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Apr 29, 2016 - Keywords: magnetic field sensor; Fabry-Perot Cavity; magnetic fluid; Fiber ... widely applied for navigation, vehicle detection, current sensing,.
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A Magnetic Field Sensor Based on a Magnetic Fluid-Filled FP-FBG Structure Ji Xia 1 , Fuyin Wang 1 , Hong Luo 1 , Qi Wang 2 and Shuidong Xiong 1, * 1

2

*

Academy of Ocean Science and Engineering & College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha 410073, China; [email protected] (J.X.); [email protected] (F.W.); [email protected] (H.L.) College of Information Science and Engineering, Northeastern University, Shenyang 110819, China; [email protected] Correspondence: [email protected]; Tel.: +86-138-0847-6806

Academic Editor: Vittorio M. N. Passaro Received: 3 March 2016; Accepted: 21 April 2016; Published: 29 April 2016

Abstract: Based on the characteristic magnetic-controlled refractive index property, in this paper, a magnetic fluid is used as a sensitive medium to detect the magnetic field in the fiber optic Fabry-Perot (FP) cavity. The temperature compensation in fiber Fabry-Perot magnetic sensor is demonstrated and achieved. The refractive index of the magnetic fluid varies with the applied magnetic field and external temperature, and a cross-sensitivity effect of the temperature and magnetic field occurs in the Fabry-Perot magnetic sensor and the accuracy of magnetic field measurements is affected by the thermal effect. In order to overcome this problem, we propose a modified sensor structure. With a fiber Bragg grating (FBG) written in the insert fiber end of the Fabry-Perot cavity, the FBG acts as a temperature compensation unit for the magnetic field measurement and it provides an effective solution to the cross-sensitivity effect. The experimental results show that the sensitivity of magnetic field detection improves from 0.23 nm/mT to 0.53 nm/mT, and the magnetic field measurement resolution finally reaches 37.7 T. The temperature-compensated FP-FBG magnetic sensor has obvious advantages of small volume and high sensitivity, and it has a good prospect in applications in the power industry and national defense technology areas. Keywords: magnetic field sensor; Fabry-Perot Cavity; magnetic fluid; Fiber Bragg Grating; temperature compensation

1. Introduction Magnetic field sensors have been widely applied for navigation, vehicle detection, current sensing, and spatial and geophysical researches. Compared with the other types of magnetic field sensor, all-fiber based sensors have been extensively investigated owing to their portability, high geometric adaptability, immunity from electromagnetic interference, long distance signal transmission for remote operation, and resistance to high pressure and corrosion. Magnetic fluids (MFs) have numerous interesting optical characteristics [1–3], such as tunable refractive index, tunable transmittance, birefringence and thermal lens effects, etc. Generally, the components of a MF are magnetic particles, a carrier liquid and surfactants. When an external magnetic field or thermal effect is applied to a MF, then the refractive index of the MF varies with the changing magnetic field or thermal effect. Various MF-based optical devices have been developed [4–6], such as magnetic fluid light modulators, magnetic fluid optical gratings, and magnetic fluid optical fiber filters, etc. Recently, various optical fiber structures with MFs have been proposed for magnetic field sensing, The employed structures include Fabry-Perot cavity [7,8], polymer optical fiber [9],

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[4–6], such as magnetic fluid light modulators, magnetic fluid optical gratings, and magnetic fluid optical fiber filters, etc. Recently, various optical fiber structures with MFs have been proposed for magnetic field Sensors 2016,The 16, 620 of 10 sensing, employed structures include Fabry-Perot cavity [7,8], polymer optical fiber [9],2fiber Bragg grating [10,11] multimode interference [12,13] Michelson interferometer [14] Sagnac interferometer [15,16] and photonic crystal fiber (PCF)-based interferometers [17–19]. Homa [7] used fiber Bragg grating [10,11] multimode interference [12,13] Michelson interferometer [14] Sagnac a MF-filled extrinsic FP interrogated with an infrared wavelength spectrometer to detect magnetic interferometer [15,16] and photonic crystal fiber (PCF)-based interferometers [17–19]. Homa [7] used a fields. The sensor readily measured the magnetic field with a range of 0.5 mT to 12.0 mT with MF-filled extrinsic FP interrogated with an infrared wavelength spectrometer to detect magnetic fields. corresponding sensitivities in the 0.3 to 2.3 nm/mT range. In 2014, Lv [20] proposed a novel fiberThe sensor readily measured the magnetic field with a range of 0.5 mT to 12.0 mT with corresponding optic magnetic field sensor, which was composed of an extrinsic fiber Fabry-Perot interferometer and sensitivities in the 0.3 to 2.3 nm/mT range. In 2014, Lv [20] proposed a novel fiber-optic magnetic a magnetic fluid. Preliminary experiments illustrated that the magnetic field measurement sensitivity field sensor, which was composed of an extrinsic fiber Fabry-Perot interferometer and a magnetic fluid. was 0.0431 nm/Gs and the measurement resolution was better than 0.5 Gs in the range from 0 to 400 Preliminary experiments illustrated that the magnetic field measurement sensitivity was 0.0431 nm/Gs Gs. Their work however did not take the thermal effect of the MF into consideration. The refractive and the measurement resolution was better than 0.5 Gs in the range from 0 to 400 Gs. Their work index of the MF behaves differently under varying magnetic field and temperature conditions, which however did not take the thermal effect of the MF into consideration. The refractive index of the causes a cross-sensitivity effect from the temperature and magnetic field existing in the MF. The MF behaves differently under varying magnetic field and temperature conditions, which causes a measurement systems mentioned above don’t take the impact of the operating temperature on the cross-sensitivity effect from the temperature and magnetic field existing in the MF. The measurement characteristic refractive index into account, which makes the resulting magnetic field measurements systems mentioned above don’t take the impact of the operating temperature on the characteristic unstable and inaccurate. In this work, a modified sensor probe based on the multiplex FP-FBG refractive index into account, which makes the resulting magnetic field measurements unstable and structure is put forward for temperature compensation, which solves the cross-sensitivity effect of inaccurate. In this work, a modified sensor probe based on the multiplex FP-FBG structure is put the temperature and magnetic field in the MF. The FBG is written on the insert fiber end of the FP forward for temperature compensation, which solves the cross-sensitivity effect of the temperature cavity, and it is sensitive to the temperature variation but insensitive to magnetic field changes. The and magnetic field in the MF. The FBG is written on the insert fiber end of the FP cavity, and it is resulting FP-FBG structure is experimentally demonstrated for high resolution magnetic field sensitive to the temperature variation but insensitive to magnetic field changes. The resulting FP-FBG detection. structure is experimentally demonstrated for high resolution magnetic field detection. 2. Principles 2. Principlesof ofthe theFP-FBG FP-FBGSensor Sensor Filled Filled with with Magnetic Magnetic Fluid Fluid The multiplexing multiplexing structure structure based based on on the the FP-FBG FP-FBG sensor sensor is is shown shown in in Figure Figure 1, 1, where where the the FBG FBG is is The written on the insert fiber end of the FP cavity. When a broadband light beam with light intensity Iin written on the insert fiber end of the FP cavity. When a broadband light beam with light intensity transmits through thethe FBG, thethe reflected light Iin transmits through FBG, reflected lightintensity intensitynear nearthe theBragg Braggreflection reflectionwavelength wavelength is is I1. I1. Then the transmission light beam intensity I2 of FBG reaches the FP cavity. In a low-reflectivity FP Then the transmission light beam intensity I2 of FBG reaches the FP cavity. In a low-reflectivity FP cavity,the theinterference interferencespectrum spectrumintensity intensityof ofFP FPII3 is is generated generated and and transmitted transmitted back back through through the the FBG FBG cavity, 3 once again. Finally, the reflected light beam intensity I out from the FP-FBG sensor is combined with once again. Finally, the reflected light beam intensity Iout from the FP-FBG sensor is combined with the the second transmission beam intensity I4 and former FBG reflected light beam intensity second FBGFBG transmission lightlight beam intensity I4 and thethe former FBG reflected light beam intensity I1 , Iand 1, and the output light intensity of the FP-FBG sensor Iout can be obtained as below: the output light intensity of the FP-FBG sensor I can be obtained as below: out

I

 I  I  I [ f

 (1  f

)2  f

out FBG FBG 2 Iout “ I11 ` I44 “ Iinin ¨ r f FBG ` p1 ´ f FBG q ¨ f FF´PPs

]

(1) (1)

where, fFBG is the reflection coefficient of FBG and it is defined as f FBG  R  exp[  (    B ) 2 / c 2 ] , R,,c where, fFBG is the reflection coefficient of FBG and it is defined as f FBG “ R ¨ expr´pλ ´ λ B q2 {c2 s, R„c are the Bragg peak reflectivity, the center-reflected wavelength of FBG, and the bandwidth of the FBG are the Bragg peak reflectivity, the center-reflected wavelength of FBG, and the bandwidth of the FBG reflected peaks. Accordingly, f  P  2 r  [1  cos(4 L /    )] is the reflection coefficient of FP reflected peaks. Accordingly, f F´PF “ 2r ¨ r1 ` cosp4πL{λ ` πqs is the reflection coefficient of FP cavity, cavity, r is the reflectivity fiber L is theof length of FP cavity. and r isand the reflectivity of fiber of end, L isend, the length FP cavity.

Figure Figure 1. 1. The The structure structure of of aa FP-FBG FP-FBG sensor. sensor.

Meanwhile, the resonant peak wavelengths of FBG and FP should be set within a proper measurement wavelength-range from the input light and both of them can be distinguished through one another. In order to maintain the FP interference fringes and the FBG reflected peaks at a same

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Meanwhile, the resonant peak wavelengths of FBG and FP should be set within a proper 3 of 10 them can be distinguished through one another. In order to maintain the FP interference fringes and the FBG reflected peaks at a same order of magnitude, the reflectivity of FBG should be set to close to that of the low fitness FP sensor. order of magnitude, the reflectivity of FBG should be set to close to that of the low fitness FP sensor. Figure 2 shows the reflected spectrum simulation of the FP-FBG sensor. Figure 2 shows the reflected spectrum simulation of the FP-FBG sensor.

Sensors 2016, 16, 620 measurement wavelength-range from the input light and both of

Reflectance / mW

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Figure 2. Simulation of the output spectrum under different different temperatures temperatures (H (H == 0).

In the the simulation, μm, the center-reflected wavelength of In simulation, the the length lengthof ofFP FPcavity cavityisisset setasasL L= =4040 µm, the center-reflected wavelength ˝   1550 nm FBG at room temperature 25 °C is with a reflectivity of 4%. The intensity of the of FBG at room temperature 25 C is λB B “ 1550 nm with a reflectivity of 4%. The intensity of the mW with with aa spectrum spectrum range range of of 1525 1525 nm–1565 nm–1565 nm. nm. The The simulated simulated spectrum of the incident light is 1 mW FP-FBG is displayed clearly with combination of two reflected spectra at a same same spectral spectral resolution resolution the reflected reflected spectra spectra moves moves through through one one another another without without interference. interference. As the temperature temperature and the sensor shifts towards towards the short short increases from 20 ˝°C C to 50 ˝°C, C, the interference spectrum of the FP sensor wavelength direction, however, the center-reflecting wavelength of the FBG moves towards along wavelength direction, however, the center-reflecting wavelength of the FBG moves towards along the the long wavelength direction. In Figure 2, amount the amount of movement of FBG the FBG resonant peaks is long wavelength direction. In Figure 2, the of movement of the resonant peaks is less less than ofFP theinterference FP interference fringes. than that that of the fringes. With reference referenceto tothe theresearch researchresults resultsofofChen Chenetetal.al.[21], [21],under under a constant temperature value With a constant temperature value of of T, T, the relationship between refractive index of the magnetic field is below: as below: the relationship between thethe refractive index of the MFMF andand thethe magnetic field is as

H  Hc 11 )[coth( H ´ Hc )q ´ ] s` n0n0 n MFnMF “ pn(sn´ s nn 00qrcothpα T ( H ´HHc )c q αpH T

(2) (2)

Hc ), nn00 is the refractive index of the where, Hc Hc is is the the critical critical value value of of the the applied applied magnetic magnetic field field (H ( Hą Hc), where, MF with the critical magnetic field and nss is the saturated saturated refractive refractive index index of of MF, MF, and α α is a fitting coefficient. Generally, Generally, the parameters of nss,, nn00,, α, α, Hc Hc for for aa certain kind of magnetic fluid film are regarded as as constants. constants. Therefore, Therefore, at a certain experimental temperature temperature T, there there is only one refractive regarded a certain magnetic field H. The refractive index of the MF isntested under index for the theMF MFnnMFMFforfor a certain magnetic field H. The refractive index ofMF thenMF MF is tested different magnetic field field and and temperature conditions, andand thethe experimental under different magnetic temperature conditions, experimentalresults resultsare are used used for field detection detection with with temperature temperature compensation. compensation. magnetic field In the sensor probe with a FP-FBG structure, the FBG is written on the insert fiber end of the FP cavity. Being Beinginspired inspiredbybythe the concept that central wavelength the are FBG are applied to cavity. concept that thethe central wavelength shiftsshifts of theofFBG applied to detect detect the external temperature, the central wavelength shift canby beEquation defined (3): by the external varying varying temperature, the central wavelength shift of FBG can of be FBG defined Equation (3): (3) ∆λ B “ λ B pβ Tn ` β Tl q ∆T B  B  Tn  Tl  T (3) where, βTn , βTl are the thermal-optical effect coefficient of 8.0 ˆ 10´−66 /˝ C and thermal expansion effect where, βTn, βTl are the thermal-optical effect coefficient of 8.0 × 10 /°C and thermal expansion effect coefficient of 0.55 ˆ 10−6´6 /˝ C in the FBG. ∆T is the variation value of the operating temperature. It coefficient of 0.55 × 10 /°C in the FBG.  T is the variation value of the operating temperature. It is is noted that the central wavelength shift of FBG is not sensitive to the magnetic field applied on the noted that the central wavelength shift of FBG is not sensitive to the magnetic field applied on the FP-FBG sensor, which is used for the measurement of magnetic field with temperature compensation. FP-FBG sensor, which is used for the measurement of magnetic field with temperature compensation. Due to the cross-sensitivity effect of the temperature and magnetic field in MF, the characteristic magnetic fluid refractive index are defined as follows: ∆n MF “ α Hn ¨ ∆H ` α Tn ¨ ∆T

(4)

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where ∆nMF is the change of the magnetic fluid refractive index, and αHn , αTn are the magnetic field sensitive coefficient and temperature sensitive coefficient of the magnetic fluid, respectively. Considering the thermal expansion effect of optical fiber, the central wavelength shift in the output spectrum of the FP-FBG magnetic sensor is given by Equation (5): ∆λm “ λm rα Hn ¨ ∆H ` pα Tn ` α Tl q ¨ ∆Ts

(5)

where, ∆λm is the central wavelength shift of the FP-FBG magnetic sensor, and αTl is the optical fiber thermal expansion effect coefficient. Combining Equations (3) and (5), a relationship matrix between the FBG output wavelength shifts and the two under-test parameters is obtained in Equation (6). Equation (7) achieves the measurement of the temperature and magnetic field through calculating the matrix in Equation (6): «

«

∆λm ∆λ B

∆H ∆T

ff

« “

ff

ff « α Hn λm 0

pα Tn ` α Tl q λm pβ Tn ` β Tl q λ B ff´1 «

« “

α Hn λm 0

pα Tn ` α Tl q λm pβ Tn ` β Tl q λ B

∆H ∆T ∆λm ∆λ B

ff (6) ff (7)

Obviously, when the spectrum drifts and the temperature detected by the FBG are measured in an experimental system, then the change of the magnetic field ∆H can be obtained by the matrix in Equation (7). According to Equation (7), the MF-filled FP-FBG sensor can achieve the simultaneous measurement of the magnetic field and the temperature, and the temperature detected in real-time can be used for the compensation of the magnetic field measurement. Finally, the cross-sensitivity effect of the temperature and magnetic field in the magnetic fluid is eliminated. 3. Experiment System and Analysis The magnetic field measurement system setup is shown in Figure 3. The light beam output from a 1550 nm DFB is injected into the optical fiber circulator via port1, and it transmits into the MF-filled FP-FBG sensor for magnetic field and temperature detection. The programmable DC controls the power of the output electric current to generate a stable magnetic field through a set of coils. When the applied magnetic field varies, the refractive index of the MF changes and the light signal is modulated. The reflected light passes through port 2 to port 3 and it is detected by the spectrometer (AQ6370 OSA, YOKOGAWA, Tokyo, Japan, with a wavelength resolution of 0.02 nm). The MF-filled FP-FBG sensor is located in a temperature control oven (FLYSET Temperature Controller, Shenzhen Dragon Born Hot Runner Technology Co., LTD, Shenzhen, China, with a temperature resolution of ˘1 ˝ C) for the tests at different stable temperatures, and the thermometer is put close to the sensor head to detect the operating temperature. In addition, a Gauss meter is also located near the sensor head to measure the varying magnetic fields. The temperature variation detected by thermometer and the magnetic field variation detected by the Gauss meter are taken to compare with the measurement results of the MF-filled FP-FBG sensor. As shown in the inset of Figure 3, the MF-filled FP-FBG sensor has a FBG length of 10 mm with a refractive index of R = 4% (the grating wavelength is 1550 nm). The length of MF filled in the FP cavity is fabricated with 32 µm. First, the fiber end written with a FBG inserts into the capillary tube; after the fiber is aligned with the capillary it is observed under a microscope; the MF (EMG605, Ferrotec USA Corporation, Bedford, NH, USA) with a volume content of C = 1.8% is infiltrated into the capillary tube. Finally, the reflected fiber is inserted into the capillary tube and sealed with UV glue under ultraviolet light irradiation for 24 h.

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Figure Figure 3. 3. Experimental Experimental setup setup configuration configuration for for the the FP-FBG FP-FBG sensing sensing system. system. Inset: Inset: the the cross-section cross-section schematic diagram of the FP sensing head. Figure 3. Experimental setup configuration for the FP-FBG sensing system. Inset: the cross-section schematic diagram of the FP sensing head. schematic diagram of the FP sensing head.

To illustrate illustrate the the operation, operation, the optical optical fiber end end face face reflection reflection method method based on the Fresnel Fresnel To To illustrate the operation, the optical fiber end face reflection method based on the Fresnel reflection principle is performed to measure the characteristics of refractive index of the MF under reflection principle is performed to measure the characteristics of refractive index of the MF under different magnetic fields and temperatures, as shown in Figure 3. refractive The refractive indexthe of the MF different magnetic fields and temperatures, as shown in Figure 3. The index MF different magnetic fields and temperatures, as shown in Figure 3. The refractive indexofofthe MFunder under parallel magnetic fields behaves as shown in Figure 4a, which shows that n MF = 1.3414 without parallel magnetic fields behaves as shown in Figure 4a, which shows that n = 1.3414 without under parallel magnetic fields behaves as shown in Figure 4a, which shows thatMF nMF = 1.3414 without any any applied magnetic field. applied magnetic field. any applied magnetic field.

Refractive index

Refractive index

1.36 1.36

1.355

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1.35

1.35 1.345

1.345 1.34 0

1.34 0

0.01

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0.03 0.04 0.05 (a) Magnetic field/T

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(a)

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10

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30 40 Temperature/℃

50

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70

(b) 10

20

30 40 50 60 70 Figure 4. (a) Magnetic fluid refractive index variation versus transverse magnetic field; (b) Magnetic Temperature/℃ Figure 4. (a) Magnetic fluid refractive index variation versus transverse magnetic field; (b) Magnetic

fluid refractive index variation versus temperature.

fluid refractive index variation versus temperature. (b)

Figure 4. (a) Magnetic fluid refractive index variation versus transverse magnetic field; (b) Magnetic fluid refractive index variation versus temperature.

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When H is less than 20 mT, nMF increases gradually while the variation is very little. With the H When H is 20 lessmT than gradually while thefrom variation is very little.with Withhigh the MF increases increases from to 20 60 mT, mT,nthe corresponding nMF increases 1.3446 to 1.3600 H increases from 20 mT to 60 mT, the corresponding n increases from 1.3446 to 1.3600 with high MFthe effective operating magnetic field range sensitivity, which plays an important role in determining sensitivity, which plays an important role intodetermining the 60 effective operating magnetic range in the experiment. Although H continues increase from mT, nMF does not change field obviously, in the experiment. Although H continues to increase from 60 mT, n does not change obviously, MF which indicates that nMF has reached its saturation value under the strong magnetic field. Therefore, which that nMFworking has reached its saturation value the strongand magnetic field.ofTherefore, the MFindicates has an effective magnetic field range in under the experiment, the range magnetic the MF has an effective working magnetic field range in the experiment, and the range of magnetic field H is set from 0 mT to 40 mT. When the direction of magnetic field is transverse to the direction field is set from 0 mT tothe 40 mT. When the of direction of magnetic fieldincrease is transverse the direction of theHincident light, and polarizability MF increases with the of thetomagnetic field of the incident light, and The the change polarizability ofsimilar MF increases with the increase the magneticand field (magneto-electric effect). of nMF is to the performance of MFofpolarizability, it (magneto-electric effect). The change of n is similar to the performance of MF polarizability, and it MF is dependent on the counter-direction between the applied magnetic field and the light transmitting is dependent on the counter-direction between magnetic index field and theislight transmitting through the MF. When the magnetic field is setthe as 0applied T, the refractive of MF shown in Figure through When thevaries magnetic set70as°C, 0 T,the therefractive refractiveindex indexof of the MFMF is shown in Figure 4b. 4(b). As the the MF. temperature fromfield 0 °Cisto decreases linearly ˝ C to 70 ˝ C, the refractive index of the MF decreases linearly with a As the temperature varies from 0 with a temperature sensitivity of −0.00008 RIU/°C. When MF is simultaneously subjected to an temperature sensitivity of ´0.00008 RIU/˝ C.temperature, When MF is simultaneously subjected to an operating magnetic field and a changing the refractive index of the MFoperating behaves magnetic field and a changing temperature, the refractive index of the MF behaves according to both according to both of them, making it hard to determine the refractive index of the MF as it responds of them, making it hard to determine the refractive index of the MF as it responds to the the changing to the the changing magnetic field or changing temperature and this will lead to an inaccurate magnetic field detection. or changing temperature and this willeffective lead to an inaccurate magnetic field magnetic field Hence, it is necessary to take measures to compensate the detection. operating Hence, it is necessary to take effective measures to compensate the operating temperature in the temperature in the magnetic field measurement. With PW*@work the temperature in the experiment magnetic field measurement. With PW*@work the temperature in the experiment system is to system is set to 25 °C, and the FP-FBG sensor filled with MF is located in a temperature controlset oven ˝ 25 C, anda the FP-FBG filled with MF is located a temperature between setthe of between set of coils. sensor The magnetic field direction is in transverse to thatcontrol of the oven incident light.aAs coils. The magnetic field direction is transverse to that of the incident light. As the applied magnetic applied magnetic field controlled by the programmable DC power increases from 0 mT to 39.12 mT, field controlled by the programmable increases fromshift 0 mT to 39.12the mT,long the normalized the normalized interference spectrumDC of power the FP-FBG sensor towards wavelength interference spectrum of the FP-FBG sensor shift towards the long wavelength direction (near the direction (near the wavelength of 1550 nm) as shown in Figure 5. wavelength of 1550 nm) as shown in Figure 5. 1

0mT 5.05mT 8.32mT 12.07mT 18.09mT 22.01mT 27.03mT

0.9

Normalized Intensity

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1535

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1545 1550 Wavelength(nm)

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Figure 5. Spectrograms under a magnetic field range of 0~30 mT. Figure 5. Spectrograms under a magnetic field range of 0~30 mT.

Figure 6 gives gives the the FP-FBG FP-FBG sensor sensor test test results results under under two two magnetic magnetic fields. fields. At room room temperature temperature ˝ C) it can be obtained that the interference fringes of FP move with the magnetic field variation but (25 (25 °C) it can be obtained that the interference fringes of FP move with the magnetic field variation the peakpeak of the is unchanged. but reflected the reflected ofFBG the FBG is unchanged. The result in Figure 6 is in good agreement result Figure 6 agreement with with the conclusion conclusion that that the the FBG FBG written written in the insert end of FP cavity is insensitive to magnetic field changes. The tests (the test was repeated three times) for a MF-based FP-FBG sensor under different different magnetic magnetic fields fields are are shown shown in in Figure Figure 7, where where the curve fitting of the relationship between resonance peak drifts and the magnetic field indicates the MF-based fitting of the relationship between resonance peak drifts and the magnetic field indicates the MFFP-FBG sensor sensor has a magnetic field sensitivity of 0.34 of nm/mT with awith repeatability error of R2 =of1.5%. based FP-FBG has a magnetic field sensitivity 0.34 nm/mT a repeatability error R2 = The interference spectrum of the MF-filled FP-FBG sensor which shifts under different temperature 1.5%. behaves as seen in Figures 8 and 9.

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0.04T, 25℃ 0.03T,25℃ 25℃ 0.04T,

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13 12

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Figure 6. 6. Spectrograms Spectrograms under under aa magnetic magnetic field fieldrange rangeof of0~30 0~30 mT. mT. Figure Figure 6. Spectrograms under a magnetic field range of 0~30 mT. 1555

Test1 Test2 Test1 Test3 Test2 Average value curve fitting Test3 Average value curve fitting

W avelength/nm W avelength/nm

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y=1540.1+340x, r=0.9954, Repeatability error:1.5% y=1540.1+340x, r=0.9954, Repeatability error:1.5%

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0.035 0.035

0.04 0.04

Magnetic field/T

Figure 7. FP peak wavelength variation versus magnetic field. Figure Figure 7. FP FP peak peak wavelength wavelength variation variation versus magnetic field.

The interference spectrum of the MF-filled FP-FBG sensor which shifts under different The interference spectrum of the8 MF-filled FP-FBG sensor under different temperature behaves seen in Figures andof9.the MF-filled Considering thatas the output spectrum FP-FBGwhich sensorshifts is combined with the temperature behaves as seen in Figures 8 and 9. reflected spectra of the FP sensor and FBG sensor and their resonance peak shifts, the analysis of 1533

Wavelength/nm Wavelength/nm

the interference spectrum of FP-FBG sensor under different temperatures can be equally separated Test1 1533 Test2 1532and FBG sensor. As the temperature into those of the FP sensor increases, the refractive index of the Test1 Test3 Test2 1532 Average value curve fittingshifts in a shorter wavelength MF decreases and the output interference spectrum of the FP sensor Test3 1531 Averagewithin value curve fitting direction. When the resonance peak of the FP sensor moves the temperature range 20 ˝ C < T < 1531 y=1535-0.0919x,r=0.995 ˝ 1530 sensor has a temperature sensitivity of 0.092 nm/ C with a repeatability 95 ˝ C, the MF-filled FP-FBG Repeatability error:0.8% y=1535-0.0919x,r=0.995 2 1530 error R = 0.8%. As illustrated in Figure 9, the center wavelength of the FBG sensor shifts less than that Repeatability error:0.8% 1529 of the FP sensor, and the FBG has a temperature sensitivity of 0.013 nm/˝ C with a repeatability error 1529 1528 R2 = 1.2%. 1528 Finally, when the magnetic field and temperature are applied to the MF-filled FP-FBG sensor, the 1527 corresponding magnetic field and temperature can be calculated from Equation (7) combined with the 1527 analysis of Figures 7–9. In1526the system, the temperature measurement can be 100 used as a compensation 20 30 40 50 60 70 80 90 Temperature/℃ for the magnetic field detection by the FP-FBG sensor filled with MF. According to Equation (7), a 1526 20 30 40 50 60 70 80 90 100 ˝ C in the MF-filled FP Temperature/℃ magnetic field sensitivity of 0.34 nm/mT, temperature sensitivity of 0.092 nm/ Figure 8. FP peak wavelength shift variation versus temperature. sensor and a temperature sensitivity of 0.013 nm/˝ C in the FBG sensor can be obtained: Figure 8. FP peak wavelength shift variation versus temperature. «

∆H ∆T

ff

« “

0.34 nm{mT ´0.092 nm{˝ C 0 0.013 nm{˝ C

ff´1 «

∆λm ∆λ B

ff (8)

Wavelength/nm

Figure 6. Spectrograms under a magnetic field range of 0~30 mT. 1555

Test1 Test2 Test3 Average value curve fitting

W avelength/nm

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y=1540.1+340x, r=0.9954,

Repeatabilitymatrix error:1.5% Based on the sensing characteristic in Equation (8) of the FP-FBG magnetic sensor, the MF-filled FP-FBG sensor (after compensation) and the MF-filled FP sensor (before compensation) are 1545 simultaneously tested in the magnetic field range 0.02T < H < 0.06T. First, the temperature in the sensor head area is accurately measured by the reflected peak wavelength of the FBG; second, the wavelength of the FP-FBG varying with the magnetic field is modified according to the sensing characteristic 1540 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 matrix in Equation (8) and the0magnetic field with temperature compensation is obtained in Figure 10. Magnetic field/T Figure 10 illustrates the fitted curves based on the test points. The magnetic field sensitivity after Figure 7. FP peak wavelength variation versus magnetic field. compensation is improved to 0.53 nm/mT with the comparison of the magnetic field sensitivity before compensation 0.23 nm/mT. As the wavelength measurement resolution OSAdifferent is 20 pm, the The of interference spectrum of the MF-filled FP-FBG sensor which shifts of under temperature behaves as seen in Figures and 9. sensor could reach 37.7 µT. magnetic field measurement resolution of8FP-FBG 1533

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Figure 8. peak FP peak wavelength shift shift variation versus temperature. 8. FP wavelength variation versus temperature.

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Figure 9. FBG wavelengthshift shift variation temperature. Figure 9. FBG wavelength variationversus versus temperature. Sensors 2016, 16, 620

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Considering that the output spectrum of the MF-filled FP-FBG sensor is combined with the reflected spectra of the FP1570 sensor and FBG sensor and their resonance peak shifts, the analysis of the interference spectrum of FP-FBG sensor under different temperatures can be equally separated into 1565 Before compensation those of the FP sensor and FBG sensor. As the temperature increases, the refractive index of the MF After compensation decreases and the output1560 interference spectrum of the FP sensor shifts in a shorter wavelength direction. When the resonance peak of the FP sensor moves within the temperature range 20 °C < T < 1555 95 °C, the MF-filled FP-FBG sensor has a temperature sensitivity of 0.092 nm/°C with a repeatability 1550 error R2 = 0.8%. As illustrated in Figure 9, the center wavelength of the FBG sensor shifts less than that of the FP sensor, and the FBG has a temperature sensitivity of 0.013 nm/°C with a repeatability 1545 error R2 = 1.2%. 1540 Finally, when the magnetic field and temperature are applied to the MF-filled FP-FBG sensor, the corresponding magnetic field and temperature can be calculated from Equation (7) combined 1535 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 with the analysis of Figures 7–9. In the system, the field/T temperature measurement can be used as a Magnetic compensation for the magnetic field detection by the FP-FBG sensor filled with MF. According to 10.test The comparison test comparison magnetic field field sensitivity in in thethe MF-filled FP-FBG sensor.sensor. Figure Figure 10. ofof magnetic sensitivity MF-filled FP-FBG Equation (7), aThe magnetic field sensitivity of 0.34 nm/mT, temperature sensitivity of 0.092 nm/°C in the MF-filled FP sensor and a temperature sensitivity of 0.013 nm/°C in the FBG sensor can be obtained: 4. Conclusions

1 Based on the characteristics the4refractive ofnm a MF, FP-FBG magnetic field nm / mT index / ℃a fiber 0.092  optic  H  of0.3 m  (8) sensor is proposed and demonstrated for magnetic field measurements with temperature   0 0.013nm / ℃   B   Tin the magnetic compensation. The key point field measurement is to overcome the cross-sensitivity effect of the temperature and magnetic field in the MF. The FBG is written on the insert fiber of FP Based on operating the sensing characteristic matrix in Equation (8) of FP-FBG magnetic sensor, the cavity for the temperature detection. Due to the fact thethe FBG is sensitive to temperature MF-filled FP-FBG sensor (after compensation) and the MF-filled FP sensor (before compensation) are

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4. Conclusions Based on the characteristics of the refractive index of a MF, a fiber optic FP-FBG magnetic field sensor is proposed and demonstrated for magnetic field measurements with temperature compensation. The key point in the magnetic field measurement is to overcome the cross-sensitivity effect of the temperature and magnetic field in the MF. The FBG is written on the insert fiber of FP cavity for the operating temperature detection. Due to the fact the FBG is sensitive to temperature variations, the operating temperature in the sensing area can be measured and compensated for the magnetic field measurement. Preliminary experimental results show that the sensitivity of magnetic field measurement could reach 0.53 nm/mT and the magnetic field measurement resolution could reach 37.7 µT. The FP-FBG magnetic field sensor probe has the advantages of simple structure, easy fabrication, anti-corrosion properties, low cost, and so on, and this sensor would find potential applications in the measurement of electromagnetic fields. Acknowledgments: This work was supported by the National High Technology Research and Development Program of China (863 Program) under Grant 2013AA09A412-1, the Major Application Basic Research Project of NUDT under Grant number ZDYYJCYJ20140701, the National Natural Science Foundation of China under Grant 61203206, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant 20120042120038. Author Contributions: J.X. has developed the EF-DCM algorithm, conceived and designed the MF-filled FP-FBG sensor experiments and drafted the paper. And he played an important role in interpreting the results. F.W. has performed the experiments, contributed experiment materials and analysis tools, and contributed significantly to acquisition of data, analysis and interpretation of data. Both J.X. and F.W. have contributed equally to this work. H.L. and S.X. has contributed to the conception of the study, and helping perform the analysis with constructive discussions. Q.W. and S.X. has contributed to manuscript preparation, revising it critically for important intellectual detail and the final approval of the version to be submitted. Conflicts of Interest: The authors declare no conflict of interest.

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