A Simple, Low-Cost, High-Sensitivity Fiber-Optic Tilt Sensor

Jovan S. Bajić a,*, Dragan Z. Stupar a, Lazo M. Manojlović b, Miloš P. Slankamenac a and Miloš B. Živanov a a University of Novi Sad, Faculty of Technical Sciences, Department of Power, Electronics and Communication Engineering, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia b Zrenjanin Technical College, Đorđa Stratimirovića 23, 23000 Zrenjanin, Serbia *Corresponding author. Tel.: +381214852555; Fax: +381214750572. E-mail address: bajic@uns.ac.rs (J. S. Bajić)

Abstract - The paper presents a simple, low-cost and high-sensitivity fiber-optic tilt sensor. The sensor consists of two optical fibers and a container filled with transparent liquid to the half of the total volume of the container. The sensor principle is based on the change in angle of the liquid surface with respect to the fibers with the tilt angle. The achieved sensor sensitivity and resolution are 1 V/° and 0.02°, respectively.

Keywords - Optical fiber, transparent liquid, tilt sensor.

1. INTRODUCTION Tilt sensors play an important role in today’s life. There are many applications of the tilt sensors such as:

determination of the angle of drilling in boreholes, measuring walls or ground movements in civil engineering projects, measuring the depth and rate of landslide movement, indication of the vehicles and aircrafts pitch and roll and so on. Development of a rugged, cheap, simple-structured tilt sensor with wide measuring range and high accuracy is important for satisfying the market needs.

There are many operational principles and implementations of tilt sensors such as resistive [1], capacitive [2], inductive [3]-[6], optical [7]-[11] and fiber-optic [12]-[17]. In [1] is given a high-performance impedance-type resistive inclinometer with a wide linear range of 320° and a tilt angle resolution of 0.3°. An innovative low-cost concept for the fabrication of micromechanical capacitive inclination sensors with the range of ±180° is reported in [2]. Magnet and magnetic fluids may be used in devices to measure the inclination [3]-[6]. Magnetic tilt transducer with ferrofluid, aimed for small inclination angles measurement with a high resolution of 0.01 mm/m is reported in [3]. An all refractive optical design for a beam dissector that can be used to obtain optimal tip-tilt measurements with high sensitivity is described in [7]. A tilt sensor with a large measurement range using four fiber Bragg gratings (FBGs) attached on a cylindrical cantilever-based pendulum is demonstrated in [14], [15]. A tilt accuracy of ±0.2° and resolution of 0.013° in the range of -40°–40° was achieved. The paper [16] deals with the theory, design, fabrication and test results of a fiber-optic tilt sensor based upon the modulation of light intensity with the change in the level of mercury (Hg) surface with the tilt. The sensitivity of the sensor realized in [16] is 0.013 Vmrad-1 and the maximum range covered is 53.4 mrad. Small in size, electrolytic tilt sensor fabricated by MEMS process is presented in [18] and [19].

The resistive [1], capacitive [2] and inductive [3]-[6] implementations can be affected by electromagnetic interference. Proposed solution for tilt angle measurement given in [7] requires relatively complex experimental setup. Fiber-optic sensors with high sensitivity, described in [12]-[15], are quite expensive. In the transducer implementation presented in [16] mercury is used, which is toxic. The sensors presented in [18] and [19] require relatively complex fabrication process.

The recent activity in the field of fiber-optic sensors resulted in a great variety of devices using interference, polarization or wavelength modulation techniques in sensing applications. While all of these methods offer great promise for certain specific applications and sensors, the intensity modulated fiber-optic transducers offer a powerful combination of simplicity, performance, and low-cost, which makes it well suited for a wide variety of

laboratory and industrial applications. Fiber-optic sensors are small in size, immune to electromagnetic interference, and can be easily integrated with existing optical fiber communication links.

In this paper a simple, low-cost and high-sensitivity fiber-optic tilt sensor based on the change in angle of the liquid surface with respect to the fibers with the tilt angle, is presented.

The proposed sensor represents an extension of our previous work. In [20] a simple and low-cost fiber-optic inclination transducer is presented. The sensor principle is based upon the refraction of light. The implemented sensor has four linear regions, each extending along 30°. Accuracy of 0.5° and resolution of 0.12° have been obtained. A characteristic of the sensor was measured in the range of 360°. The results are shown in Fig 1.

Fig. 1. Charasteristic of the sensor presented in [20].

It should be noted that there are two peaks on 90° and 270°, indicated by dashed lines, which are very

interesting. In this paper we give detailed theoretical and experimental results of the sensor behavior around 90° and 270°. Due to its symmetrical structure, the sensor shows the same behavior around 90° and around 270°. Therefore, hereinafter only one of these ranges will be considered (eg range of about 90°). Additionally, due to the simpler theoretical analysis 90° will be replaced with 0°, so below it will be described behavior of the sensor around 0° that corresponds to the behavior of the sensor around 90° (or 270°) in Fig. 1.

2. PRINCIPLE OF OPERATION In Fig. 2 and Fig. 3 the principle of operation of the proposed sensor is presented. Two optical fibers are placed

axially symmetric at the distance 2h. The fibers are mounted at the opposite sides of the container, which is filled with transparent liquid to the half of the total internal volume of the container. The surface of the liquid within the container under the influence of the gravity does not change its level while the container is tilted or inclined. In the zero position, with no inclination, (Fig. 2) half of the total power emitted by the transmitting fiber is directed towards the receiving fiber through the air and half through the liquid. Assuming that there is no surface tension in the container and the surface of the liquid is ideally flat, the radiating areas of the transmitting fiber in the liquid and in the air are the same. The same goes for the reception areas of the receiving fiber. However, due to the different numerical apertures and acceptance angles of the fibers in different mediums amount of light collected by the parts of the receiving fiber in the liquid and in the air are not the same. Additionally, when the sensor is tilted (Fig. 3), transmitting and receiving fiber areas in the air and in the liquid are changed, which leads to the changes in total power collected by the receiving fiber with respect to the zero position.

Fig. 2. Zero position, tilt angle α=0.

Fig. 3. Tilted sensor with tilt angle α.

Some crucial conclusions can be drawn by closer observation of the light rays passing from the transmitting to

the receiving fiber. Light rays passing from the liquid into the air will be totally reflected at the boundary surface due to high incident angles (occurrence of total reflection). On the other side, light rays coming from the air into the liquid will be either refracted in such a way that does not reach the receiving fiber or due to the high incident angles (low transmission coefficient) reach the receiving fiber with very low intensity and as such can be ignored. Therefore, only the rays arriving entirely through the liquid or through the air from the transmitting to the receiving fiber will affect the light intensity at the end of the receiving fiber. The total light power at the output of the receiving fiber will be determined by the sizes of the radiating and reception areas of the fiber parts in the liquid and in the air. As it can be seen from Fig. 3 when tilt angle α reaches critical value:

( )tan ,k h aα= ⋅ ≥ (1)

practically there are no more light rays that reach the receiving fiber area and the light intensity at the fiber output is zero. 2h is the distance between the fibers, and a is the radius of the fiber core.

By imagining that the transmitting fiber emits entirely in one medium (e.g. air), then at the receiving fiber plane light appears to form a cone from the transmitting fiber, with a cone angle θmax given by the numerical aperture NA [21]. At the output of the transmitting fiber conical beam of light forms a circular pattern in the receiving fiber plane, with the radius Rmax given by:

max max2 tan( ),R a h θ= + (2)

Fig. 4. a) Cross section at input of the receiving fiber b) Cross section at output of the transmitting fiber.

The optical power emitted by the transmitting fiber gets spread over the entire circle area. The amount of light

collected by the receiving fiber depends on the fiber reception areas in the liquid and in the air. By following similar procedure as given in [21] and [22], the power collected by the parts of the receiving optical fiber in the air and in the liquid will be due to tilted surface:

11 1 2

max1

2 sin arccos ,a

oi

k

P rP T a drR aπ

= ∫ (3)

22 2 2

max 2

2 sin arccos ,k

oi

a

P rP T a drR aπ −

= ∫ (4)

respectively, where T1 and T2 represent the Fresnel transmission coefficients at the fiber input in the air and in the liquid, respectively. Rmax1 is the radius of the conical beam of light launched in the air, given by (2). The same goes for Rmax2 in case of the liquid medium. Po1 and Po2 are the optical powers launched from the transmitting fiber in the air and in the liquid, respectively. The expression under integral represents shaded area in Fig. 4. The powers emitted in the air and in the liquid can be obtained as:

1 ( )2 sin arccos ,k

oa

rP I r a dra−

= ∫ (5)

2 ( )2 sin arccos ,a

ok

rP I r a dra

= ∫ (6)

where I(r) is the light intensity distribution at the output of the transmitting fiber. By substituting expressions (5) and (6) in (3) and (4), respectively, and by summing expressions (3) and (4) the total power collected by the receiving fiber is obtained.

It should be noted that above presented theoretical analysis is just an approximation. In the theoretical model it is assumed that the light losses in the fiber are negligible. The influence of the liquid surface tension is also ignored. The influence of the rays passing through both mediums is considered as insignificant.

3. EXPERIMENTAL SETUP

Fig. 5 shows a photograph of the implemented tilt sensor.

Fig. 5. Photograph of the implemented tilt sensor.

Sensor container is cylindrically shaped and made of plastic. As the liquid medium, the water is used. The

optical fibers are mounted at the center of the top and bottom base of the cylinder. The cylinder height and diameter are 32 mm and 30.7 mm, respectively. The fiber diameters are 1.5 mm. The sensor housing is filled with water to the half of the height of the cylinder. The sensor is mounted on the precise manual rotation stage PRM1/M produced by Thorlabs. As the angle of the rotation stage increases, the water within the container does not change its level under the influence of the gravity. This causes the changes in angle of the boundary surface water-air with respect to the fibers. As a result, the amount of the light, collected by the receiving optical fiber, changes in dependence of the rotation stage angle.

Plastic optical fibers are used in the fabrication of the transducer because they are cheap, robust and easy to handle. Glass fibers can also be used. They have further more advantages over the plastic type such as higher sensitivity and lower attenuation. However, they are costly, fragile and difficult to handle. The cylinder size is a trade-off between the size of the sensor and the influence of the liquid surface tension.

The block diagram of the implemented hardware solution for the tilt angle measurement is given in [20]. As already mentioned in [20], PMMA (polymethyl methacrylate) optical fiber shows minimum losses of light at the wavelength of about 650 nm [23], which represents the red color. Therefore, as the light source for the fiber an ultra bright red LED with peak wavelength of 630 nm is used. LED is configured to operate in pulsed mode in order to eliminate daylight effects. The phototransistor BPW17 that works in conjunction with common-collector (emitter follower) is chosen as a light detector [20]. The phototransistor signal is amplified by rail-to-rail operational amplifier MCP6022 from Microchip Technology. As a microcontroller, dsPIC30f4013 from Microchip Technology is used. It generates pulses and drives LED at the frequency of 1 kHz. Also the microcontroller performs A/D conversion by using 12 bit A/D converter, and displays results on a graphical display.

4. RESULTS AND DISCUSSION As the light intensity distribution at the output of the transmitting fiber, Gaussian, parabolic and uniform

distributions were tested. In Fig. 6, the normalized power, collected by the receiving optical fiber in dependence of the tilt angle for the parabolic intensity distribution is presented. The power, collected through air, water, and total power, are shown. The same results for uniform distribution are displayed in Fig. 7. For the Gaussian intensity

distribution very similar results, as for the parabolic distribution, were obtained. The characteristics in Fig. 6 and Fig. 7 are obtained using equations (3) and (4).

Fig. 6. Results obtained for the parabolic light intensity distribution at the transmitting fiber output: P1-power

collected through the air; P2- power collected through the water; Ptotal- total power collected by the receiving fiber in dependence of the tilt angle.

Fig. 7. Results obtained for uniform light intensity distribution at the transmitting fiber output: P1-power

collected through the air; P2- power collected through the water; Ptotal- total power collected by the receiving fiber in dependence of the tilt angle.

As it can be noticed from Fig. 6 and Fig. 7, in the case of total collected power, the type of the light intensity

distribution at the output of the transmitting fiber does not play a significant role in the characteristics shape. Both characteristics in Fig. 6 and Fig. 7 are approximately symmetric and have a peak value at about -0.1°. The contributions of the light rays passing through different mediums on the total power collected by the receiving fiber should be also noticed. As it is expected, more light rays were collected through the water due to less numerical aperture or a smaller scattering of the light beam at the output of the transmitting optical fiber. Also, the characteristics through various mediums are dependent on the type of the light intensity distribution. If using an opaque liquid (e.g. mercury), then it would be important what type of the light intensity distribution at the output of the transmitting fiber is used.

In order to verify the theoretical analysis, the simulation of the proposed sensor is performed in TracePro software from Lambda Research. TracePro is an optical engineering software for designing and analyzing optical and illumination systems. In Fig. 8, 3D model of the proposed sensor in TracePro software is given. A source with Gaussian spatial profile and the total number of 100000 rays was used to simulate the sensor. Simulation was performed in two iterations in steps of 0.5° along ±5° range. In the first iteration only optical power collected through air is considered. This is accomplished by having the water set as a totally absorbing medium. In the next iteration in a similar way, only optical power collected through the water is recorded. Total power collected by the receiving fiber in dependence on the tilt angle was obtained by summing the values obtained in the previously described two iterations. In Fig. 9, a comparison of the results obtained by using the presented theoretical analysis and software simulation is given. As it can be seen, an excellent matching of the results has been achieved.

Fig. 8. 3D model of the proposed sensor in TracePro software.

Fig. 9. Comparison of the results obtained using the given theoretical analysis and TracePro software: P1-

power collected through the air; P2- power collected through the water; Ptotal- total power collected by the receiving fiber in dependence of the tilt angle.

As earlier mentioned, the implemented tilt sensor is mounted on the precise manual rotation stage.

Measurement was performed by rotating the stage in steps of 0.2° along approximately 10° range. In Fig. 10, the

comparison of experimental and theoretical results is given. It can be noticed that the experimental curve corresponds well to the theory. In the experiments, because the measured tilt angle is transformed into the light intensity variation, the fluctuation of the light intensity will result in the measurement errors. Fig. 11 indicates measurement stability of the system consisted of LED, sensor and photodetector, captured during one hour. As it can be seen from Fig. 11, by linear fitting of the measurement data, captured during one hour, a tilt angle drift of only 0.00006° per minute was obtained. In addition, by measuring the LED optical power coupled into the fiber and after the normalization of the sensor signal even better stability can be achieved. The resolution of the tilt angle measurement depends on the signal/noise ratio, resolution of A/D converter and the aforementioned sensitivity. The resolution of the implemented sensor is around 0.02°. The achieved transducer sensitivity is around 1 V/°. As it can be seen from Fig. 10, the sensor measurement range is around ±2.5°. By increasing the radius of the optical fiber and/or by decreasing the distance between fibers, it is possible to increase the measuring range. However, during the performed experiments it has been noticed that by reducing the distance between fibers, the effect of the liquid surface tension increases and the sensor no longer behaves as predicted by the theoretical analysis.

Fig. 10. Comparison of experimental and theoretical results.

Fig. 11. Measurement stability of the system consisting of LED, sensor and photodetector, captured during one

hour (MV - mean value, SD - standard deviation).

In Fig 12. temperature and humidity stability of the sensor is presented. The sensor is placed in a temperature chamber. The chamber is firstly heated to about 60°C, which caused a simultaneous decrease in relative humidity to about 10%. Afterwards, the chamber is left to cool down gradually to the room temperature of around 27°C. Peak temperature of about 60°C is selected in accordance with the operating temperatures of the plastic optical fibers, because above this temperature comes to the deformation of the optical fiber. As it can be observed from the Fig. 12, the sensor shows good stability in the observed range of temperature and relative humidity.

Fig. 12. Temperature and humidity stability of the sensor captured during one hour.

5. CONCLUSIONS

A simple, low-cost and high-sensitivity fiber-optic tilt sensor is fabricated and tested. Both theoretical

explanation and experimental results are presented. The experimental curve corresponds well to the theory. The resolution of the tilt angle measurement of 0.02° is obtained. The presented sensor has high resistance to environmental influences and can be easily multiplexed, resulting in the long distributed sensor networks. The proposed sensor, together with the sensor presented in [20], represents a unique combination of two distinct sensors packaged in the same housing, and as such can be used both in applications where high sensitivity is required or where a wide measuring range is needed.

ACKNOWLEDGMENTS The authors gratefully acknowledge the funding provided by The Ministry of Education and Science of the

Republic of Serbia under projects “Development of methods, sensors and systems for monitoring quality of water, air and soil”, number III43008 and “Optoelectronic nanodimension systems – route towards applications”, number III45003.

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Jovan S. Bajić was born in Sremska Mitrovica, in 1986. He received the B.S. and M.Sc. degrees in electrical engineering from the Faculty of Technical Sciences (FTS), University of Novi Sad (UNS), Serbia in 2009 and 2010, respectively. Currently, he is a Research Assistant at the FTS, UNS. His areas of interest are applied electronics and sensing applications. He received “Mihajlo Pupin” award for the significant scientific contribution in Serbia in 2011. Dragan Z. Stupar was born in Bačka Palanka, Serbia, in 1986. He received the B.Sc., M.Sc. degrees in electrical engineering from the Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia, in 2010. Currently,

he is a Research Assistant in the Department on Electronics at the Faculty of Technical Sciences. His current research interests include applied electronics, optoelectronics and digital signal processing. Lazo M. Manojlović was born in Vranje, Serbia, in 1972. He received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Belgrade, Belgrade, Serbia, in 1996 and 2003, respectively, and the Ph.D. degree from the University of Novi Sad, Novi Sad, Serbia, in 2010, all in electrical engineering. He is currently a Full Professor at Zrenjanin Technical College, Zrenjanin, Serbia. His current research interests include interferometry, optical sensing systems, and laser rangefinders. Miloš P. Slankamenac was born in Novi Sad, in 1977. He received the B.S., M.Sc., and Ph.D. degrees in electrical engineering from the Faculty of Technical Sciences (FTS), University of Novi Sad (UNS), Serbia in 2001, 2004 and 2010, respectively. Currently, he is a Assistant Professor at the FTS, UNS and the Head of the Optoelectronic Laboratory. He has more than 9 years of experience in research and education in the field of electronic components, microprocessors, solid state, and optoelectronics. He received “Mihajlo Pupin” and “Nikola Tesla” Awards for the significant scientific contribution in Serbia in 2005 and 2011, respectively. Miloš B. Živanov was born in Novi Sad, Serbia, in 1948. He received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from the Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia, in 1973, 1978, and 1992, respectively. He is currently a Full Professor at Faculty of Technical Sciences, University of Novi Sad, Serbia. His current research interests include electronics, optoelectronics, geophysical well logging, and electrical vehicles.