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The liquid level detection principle of cladding mode frustrated total internal reflection (CMFTIR) effect is proposed. The significant enhancement of CMFTIR effect is realized through macro-bend coupling system in which the dark-field coupling phenomenon between two multimode polymer optic fibers is observed through experiment. Especially twisted macro-bend coupling structure (TMBCS) is adopted to achieve stable coupling of two naked POF. The testing result showed that the dark-filed forward coupling efficiency reached 2‰ and the extinction ratio of the liquid level probe reached 4.18dB. Compared with existing optical fiber liquid level sensors, the TMBCS probe is simpler, robuster, and cheaper. In addition, the TMBCS has the potential for displacement or stress sensing.
© 2014 Optical Society of America
1. Introduction
When it comes to optical fiber sensors people usually associate with difficult processing technology with high accuracy such as fiber gratings [1,2], side-polishing on fibers [3] and fused-taper [4] with nanometer or micron scale. It is hard to believe that two ordinary commercial bare POF without any pretreatment which are just twisted together and then made a curve can be an effective sensing system. The system is called macro-bend coupling system(MBCS), which we will introduce in this paper. Actually, many optical sensors can be regarded as an energy coupling system. These coupling systems have a common character in which some optical parameters can be modulated by external environment in the process of coupling. Constructing and using a new coupling system usually means the birth of a novel type sensor. Montero, et al. [5] used side-polishing technique on POF to make fiber coupler as refraction index and liquid level sensor. Yan et al. [6] reported a thermal sensor which had been made by micro sphere-taper coupling system. The system needs to detect the resonant spectrum shift to get sensing signal. Ding, et al. [7] presented a temperature sensor that has the structure of ~2.5um Micro fiber Coupler Tip made through fused taper technique. From a new Angle of energy coupling system to re-examine these sensors mentioned above, it is easier to find out some common problems. The structures of systems [5,6] are not stable so the consistency of the sensors is not satisfactory. These sensors must be fixed by glue, so that the losses of radiation and absorption are inevitable. The systems [6,7] are fragile, so these two sensors are not robust. The producing technologies of the systems [5,6] are complicated, so the yield of sensors is low and the productive cost is high. The signal detection method of the systems [6,7] is very expensive. It is because high-resolution optical spectrum analyzer is needed. Overall, the characteristics of these sensors are essentially conditioned by the coupling system themselves.
Currently, as a representative liquid level probe type, the principle of frustrated total internal reflection is wildly used. Golnabi et al. [8] utilized prism to make reflection inclined plane as liquid level probe and realized the extinction ratio 0.03dB. Bottacini et al. [9] reported a liquid level probe whose reflected tip was made by standard 980/1000 POF with 90 ° angle tip polished at the fiber’s end face and the extinction ratio of the probe can reach 1.09dB. Compared with these existing optical fiber liquid level sensors, the liquid level probe reported in this paper, as shown in Fig. 1, has realized extinction ratio more than 4.18dB. The facture of probe is simpler and cheaper. In addition, the probe has better robustness.
Fig. 1 Macro-bend coupling phenomenon is exhibited by 650nm red light laser coupling in TMBCS(P0:light input port; P1:straight output port; P2:forward coupling port;P3:backward coupling port).
2. Macro-bend coupling phenomenon and coupling experiments of MBCS
As is known, coupling can occur between two parallel optical fibers whose cores must be close enough with each other [10]. In order to avoid crosstalk, thick enough cladding is generally set up outside the core of communication optical fibers [11]. Therefore, when making fiber couplers, the usual approach is to destroy the original cladding structure, such as fused-taper [12] or side polishing [13]. But such production methods restrict their sensing applications, because these coupling structures are very fragile. And it is difficult to ensure consistency of sensors due to sophisticated processing technology.
In this paper, we propose the realization of light coupling between two POF by using light radiation caused by macro-bend effect. To the best of our knowledge, it is the first time that the macro-bend coupling phenomenon is observed through experiment. And it is also the first time that MBCS is reported and used as liquid level sensor (see section 4). As is shown in Fig. 1, MBCS is made by two ordinary untreated naked POF (Mitsubishi, SK40), so the structure is robust. Stable coupling is achieved by adopting twisted macro-bend coupling structure (TMBCS), which means two naked POF are just twisted together and then bent to a loop. We can see from Fig. 1, the light emitted by red laser propagates in a fiber and couples into the neighboring fiber simultaneously.
We know that when the bending radius of the fiber is smaller than a certain threshold, bending can change core mode into radiation mode [14]. This effect is called macro-bend radiation loss, as shown in Fig. 2.
In the bending area of optical fiber, more lights refract at the core-cladding interface and a fraction of the power of the incident lights radiate out of the active fiber. The power of radiation light can be calculated from:
where, is the power in the incident rays and T is the Fresnel transmission coefficient in the POF and can be represented as [15]:where, is the incident angle,is the total internal reflection critical angle. It can be proved that when the bending radius R decreases, the incident anglewill increases [16]. From Eq. (2), we know that the greater of the, the greater of the T and the same as the macro-bend radiation loss is. As long as choosing the POF whose cladding is thin and flexibility is good and due to macro-bend effect, radiation light field will form around the outside space of cladding at the bending part of fiber (Fig. 2). Under this coupling pattern, with the decrease of the parameter R of the active fiber, more energy will transfer to the outside of the active fiber, and then the coupling power in passive fiber increases significantly. It is the macro-bend effect that brings the happening of the coupling and the coupling power is directly modulated by macro-bend radius. So we name this phenomenon as “macro-bend coupling (MBC) “.In this section forward coupling power of PMBCS(parallel macro-bend coupling structure) and TMBCS was studied through the experiment. The experiment system is shown in Fig. 3, 660 nm LED (Thorlabs, M660F1) light source was used. P1 and P2 port were monitored by optical power meter (Thorlabs, PM100USB). The initial output power of P1 was 3.051 mw when the active fiber was straight and there was no macro-bend radiation loss either. In order to exclude the influence of visible light, the fibers were put into black thermal shrinkage casing before test (Fig. 4).
The PMBCS was made by two parallel naked POF without twisting and was put into black jacket as the same. It can be seen that one end of the macro-bend loop was fixed by the device in Fig. 4, and the other end could move freely and horizontally along the groove. Because it is difficult to make the macro-bend loop be a perfect circle, it is also hard to guarantee the accuracy of the test when the macro-bend radius is used as the independent variable. In our experiment the perimeter of the macro-bend loop was used as independent variable. As shown in Fig. 4, the scales were tagged on the black jacket with the interval of 5 mm. If the fiber moves one scale toward one direction, it means the perimeter of the macro-bend loop increases or decreases 5mm.
3. Test results and analysis
Six repeated test results of PMBCS are shown in Fig. 5, it can be seen that the forward coupling power has gradually increased along with the decrease of the perimeter of the macro-bend loop. Since the perimeter relating to the macro-bend radius is shorter,the stronger the macro-bend radiation is, and the higher the forward coupling power is. It can also be seen that the coupling power of PMBCS was not stable because of the unstableness of the relative position of the two parallel fibers of PMBCS. Especially at the moving situation, the stableness of PMBCS will be worse. It leads to the breakage of the consistency of the measuring results.
Fig. 5 Forward coupling power of PMBCS changes with perimeter of macro-bend loop (A-F are the numbers of tests).
In order to achieve stable macro-bend coupling, the TMBCS was adopted. As shown in Fig. 6, the tests were repeated four times and the results showed that the stability of the TMBCS was good. Among these four tests, A and C showed the state that the free end of the TMBCS moved to right direction, B and D to the opposite situation. It can also be found from Fig. 6 that the forward coupling power of TMBCS is much higher than that of PMBCS (about 18 times at 90mm). This demonstrates that the TMBCS is more suited to be a liquid level probe and has the potential as a stress or displacement sensor.
Fig. 6 Forward coupling power of TMBCS changes with perimeter of macro-bend loop (A-D are the numbers of the tests).
We know that the center-to-center spacing is an important parameter which influences the coupling effect of two parallel fibers. According to the coupled-mode theory, the coupling coefficient C between two adjacent parallel fibers can be represented as [10]:
Among them, d is the center-to-center spacing of two fibers,is core radius, is dimensionless frequency.determines the degree of isolation between the fibers. Numerical calculation is carried out in literature [17] by using Eq. (3), and the result shows that the coupling coefficient C decreases significantly with the increase of d. It means the coupling capability between the fibers is been reduced apparently when the center-to-center spacing is getting large. In the experiments shown in Fig. 5 and Fig. 6, the fibers are put into thermal shrinkage tube. Although the tube could fix and tight the fibers at a certain degree, in fact it is a bad method when the fibers is parallel. When two fibers are put into tube in parallel, the large center-to-center spacing is not only easy to exist, but the spacing d is not stable. It is because the relative position of the two fibers is easy to change. This causes the lowness and unstableness of the forward coupling power. It is the twisting which solves the problems by making the two fibers keep close to each other tightly and hold stable d.
Although we qualitatively explained the change of coupling power in Fig. 5 and Fig. 6 by Eq. (3), it is not suitable for quantitative calculation in this paper’s situation. It is because the Eq. (3) neither considers the change caused by bending nor the influence of radiation fields [18]. And we know that the fiber is isotropic, but the bend has directions. When two parallel fibers are simultaneously bent upwards and downwards the result of coupling is different from the forwards and backwards. And under the condition of twisted fibers, the two different situations exist in TMBCS at the same time. It makes the calculation more complicated and difficult.
From the experiment we can also see that the forward coupling power which comes from the radiation light field is significantly weaker than the energy inside the active fiber and the coupling light is separated from light source path. So the radiation light field is called dark-field, and the coupling light is called dark-field signal. As shown in Fig. 3, the dark-field light couples into the neighboring passive fiber waveguide which is bent as the same as the active fiber. And the coupling light propagates towards forward and backward directions. Because the coupling power of MBC comes from dark-field light, a new parameter is needed to describe this effect. We call it “dark-field forward coupling efficiency”, and define as follows:
where, is the output power of forward coupling port, appeared in Fig. 3, and is the macro-bend loss tested in port P1. Factors influencing are very complicated. POF support a large amount of modes, and every mode has particular macro-bend radiation characteristic [19]. So the radiation field which plays the major role in the process of macro-bend coupling is very complicated. In addition, macro-bend will lead to the change of the refractive index profile (induced-anisotropy) [20] at the bend part of the fiber and change the mode field distribution in fiber [21]. Meanwhile, twisted structure in this paper makes the problem more complicated.According to Eq. (4), the dark-field forward coupling efficiencyof TMBCS was plotted, and showed in Fig. 7. From Fig. 7 we can see that increases with the decrease of the perimeter, but it is still less than 2‰ when the perimeter is 90mm. We know that the macro-bend coupling energy comes from the dark-field. Originally weak energy and low will increase the difficulty of detection. In this paper, TMBCS is adopted, and is enhanced effectively to reach up to hundreds of nanowatts so that the forward coupling power is not so difficult to be detected. But the dark-field forward coupling efficiency is still so small that the coupling power is quite easy to be disturbed by visible light existing in the testing environment. So the optical isolation is necessary in our experiment.
Fig. 7 Dark-field forward coupling efficiency of TMBCS changes with perimeter of macro-bend loop (A-D are the numbers of the tests).
4. CMFTIR enhancement and TMBCS liquid level sensing experiment
In this section, the liquid level sensing principle of cladding mode frustrated total internal reflection (CMFTIR) in POF is proposed. It is the first time to find that the TMBCS proposed in this paper can significantly enhance the CMFTIR effect from experiment. At theoretical calculation, the optical fiber is usually regarded as infinite cladding structure, which means that the lights refract on the core-cladding interface and lose forever after refraction. But in practical optical fibers, cladding itself plays the role of waveguide [22].After the reflection at cladding-environment interface, partial power of the rays are still allowed to return to the fiber core, and the energy of the light rays returning to the core is related to the refractive index of external environment. When the external environment of the optical fiber is changed from air to liquid, the refractive index of environment becomes larger, approaching or even exceeding the refractive index of cladding(1.402 for SK40 [23]). So the total internal reflection condition of cladding will be restrained or damaged, and then partial light rays reflected at the cladding-environment interface cannot return. As shown in Fig. 3, when the macro-bend coupling system is immersed in liquid, the output power at P1 and P2 declines. We call this effect as “cladding mode frustrated total internal reflection (CMFTIR)”. In paper [16], Zhao et al. have reported that the radiation mode power in the scattering light of side-emitting optical fiber is determined by the ambient refractive index. Now we can claim that this effect is the same effect that was depicted above and should be called as CMFTIR effect.
But usually in straight fiber with integral structure, the CMFTIR effect is not significant. It is because the power of the cladding mode which can be modulated by external refraction index is negligible. Formerly, in the theoretical derivation, due to the need of simplifying calculation, this cladding part of the fiber modes is usually omitted. The CMFTIR effect in the current fiber sensing systems is seen as interference, and is often stripped by cladding mode stripper in order to avoid the impact of this effect [24].In order to understand the CMFTIR effect in fibers, we separately tested the influence of finger touching on fibers which separately have three different kind of structures (straight, macro-bend and TMBCS). It is already known that some cladding mode light power will lose when the cladding of the naked fiber is touched by finger because of CMFTIR effect. So the strength of the CMFTIR effect can be estimated by the decline of the normalized output power, as shown in Fig. 8.
It can be seen from Fig. 8 that there was no power decline in straight fiber under finger touch. So it can be concluded that the CMFTIR effect hardly exist in straight fiber. We can utilize the macro-bend effect to change mode field distribution within the POF. And this change will prompt a lot of cladding modes in bent fiber. It means that the CMFTIR effect is enhanced. As shown in Fig. 8, there was nearly 5% power decline, when the macro-bend fiber was touched at the top of the bending area of the fiber. Although the macro-bend effect increases the proportion of cladding mode which can be modulated by external environment, the power of cladding mode is still very weak compared with the power of light source. So the sensing signal is still very easy to submerge in light source fluctuations. In the previous work [16], the techniques of difference and correlation detection are used to improve the system’s signal-to-noise ratio. And lock-in amplifier is needed to make correlation operation and obtain the weak signals which are submerged in noise. So the ideal sensing applications cannot be achieved just relying on macro-bend effect. In this paper, the significant enhancement of CMFTIR effect by TMBCS was found. It can be seen in Fig. 8 that the normalized power declines about 30%-40% when the TMBCS is slightly touched by finger. So the TMBCS was utilized to measure the dark-field coupling signal (P2, Fig. 3) and to achieve three purposes:
1. The dark-field signals separate from the light source path, so the influence of the light source fluctuation is reduced. Although the dark-field signal is coupled from the light source path and its background noises contain the composition from the light source fluctuations, the background noises of dark-field are extremely different from that of bright-field. The light source fluctuation detected through fiber is the total sum of fluctuations of all the light modes (core and cladding mode) propagating in the fiber. Because the light source energy in fiber is mainly concentrated in the core, the fluctuation of core mode energy is the main background noises in bright-field. And this part of lights does not go through the reflection at the cladding-environment interface, so its energy has no contribution to the effect of CMFTIR, but has destructive effect to the signal-to-noise ratio of sensor. The core mode fluctuations will be completely received by detecting the bright-field signal through straight output port P1. In the situation of detecting the dark-field signal, the active fiber core mode energy is well restricted. Only the fluctuations of partial cladding mode is transferred to the outside of the active fiber and retained in the passive fiber through macro-bend radiation and coupling. So the background noises of dark-field signals include the fluctuations coming from the active fiber cladding mode and visible lights in surrounding. The results of experiment showed that the fluctuations coming from cladding mode is negligible, when the stable LED light source (Thorlabs, M660F1) is used. And the fluctuations of visible lights in surrounding become the major part of background noises in dark-field.
2. In the passive fiber the proportion of the cladding mode is higher, which can be modulated by external environment. This means the effect of CMFTIR is more obvious.
3. In coupling process, when light radiates out of the active fiber, the light is modulated by environment refractive index for the first time. Then the light is secondary modulated by environment when the light propagates in the bent passive fiber. This increases the depth of modulation.
Therefore, through analysis we believe that liquid level sensor based on macro-bend coupling system can achieve good signal-to-noise ratio through testing the dark-field coupling signal output by P2 port (Fig. 3). In our experiment, in order to exhibit the natural characteristic of TMBCS liquid level senor, signal processing techniques were not used. The test results obtained directly by optical power meter (Thorlabs, PM100USB) intrinsically represent the advantage of dark-field signals. The performance of liquid level probes is usually described through extinction ratio, and defined as follows:
Among them, is the output power of the forward coupling port P2 (Fig. 3), when sensor probe is immersed in liquid; is in the air. Before test we packaged TMBCS by binding the fibers at the macro-bend position with common conducting wire for further stabilizing the structure (Fig. 9). In addition, we use silica gel (GD414) to fix the cross position of the fibers which is sensitive to stress. We selected 95mm as the perimeter of TMBCS probe so that the coupling power could approximately reach 650nW when the initial output power of P1 was 3.051 mw.
The liquid level probe was tested using a bucket of water in dark room, and the result is shown in Fig. 10. It can be seen that “first bath” [25] phenomenon appeared at the beginning. When the originally dry probe was put into water for the first time, the change of the forward coupling power was dramatic, and the extinction ratiowas about 5.14dB at this moment. Since then, a little of water had been hung on the probe after the probe was taken out of the water. The amount of the water hanging on the probe was random, so the peak of the curve is not smooth. And at the influence of the hanging water, was declined but still higher than 4.18dB.
Fig. 10 20 times repeated water immersion test for TMBCS liquid level probe (when the power is above the red line the probe is in the air and dry; when in the middle of the red and green it is also in the air but wet; when under yellow it is in the water).
In addition, we can also see the power of the forward coupling port was about 550nW before “first bath”. This value is less than that in Fig. 6 when the perimeter of macro-bend loop is 95mm. We think this loss is caused by packaging process, so the packaging technology should be studied carefully to reduce the additional loss.
4. Discussion and conclusion
Optical fiber liquid level sensors are divided into two kinds [26]: the sensors for punctual measurement and for continuous measurement. The continuous liquid level sensor can accomplish real-time measuring of the continuously changing liquid level [16,26]. In this situation, the changing level will cause the change of the submerged length or percentage of the sensor. The sensors for punctual measurement are usually arranged in different places with many sensors [27]. They can also be controlled by a stepping motor system to move up and down with only one sensor [28]. The sensing probe designed in this paper is used for punctual measurement, and needs many probes horizontally fixed in different positions or just one probe controlled by a stepping motor system. Naturally, immersing the entire device into liquid will more or less influence the measurement accuracy of the liquid level sensor. But when the TMBCS probe is arranged horizontally, it can be entirely immersed by 2mm high liquid. It is because the probe is made by two naked fibers whose diameters are 1mm, and the total thickness is 2mm after twisting. In the practical application, 2mm measurement accuracy is already enough in most situations. Certainly the punctual liquid level probe has some undeniable defects, such as the lack of real-time, low accuracy and complicated control system. But in some fields, i.e. oil field, the punctual liquid level probe is playing important role. The continuous liquid level sensor is the trend of development, but the sensor based on optical fiber, which can satisfy the needs of practical use, is rare now. Utilizing the liquid level detection principle of CMFTIR and the TMBCS proposed in this paper, a breakthrough will hopefully be made in this field. We are dedicating to this purpose, and carrying on the research and experiment. But limited by the length of paper, we can only report the relevant work in the following papers.
In summary, the macro-bend coupling phenomenon in TMBCS has been first showed through experiment. By using TMBCS we enhanced the dark-filed coupling power and the stability of the coupling structure. We have experimentally studied the coupling characteristics of TMBCS and demonstrated its potential as sensors. In addition, we have firstly found that the TMBCS could significantly enhance the CMFTIR effect. Little attention has been paid to the CMFTIR effect in existing researches, because the CMFTIR effect is more like a pure interference [24] when there is no effective enhancement method. Theoretical analysis shows that good signal-to-noise ratio could be achieved by measuring the dark-field coupling power with P2 port of TMBCS. The testing result of the liquid level probe made by TMBCS showed that the extinction ratiowas higher than 4.18dB. Compared with the existing fiber optic liquid level sensor [8,9], the TMBCS probe greatly reduces production costs and complexity, and has better robustness and performance. The main existing problem of TMBCS probe is that it is easy to be disturbed by visible light because of the small. So it is important to find out methods to increaseeffectively in next research step. Besides, the additional loss of TMBCS probe is high and affected by many factors in the process of packaging. In order to ensure the consistency of the sensor, the additional loss caused by encapsulation must be studied carefully next. After all, the TMBCS proposed in this paper will play an important role in the field of liquid level detection, and in other fields such as stress and displacement measurement.
Acknowledgments
This work was supported by the Major State Basic Research Development Program of China (Grant No. 2012CB723404) and the National Natural Science Foundation of China (No. 51275491 and NO. 61275166).
References and links
1. K. R. Sohn and J. H. Shim, “Liquid-level monitoring sensor systems using fiber Bragg grating embedded in cantilever,” Sens. Actuators A Phys. 152(2), 248–251 (2009). [CrossRef]
2. X. Dong and R. Zhao, “Highly sensitive distributed liquid-droplet sensor based on evanescent-wave linearly chirped fiber Bragg grating,” Opt. Commun. 282(4), 535–539 (2009). [CrossRef]
3. X. Dong and R. Zhao, “Detection of liquid-level variation using a side-polished fiber Bragg grating,” Opt. Laser Technol. 42(1), 214–218 (2010). [CrossRef]
4. X. Dong, W. Liu, and R. Zhao, “Liquid-level sensor based on tapered chirped fiber grating,” Sci. China Technol. Sci. 56(2), 471–474 (2013). [CrossRef]
5. D. S. Montero, C. Vázquez, I. Möllers, J. Arrúe, and D. Jäger, “A self-referencing intensity based polymer optical fiber sensor for liquid detection,” Sensors 9(8), 6446–6455 (2009). [CrossRef] [PubMed]
6. Y. Z. Yan, C. L. Zou, S. B. Yan, F. W. Sun, Z. Ji, J. Liu, Y. G. Zhang, L. Wang, C. Y. Xue, W. D. Zhang, Z. F. Han, and J. J. Xiong, “Packaged silica microsphere-taper coupling system for robust thermal sensing application,” Opt. Express 19(7), 5753–5759 (2011). [CrossRef] [PubMed]
7. M. Ding, P. Wang, and G. Brambilla, “Fast-response high-temperature microfiber coupler tip thermometer,” IEEE Photon. Technol. Lett. 24(14), 1209–1211 (2012). [CrossRef]
8. H. Golnabi, “Design and operation of a fiber optic sensor for liquid level detection,” Opt. Lasers Eng. 41(5), 801–812 (2004). [CrossRef]
9. M. Bottacini, N. Burani, M. Foroni, F. Poli, and S. Selleri, “All-plastic optical-fiber level sensor,” Microw. Opt. Technol. Lett. 46(6), 520–522 (2005). [CrossRef]
10. A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. 62(11), 1267–1277 (1972). [CrossRef] [PubMed]
11. A. H. Cherin and E. J. Murphy, “Quasi-ray analysis of crosstalk between multimode optical fibers,” Bell Syst. Tech. J. 54(1), 17–45 (1975). [CrossRef]
12. D. Irawan, J. Saktioto, Ali, and M. Fadhali, “Birefringence analysis of directional fiber coupler induced by fusion and coupling parameters,” Optik 124(17), 3063–3066 (2013). [CrossRef]
13. M. Yasin, S. W. Harun, Samian, Kusminarto, and H. Ahmad, “Simple design of optical fiber displacement sensor using a multimode fiber coupler,” Laser Phys. 19(7), 1446–1449 (2009). [CrossRef]
14. D. Gloge, “Bending loss in multimode fibers with graded and ungraded core index,” Appl. Opt. 11(11), 2506–2513 (1972). [CrossRef] [PubMed]
15. J. Arrue, J. Zubia, G. Fuster, and D. Kalymnios, “Light power behaviour when bending plastic optical fibres,” IET Optoelectron. 145(6), 313–318 (1998). [CrossRef]
16. C. Zhao, L. Ye, J. Ge, J. Zou, and X. Yu, “Novel light-leaking optical fiber liquid-level sensor for aircraft fuel gauging,” Opt. Eng. 52(1), 014402 (2013). [CrossRef]
17. B. Cheng and X. Lu, “Analysis of power transfer characteristics among many parallel optical fibers,” Acta Photon. Sinica. 35(1), 29–32 (2006).
18. W. P. Huang and J. W. Mu, “Complex coupled-mode theory for optical waveguides,” Opt. Express 17(21), 19134–19152 (2009). [CrossRef] [PubMed]
19. D. Donlagic, “A low bending loss multimode fiber transmission system,” Opt. Express 17(24), 22081–22095 (2009). [CrossRef] [PubMed]
20. F. El-Diasty, H. A. El-Hennawi, and M. A. Soliman, “Chromatic and opto-mechanical dispersion of some characteristic parameters of optical fiber undergoing macrobending,” Opt. Commun. 267(2), 394–401 (2006). [CrossRef]
21. T. Z. N. Sokkar, W. A. Ramadan, M. A. Shams El-Din, H. H. Wahba, and S. S. Aboleneen, “Bent induced refractive index profile variation and mode field distribution of step-index multimode optical fiber,” Opt. Lasers Eng. 53, 133–141 (2014). [CrossRef]
22. G. Durana, J. Zubia, J. Arrue, G. Aldabaldetreku, and J. Mateo, “Dependence of bending losses on cladding thickness in plastic optical fibers,” Appl. Opt. 42(6), 997–1002 (2003). [CrossRef] [PubMed]
23. I. R. Husdi, K. Nakamura, and S. Ueha, “Sensing characteristics of plastic optical fibres measured by optical time-domain reflectometry,” Meas. Sci. Technol. 15(8), 1553–1559 (2004). [CrossRef]
24. A. A. Boechat, D. Su, D. R. Hall, and J. D. Jones, “Bend loss in large core multimode optical fiber beam delivery systems,” Appl. Opt. 30(3), 321–327 (1991). [CrossRef] [PubMed]
25. G. Betta, A. Pietrosant, and A. Scaglione, “A digital level transducer based on optical fiber,” in Instrumentation and Measurement Technology Conference, USA, 24–26 Apr 1995. [CrossRef]
26. M. Lomer, A. Quintela, M. Lopez-Amo, J. Zubia, and J. M. Lopez-Higuera, “A quasi-distributed level sensor based on a bent side-polished plastic optical fibre cable,” Meas. Sci. Technol. 18(7), 2261–2267 (2007). [CrossRef]
27. K. E. Romo-Medrano and S. N. Khotiaintsev, “An optical-fibre refractometric liquid-level sensor for liquid nitrogen,” Meas. Sci. Technol. 17(5), 998–1004 (2006). [CrossRef]
28. B. Dong, Q. Zhao, J. Lu, T. Guo, L. Xue, S. Li, and H. Gu, “A digital liquid level sensor system based on parallel fiber sensor heads,” Proc. SPIE 6595, 659541 (2007).
