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Abstract
This paper highlights a novel approach towards a three-dimensional displacement measurement sensor. The designed sensor structure is simple, low cost, flexible, and easy to assemble. The sensor works on the twisted macro-bending coupling method. We realized displacement in three different dimensions using the single light transmitting fiber and the dimensions can be further extended by cascading. For sensing in each direction, the transmitting fiber was three-time circular-bended and twisted. The beam quality analyzer was used to analyze the coupling of optical power in receiving fibers when the displacement moves. The displacement has been achieved up to 140 mm in each direction with good consistency, and the system could operate up to 70°C. In comparison with the other methods, the aforementioned method is well suited, holistic, and optimal.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The displacement is the crucial parameter in various industrial applications. The displacement sensors are installed in the civil structure such as dams, bridges mines, in transportation, aerospace, energy sector, marine vessels, industrial robotics and many more. However, in particular cases, the directional displacement sensor needs to be deployed for measurement of two or three-dimensions [1].
The traditional displacement sensors are Magnetic induction, Photoelectric, Potentiometer, Transformer, Hall type, Winding, Capacitive types [2]. These conventional displacement sensors principle has been more mature technology and deployed in different industrial usage. However, traditional methods have some merit as well as have demerit, and compatible technology over traditional technology is optical fiber based system. The prominent plus points of these optical fiber sensors are nonelectrical, explosion proof, small size, lightweight, high accuracy, high precision. Moreover, breakthrough characteristic of the fiber optic sensor is immune to radio frequency interference RFI and electromagnetic interference EMI and can facilitate distributed sensing [3–4].
Marvelous progress has been made in the past few decays; the FOS has attained much growth in research and implementation in the physical environment. Most of the research has been carried out on one-dimensional 1D displacement measurement sensors, and numerous technique has been invented. For 1D sensing technique used in commercial systems are Intensity-Based Sensors, Triangulation Sensors, time-of-flight sensors, confocal sensors, interferometric sensors, measurements of velocity and vibration based on successive distance measurements and direct velocity measurement—Doppler sensing [5]. Whereas some optical system based are multiple-wavelength and scanning interferometry, frequency modulated continuous wave time-of-flight and self-mixing interferometry. All these reported methods are non-contact based 1D displacement system whereas the macro-bending, fiber Bragg Grating FBG are the contact type 1D displacement sensor [6–8]. However, one dimension is not necessary for particular conditions still need to measure another direction; for instance the measurement of the x-axis and y-axis.
Measurement of two dimensions, a straightforward approach is to take two sets of the 1D displacement sensor to achieve a 2D displacement measurement sensor. Whereas in this concept, the system became more complicated and congested and was operating as two different setups [9]. This concept inconvenient to use and it increases the cost of the whole system. For 2D displacement measurement, most research has done on the optical-based method that includes speckle pattern interferometry, image-processing algorithm, speckle-gram, Laser Doppler and Grating interferometry [10]. These systems have been suitable for 2D whereas one direction is still lacking in 2D displacement measurement when there needs to sense in the real environment which needs to measure in three-directions to compete for three axes (x, y, and z-axis). The three-dimensional system is very suitable for the measuring of x, y and z-axis that problem is focused on this research.
Previously conventional 3D sensor based on piezoelectric semiconductors (PSCs) method that was first given by Hutson [11]. Likewise several techniques presented to extend the range of PSCs sensor like extended element method, extended displacement discontinuity method, boundary element method, distributed dislocation method. These methods have high sensitivity and accuracy although these systems have a complex mathematical and numerical model [12–13]. In the choice of high resolution, fast speed, small measurement range, the laser interferometers have goodness, but these systems are susceptible to environmental influences such as air humidity, air pressure and air temperature [14–16]. The alternative system for the measurement of 3D displacement is a combination of XY-grid encoder that measures the x-y axes and the third direction z-axis measured by a capacitive displacement sensor [17–18].
To avoid environmental perturbation, the optical fiber-based displacement sensor is a suitable choice to attain such a high resolution, accuracy, and sensitivity. For the sensing purpose, glass and polymer optical fiber are commonly used. Compare to the standard glass optical fiber (GOF), the polymer optical fiber (POF) has a specific advantage, as POF is much flexible, inexpensive and easy to bend [19–20]. Fiber Bragg grating FBG fiber used by some researchers to measure the 3D as well as multidimensional displacement. This method needs three FBG and three optical filters that ensure to operate at different wavelengths although this method is relatively expensive and needs to be carried out signal processing and unable to use for a wide range [21].
In this paper, we presented a novel system for three-dimensional displacement measurement sensor and introduced a concept of multiple time macro-bending and twisting on a single light transmitting fiber. This system works on twisted macro-bending coupling phenomena that ensure the optical power loss when its bend radius is increased or decrease. The twisting structure has been employed to couples the optical power loss that will be used for measurement purpose in each directions corresponding to displacement change. In addition, we have constructed three-time macro-bend twisting on a single transmitting fiber to achieve three-dimensional system, and the macro-bend twisting can be further cascaded to multiple-time macro-bend twisting to achieve the multi-dimensional displacement purpose.
2. Twisted macro-bend coupling phenomena
The three-dimensional displacement measurement sensor operates on two phenomena of the optical system that is macro-bending effect and the optical power coupling method. The macro-bend loss radiates when the fiber is going to be bend and this radiated power from transmitting fiber can be coupled by another fiber named as receiving fiber via the twisting method. This phenomenon is called twisted macro-bend coupling phenomena. The proposed method is shown in Fig. 1; in which three circular-bends are shown and three separate twistings are mentioned.
Fig. 1. Three-dimensional dimensional displacement sensor, red line indicates illumination fiber (IF) which will be connected with light source. Blue, green and yellow are receiving fibers twisted with IF, forward ends of each receiving fibers will be connected with power meters.
Only one light source used in the experiment that coupled with the fiber named as illumination fiber and three other separate fibers were taken to twist with IF and these three separate receiving fibers (RFs) were not coupled with the light source. In Fig. 1, the red line indicates for illuminating fiber whereas the green, yellow and blue line indicating for receiving fiber. These three RFs have been employed for measurement of displacement in certain directions like the first RF1 for x-axis measurement, the second RF2 for y-axis measurement and the third RF3 for z-axis measurement respectively. For the sake of simplicity, the block diagram of the system is shown in Fig. 2.a. The terminal 1, 2 and 3 are the output from twisted macro-bend coupling block and these terminals connected with power meters. Moreover, the sensing part of the sensor is the bend-radius of fiber for each x, y, and z-direction shown in Fig. 2.b.
Fig. 2. (a): The block diagram of the 3D sensor. (b): Illustration of the circular-bend radius. When displacement will drifting the bend-radius will change.
There is R1 which is bend-radius considered at 00 mm and R2 is for maximum 140 mm displacement of our proposed sensor. When x-axis move, it can interact with y-axis that can produce the cross-talk. To avoid the influence of movement on fibers due to the movement of one direction to the other direction fiber; we fixed the fiber at the certain point as mention in Fig. 1.
Some analytical and numerical methods are presented by researchers to estimate the macro-bending loss. The analytical method is; total power loss model, power loss coefficient model, external field model based on going waves, 2D scalar field model and Finite-cladding model. However, the accurate and relevant model is the Finite-cladding model [22–24]. While the other numerical model is; MATLAB simulation, the method of using strength segments to approximate the curved fiber, beam propagation method, and mode-solving simulation. Among them MATLAB simulation was developed to perform bend loss in step index, multimode fiber also for POF and this model have very much relevancy and accurate [25].
The loss of energy in IF due to bending-effect that radiates energy in the environment and the coupling method used to couple the radiated optical energy as mentioned in Fig. 4. When the fiber moves the bend-radius become shorter and the propagating angle exceeds the critical angle. At this point, the total internal reflection no further exists and some rays refracting from fiber and as a result bend loss emerge. The refracting power ${P_r}$ from IF can be calculated as [26]:
Fig. 4. Experimental setup for three axes (x, y and z-axis); (a) LED (M660F1, Thorlabs); (b) connector coupled with active fiber and LED; (c-d)single illuminating fiber; (e-g) three separate receiving fibers; (h-j) optical power meters; (k-m) the moving plates. The sensing portion was twisted macro-bend. For k and l moving plates the sensing part placed together whereas sensing part of m placed separately.
whereas, T is Fresnel transmission coefficient, ${P_i}$ is the incident power, ${\theta _c}$ is the critical angle. In the further step, the ${P_r}$ from IF will be easily couples in adjacent RF because the SK-40 POF has core-radius about 980 µm and cladding has 10 µm. It is common fact that when two fibers brought closer to each other the optical power coupling happens. The coupling coefficient C between two adjoining parallel fibers can be expressed from the coupled-mode theory:
However, these are distractive methods; formerly, these methods need to destroy the actual cladding portion and need precise work to develop it. The twisting method has been used as an alternative method for optical power coupling [29]. The fruitiness of twisting structure is neat, not complicated, no need for any extra cost because it can make with the hand at any time and easy to separate fibers. Best of our knowledge, there is not the mathematical model has been presented yet for the twisting structure particularly in twisting macro-bending coupling method TMBCM. This model slightly complicated to estimate the optical power coupling OPC in receiving fiber then find the bend loss in receiving fiber; in fact, the RF is also in bending position because of twisted with IF. The loss of radiation from RF also coupling in active fiber which is the pretty small amount.
3. Experimental results and discussion
The practical implementation of three-dimensional displacement measurement sensor shown in Fig. 3. We have accomplished three perpendicular directions like x-axis, y-axis, and z-axis respectively. In the experiment, one light source (LED, M660F1, Thorlabs) that coupled with IF through the connector. There were three cascaded circular-bends on the IF, and each bend was twisted with three separate RFs, which receives the optical bend-loss. The LED’s output power was 30 mW, and the resolution of the power meter is 1nW. The systems-operating wavelength is 660 nm as the Sk-40 POF have minimum attenuation at this wavelength [30].
The multimode polymer optical fiber MMPOF (SK-40, Mitsubishi, Tokyo, Japan) was chosen for this experiment. It has two reasons first it produces too much loss when the fiber is going to be bend. The MMPOF has the advantage as compared to single mode fiber SMF which not able to produce such a significant loss. Second, in the MMPOF side coupling power in more than SMF. Another reason to choose plastic optical fiber is that POF is more flexible as compared to glass optical fiber GOF. The POF easily bends but GOF as slightly harder and cannot bend easily.
There were four pieces of MMPOFs used in the experiment setup in which one used for the light transmitting fiber. The remaining three were receiving fiber used as the receiving of macro-bending loss. These three RFs separately twisted on IF, and the forward end of each PFs connected to the optical power meters (PM100USB, Thorlabs). The power meter1 coupled with first receiving fiber associated with the measurement of the x-axis. The second power meter coupled with second receiving fiber related for the measurement of the y-axis and the third power meter coupled with third receiving fiber associated for the measurement of the z-axis. To avoid the interaction between the first and second circular-bend which may produce cross-talk for that, we used glue to fix the fiber at the end of the first and second circular-bend.
In the experiment, the Beam quality analyzer (BC106N-VIS/M, Thorlabs) used to analyze the optical power coupling in PFs. The results of power coupling in RFs from beam quality analyser is shown in Fig. 5. The results of W related to direct power in illuminating fiber while X, Y and Z related to three separate receiving fibers of each direction. In Fig. 5 X.1 the result was taken at the displacement of 0 mm, X.2 at 70 mm and X.3 at 140 mm respectively. As the displacement increasing from 0 mm to 140 mm, the coupling power was increasing in RFs. The power coupling in each direction was not accurate equal because the twisting was not accurately aligned.
Fig. 5. Optical power coupling response of transmitting and receiving fibers. W for active fiber response, X for first direction, Y for second direction and Z for the third direction. (1) =0 mm, (2) =70 mm (3) =140 mm.
The receiving power in receiving fiber was calibrated according to the displacement change. This sensor is a contact type that should need to attach to the moving structure. For that, we fixed the fiber on moving plates with glue during experiment. While designing of the experimental platform, the moving plates were moved in the groove, and the length of the groove was fixed up to 140 mm. In this mechanical structure, the moving plates were not able to move beyond that certain length due to designed structure. Secondly, to prevent the anxiety of fiber breakage beyond the threshold value of bending the fiber. For the origin, the initial coupling power from each axis taken as the origin of the direction. At the 0 mm distance, the initially coupling power was 88nW in the x-axis, 62nW in the y-axis and 43nW in the z-axis.
In this research, the independent measurement of each direction considered and the measurement was taken for forward and backhaul movements. The calibrated values of received optical power versus displacement shown in Fig. 6,7 and 8. The experiment was performed for outward, and backhaul movement and the results achieved up to 140 mm displacement having an average sensitivity of 6.91nW\mm, the resolution is 0.1434 mm and the step change for each movement was 10 mm.
4. Temperature dependence
Temperature is an important parameter that influences the performance of the sensor. According to SK-40 multimode POF design parameter, it is suitable from -55 to ∼70°C. The heating machine (kaisi 818) was used to perform temperature influence on the designed sensor. Figure 9 shows the results of the temperature effect on the sensor. As temperature further increases from 70°C, the performance of the sensor gets worse and sensitivity reduces which due to light in fiber get worse. When the temperature rises the optical power coupling become slightly weak.
The bared Mitsubishi SK-40 POF has the influence of external light that produce signal-to-noise SNR. The experiment needs to be carried out in the darkness to avoid external light for that the plastic tube was coated on the POF. Furthermore, the twisting was not robotically constructed. So, it was not precisely aligned. The stability of TMBCM method has been discussed in previous work [26]. The TMBCM based method has the influences of weak and tight twisting. When making tight twisting, the fiber reduced its flexibility and difficult to bend while in weak twisting fiber still flexible and soft. The three-dimensional displacement sensors have applications particularly in the aerospace industry, military vehicles, machine tools, hydraulics, material testing, robotics, and 3D printers. In this work, the designed 3D displacement sensor has been employed for three-direction, and the directions can be further extended.
5. Conclusion
The novel 3D displacement sensor has been experimentally proposed in this research work which depends on the single transmitting fiber. The 3D displacement system works on the principle of TMBCM. The design structure able to detect three dimensions (x, y, and z-axis) and is also flexible extend to more dimensions. In this research, the cascading of twisted macro-bend has introduced. Each dimension can measure displacement up to 140 mm, having average sensitivity of 6.91nW\mm, and the resolution is 0.1434 mm. The designed sensor is cheaper, easy to construct, and there is no need to perform signal processing or other sophisticated techniques required. Furthermore, this concept of multiple times macro-bend twisting on single light transmitting fiber has advantages to simultaneous measurements of different physical parameters. This work can be further extend to the simultaneous measurement of all directions and dynamic measurement.
Funding
National Natural Science Foundation of China (NSFC) (51405454); Fund for Shanxi “1331Project” Key Subject Construction.
Acknowledgments
This work was supported by the National Science Fund for Distinguished Young Scholars of China (51425505); National Natural Science Foundation of China (51405454); Fund for Shanxi “1331Project” Key Subject Construction.
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