sensors
Article
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],
Sensors 2016, 16, 620; doi:10.3390/s16050620
www.mdpi.com/journal/sensors
[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
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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.
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2016, 16, 620
measurement
wavelength-range from the input light and both of
Reflectance / mW
0.03
T=20C
T=30C
T=40C
T=50C
0.025
0.02
0.015
0.01
0.005
0
1530
1535
1540
1545
1550
Wavelength  / nm
1555
1560
1565
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
1.355
1.35
1.35
1.345
1.345
1.34
0
1.34
0
0.01
0.01
0.02
0.02
1.348
0.03
0.04
0.05
Magnetic field/T
0.03
0.04
0.05
(a)
Magnetic
field/T
0.06
0.06
0.07
0.07
(a)
1.347
1.348
Refractive index
1.346
1.347
1.345
Refractive index
1.346
1.344
1.345
1.343
1.344
1.342
1.343
1.341
0
10
20
1.342
1.341
0
30
40
Temperature/℃
50
60
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
1540
1545
1550
Wavelength(nm)
1555
1560
1565
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.
Sensors 2016, 16, 620
Sensors 2016, 16, 620
7 of 10
7 of 10
Sensors 2016, 16, 620
7 of 10
14
0.04T, 25℃
0.03T,25℃
25℃
0.04T,
14
13
LightLight
intensity/nW
intensity/nW
13
12
0.03T, 25℃
12
11
11
10
10
9
9
8
8
7
7
6
1530
6
1530
1535
1540
1535
1545
1550
1555
Wavelength/nm
1540
1545
1550
1560
1555
1565
1560
1565
Wavelength/nm
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
1555
1550
y=1540.1+340x, r=0.9954,
Repeatability error:1.5%
y=1540.1+340x, r=0.9954,
Repeatability error:1.5%
1550
1545
1545
1540
1540
0
0.005
0
0.005
0.01
0.01
0.015
0.015
0.02
Magnetic field/T
0.02
0.025
0.025
0.03
0.03
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
Sensors 2016, 16, 620
8 of 10
1550
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
Test1
Test2
Test3
Average value curve fitting
1532
Wavelength/nm
1531
y=1535-0.0919x,r=0.995
Repeatability error:0.8%
1530
1529
1528
1527
1526
20
30
40
50
60
70
80
90
100
Temperature/℃
Figure
8. peak
FP peak
wavelength shift
shift variation
versus
temperature.
8. FP
wavelength
variation
versus
temperature.
Sensors 2016, 16, 620Figure
8 of 10
1556.6
1556.4
Test1
Test2
Test3
Average value curve fitting
FBGWavelength/nm
1556.2
1556
y=1555+0.0131x, r=0.993
Repeatability error:1.2%
1555.8
1555.6
1555.4
1555.2
20
30
40
50
60
70
80
90
100
Temperature/℃
Figure
9. FBG
wavelengthshift
shift variation
temperature.
Figure
9. FBG
wavelength
variationversus
versus
temperature.
Sensors 2016, 16, 620
9 of 10
Wavelength/nm
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
Sensors 2016, 16, 620
9 of 10
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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© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).