser before it is cured by a UV light. Finally, the sensing tape with the fiber bonded on the PET film is wound on the big spool on the left. Note that two fiber clamps are also used to clamp down the fiber in the image observation window in the vertical direction, but still allowing the fiber to rotate. They can be made with electro-magnets and controlled by the computer, although in our experiment we manually put two glass carriers as the clamps because such electrically activated clamps were not implemented by the time of experiment. Figure 5 shows the flow chart for the process described above.
3.4 Image analysis
The system uses the Polarization Observation by Lens Effect (POL) method  originally developed for PM fusion splicers for analyzing the fiber side images to determine fiber birefringence axis orientation. Due to the different refractive index values of the coating, cladding, stress axis and core of the PM fiber, incoherent parallel light passing through the fiber will refract to form an image representative of the internal structure of the PM fiber, as shown in Fig. 6 in which fiber side images corresponding to fiber axis orientation angles of 0°, 45° and 90° are displayed. In particular, the widths of the vertical stripes in Figs. 6(a)–6(c) represent the projection distances between different boundaries of the fiber internal structure at different fiber axis orientation angles. For example, the 1st stripe from the left in Fig. 6(a) correspond to the projection distance between the outer and the inner boundaries of the outer most fiber coating of the PM fiber, which does not change when the fiber orientation angle is changed. Similarly, the width of the 2nd stripe in Fig. 6(a) represents the projection distance between the outer and the inner boundaries of the inner fiber coating of the PM fiber, which also does not change when the fiber orientation angle is changed. Figures 6(g)–6(i) are the brightness graph derived from Figs. 6(a)–6(c) with which the width of the stripes can be easily extracted.
We find that the width d3 of the 3rd stripe from the left in Fig. 6 is the most sensitive and best behaved to the changes of the PM fiber’s orientation angle, as shown in Fig. 7. This width actually corresponds to the projection distance between the boundaries of the cladding and one of the stress rods of the PM fiber, and therefore can be used as a characteristic variable to determine the fiber axis orientation angle. The theoretical expression for d3 is2(b). The fiber structure dimensions r1, r2, r3, r4, r5, can be obtained by first taking a fiber end picture as Fig. 2(b) and then measuring the relative dimensions of r2, r3, r4, r5 with respect to r1. Since the fiber outer diameter 2r1 can be determined with a caliber or other means, the absolute dimensions of r2, r3, r4, r5 can be accurately determined. With carefully measured r3, r4, r5, we obtain
On the other hand, stripe width d3 can be experimentally obtained with the brightness graphs as in Figs. 6(g)–6(i) for different orientation angles α as shown in Fig. 7. The magnification factor k can be readily obtained by taking the ratio of d3 in Fig. 6(a) (the number of pixels across d3 multiplied by the pixel size of 3.45 µm) and (r3-r4) obtained previously for the case of α=90°, which is further verified using the CCD image of a resolution chart having some lines with known widths by taking the ratio of the width of a line on the CCD image (the number of pixels across the line multiplied by the pixel size of 3.45 µm) and the physical width of the line. Curve-fitting the data in Fig. 7 obtains the formula below:5).
Note that because of the manufacturing tolerances, the structural dimensions of the PM fiber may vary slightly from batch to batch. Therefore, the curve-fitted formula for each fiber batch will be obtained first by the machine vision system before making the PM fiber sensing tape in practice. The fiber axis orientation angle of each fiber section can be determined with the knowledge of by the computer, which then feedback to the fiber axis rotation apparatus for adjusting the fiber axis orientation as described previously. As will be shown in the next section, any orientation angles can be obtained with this method, although we aim at laying the fiber at the optimal orientation angle of 45° on the PET film.
Because of the rotational symmetry of the PM fiber internal structure, d3 is symmetric with respect to the orientation angle α so that both +α and -α result in the same d3 value, as shown in Fig. 6. Therefore, it is possible that the computer may get confused and cause abrupt fiber rotation in the process. This problem can be resolved by noting that in Fig. 7 the two slopes of the curve have the opposite signs around the +45° and -45° as the fiber orientation angle is changed. We include an algorithm to obtain this slope information by slightly rotating the fiber axis, which in turn is able to identify fiber’s angular position unambiguously for avoiding the abrupt fiber rotations.
4. Results and discussion
4.1 Verification of the theoretical results
As described in Eq. (1), when a load or force is applied onto a PM fiber at a particular location, a polarization crosstalk peak will occur at the location and its amplitude is sensitive to the angle between the direction of the force/pressure and the fiber’s birefringence axis angle, which can be measured and validated with a DPXA (PXA-1000, General Photonics Corporation) [8,26]. The instrument was specially modified with about 5 times less spatial measurement uncertainty than that of a standard unit for distributed sensing applications and has a polarization cross-talk measurement floor of -80 dB, cross-talk repeatability and accuracy of ±0.5 dB, a spatial resolution of 4 cm, and a spatial measurement uncertainty of ± 2.53 cm.
To experimentally verify Eq. (1), we fabricated a 2m-long sensing tape using the equipment and process described above, with different sections having different fiber axis orientation angles ranging from 0° to 90°, measured again with the POL method described in the previous section after the tape was made. The PM fiber is of PANDA for operating at 1550nm with a core, cladding, and coating diameters of 6.92 µm, 125 µm, and 250 µm, respectively. In order to apply a consistent force on all fiber sections, we designed and made a pressure plate with the dimensions of 15×10×0.3 mm and a weight of 5g, as shown in Fig. 8(a). The long dowel pin on the right end was designed to be in contact with the sensing fiber, and the two short dowel pins with the same diameter were to be on both sides of the sensing fiber for balancing purpose. We also slightly elevated the two short dowel pins with two waste optical fibers of the same size as the sensing fiber to ensure the pressures plate is leveled when sitting on top of the sensing fiber, as shown in Fig. 8(b). All dowel pins and the waste fibers were all glued onto the steel plate with the same UV adhesive for fixing the fiber on the PET film. In the experiment, the pressure plate was put on top of the sensing fiber and a weight of 100g was placed on the center of the pressure plate for applying a constant force on the sensing fiber. Finally, a DPXA was used to measure the polarization crosstalk value at each point the pressure was applied using the pressure plate, with 21 points all together, one at a time, as shown in Fig. 8(a). The measurement results are shown in Fig. 9.
The diameter of the force applying dowel pin on the pressure plate is 1.5 mm and the force acting width was estimated to be 0.1 mm, resulting in an effective stress on the PM fiber of approximately 3.5 N/mm. In the calculation, only 1/3 of the weight was included because the pressure plate had 3 dowel pins of the same diameter to share the load applied. Using the expression for the crosstalk ratio h given in Eq. (1) and Eq. (3), the polarization crosstalk as a function of the fiber axis orientation angle was obtained for a wavelength at 1550 nm, with the results also shown in Fig. 9.
Overall, the experimental and theoretical results agreed reasonably well, except at fiber axis orientation angles less than 5° or larger than 85° where the polarization crosstalk values were too small so that the measurement accuracy were affected by the residual polarization crosstalk induced in the manufacturing process. This experimental result further confirms the necessity for orienting the PM fiber axis 45° from the tape surface.
4.2 Validation of 70 m-long sensing tape
With the equipment and process described above, a 70 m-long PM fiber based sensing tape operating at 1550 nm band was successfully fabricated with the fiber birefringence axis align nominally 45° with respect to the tape surface. To verify the accuracy of the fiber axis orientation, we randomly selected 20 points in the 70 m-long PM fiber sensing tape, and then applied the POL method to measure the angle between the fiber birefringence axis and the PET film, with the result shown in Fig. 10. It can be observed that the repeatability of the measured angle is within ±0.6° and the average angles of the 20 points range between 42° and 48°, resulting in an angular accuracy of ±3° around 45°.
One may also use a DPXA to further validate the quality of the sensing tape, particularly the consistency of PM fiber’s birefringence orientation angle with respect to the tape surface. We therefore randomly selected 14 points in the 70 m-long PM fiber sensing tape to use the DPXA and the pressure plate described in Fig. 8 to measure the polarization crosstalk induced by 100 g weight. In this experiment, 14 identical pressure plates described in Fig. 8(a) were made and placed onto the 14 points on the sensing tape, with a 100g weight placed on each pressure plate. The DPXA was used to simultaneously measure all induced polarization crosstalk peaks, with the resulting polarization crosstalk measurement shown in Fig. 11. It is evident that there appeared 14 polarization crosstalk peaks of similar heights, with a maximum difference less than 2.11 dB and standard deviation of 0.62 dB, indicating an excellent uniformity of fiber orientation angle alignment along the sensing tape. The experiment above is also in fact an excellent demonstration for the distributed force sensing using the PM sensing tape. One may notice that in Fig. 11 the residual polarization crosstalk (RPC) peaks (black curve) of the sensing tape are not consistent at different locations along the tape and appeared to be higher at larger distances. Some of these RPC peaks are caused by unwanted stresses on the PM fiber from the shrinkages of the adhesive at the bonding points (Fig. 3). In the experiments, the curing time of UV adhesive, the amount of adhesive and the irradiation power of the light source all lead to the difference of the stress on the fiber and therefore the variations of the RPC peaks. In addition, due to the limited space in the laboratory, it is difficult to lay the 70 m long sensing tape flat, resulting in bending and twisting of the sensing tape and hence the additional RPC peaks. We believe the unwanted stresses are more severe in the fiber section from 40 m to 70 m, which leads to the increased RPC peaks. Further improvements on the fabrication and handling of the sensing tapes are required to reduce the RPC peaks. Nevertheless, there are also valleys in the RPC curve to support more sensitive stress sensing.
Finally, we further demonstrated distributed transversal load sensing with the 70 m sensing tape using 7 pressure plates randomly placed on the sensing tape, with weights ranging from 10 g to 200 g, as shown in Fig. 12(a). It is evident that the system can clearly distinguish weights less than 10 g (corresponding to a line force of 0.33 N/mm). We also obtained the calibration curves of crosstalk vs. weight at five randomly selected sensing points, compared with the theoretical curve of Eq. (1), as shown in Fig. 12(b). As can be seen that these calibration curves have reasonably good repeatability, however, they deviate significantly from the theoretical curve when the weights applied to the PM fiber are small. This deviation is mainly due to the cushion effect of the fiber buffer (250 µm) on the PM fiber used because Eq. (1) did not take the buffer into account. Therefore in practice, the calibration curves must be used for converting the polarization crosstalk values to the weight values. Note that the nonlinear response may complicate the implementation of the sensing system and compromise the sensing accuracy across the sensing range, however, with a properly implemented calibration procedure using the calibration curves, the inaccuracy caused by the nonlinearity can be minimized digitally. Note from Eq. (1) that the sensing sensitivity can be controlled by changing the acting width l of the force with respect to the PM fiber beat length. The maximum sensitivity occurs when the force acting width is (2n-1)/2 of the fiber beat length. Therefore, for small scale weight sensing, one can design the sensing plate with a force acting width close to (2n-1)/2 of the beat length. For large scale force sensing, the force acting width can be designed away from (2n-1)/2 beat length.
In summary, we report in this paper what we believe the first equipment and process for fabricating PM fiber sensing tape with fiber birefringence axis oriented 45° from the tape surface for distributed force/pressure sensing applications. We developed a machine vision system and adopted the POL method for the fiber axis orientation angle determination to enable automatic alignment of the fiber orientation while laying the fiber on a PET film. We successfully fabricated such a 70 m-long sensing tape, achieved a tolerance of ±3° for the fiber axis orientation angle, and demonstrated distance resolved transversal force/load sensing with good uniformity and repeatability using the tape. We point out that the same sensing tape also be used for pressure sensing using properly designed fixtures to convert pressure into transversal load. We also experimentally verified the theoretical expression relating the polarization crosstalk with the fiber axis orientation angle, using a fabricated sensing tape while obtaining the fiber orientation angle at different positions along the sensing tape using the machine vision system.
It is important to point out that the biggest remaining hurdle preventing using PM fiber for distributed sensing in practice is how to align the fiber birefringence axis orientation in the field, although both the theory and the interrogation method [8,13,24] for using PM fiber for distributed sensing have already been reported. The work presented in this paper demonstrated a practical solution for solving this last major hurdle, which was never reported previously to the best of authors’ knowledge. We believe the development of the equipment, process, and method described in this paper is an important advancement for the practical use of PM fiber for distributed force/pressure sensing.
National Natural Science Foundation of China (61705057, 61975049); Research Start-up Foundation of High-Level Talents Introduction (801260201243, 8012605); Key R & D project of Hebei Province (19212109D).
XSY is also a consultant for General Photonics Corporation, a division of Luna Innovations, USA.
The authors declare no conflicts of interest.
1. C. Hong, Y. Zhang, G. Li, M. Zhang, and Z. Liu, “Recent progress of using Brillouin distributed fiber optic sensors for geotechnical health monitoring,” Sens. Actuators, A 258, 131–145 (2017). [CrossRef]
2. A. K. Singh, S. Berggren, Y. Zhu, M. Han, and H. Huang, “Simultaneous strain and temperature measurement using a single fiber Bragg grating embedded in a composite laminate,” Smart Mater. Struct. 26(11), 115025 (2017). [CrossRef]
3. L. Schenato, A. Pasuto, A. Galtarossa, and L. Palmieri, “An Optical fiber distributed pressure sensing cable with Pa-sensitivity and enhanced spatial resolution,” IEEE Sens. J. 20(11), 5900–5908 (2020). [CrossRef]
4. U. Abdulkadir, J. Hashim, M. Alkali, and A. Kumar, “Application of thermal investigation methods in developing heavy-oil recovery: phase one,” International Journal of Advance Research Ideas and Innovations in Technology 2(5), 102–120 (2017).
5. Q. Zou, S. Dou, C. Hu, Y. Pan, S. Xie, W. Wang, M. Zhang, and Y. Liao, “A novel noise suppression method for white light extrinsic Fabry-Perot interferometric fiber-optic pressure sensor in heavy oil thermal recovery downhole environment,” Proc. SPIE 8421, 8421BI (2012). [CrossRef]
6. B. Qi, G. R. Pickrell, P. Zhang, Y. Duan, W. Peng, J. Xu, Z. Huang, J. Deng, H. Xiao, Z. Wang, W. Huo, R. G. May, and A. Wang, “Fiber optic pressure and temperature sensors for oil down hole application,” Proc. SPIE 4578, 182–190 (2002). [CrossRef]
7. M. Tsubokawa, T. Higashi, and Y. Negishi, “Mode couplings due to external forces distributed along a polarization-maintaining fiber: An evaluation,” Appl. Opt. 27(1), 166–173 (1988). [CrossRef]
8. Z. Li, X. S. Yao, X. Chen, H. Chen, Z. Meng, and T. Liu, “Complete characterization of polarization-maintaining fibers using distributed polarization analysis,” J. Lightwave Technol. 33(2), 372–380 (2015). [CrossRef]
9. Z. Zhang, T. Feng, Z. Li, J. Zhou, P. Hao, and X. S. Yao, “Experimental study of transversal-stress-induced polarization crosstalk behaviors in polarization maintaining fibers,” in SPIE/COS Photonics Asia(Proc. SPIE 11191, Advanced Sensor Systems and Applications IX, 2019), p. 111910W.
10. T. Feng, D. Ding, Z. Li, and X. S. Yao, “First quantitative determination of birefringence variations induced by axial-strain in polarization maintaining fibers,” J. Lightwave Technol. 35(22), 4937–4942 (2017). [CrossRef]
11. K. Hotate and S. O. S. Leng, “Transversal force sensor using polarization-maintaining fiber independent of direction of applied force: proposal and experiment,” in 15th Optical Fiber Sensors Conference Technical Digest. OFS 2002(Cat. No.02EX533), Portland, OR, USA, 2002, pp. 363–366.
12. T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009). [CrossRef]
13. H. Zhang, Y. Wang, G. Wen, D. Jia, and T. Liu, “Frequency demodulation of dynamic stress based on distributed polarization coupling system,” J. Lightwave Technol. 36(11), 2094–2099 (2018). [CrossRef]
14. Z. Zhang, T. Feng, X. Wang, Y. Shang, M. Wang, and X. S. Yao, “Demonstration of liquid pressure fiber sensing based on distributed polarization crosstalk analysis,” in 2018 Asia Communications and Photonics Conference (ACP), Hangzhou, 2018, pp. 1–3.
15. Z. Ding, Z. Meng, X. S. Yao, X. Chen, and M. Qin, “Accurate method for measuring the thermal coefficient of group birefringence of polarization-maintaining fibers,” Opt. Lett. 36(11), 2173–2175 (2011). [CrossRef]
16. H. Su, Z. Zhao, T. Feng, D. Ding, Z. Li, and X. S. Yao, “Demonstration of distributed fiber-optic temperature sensing with PM fiber using polarization crosstalk analysis technique,” in SPIE/COS Photonics Asia (2016), pp. 100251F.
17. D. Ding, T. Feng, Z. Zhao, H. Su, Z. Li, and X. S. Yao, “Demonstration of distributed fiber optic temperature sensing using polarization crosstalk analysis,” in Conference on Lasers and Electro-Optics (Optical Society of America, San Jose, California, 2016), p. JTu5A.105.
18. M. Maheshwari, S. C. Tjin, Y. Yang, and A. Asundi, “Wavelength-shifted chirped FBGs for temperature compensated strain measurement,” Sens. Actuators, A 265, 231–235 (2017). [CrossRef]
19. M. Ramakrishnan, G. Rajan, Y. Semenova, and G. Farrell, “Overview of fiber optic sensor technologies for strain/temperature sensing applications in composite materials,” Sensors 16(1), 99 (2016). [CrossRef]
20. R. Xing, C. Dong, Z. Wang, Y. Wu, Y. Yang, and S. Jian, “Simultaneous strain and temperature sensor based on polarization maintaining fiber and multimode fiber,” Opt. Laser Technol. 102, 17–21 (2018). [CrossRef]
21. M. Zhu, H. Murayama, D. Wada, and K. Kageyama, “Dependence of measurement accuracy on the birefringence of PANDA fiber Bragg gratings in distributed simultaneous strain and temperature sensing,” Opt. Express 25(4), 4000–4017 (2017). [CrossRef]
22. C. Wei, H. Chen, X. Chen, D. Chen, Z. Li, and X. S. Yao, “Distributed transverse stress measurement along an optic fiber using polarimetric OFDR,” Opt. Lett. 41(12), 2819–2822 (2016). [CrossRef]
23. T. Feng, Y. Shang, X. Wang, S. Wu, A. Khomenko, X. Chen, and X. S. Yao, “Distributed polarization analysis with binary polarization rotators for the accurate measurement of distance-resolved birefringence along a single-mode fiber,” Opt. Express 26(20), 25989–26002 (2018). [CrossRef]
24. F. Tang, “Measurement of polarization coupling in polarization-maintaining fiber using white light interferometry and its applications,” Ph. D. Thesis, Tianjin University, (2005) (in Chinese).
25. J. Yan, L. Miao, T. Huang, S. Che, and X. Shu, “Development of method for polarization alignment of PANDA polarization maintaining fiber,” Opt. Fiber Technol. 53, 101999 (2019). [CrossRef]