Bio-Medical Materials and Engineering 24 (2014) 771–780 DOI 10.3233/BME-130867 IOS Press
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Development of an Optical Fiber Sensor for Angular Displacement Measurements Gu-In Jung a,b, Ji-Sun Kim a,b, Tae-Hee Lee a,b, Ju-Hyeon Choi a,b, Han-Byeol Oh a,b, A-Hee Kim a,b, Gwang-Moon Eom a,b, Jeong-Hwan Lee a,b, Soon-Cheol Chung a,b, Jong-Rak Park c, Young-Jae Lee a,b, Hee-Jung Park a,b, and Jae-Hoon Jun a,b* a
Department of Biomedical Engineering, College of Biomedical and Health Science, Konkuk University, Chungju, South Korea b Department of Biomedical Engineering, Research Institute of Biomedical Engineering, Konkuk University, Chungju, South Korea c Department of Photonic Engineering, Chosun University, Gwangju, South Korea
Abstract. For diagnostic and therapeutic purposes, the joint angle measurement of a patient after an accident or a surgical operation is significant for monitoring and evaluating the recovering process. This paper proposed an optical fiber sensor for the measurement of angular displacement. The effect of beveled fiber angle on the detected light signal was investigated to find an appropriate mathematical model. Beveled fiber tips redirected the light over a range of angles away from the fiber axis. Inverse polynomial models were applied to directly obtain and display the joint angle change in real time with the LabVIEW program. The actual joint angle correlated well with the calculated LabVIEW output angle over the test range. The proposed optical sensor is simple, cost effective, small in size, and can evaluate the joint angle in real time. This method is expected to be useful in the field of rehabilitation and sport science. Keywords: Optical fiber, Angular sensor, Beveled tip, Asymmetric beam profile, Goniometer
1. Introduction Human joint movement can be used to evaluate the rehabilitation process of patients and the optimal performance of sport activities [1-3]. For diagnostic and therapeutic purposes, it may be necessary to evaluate and monitor the joint angle of a patient after an accident or a surgical operation to ensure that the patient is doing one of the different exercises for each patient in the correct posture [4-6]. Different kinds of angular sensors have been reported in the past. The most widely used is a goniometer using a circular potentiometer as the sensitive element [7-10]. Another kind is the strain gauge [11-14]. During repeated use of mechanical and electrical parts, current goniometers show some disadvantages in accuracy and repeatability. In addition, these sensors are quite expensive and sometimes fragile as well. *Adress for Correspondence : Department of Biomedical Engineering, College of Biomedical and Health Science, Konkuk University, 268 Chungwondaero, Chungju-si, Chungcheongbuk-do, 380-701, South Korea, Tel.: +82 43 8403799; E-mail: [email protected]. 0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
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G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements
The camera based three-dimensional (3-D) motion capture system [15-18] is accurate but very expensive, complicated to use, and only effective in the special lab with bulky camera systems. Furthermore, to process data, specialists are required and the data processing time is relatively long. The system requires calibration in each test set and long preparation time. Sometimes patients claim inconvenience in attaching reflection markers on their body, and the markers can be obscured from vision resulting in incomplete data. This study used beveled fiber tips and studied the beam profile to find out the way of increasing detection range. The aim of this study is to suggest an alternative method for the identification of the joint angle which can be convenient, cost effective, and operated in real time. Therefore, a new design concept of the optical fiber sensor was proposed to measure joint angle. 2. Materials and Methods 2.1. Beveled fiber Snell’s law describes the relationship between the angles of incidence and refraction, when referring to light passing through a boundary between two different isotropic media, such as water, glass, and air. Thus, the law is used in ray tracing to compute the angles of incidence or refraction [19-20]. For fiber characterization, the acceptance angle is typically reported in terms of a numerical aperture (NA). Light enters (or leaves) the fiber within an acceptance cone of 2 (see Fig. 1(a)). From Eq. (1), the NA can be expressed in terms of the refractive indices of the fiber material, depending on the refractive index of the surrounding environment (nair). The NA of an optical fiber characterizes its ability to collect light from a source and to preserve the light inside the fiber.
NA = nair sin = n 2 core ڈn 2 cladding
,
(1)
Where is the acceptance angle (light enters /leaves the fiber within an acceptance cone), nair is the refractive index of air, ncore is the refractive index of core, and ncladding is the refractive index of cladding. If the surface of the fiber is fabricated with a bevel angle with respect to the fiber axis, the output light from the fiber is refracted by an angle (see Eqs. (2)-(4) and Fig. 1 (b)). The refracted angle can be described as a function of the bevel angle of the fiber.
nair sin air = ncore sin ,
(2)
air = sin 1 (ncore sin / nair ) ,
(3)
= air ڈ
,
(4)
Where air is the angle at which the peak propagates in air, relative to the face normal, is the bevel angle, and is the angular limit of the refraction angle.
G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements
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Fig. 1. The change of the refracted angle due to the bevel angle
2.2. Fiber optic sensor Fig. 2 shows the fiber optic sensor developed in this study. A red chip LED (IWS-165-RXWF, ITSWELL, Korea) with the wavelength range of 618 - 635nm, was attached on the right end of the polished beveled fiber. The fiber (BFL48-1000, Thorlabs, Newton, New Jersey) is step index multimode (the refractive index of core = 1.457, the refractive index of cladding = 1.3756, and NA=0.48) made of silica core and hard polymer cladding. With a total diameter of 1.4 mm, the core and cladding diameters of the fiber are 1mm and 1.035mm, respectively. A phototransistor (ST-23G, KODENSHI CORP., Japan) was used as a detector to monitor the change of light signal from the fiber due to the change of the joint angle. The sensing range of the phototransistor is from 500 to 1050nm and its half angle of detection is s30rU With the developed fiber optic sensor, various distances between the detector and the optical fiber tip (d = 3.3mm, 4.3mm, 5.3mm), beveled fiber angles ( = 0°, 20°, 30°, 45°), and joint angles ( = 0° ~ 180°, with increment of 5°) were applied to find the optimal combination of these variables for joint angle measurements. The beveled optical fibers were fabricated by polishing the fiber tips at certain angles with a rotating sandpaper tool. Our aim of this study is to find the conditions for a wide detection range with the minimum error.
Fig. 2. Fiber optics sensor
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2.3. Data acquisition and Modeling As shown in Fig. 3, output signals from phototransistor were collected using DAQ board (NI USB6008, National Instrument) in digital form, and saved in a computer with LabVIEW 8.0 (National Instruments, Austin, Texas). Modeling of the experimental data was done by using Matlab (R2008a, Mathworks, Portola Valley, California). Polynomial equations were tested for the modeling. Two types of modeling were selected to obtain the joint angle. First, the relationship between phototransistor output and joint angle was mathematically modeled (see Eq. (5)). Next, the inverse relationship was used to derive the joint angle (see Eq. (6)). The inverse model is possible when the functions show monotonic pattern (increase or decrease). Using the obtained inverse model, the joint angle change with LabVIEW in real time could be calculated and displayed.
y = a0 x n + a1 x n-1 + a2 x n-2 + ! + an x 0 x = b0 y n + b1 y n-1 + b2 y n
2
(5)
+ ! + bn y 0 ,
(6)
Where a0 ~ an are the coefficients of the polynomial equation, b0 ~ bn are the coefficients of the inverse polynomial equation, x is the joint angle [Deg.], and y is the phototransistor output voltage [V].
Fiber optic sensor
DAQ board
- signal detection
- A/D conversion
Matlab - data analysis - data modeling
LabVIEW - joint angle display
Fig. 3. Schematic of experimental procedures
3. Results and Discussion 3.1. The effect of the bevel angle and the distance between detector and fiber tip Fig. 4 shows the change of light signal by the joint angle ( = 0° ~ 180°, with an increment of 5°) with different beveled fiber tips (bevel angle = 0°, 20°, 30°, 45°). Similar experiments had been repeated at different distances between the detector and fiber tip (d = 3.3mm, 4.3mm, 5.3mm). The detected light signal has different peak patterns and beam profiles due to the beveled fiber angle and the distance between detector and fiber tip. Thus, the fiber tip angle and the distance must be considered to develop an efficient optical fiber sensor for angular measurements. Fig. 5 shows the effect of the bevel angle on detected light signal. For a flat fiber ( = 0°), the light signal shows the symmetric beam profile. However, for beveled fibers ( = 20°, 30°, 45°), the signal shows that the asymmetric beam profile and the asymmetric nature are increased with the increase of the bevel angle. Beveled tips redirect the light over a range of angles away from the fiber axis. In an extreme case such as = 45°, the light signal has two peaks which can be caused by the outof-range in critical angle condition. Thus this extreme case is not suitable for joint angle measurements. Since the range of joint angle measurement increases as the bevel angle increases, the beveled fiber of = 30° is selected for application in an angular sensor.
G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements
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β=0
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Fig.6 shows the effect of the distance between detector and fiber tip (d = 3.3mm, 4.3mm, and 5.3mm) on detected light signal with the bevel angle, = 30°. As the distance increases, the value of the peak point decreases but the range of light signal measurement is on the rise with enough resolution. This result implies that d= 5.3mm is the efficient distance in the test range for joint angle measurements. 5
d = 3.3mm d = 4.3mm d = 5.3mm
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Fig. 6. The effect of the distance between the detector and fiber tip ( = 30°)
3.2. Modeling and the measured angle display Fig. 7 shows two sections (section A and section B) for inverse mathematical modeling. The section A (joint angle, = 0 ~ 85°) is monotonically increasing region and the section B (joint angle, = 85° ~ 120°) is monotonically decreasing region. The inverse model is possible when the functions show monotonic pattern (increase or decrease). The other region ( = 120° ~ 180) is excluded from modeling because the resolution is too low.
G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements 5
β = 30
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Fig. 7. Two monotonic regions for inverse modeling
Fig. 8 shows inverse modeling results with inverse polynomial equations for section A and section B with the bevel angle, = 30° and the distance, d= 5.3 mm. Only monotonically increasing or decreasing region was used to get inverse polynomial equations. The inverse 5th order equation showed the best fit in section A while the inverse 7th order equation showed the best fit in section B. Inverse of polynomial equations had coefficients of determination (R2) of section A and section B, 0.9918 and 0.9999, respectively. Fig. 9 shows the example of LabVIEW display of calculated joint angle. Using the obtained inverse models, one can directly calculate and display the joint angle with detected light signal in real time. Fig. 10 shows the relationship between the actual joint angle and the LabVIEW output angle. The result shows that actual joint angle correlates well with the calculated LabVIEW output angle. Experimental results show that the maximum error is ± 1.2596° and root-mean-square error is ± 0.0096°. 5
o
Experimental data [β = 30 ] Inverse 5th order equation
Light signal [V]
4 x = 11.72y5 - 64.95y4 + 132.48y3 - 117.95y2 + 71.0416y - 4.79
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4 Light signal [V]
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x = -242.34y + 2116.93y - 7484.40y + 13757.54y - 14067.57y + 7941.46y - 2298.62y + 380.45
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(b) Section B Fig. 8. Inverse models with polynomial equations (d = 5.3mm, = 30°)
Fig. 9. Example of LabVIEW display 150
Labview output Angle [Deg.]
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Fig. 10. Actual joint angle versus LabVIEW output angle
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The developed optical sensor is valid in the measuring range of = 85° ~ 120°. Future study should be done to increase the measuring range up to 180 degree. The design for 3-D angular measurement and a wireless module will be added for an upgraded optical sensor in future study. Our final goal is to develop a low-cost device that can be used by patients at home to record and provide the real-time feedback without space limitations using a wireless module. 4. Conclusions This study proposed an optical fiber sensor and investigated the effects of beveled fiber angle on joint angle measurements. The detected light signal depends on the distance between the detector and fiber tip. In general, as the bevel angle and the distance increase, the range of joint angle measurement increases. The best combination of parameters is applied to find the appropriate model. Using inverse polynomial models, the joint angle change in real time with LabVIEW display is obtained. The suggested sensor is expected to be used in the fields of rehabilitation and sport science. 5. Acknowledgements This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 20100023158) and the Pioneer Research Center Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future planning (No.2011-0027920). References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
S.T. West and C.L. Chen, Optical fiber rotary displacement sensor, Appl. Opt. 28(1989), pp. 4206-4209. A.J. Wixted, D.V. Thiel, A.G. Hahn, C.J. Gore, D.B. Pyne, and D.A. James, Measurement of energy expenditure in elite athletes using MEMS-based triaxial accelerometers, IEEE Sensors J. 7 (2007), pp. 481–488. D.A. James, N. Davey, and T. Rice, An accelerometer based sensor platform for insitu elite athlete performance analysis, in Proc. IEEE Sensors, 2004, pp. 1373–1376. D.M. Karantonis, M.R. Narayanan, M. Mathie, N.H. Lovell, and B.G. Celler, Implementation of a real-time human movement classier using a triaxial accelerometer for ambulatory monitoring, IEEE Trans. Inf. Technol. Biomed. 10 (2006), pp. 156–167. J.W. Kim, B.K. Lee, J.H. Hong, and G.M. Eom, The trend and prospect of silver/rehabilitation engineering, KIC News. 11 (2008), pp. 11-23. L.E. Dunne, P. Walsh, S. Hermann, B. Smyth, and B. Caulfiel, Wearable monitoring of seated spinal posture, IEEE Trans. Biom. Cirt. Syst. 2 (2008), pp. 97-105. D.S. Park, and S.G. Lee, A review of AMA guides to the evaluation of permanent impairment, J. Korea Med. Assoc. 52 (2009), pp. 567-572. L. Tesio, M. Monzani, R. Gatti, and F. Franchigioni, Flexible electrogoniometers: kinesiological advantages with respect to potentiometric goniometers, Clin. Biomech. 10(1995), pp. 275–277 D. Marcuse, Curvature lose formula for optical fibers, J. Opt. Soc. Am. 66 (1976), pp. 216-220. D.A. Winter, Biomechanics and motor control of human movement, Wiley and Sons, New York, 1990. D.B. Chaffin , G. Andersson, and B.J. Martin, Occupational biomechanics, Wiley and Sons, New York, 1991. G.J. Donatell, D.W. Meister, J.R. O’Brien, J.S. Thurlow, J.G. Webster, and F.J. Salvi, A simple device to monitor flexion and lateral bending of the lumbar spine, IEEE Trans. Neural. Syst. Rehabil. Eng. 13(2005), pp. 18-23. Y.S. Park, S.H. Lee, and S.B. Yoon, Calibration of glove-like hand input system for wearable computer, J. Korean Sco. Precis. Eng. 17 (2000), pp. 209-216. R. Roduit, P.A. Besse, and J.P. Micallef, Flexible angular sensor, IEEE Trans. Inst. Meas. 47 (1998), pp. 1020-1022.
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[15] M.W. Whittle, Calibration and performance of a 3-dimensional television system for kinematic analysis, J. Biom. 15 (1982), pp. 185-196. [16] B. Auvinet, D. Chaleil and E. Barrey, Accelerometric gait analysis for use in hospital outpatients, Rev. Rhum. Engl. Ed. 66 (1999), pp. 389-397. [17] C.M. Wu and Y.T. Chuang, Roll angular displacement measurement system with microradian accuracy, Sens. Actuat. A 116 (2004), pp. 145-149. [18] P.S. Huang, Use thin films for high-sensitivity angle measurement, Appl. Opt. 38(1999), pp. 4831-4836. [19] M. Born, E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, Cambridge: Cambridge University Press, 1999. [20] B.E.A. Saleh and M.C. Teich, Fundamentals of photonics, Wiley and Sons, New York, 2007.
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771
Development of an Optical Fiber Sensor for Angular Displacement Measurements Gu-In Jung a,b, Ji-Sun Kim a,b, Tae-Hee Lee a,b, Ju-Hyeon Choi a,b, Han-Byeol Oh a,b, A-Hee Kim a,b, Gwang-Moon Eom a,b, Jeong-Hwan Lee a,b, Soon-Cheol Chung a,b, Jong-Rak Park c, Young-Jae Lee a,b, Hee-Jung Park a,b, and Jae-Hoon Jun a,b* a
Department of Biomedical Engineering, College of Biomedical and Health Science, Konkuk University, Chungju, South Korea b Department of Biomedical Engineering, Research Institute of Biomedical Engineering, Konkuk University, Chungju, South Korea c Department of Photonic Engineering, Chosun University, Gwangju, South Korea
Abstract. For diagnostic and therapeutic purposes, the joint angle measurement of a patient after an accident or a surgical operation is significant for monitoring and evaluating the recovering process. This paper proposed an optical fiber sensor for the measurement of angular displacement. The effect of beveled fiber angle on the detected light signal was investigated to find an appropriate mathematical model. Beveled fiber tips redirected the light over a range of angles away from the fiber axis. Inverse polynomial models were applied to directly obtain and display the joint angle change in real time with the LabVIEW program. The actual joint angle correlated well with the calculated LabVIEW output angle over the test range. The proposed optical sensor is simple, cost effective, small in size, and can evaluate the joint angle in real time. This method is expected to be useful in the field of rehabilitation and sport science. Keywords: Optical fiber, Angular sensor, Beveled tip, Asymmetric beam profile, Goniometer
1. Introduction Human joint movement can be used to evaluate the rehabilitation process of patients and the optimal performance of sport activities [1-3]. For diagnostic and therapeutic purposes, it may be necessary to evaluate and monitor the joint angle of a patient after an accident or a surgical operation to ensure that the patient is doing one of the different exercises for each patient in the correct posture [4-6]. Different kinds of angular sensors have been reported in the past. The most widely used is a goniometer using a circular potentiometer as the sensitive element [7-10]. Another kind is the strain gauge [11-14]. During repeated use of mechanical and electrical parts, current goniometers show some disadvantages in accuracy and repeatability. In addition, these sensors are quite expensive and sometimes fragile as well. *Adress for Correspondence : Department of Biomedical Engineering, College of Biomedical and Health Science, Konkuk University, 268 Chungwondaero, Chungju-si, Chungcheongbuk-do, 380-701, South Korea, Tel.: +82 43 8403799; E-mail: [email protected]. 0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
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G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements
The camera based three-dimensional (3-D) motion capture system [15-18] is accurate but very expensive, complicated to use, and only effective in the special lab with bulky camera systems. Furthermore, to process data, specialists are required and the data processing time is relatively long. The system requires calibration in each test set and long preparation time. Sometimes patients claim inconvenience in attaching reflection markers on their body, and the markers can be obscured from vision resulting in incomplete data. This study used beveled fiber tips and studied the beam profile to find out the way of increasing detection range. The aim of this study is to suggest an alternative method for the identification of the joint angle which can be convenient, cost effective, and operated in real time. Therefore, a new design concept of the optical fiber sensor was proposed to measure joint angle. 2. Materials and Methods 2.1. Beveled fiber Snell’s law describes the relationship between the angles of incidence and refraction, when referring to light passing through a boundary between two different isotropic media, such as water, glass, and air. Thus, the law is used in ray tracing to compute the angles of incidence or refraction [19-20]. For fiber characterization, the acceptance angle is typically reported in terms of a numerical aperture (NA). Light enters (or leaves) the fiber within an acceptance cone of 2 (see Fig. 1(a)). From Eq. (1), the NA can be expressed in terms of the refractive indices of the fiber material, depending on the refractive index of the surrounding environment (nair). The NA of an optical fiber characterizes its ability to collect light from a source and to preserve the light inside the fiber.
NA = nair sin = n 2 core ڈn 2 cladding
,
(1)
Where is the acceptance angle (light enters /leaves the fiber within an acceptance cone), nair is the refractive index of air, ncore is the refractive index of core, and ncladding is the refractive index of cladding. If the surface of the fiber is fabricated with a bevel angle with respect to the fiber axis, the output light from the fiber is refracted by an angle (see Eqs. (2)-(4) and Fig. 1 (b)). The refracted angle can be described as a function of the bevel angle of the fiber.
nair sin air = ncore sin ,
(2)
air = sin 1 (ncore sin / nair ) ,
(3)
= air ڈ
,
(4)
Where air is the angle at which the peak propagates in air, relative to the face normal, is the bevel angle, and is the angular limit of the refraction angle.
G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements
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Fig. 1. The change of the refracted angle due to the bevel angle
2.2. Fiber optic sensor Fig. 2 shows the fiber optic sensor developed in this study. A red chip LED (IWS-165-RXWF, ITSWELL, Korea) with the wavelength range of 618 - 635nm, was attached on the right end of the polished beveled fiber. The fiber (BFL48-1000, Thorlabs, Newton, New Jersey) is step index multimode (the refractive index of core = 1.457, the refractive index of cladding = 1.3756, and NA=0.48) made of silica core and hard polymer cladding. With a total diameter of 1.4 mm, the core and cladding diameters of the fiber are 1mm and 1.035mm, respectively. A phototransistor (ST-23G, KODENSHI CORP., Japan) was used as a detector to monitor the change of light signal from the fiber due to the change of the joint angle. The sensing range of the phototransistor is from 500 to 1050nm and its half angle of detection is s30rU With the developed fiber optic sensor, various distances between the detector and the optical fiber tip (d = 3.3mm, 4.3mm, 5.3mm), beveled fiber angles ( = 0°, 20°, 30°, 45°), and joint angles ( = 0° ~ 180°, with increment of 5°) were applied to find the optimal combination of these variables for joint angle measurements. The beveled optical fibers were fabricated by polishing the fiber tips at certain angles with a rotating sandpaper tool. Our aim of this study is to find the conditions for a wide detection range with the minimum error.
Fig. 2. Fiber optics sensor
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G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements
2.3. Data acquisition and Modeling As shown in Fig. 3, output signals from phototransistor were collected using DAQ board (NI USB6008, National Instrument) in digital form, and saved in a computer with LabVIEW 8.0 (National Instruments, Austin, Texas). Modeling of the experimental data was done by using Matlab (R2008a, Mathworks, Portola Valley, California). Polynomial equations were tested for the modeling. Two types of modeling were selected to obtain the joint angle. First, the relationship between phototransistor output and joint angle was mathematically modeled (see Eq. (5)). Next, the inverse relationship was used to derive the joint angle (see Eq. (6)). The inverse model is possible when the functions show monotonic pattern (increase or decrease). Using the obtained inverse model, the joint angle change with LabVIEW in real time could be calculated and displayed.
y = a0 x n + a1 x n-1 + a2 x n-2 + ! + an x 0 x = b0 y n + b1 y n-1 + b2 y n
2
(5)
+ ! + bn y 0 ,
(6)
Where a0 ~ an are the coefficients of the polynomial equation, b0 ~ bn are the coefficients of the inverse polynomial equation, x is the joint angle [Deg.], and y is the phototransistor output voltage [V].
Fiber optic sensor
DAQ board
- signal detection
- A/D conversion
Matlab - data analysis - data modeling
LabVIEW - joint angle display
Fig. 3. Schematic of experimental procedures
3. Results and Discussion 3.1. The effect of the bevel angle and the distance between detector and fiber tip Fig. 4 shows the change of light signal by the joint angle ( = 0° ~ 180°, with an increment of 5°) with different beveled fiber tips (bevel angle = 0°, 20°, 30°, 45°). Similar experiments had been repeated at different distances between the detector and fiber tip (d = 3.3mm, 4.3mm, 5.3mm). The detected light signal has different peak patterns and beam profiles due to the beveled fiber angle and the distance between detector and fiber tip. Thus, the fiber tip angle and the distance must be considered to develop an efficient optical fiber sensor for angular measurements. Fig. 5 shows the effect of the bevel angle on detected light signal. For a flat fiber ( = 0°), the light signal shows the symmetric beam profile. However, for beveled fibers ( = 20°, 30°, 45°), the signal shows that the asymmetric beam profile and the asymmetric nature are increased with the increase of the bevel angle. Beveled tips redirect the light over a range of angles away from the fiber axis. In an extreme case such as = 45°, the light signal has two peaks which can be caused by the outof-range in critical angle condition. Thus this extreme case is not suitable for joint angle measurements. Since the range of joint angle measurement increases as the bevel angle increases, the beveled fiber of = 30° is selected for application in an angular sensor.
G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements
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Fig.6 shows the effect of the distance between detector and fiber tip (d = 3.3mm, 4.3mm, and 5.3mm) on detected light signal with the bevel angle, = 30°. As the distance increases, the value of the peak point decreases but the range of light signal measurement is on the rise with enough resolution. This result implies that d= 5.3mm is the efficient distance in the test range for joint angle measurements. 5
d = 3.3mm d = 4.3mm d = 5.3mm
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3.2. Modeling and the measured angle display Fig. 7 shows two sections (section A and section B) for inverse mathematical modeling. The section A (joint angle, = 0 ~ 85°) is monotonically increasing region and the section B (joint angle, = 85° ~ 120°) is monotonically decreasing region. The inverse model is possible when the functions show monotonic pattern (increase or decrease). The other region ( = 120° ~ 180) is excluded from modeling because the resolution is too low.
G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements 5
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Fig. 7. Two monotonic regions for inverse modeling
Fig. 8 shows inverse modeling results with inverse polynomial equations for section A and section B with the bevel angle, = 30° and the distance, d= 5.3 mm. Only monotonically increasing or decreasing region was used to get inverse polynomial equations. The inverse 5th order equation showed the best fit in section A while the inverse 7th order equation showed the best fit in section B. Inverse of polynomial equations had coefficients of determination (R2) of section A and section B, 0.9918 and 0.9999, respectively. Fig. 9 shows the example of LabVIEW display of calculated joint angle. Using the obtained inverse models, one can directly calculate and display the joint angle with detected light signal in real time. Fig. 10 shows the relationship between the actual joint angle and the LabVIEW output angle. The result shows that actual joint angle correlates well with the calculated LabVIEW output angle. Experimental results show that the maximum error is ± 1.2596° and root-mean-square error is ± 0.0096°. 5
o
Experimental data [β = 30 ] Inverse 5th order equation
Light signal [V]
4 x = 11.72y5 - 64.95y4 + 132.48y3 - 117.95y2 + 71.0416y - 4.79
3 R2 = 0.9918
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G.-I. Jung et al. / Development of an optical fiber sensor for angular displacement measurements 5
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Experimental data [β = 30 ] Inverse 7th order equation
4 Light signal [V]
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x = -242.34y + 2116.93y - 7484.40y + 13757.54y - 14067.57y + 7941.46y - 2298.62y + 380.45
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(b) Section B Fig. 8. Inverse models with polynomial equations (d = 5.3mm, = 30°)
Fig. 9. Example of LabVIEW display 150
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Fig. 10. Actual joint angle versus LabVIEW output angle
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The developed optical sensor is valid in the measuring range of = 85° ~ 120°. Future study should be done to increase the measuring range up to 180 degree. The design for 3-D angular measurement and a wireless module will be added for an upgraded optical sensor in future study. Our final goal is to develop a low-cost device that can be used by patients at home to record and provide the real-time feedback without space limitations using a wireless module. 4. Conclusions This study proposed an optical fiber sensor and investigated the effects of beveled fiber angle on joint angle measurements. The detected light signal depends on the distance between the detector and fiber tip. In general, as the bevel angle and the distance increase, the range of joint angle measurement increases. The best combination of parameters is applied to find the appropriate model. Using inverse polynomial models, the joint angle change in real time with LabVIEW display is obtained. The suggested sensor is expected to be used in the fields of rehabilitation and sport science. 5. Acknowledgements This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 20100023158) and the Pioneer Research Center Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future planning (No.2011-0027920). References [1] [2] [3] [4]
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[15] M.W. Whittle, Calibration and performance of a 3-dimensional television system for kinematic analysis, J. Biom. 15 (1982), pp. 185-196. [16] B. Auvinet, D. Chaleil and E. Barrey, Accelerometric gait analysis for use in hospital outpatients, Rev. Rhum. Engl. Ed. 66 (1999), pp. 389-397. [17] C.M. Wu and Y.T. Chuang, Roll angular displacement measurement system with microradian accuracy, Sens. Actuat. A 116 (2004), pp. 145-149. [18] P.S. Huang, Use thin films for high-sensitivity angle measurement, Appl. Opt. 38(1999), pp. 4831-4836. [19] M. Born, E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, Cambridge: Cambridge University Press, 1999. [20] B.E.A. Saleh and M.C. Teich, Fundamentals of photonics, Wiley and Sons, New York, 2007.
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