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Theoretical and experimental research on MZI frequency detection method based on orthogonal signal processing technology
Optik 126 (2015) 3554–3557
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Theoretical and experimental research on MZI frequency detection method based on orthogonal signal processing technology Bo Han a,∗ , Da Sun a , Kuihe Gao a , Yonggang Jia a , Xiaoyu Zhang b a b
Liaoning Provincial Institute of Measurement, Shenyang 110819, China College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
a r t i c l e
i n f o
Article history: Received 31 August 2014 Accepted 25 August 2015 Keywords: MZI Frequency detection Orthogonal signal processing technology 4 × 4 coupler Fiber Bragg grating
a b s t r a c t A novel MZI structure was proposed by taking advantage of orthogonal signal processing technology (OSPT) and used for frequency detection. The proposed MZI was made up of a 4 × 4 coupler and a 2 × 2 coupler, and the signal processing was realized by a numerical oscilloscope. The theoretical and experimental results demonstrated that the proposed MZI structure could decrease the influence of input power vibration and the output profile was linearity and the measurement range was enlarged to more than 6 times as large as before. The achievement in this research could not only make up for the weakness of conventional MZI, but also extent the application ranges of interferometer. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction Fiber Bragg grating (FBG) has attracted increasing attention for its promising application in the measurements of physical and chemical parameters, such as temperature [1,2], strain [3–5], displacement [6,7], and so on [8,9]. The sensing principle of FBG is that the reflected frequency of FBG would change with the variations of these surrounding parameters. To demodulate the frequency change of the reflected signal of FBG, many methods have been reported, such as spectral-splitting based demodulation technology [10], filter based demodulation technology [11], and interferometer based demodulation technology [12]. Among which the Mach–Zehnder interferometer (MZI) based light frequency detection method, with high-precision, low cost, and high response rate, has been widely used to demodulate the reflected frequency of FBG [13,14]. The demodulation principle of traditional MZI is to transform light frequency to power variation. However, since the output power of MZI appears as sine-profile with input frequency changing, the output profile could not be regard as linear and there exist measurement dead zones in it. Besides, the measurement range is limited by the monotone interval. In this paper, a novel MZI structure was proposed based on orthogonal signal processing technology (OSPT), in which a 4 × 4
∗ Corresponding author at: Institute of mechanics, Liaoning Provincial Institute of Measurement, Shenyang, Liaoning 110819, PR China. Tel.: +86 15942368046. E-mail address: [email protected] (B. Han). http://dx.doi.org/10.1016/j.ijleo.2015.08.182 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
coupler was fabricated and the complicated numerical analysis was built. The experiment results proved that the output profile was linearity and the measurement range could be further enlarged.
2. Theory analysis In traditional MZI, the output signal is the output power I of MZI, which could be written as: I=
I0 [1 + cos ] 2
(1)
where, I0 is the input power of MZI, = (2fLn)/c is the phase of MZI, f is the frequency of input signal, L is the length difference between the two interferometer branches and is set to be 1 cm in this paper, c is the velocity of light in vacuum, n is the refractive index of fiber. Fig. 1 shows the relationship between the light frequency and the output power. Based on Eq. (1) and Fig. 1, it could be found that the profile is periodical, so only one the monotone interval with linear changing of power could be used for sensing. However, in actually, the profile of one monotone interval is nonlinear, so linear approximation would lead to linearity error. As we known, the phase is linear to light frequency, and we could avoid the linearity error by making the light phase as the output signal through inverse trigonometric function calculations. But, measurement dead zones in the profile make inverse trigonometric function calculation inaccurate. In addition, the input power vibration will also make system unreliable.
B. Han et al. / Optik 126 (2015) 3554–3557
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Fig. 1. The relationship between the light frequency and the output power in traditional MZI.
To improve all the problems above, the OSPT was adopted to transform sine-output profile to tangent-output profile, which exists no dead zone, and could avoid input power influence on system. To realize OSPT, there should be four output signals, which should be orthogonal with each other. 4 × 4 coupler is an unusual coupler with four output ports, and the phase difference between nearby ports is /2. So, we could use 4 × 4 coupler to realize OSPT. As shown in Fig. 2, the structure of OSPT based MZI is proposed. The signal from sensor goes into a MZI through a 2 × 2 coupler, and then is demodulated to 4 output signals. The power of output signals are transformed to current by four optical detectors, and processed by a numerical oscilloscope. The power of four output signals could be written as follows: I0 I1 = [1 + cos ] 2 I2 = I3 = I4 =
I0 2
1 + cos +
(2)
2
I0 [1 + cos( + )] 2
I0 2
1 + cos +
3 2
(3) (4) (5)
By orthogonal operation, the tangent-output profile could be obtained, which could be written as follows: P=
(I1 − I3 )/(I1 + I3 ) = tan (I2 − I4 )/(I2 + I4 )
Fig. 3. (a) The calculated phase profile without phase compensation; and (b) The calculated phase profile after phase compensation.
As shown in Fig. 3(a), the initial input frequency is F0 and the output phase is 0 . When the input frequency moving leads the output phase changing to 0 , there would be an unlimited number of frequency answers, as the profile is periodical. Assumed that the nearest two answers are F1 and F2 , as shown in Fig. 3(a), and it is sure that F2 − F1 = c/2nL. If we regard the nearest one as the real answer, when the frequency change F = Fx − F0 is so large that F2 − F0 = F0 − F1 , the real answer would never be found out. The upper limit of frequency change could be defined as the maxim frequency change, which could be calculated to be Fmax = c/4nL. So, when F < Fmax , we could know the direction and value of frequency change, and connect every period profile with each other. Then, the phase profile could be compensated, as shown in Fig. 3(b).
(6) 3. Experimental results and discussions
As I0 doesn’t exist in Eq. (6), the influence of input power vibration could be avoided. Based on Eq. (6), the phase value could be obtained through arc-tangent calculation. However, the scope of arc-tangent calculation is only from 0 rad to rad, so the calculated phase profile is periodical and discontinuous, as shown in Fig. 3(a), while the real phase profile is a continuous straight line. To get the real profile, phase compensation algorithm is necessary.
To prove what discussed above, a lot of efforts had been made in experiments. We customize a 4 × 4 coupler, and test the output powers of every branch to make sure that the splitting ratio of the coupler is 25:25:25:25. As MZI is so sensitive that slight temperature change or vibration would influence the stability of system, a fiber fixed equipment, as shown in Fig. 4, was designed and
Fig. 2. The structure of OSPT based MZI.
Fig. 4. The fiber fixed equipment.
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B. Han et al. / Optik 126 (2015) 3554–3557
Fig. 7. The experiment profile of orthogonal operation result. Fig. 5. The desktop of software.
fabricated to avoid interruption from air flow and slight vibration. The fibers in couplers twined tightly around the two glass sticks on fixed equipment, and one of the glass stick was pulled strongly enough to make sure that the fibers could be hold still. To avoid temperature interruption, the couplers were put into invariable temperature environment. As human manipulation will cause unavoidable interruption, we make the system run automatically. We use a tunable laser to provide input signal, which is controlled by an advanced numerical oscilloscope. The numerical Oscilloscope was produced by Lecroy and numbered Waverunner 640, which could be used to realize complicated numerical analysis. Besides, an software is programed to realize the automatic flow of experiment, and the desktop of software is shown in Fig. 5, where Sx (x = 1, 2, 3, 4) screen is utilized to filter the noise and make an analyze on system stability by numerical processing, and then Px (x = 1, 2, 3, 4) would show the output profiles of every ports. Fig. 6 shows one of the experiment records of four output ports. It could be found that the four profiles were orthogonal. Then, after numerical calculation, the profile of orthogonal operation result could be obtained by Eq. (6), which is tangent-profile and shown in Fig. 7. As the frequency change is set to 2 GHz, which was lower c than Fmax = 4nL = 5.17 GHz, we get the phase profile successfully, which is shown in Fig. 8. The experimental result is almost consistent with the calculated result as shown in Fig. 8, and could be regarded as a direct line. By comparing Fig. 1 with Fig. 8, it could be found that there exists no dead zone in output profile after orthogonal operation. Further more, the measurement range of OSPT based MZI had been enlarged to 60 GHz, while the one of traditional MZI could not be larger than 10 GHz as shown in Fig. 1, and if the band width of light source and detector was wide enough, much larger measurement range could be obtained. To analyze the influence of input power on experiment result, the output phase profiles with different input powers were studied
Fig. 8. The experiment result and calculated result of output phase after phase compensation.
Fig. 9. The comparison between experiment result with different input power.
from experiment. As shown in Fig. 9, although the input powers were different, the output profiles were overlap with each other, which meant that the proposed MZI structure could avoid the interruption from input power vibration. 4. Conclusion In this paper, a novel MZI structure was proposed, which took advantage of OSPT and was realized by a 4 × 4 coupler. The experimental results proved that the proposed MZI could avoid the interruption of input power vibration and have a linear output profile without insensible zone. Besides, we proved that when the change step of light frequency is lower than Fmax , the measurement range could be enlarged to infinite in theory, and we successfully made it enlarged to more than 6 times as large as before in experiment. References
Fig. 6. The experiment results of four output signals.
[1] S.J. Mihailov, Fiber Bragg grating sensors for harsh environments, Sensors 12 (2012) 1898–1918.
B. Han et al. / Optik 126 (2015) 3554–3557 [2] R. RajiniKumar, K.G. Narayankhedkar, G. Krieg, M. Süber, A. Nyilas, K.P. Weiss, Fiber Bragg gratings for sensing temperature and stress in superconducting coils, IEEE Trans. Appl. Supercond. 16 (2006) 1737–1740. [3] C.H. Lee, J. Lee, M.K. Kim, K.T. Kim, Characteristics of a fiber Bragg grating temperature sensor using the thermal strain of an external tube, J. Korean Phys. Soc. 59 (2011) 3188–3191. [4] G. Rajan, Y. Semenova, Q. Wang, G. Farrell, P. Wang, A method to measure reference strain in FBG strain sensor interrogation system involving actuators, Microw. Opt. Technol. Lett. 49 (2007) 2658–2661. [5] G. Rajan, Y. Semenova, Q. Wang, G. Farrell, P. Wang, Fibre bend loss ratiometric wavelength demodulation system for an FBG strain sensor, Photonics 2006 (2006) 9–11. [6] L.H. Kang, D.K. Kim, J.H. Han, Estimation of dynamic structural displacements using fiber Bragg grating strains sensors, J. Sound Vib. 305 (2007) 534–542. [7] Y. Zhao, Q. Wang, H. Huang, Wavelength demodulation method using a tilted FBG and a PSD for a fiber optic micro-displacement sensor, J. Optoelectron. Adv. Mater. 13 (2011) 845–847. [8] A.P. Zhang, S. Gao, G. Yan, Y. Bai, Advances in optical fiber Bragg grating sensor technologies, Photonic Sens. 2 (2012) 1–13.
3557
[9] G. Rajan, Y.M. Noor, B. Liu, E. Ambikairaja, D.J. Webb, G.D. Peng, A fast response intrinsic humidity sensor based on an etched singlemode polymer fiber Bragg grating, Sens. Actuators A: Phys. 203 (2013) 107–111. [10] Y. Zhao, C.B. Yu, Y.b. Liao, Differential FBG sensor for temperature-compensated high pressure (or displacement) measurement, Opt. Laser Technol. 36 (2004) 39–42. [11] S. Matthews, Y. Semenova, G. Rajan, G. Farrell, Experimental demonstration of a ferroelectric liquid crystal tunable filter for fast demodulation of FBG sensors, Conf. Opt. Sens. 7356 (2009) 20–24. [12] D.C.C. Norman, Y. Lai, D.J. Webb, High birefringence fibre interrogating interferometer for optical sensing applications, Electron. Lett. 41 (2005) 235–236. [13] Q. Wang, B. Han, C. Qin, K. Xue, Y. Zhao, Enhancing the sensitivity of interferometer sensing by slow light in a photonic crystal waveguide, Photonics Lett. Pol. 4 (2012) 131–133. [14] D. Feng, Z. Liu, W. Zhang, G. Kai, X. Dong, Optimization design of Mach–Zehnder interferometer and its application in a fiber Bragg grating phase sensor demodulation, Optoelectron. Inf. Syst. Process. 7 (2001) 7–11.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Theoretical and experimental research on MZI frequency detection method based on orthogonal signal processing technology Bo Han a,∗ , Da Sun a , Kuihe Gao a , Yonggang Jia a , Xiaoyu Zhang b a b
Liaoning Provincial Institute of Measurement, Shenyang 110819, China College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
a r t i c l e
i n f o
Article history: Received 31 August 2014 Accepted 25 August 2015 Keywords: MZI Frequency detection Orthogonal signal processing technology 4 × 4 coupler Fiber Bragg grating
a b s t r a c t A novel MZI structure was proposed by taking advantage of orthogonal signal processing technology (OSPT) and used for frequency detection. The proposed MZI was made up of a 4 × 4 coupler and a 2 × 2 coupler, and the signal processing was realized by a numerical oscilloscope. The theoretical and experimental results demonstrated that the proposed MZI structure could decrease the influence of input power vibration and the output profile was linearity and the measurement range was enlarged to more than 6 times as large as before. The achievement in this research could not only make up for the weakness of conventional MZI, but also extent the application ranges of interferometer. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction Fiber Bragg grating (FBG) has attracted increasing attention for its promising application in the measurements of physical and chemical parameters, such as temperature [1,2], strain [3–5], displacement [6,7], and so on [8,9]. The sensing principle of FBG is that the reflected frequency of FBG would change with the variations of these surrounding parameters. To demodulate the frequency change of the reflected signal of FBG, many methods have been reported, such as spectral-splitting based demodulation technology [10], filter based demodulation technology [11], and interferometer based demodulation technology [12]. Among which the Mach–Zehnder interferometer (MZI) based light frequency detection method, with high-precision, low cost, and high response rate, has been widely used to demodulate the reflected frequency of FBG [13,14]. The demodulation principle of traditional MZI is to transform light frequency to power variation. However, since the output power of MZI appears as sine-profile with input frequency changing, the output profile could not be regard as linear and there exist measurement dead zones in it. Besides, the measurement range is limited by the monotone interval. In this paper, a novel MZI structure was proposed based on orthogonal signal processing technology (OSPT), in which a 4 × 4
∗ Corresponding author at: Institute of mechanics, Liaoning Provincial Institute of Measurement, Shenyang, Liaoning 110819, PR China. Tel.: +86 15942368046. E-mail address: [email protected] (B. Han). http://dx.doi.org/10.1016/j.ijleo.2015.08.182 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
coupler was fabricated and the complicated numerical analysis was built. The experiment results proved that the output profile was linearity and the measurement range could be further enlarged.
2. Theory analysis In traditional MZI, the output signal is the output power I of MZI, which could be written as: I=
I0 [1 + cos ] 2
(1)
where, I0 is the input power of MZI, = (2fLn)/c is the phase of MZI, f is the frequency of input signal, L is the length difference between the two interferometer branches and is set to be 1 cm in this paper, c is the velocity of light in vacuum, n is the refractive index of fiber. Fig. 1 shows the relationship between the light frequency and the output power. Based on Eq. (1) and Fig. 1, it could be found that the profile is periodical, so only one the monotone interval with linear changing of power could be used for sensing. However, in actually, the profile of one monotone interval is nonlinear, so linear approximation would lead to linearity error. As we known, the phase is linear to light frequency, and we could avoid the linearity error by making the light phase as the output signal through inverse trigonometric function calculations. But, measurement dead zones in the profile make inverse trigonometric function calculation inaccurate. In addition, the input power vibration will also make system unreliable.
B. Han et al. / Optik 126 (2015) 3554–3557
3555
Fig. 1. The relationship between the light frequency and the output power in traditional MZI.
To improve all the problems above, the OSPT was adopted to transform sine-output profile to tangent-output profile, which exists no dead zone, and could avoid input power influence on system. To realize OSPT, there should be four output signals, which should be orthogonal with each other. 4 × 4 coupler is an unusual coupler with four output ports, and the phase difference between nearby ports is /2. So, we could use 4 × 4 coupler to realize OSPT. As shown in Fig. 2, the structure of OSPT based MZI is proposed. The signal from sensor goes into a MZI through a 2 × 2 coupler, and then is demodulated to 4 output signals. The power of output signals are transformed to current by four optical detectors, and processed by a numerical oscilloscope. The power of four output signals could be written as follows: I0 I1 = [1 + cos ] 2 I2 = I3 = I4 =
I0 2
1 + cos +
(2)
2
I0 [1 + cos( + )] 2
I0 2
1 + cos +
3 2
(3) (4) (5)
By orthogonal operation, the tangent-output profile could be obtained, which could be written as follows: P=
(I1 − I3 )/(I1 + I3 ) = tan (I2 − I4 )/(I2 + I4 )
Fig. 3. (a) The calculated phase profile without phase compensation; and (b) The calculated phase profile after phase compensation.
As shown in Fig. 3(a), the initial input frequency is F0 and the output phase is 0 . When the input frequency moving leads the output phase changing to 0 , there would be an unlimited number of frequency answers, as the profile is periodical. Assumed that the nearest two answers are F1 and F2 , as shown in Fig. 3(a), and it is sure that F2 − F1 = c/2nL. If we regard the nearest one as the real answer, when the frequency change F = Fx − F0 is so large that F2 − F0 = F0 − F1 , the real answer would never be found out. The upper limit of frequency change could be defined as the maxim frequency change, which could be calculated to be Fmax = c/4nL. So, when F < Fmax , we could know the direction and value of frequency change, and connect every period profile with each other. Then, the phase profile could be compensated, as shown in Fig. 3(b).
(6) 3. Experimental results and discussions
As I0 doesn’t exist in Eq. (6), the influence of input power vibration could be avoided. Based on Eq. (6), the phase value could be obtained through arc-tangent calculation. However, the scope of arc-tangent calculation is only from 0 rad to rad, so the calculated phase profile is periodical and discontinuous, as shown in Fig. 3(a), while the real phase profile is a continuous straight line. To get the real profile, phase compensation algorithm is necessary.
To prove what discussed above, a lot of efforts had been made in experiments. We customize a 4 × 4 coupler, and test the output powers of every branch to make sure that the splitting ratio of the coupler is 25:25:25:25. As MZI is so sensitive that slight temperature change or vibration would influence the stability of system, a fiber fixed equipment, as shown in Fig. 4, was designed and
Fig. 2. The structure of OSPT based MZI.
Fig. 4. The fiber fixed equipment.
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B. Han et al. / Optik 126 (2015) 3554–3557
Fig. 7. The experiment profile of orthogonal operation result. Fig. 5. The desktop of software.
fabricated to avoid interruption from air flow and slight vibration. The fibers in couplers twined tightly around the two glass sticks on fixed equipment, and one of the glass stick was pulled strongly enough to make sure that the fibers could be hold still. To avoid temperature interruption, the couplers were put into invariable temperature environment. As human manipulation will cause unavoidable interruption, we make the system run automatically. We use a tunable laser to provide input signal, which is controlled by an advanced numerical oscilloscope. The numerical Oscilloscope was produced by Lecroy and numbered Waverunner 640, which could be used to realize complicated numerical analysis. Besides, an software is programed to realize the automatic flow of experiment, and the desktop of software is shown in Fig. 5, where Sx (x = 1, 2, 3, 4) screen is utilized to filter the noise and make an analyze on system stability by numerical processing, and then Px (x = 1, 2, 3, 4) would show the output profiles of every ports. Fig. 6 shows one of the experiment records of four output ports. It could be found that the four profiles were orthogonal. Then, after numerical calculation, the profile of orthogonal operation result could be obtained by Eq. (6), which is tangent-profile and shown in Fig. 7. As the frequency change is set to 2 GHz, which was lower c than Fmax = 4nL = 5.17 GHz, we get the phase profile successfully, which is shown in Fig. 8. The experimental result is almost consistent with the calculated result as shown in Fig. 8, and could be regarded as a direct line. By comparing Fig. 1 with Fig. 8, it could be found that there exists no dead zone in output profile after orthogonal operation. Further more, the measurement range of OSPT based MZI had been enlarged to 60 GHz, while the one of traditional MZI could not be larger than 10 GHz as shown in Fig. 1, and if the band width of light source and detector was wide enough, much larger measurement range could be obtained. To analyze the influence of input power on experiment result, the output phase profiles with different input powers were studied
Fig. 8. The experiment result and calculated result of output phase after phase compensation.
Fig. 9. The comparison between experiment result with different input power.
from experiment. As shown in Fig. 9, although the input powers were different, the output profiles were overlap with each other, which meant that the proposed MZI structure could avoid the interruption from input power vibration. 4. Conclusion In this paper, a novel MZI structure was proposed, which took advantage of OSPT and was realized by a 4 × 4 coupler. The experimental results proved that the proposed MZI could avoid the interruption of input power vibration and have a linear output profile without insensible zone. Besides, we proved that when the change step of light frequency is lower than Fmax , the measurement range could be enlarged to infinite in theory, and we successfully made it enlarged to more than 6 times as large as before in experiment. References
Fig. 6. The experiment results of four output signals.
[1] S.J. Mihailov, Fiber Bragg grating sensors for harsh environments, Sensors 12 (2012) 1898–1918.
B. Han et al. / Optik 126 (2015) 3554–3557 [2] R. RajiniKumar, K.G. Narayankhedkar, G. Krieg, M. Süber, A. Nyilas, K.P. Weiss, Fiber Bragg gratings for sensing temperature and stress in superconducting coils, IEEE Trans. Appl. Supercond. 16 (2006) 1737–1740. [3] C.H. Lee, J. Lee, M.K. Kim, K.T. Kim, Characteristics of a fiber Bragg grating temperature sensor using the thermal strain of an external tube, J. Korean Phys. Soc. 59 (2011) 3188–3191. [4] G. Rajan, Y. Semenova, Q. Wang, G. Farrell, P. Wang, A method to measure reference strain in FBG strain sensor interrogation system involving actuators, Microw. Opt. Technol. Lett. 49 (2007) 2658–2661. [5] G. Rajan, Y. Semenova, Q. Wang, G. Farrell, P. Wang, Fibre bend loss ratiometric wavelength demodulation system for an FBG strain sensor, Photonics 2006 (2006) 9–11. [6] L.H. Kang, D.K. Kim, J.H. Han, Estimation of dynamic structural displacements using fiber Bragg grating strains sensors, J. Sound Vib. 305 (2007) 534–542. [7] Y. Zhao, Q. Wang, H. Huang, Wavelength demodulation method using a tilted FBG and a PSD for a fiber optic micro-displacement sensor, J. Optoelectron. Adv. Mater. 13 (2011) 845–847. [8] A.P. Zhang, S. Gao, G. Yan, Y. Bai, Advances in optical fiber Bragg grating sensor technologies, Photonic Sens. 2 (2012) 1–13.
3557
[9] G. Rajan, Y.M. Noor, B. Liu, E. Ambikairaja, D.J. Webb, G.D. Peng, A fast response intrinsic humidity sensor based on an etched singlemode polymer fiber Bragg grating, Sens. Actuators A: Phys. 203 (2013) 107–111. [10] Y. Zhao, C.B. Yu, Y.b. Liao, Differential FBG sensor for temperature-compensated high pressure (or displacement) measurement, Opt. Laser Technol. 36 (2004) 39–42. [11] S. Matthews, Y. Semenova, G. Rajan, G. Farrell, Experimental demonstration of a ferroelectric liquid crystal tunable filter for fast demodulation of FBG sensors, Conf. Opt. Sens. 7356 (2009) 20–24. [12] D.C.C. Norman, Y. Lai, D.J. Webb, High birefringence fibre interrogating interferometer for optical sensing applications, Electron. Lett. 41 (2005) 235–236. [13] Q. Wang, B. Han, C. Qin, K. Xue, Y. Zhao, Enhancing the sensitivity of interferometer sensing by slow light in a photonic crystal waveguide, Photonics Lett. Pol. 4 (2012) 131–133. [14] D. Feng, Z. Liu, W. Zhang, G. Kai, X. Dong, Optimization design of Mach–Zehnder interferometer and its application in a fiber Bragg grating phase sensor demodulation, Optoelectron. Inf. Syst. Process. 7 (2001) 7–11.