Download An Optical Fiber Lateral Displacement Measurement Method and

sensors
Article
An Optical Fiber Lateral Displacement Measurement
Method and Experiments Based on Reflective
Grating Panel
Yuhe Li *, Kaisen Guan, Zhaohui Hu and Yanxiang Chen
Department of Precision Instruments, Tsinghua University, State Key Laboratory of Precision Measurement
Technology and Instruments, Beijing 100084, China; [email protected] (K.G.);
[email protected] (Z.H.); [email protected] (Y.C.)
* Correspondence: [email protected]; Tel.: +86-10-6279-4630
Academic Editor: Jose Miguel Lopez-Higuera
Received: 10 March 2016; Accepted: 30 May 2016; Published: 2 June 2016
Abstract: An optical fiber sensing method based on a reflective grating panel is demonstrated for
lateral displacement measurement. The reflective panel is a homemade grating with a periodic
variation of its refractive index, which is used to modulate the reflected light intensity. The system
structure and operation principle are illustrated in detail. The intensity calculation and simulation of
the optical path are carried out to theoretically analyze the measurement performance. A distinctive
fiber optic grating ruler with a special fiber optic measuring probe and reflective grating panel is
set up. Experiments with different grating pitches are conducted, and long-distance measurements
are executed to accomplish the functions of counting optical signals, subdivision, and discerning
direction. Experimental results show that the proposed measurement method can be used to detect
lateral displacement, especially for applications in working environments with high temperatures.
Keywords: fiber optic sensing; lateral displacement measurement; reflective grating panel
1. Introduction
Displacement sensors and measurement techniques have been widely applied in many
fields, including advanced fabrication machines, health monitoring devices, and medicine [1–3].
Capacitive sensors could provide excellent linearity, resolution, and bandwidth in short-range
applications [4]. A sensing method with scanning probe microscopy (SPM) has become an indispensible
tool for topographical measurement with nano- and sub-nanometer resolution [5], but usually
the single scanning distance is of the order of 150 ˆ 150 µm, and the scanning speed is also a
limitation. Eddy current sensors have a large range with linearity error of less than ˘3% [6,7], but
they are not widely used because of the temperature sensitivity. Both linear variable displacement
transformers [8] and linear encoders can supply nanoscale resolution with a large measurement
range [9,10], however, they are unreliable in electromagnetic interference environments. Fiber optic
sensors (FOS) have attracted much attention of researchers over the past few decades due to some
innovative characteristics, such as high bandwidth, low loss, and can work under harsh environmental
conditions compared to traditional sensors [11].
Fiber optic displacement sensors (FODS) are playing a more important role in the area of
displacement measurement. Fiber Bragg grating-based sensors have become most widely known
in the market due to their multiple functions [12–17]. Including interferometric sensors and
intensity modulated sensors, many kinds of FODS have been presented in recent years [18–29].
The interferometric sensors could realize high sensitivity and accuracy, but they are usually complicated
and of higher cost to set up wavelength shift interrogation systems [19]. The intensity-modulated
Sensors 2016, 16, 808; doi:10.3390/s16060808
www.mdpi.com/journal/sensors
Sensors 2016, 16, 808
Sensors 2016, 16, 808
2 of 15
2 of 15
intensity-modulated
sensors,
contrast,
are [20–27].
simple and
low cost [20–27].
transmissive
fiber design
lens
sensors,
by contrast, are
simplebyand
low cost
A transmissive
fiberAlens
double-fiber
double-fiber
proposed to achieve
displacement
measurement
[20]. A seond
transmissive
is proposed
to design
achieveis displacement
measurement
[20]. A
seond transmissive
one could
realize a
one could realize
accuracy
of of
6 µm
over
range
of 3000 µm
However,
measurement
with aanmeasurement
accuracy of with
6 µman
over
a range
3000
µma[21].
However,
in [21].
the transmissive
in
the
transmissive
fiber
sensor,
the
emitting
fibers
and
receiving
fibers
are,
respectively,
arranged
fiber sensor, the emitting fibers and receiving fibers are, respectively, arranged on two sides
of the
on two sides
of the
measuring
which
occupies
tooReflective
much room
[22].
Reflective
fiber
measuring
probe,
which
usuallyprobe,
occupies
toousually
much room
[22].
fiber
optic
displacement
optic displacement
sensors
(RFODS)
simplify
their the
structure
the of
fibers
one [23,24].
side
sensors
(RFODS) could
simplify
their could
structure
by fixing
fibersby
onfixing
one side
the on
probe
of
the
probe
[23,24].
In
addition,
by
adopting
different
reflective
targets,
RFODS
show
many
In addition, by adopting different reflective targets, RFODS show many advanced characteristics
advanced characteristics and could measure different measurands [28–32]. Although RFODS have
and could measure different measurands [28–32]. Although RFODS have high accuracy and simple
high accuracy and simple structure, small measurement ranges, to some degree, limit their practical
structure, small measurement ranges, to some degree, limit their practical applications [33].
applications [33].
In this study, we propose a novel type of optical fiber measurement method based on a reflective
In this study, we propose a novel type of optical fiber measurement method based on a
grating panel for lateral displacement. The signal subdivision model with the tangent and cotangent
reflective grating panel for lateral displacement. The signal subdivision model with the tangent and
functions
is given, and error analysis and processing are studied. Based on the relationship between
cotangent functions is given, and error analysis and processing are studied. Based on the
displacement
received
optical power
phaseoptical
difference
is adopted
in order
to realize
discerning
relationshipand
between
displacement
and the
received
power
the phase
difference
is adopted
in
direction
displacement
and the center
distance ofand
twothe
receiving
fibers isofderived
order tofor
realize
discerningmeasurement,
direction for displacement
measurement,
center distance
two
theoretically
to ensure
the orthogonal
between
two receiving
A distinctive
fiber
optic
receiving fibers
is derived
theoreticallyphase
to ensure
the orthogonal
phasefibers.
between
two receiving
fibers.
grating
ruler is set
upoptic
to measure
includes
a special fiber
optic
measuring
probe
A distinctive
fiber
grating dispalcement,
ruler is set up which
to measure
dispalcement,
which
includes
a special
and
reflective
grating panel.
fiber
optic measuring
probe and reflective grating panel.
In In
this
paper,
methodfor
forlateral
lateral
displacement
is presented,
this
paper,an
anoptical
opticalfiber
fiber measurement
measurement method
displacement
is presented,
and and
a
a reflective
Themeasurement
measurementmethod
methodand
andsystem
systemforfordisplacement
displacement
reflective grating
grating panel
panel is fabricated.
fabricated. The
measurement
is detailed.
The
simulation
calculationofofthe
the
opticalpath
path
and
resolutionare
are
carred
measurement
is detailed.
The
simulation
calculation
optical
and
resolution
carred
out,
out,
and
signal
analysis
and
processing
follows.
Finally,
some
experiments
including
the
and signal analysis and processing follows. Finally, some experiments including the application test in
application test inworking
a high-temperature
working
environment,
arethe
presented
to measurement
verify the proposed
a high-temperature
environment,
are presented
to verify
proposed
method
measurement
method
andruler.
the fiber optic grating ruler.
and
the fiber optic
grating
MeasurementMethod
Methodand
and System
System for
2. 2.Measurement
for Lateral
LateralDisplacement
Displacement
Working
Principle
2.1.2.1.
Working
Principle
The
displacement
measurement
system
is composed
a light
source,
a sensor
a
The
displacement
measurement
system
is composed
of a of
light
source,
a sensor
probe, probe,
a reflective
reflective
grating
panel
(RGP), photodetectors
and anpower
opticalmeter,
poweras
meter,
as shown
in Figure
1.
grating
panel
(RGP),
photodetectors
(PD), and(PD),
an optical
shown
in Figure
1.
Figure1.1.Displacement
Displacement measurement
Figure
measurementsystem.
system.
The RGP, which comprises highly-reflective areas and low reflective areas, is attached to the
The RGP, which comprises highly-reflective areas and low reflective areas, is attached to the
measurand. An emitting fiber and two receiving fibers make up the fiber bundle. The working
measurand. An emitting fiber and two receiving fibers make up the fiber bundle. The working process
process of the measurement system can be summarized as follows. The RGP moves with the
of the measurement system can be summarized as follows. The RGP moves with the measurand and
measurand and the emitted light from the fiber is modulated by the moving RGP. When the light
theirradiates
emitted light
from the fiber is modulated by the moving RGP. When the light irradiates on the highly
on the highly reflective area, the reflected light intensity is high, and vice versa. Through
reflective
area,
the
reflected
light intensity
is high, and
Through
two receiving
two receiving fibers,
the modulated
light transmits
into vice
PDs,versa.
whose
signals enter
the opticalfibers,
powerthe
modulated light transmits into PDs, whose signals enter the optical power meter. The reflected signals
Sensors 2016, 16, 808
3 of 15
vary like sinusoidal functions, and they would vary one period when the RGP moves one grating
pitch [33]. Therefore, the displacement measurement can be achieved by counting the sinusoidal
signals. In the measurement system, the two receiving fibers are arranged at a specific location, so
that the PDs could obtain two light signals S1 and S2 with a phase difference of 90˝ , which can be
expressed as:
ˆ
˙
2π ¨ x ptq
S1 “ sin
(1)
p
ˆ
˙
2π ¨ x ptq
S2 “ cos
(2)
p
where x(t) is the measurand displacement, and p is the grating pitch. The displacement x(t) could be
inferred as follows:
ˆ ˙
p
S1
x ptq “
arctan
(3)
2π
S2
The signal processing methods adopted in the measurement system are similar to that used for
traditional grating signals [34], such as counting, subdivision, and discerning direction.
2.2. Preliminary Theoretical Derivation
The fiber-grating distance ZFG between the fiber end and the RGP has influence on the
measurement performance, as shown in Figure 2. The decreased ZFG will result in a smaller spot size
of fiber, which is related with the measurement resolution to some degree. When ZFG gets larger than
0, the optical power of the receiving fiber will become higher, and then decrease gradually [23], which
would have significant influence on the measuring sensitivity. Therefore, it is necessary to make an
analysis about the relationship between ZFG and the optical field intensity at the fiber end. On the basis
of the intensity distribution of the output optical field formed by the source fiber end [35], the optical
field intensity distribution function at the multimode fiber end is calculated by the following formula:
$
’
&
I pr, zq “
r2
,
/
.
I0
”
ı2 exp ´ ”
ı2
’
% a2 1 ` 0.146 pz{a0 q1.5 tanθ0 /
a20 1 ` 0.146 pz{a0 q1.5 tanθ0
0
(4)
where I0 is the intensity of the light source, a0 is the radius of the emitting fiber, θ 0 is the fiber maximum
exit angle, which is equivalent to the acceptance angle and can be determined by the numerical aperture
(NA), θ 0 = arctan(NA), z = 2ZFG is the axial distance between the receiving fiber end and its mirroring,
r is the radial distance from the fiber center, and I(r,z) is the light field intensity. The parameters of the
emitting fiber are: a0 = 52.5 µm, tanθ 0 = 0.22; then, by solving Equation (4), the following equation can
be obtained:
#
+
r2
I0
(5)
I pr, zq “ `
˘2 exp ´ `
˘2
52.5 ` 0.00445 ˆ z1.5
52.5 ` 0.00445 ˆ z1.5
As shown in Figure 2, the emitting and receiving fibers are placed closely and parallelly, and the
fiber ends are aligned as much as possible. The gray ring Lin Lout is the emitted optical field. It can
be known that the optical power of the receiving fiber is proportional to the light flux BZ in the area
between the rings Lin and Lout . It can be expressed as:
Bz “
ş a0 `δ`2a
a 0 `δ
I pr, zq dr “
ş1137.5
137.5
?
I pr, zq dr “
I0 π
105`0.0089ˆz1.5
´
¨ erf
r
52.5`0.00445ˆz1.5
ˇ
¯ ˇ 1137.5
ˇ
ˇ
ˇ 137.5
(6)
where a = 500 µm is the radius of the receiving fibers, and δ = 85 µm is the interval between the emitting
fiber and receiving fiber. It can be known from the numerical solution obtained by MATLAB software
(MathWorks Inc., Natick, MA, USA) that BZ reaches a maximum value at the point of Z = 1292 µm.
Sensors 2016, 16, 808
Sensors 2016, 16, 808
4 of 15
4 of 15
where a = 500 µm is the radius of the receiving fibers, and δ = 85 µm is the interval between the
where
a = 16,
500808µm is the radius of the receiving fibers, and δ = 85 µm is the interval between
the
Sensors 2016,
4 of
15
emitting fiber and receiving fiber. It can be known from the numerical solution obtained by
emitting fiber and receiving fiber. It can be known from the numerical solution obtained by
MATLAB software (MathWorks Inc., Natick, MA, USA) that BZ reaches a maximum value at the
MATLAB software (MathWorks Inc., Natick, MA, USA) that BZ reaches a maximum value at the
point of Z =when
1292 µm.fiber-grating
Therefore, when
the fiber-grating
distance
ZFG = 646 µm,
the
optical power
of
Therefore,
distance
the optical
of the
receiving
fiber will
FG = 646 µm,distance
point
of Z = 1292 the
µm. Therefore, when
the Zfiber-grating
ZFGpower
= 646 µm,
the
optical power
of
the receiving
fiber will
reach its maximum value.
reach
its maximum
value.
the
receiving
fiber will
reach its maximum value.
(a)
(a)
(b)
(b)
Figure 2. Schematic diagram of measurement method. (a) Layout of measurement units; and (b)
measurement
method.
(a) Layout
of measurement
units; units;
and (b)and
spatial
Figure 2.
2. Schematic
Schematicdiagram
diagramofof
measurement
method.
(a) Layout
of measurement
(b)
spatial relations and dimension parameters.
relations
and
dimension
parameters.
spatial relations and dimension parameters.
3. Simulation Calculation
3. Simulation
SimulationCalculation
Calculation
3.1. Optical
Modeling
3.1.
Optical Modeling
Modeling
3.1.
Optical
Simulation isisconducted
conducted by
using
the
optical
design
software,
ZEMAX
software
(Radiant
Simulation
using
the the
optical
design
software,
ZEMAX
software
(Radiant(Radiant
Zemax,
Simulation
is conductedbyby
using
optical
design
software,
ZEMAX
software
Zemax,
LLC,
Redmond,
WA,
USA).
As
shown
in
Figure
3,
the
simulation
model
consists
of one
LLC, Redmond,
WA, USA).
shown
Figurein
3, Figure
the simulation
model consists
one LED
Zemax,
LLC, Redmond,
WA,AsUSA).
Asinshown
3, the simulation
modelofconsists
oflight
one
LED
light
source,
one
emitting
fiber,
two
receiving
fibers
and
a
RGP.
The
emitting
fiber
core
source,
one
emitting
fiber,
two
receiving
fibers
and
a
RGP.
The
emitting
fiber
core
diameter
is
105
µm,
LED light source, one emitting fiber, two receiving fibers and a RGP. The emitting fiber core
diameter
is
105
µm,
and
its
numerical
aperture,
NA
1 = 0.236. The receiving fiber core diameter 2a =
and its numerical
NA1 = 0.236.
The NA
receiving
fiber
diameter
= 1000
µm, 2a
and
diameter
is 105 µm,aperture,
and its numerical
aperture,
1 = 0.236.
Thecore
receiving
fiber2acore
diameter
=
1000 µm,
and NA
2 = 0.467. The RGP grating pitch p is 300 µm. For simplicity, the reflectivity of high
NA
=
0.467.
The
RGP
grating
pitch
p
is
300
µm.
For
simplicity,
the
reflectivity
of
high
and
low
2
1000 µm, and NA2 = 0.467. The RGP grating pitch p is 300 µm. For simplicity, the reflectivity of high
and low reflective
areas
were
set to 1 and 0, respectively,
and the highly-reflective
area
width p1 is
reflective
areas were
set to
1 and
and the highly-reflective
area width parea
1 is equal
and
low reflective
areas
were
set0,torespectively,
1 and 0, respectively,
and the highly-reflective
widthtopthe
1 is
equal
to
the
low
one
p
2.
low one
2 . low one p2.
equal
to pthe
(a)
(a)
(b)
(b)
Figure 3. Simulation model of fibers and the RGP. (a) Overall view; and (b) partial enlarged view.
Figure
enlarged view.
view.
Figure 3.
3. Simulation
Simulationmodel
modelof
offibers
fibers and
and the
the RGP.
RGP. (a)
(a) Overall
Overall view;
view; and
and (b)
(b) partial
partial enlarged
3.2. Relationship between Fiber-Grating Distance and Received Optical Power
3.2. Relationship between Fiber-Grating Distance and Received Optical Power
3.2. Relationship between Fiber-Grating Distance and Received Optical Power
The relationship between the fiber-grating distance ZFG and the fiber received optical power
The relationship between the fiber-grating distance ZFG and the fiber received optical power
The relationship
between
thenow
fiber-grating
the fiber
received optical
power
FG and
has been
derived above,
and can
be verifieddistance
throughZthe
following
simulations.
Assuming
the
has been derived above, and can now be verified through the following simulations. Assuming the
has
been fiber
derived
above,on
and
nowof
bethe
verified
through thearea,
following
simulations.
Assuming
the
emitting
is located
thecan
center
highly-reflective
and ZFG
increases from
0 to 4 mm
emitting fiber is located on the center of the highly-reflective area, and ZFG increases from 0 to 4 mm
emitting
fiber
on average
the center
of the
area,
and
ZFG
increases
fromis0obtained
to 4 mm
with a step
of is
0.1located
mm, the
value
of highly-reflective
optical power from
the
two
receiving
fibers
with a step of 0.1 mm, the average value of optical power from the two receiving fibers is obtained
with
a
step
of
0.1
mm,
the
average
value
of
optical
power
from
the
two
receiving
fibers
is
obtained
and normalized, then the curve of ZFG and the received optical power can be fitted numerically,and
as
and normalized, then the curve of ZFG and the received optical power can be fitted numerically, as
normalized,
then 4.
theThe
curve
of ZFG and
the received
power cancurves
be fitted
numerically,
as shown
shown in Figure
comparison
between
fittingoptical
and theoretical
indicates
that both
agree
shown in Figure 4. The comparison between fitting and theoretical curves indicates that both agree
in
Figure 4. The
betweendistance
fitting and
curves indicates
that both
reasonably
well.comparison
The fiber-grating
ZFGtheoretical
and the received
optical power
areagree
of a reasonably
non-linear
reasonably well. The fiber-grating distance ZFG and the received optical power are of a non-linear
well. The fiber-grating distance ZFG and the received optical power are of a non-linear relationship,
and the maximum value of optical power is reached when ZFG equals 600 µm. When the RGP moves
Sensors 2016, 16, 808
Sensors 2016, 16, 808
Sensors 2016, 16, 808
5 of 15
5 of 15
5 of 15
relationship, and the maximum value of optical power is reached when ZFG equals 600 µm. When
relationship, and the maximum value of optical power is reached when ZFG equals 600 µm. When
the RGP moves with the measurand, the received optical power signal varies like a sinusoidal
the
moves withthe
the measurand,
the
received
optical
power
signal varies
like aIf sinusoidal
withRGP
the measurand,
optical
power
varies like
a sinusoidal
function.
the optical
function.
If the optical received
power gets
larger,
thesignal
peak-peak
value
of the signal
becomes
larger,
function.
If
the
optical
power
gets
larger,
the
peak-peak
value
of
the
signal
becomes
larger,
power
gets
larger,
the
peak-peak
value
of
the
signal
becomes
larger,
accordingly.
The
measurement
accordingly. The measurement sensitivity is proportional to the optical power, theoretically. On the
accordingly.
The
measurement
sensitivity
is
proportional
to
the
optical
power,
theoretically.
On
the
sensitivity
proportional
the optical
power,
the the
other
hand, the light
other
hand,is the
light spottocan
be changed
intheoretically.
size linearlyOn
with
parementer
ZFG, spot
and can
the
other
hand, in
thesize
light
spot with
can be changed
in size
the parementer
ZFG, will
andvary
the
be changed
linearly
parementer
ZFG ,linearly
andthere
the with
identifiable
grating
pitch
identifiable
grating
pitch
will varythe
accordingly.
Therefore,
is an inverse
relationship
between
identifiable
grating
pitch
will
vary
accordingly.
Therefore,
there
is
an
inverse
relationship
between
accordingly.
Therefore,
there
an inverse
relationshipresolution
between the
distance
ZFG and
the
the
fiber-grating
distance
ZFGisand
the measurement
onfiber-grating
the whole. In
summary,
among
the
fiber-grating
distance
Z
FG and the measurement resolution on the whole. In summary, among
measurement
the whole.
In summary,
the points
1, 2, and
and 3medium
in Figure
4, point 1
the
points 1, 2,resolution
and 3 inon
Figure
4, point
1 has the among
maximum
resolution
sensitivity,
the
1, 2, and
3 in Figure
4,
point 1sensitivity,
has the maximum
resolution
and medium
has points
the
maximum
resolution
and
medium
pointand
2 has
medium
andsensitivity,
maximum
point
2 has
medium
resolution
and
maximum sensitivity,
point
3 has resolution
the minimum
resolution
point
2 has and
medium
and maximum
sensitivity,
and point
3 has theTominimum
resolution
sensitivity,
pointresolution
3 has
minimum
resolution
medium
sensitivity.
resolution
and
medium
sensitivity.
Tothe
improve
resolution
and and
sensitivity,
we
choose the
Zimprove
FG of point
1 in the
and
sensitivity.
To improve
resolution
and
sensitivity,
we choose
theexperiments.
ZFG of point 1 in the
and medium
sensitivity,
we choose
ZFG of point
1 in the
remaining
simulations
and
remaining
simulations
andthe
experiments.
remaining simulations and experiments.
Figure
Figure 4.
4. Comparisons
Comparisons between
between simulation
simulation fitting
fitting curve
curve and
and theoretical
theoretical curve.
curve.
Figure
4.
Comparisons
between
simulation
fitting
curve
and
theoretical
curve.
3.3. Relationship between Lateral Displacement and Received Optical Power
3.3. Relationship
Relationship between
between Lateral
Lateral Displacement
Displacement and
and Received
Received Optical
Optical Power
Power
3.3.
The simulation on the relationship between the lateral displacement and received optical
The simulation
between
the the
lateral
displacement
and received
opticaloptical
power
The
simulation on
onthe
therelationship
relationship
between
lateral
displacement
and received
power is conducted with the fiber-grating distance ZFG = 0.3 mm, the pitch of RGP p1 = p2 = 0.5p =
is
conducted
with
the
fiber-grating
distance
Z
=
0.3
mm,
the
pitch
of
RGP
p
=
p
=
0.5p
=
150
µm.
FG
2 p1 = p2 = 0.5p
power is conducted with the fiber-grating distance
ZFG = 0.3 mm, the pitch of1 RGP
=
150 µm. In order to get a phase difference
of 90° between the two receiving fiber signals, the center
˝
In order
a phase
of 90 between
two receiving
signals,
thesignals,
center distance
of
150
µm. to
In get
order
to getdifference
a phase difference
of 90°the
between
the twofiber
receiving
fiber
the center
distance of two receiving fibers D as shown in Figure 2, should be approximately equal to (k + 1/4)p;
two receiving
D as fibers
shownDinasFigure
equal to (kequal
+ 1/4)p;
k is
distance
of twofibers
receiving
shown2,inshould
Figurebe
2, approximately
should be approximately
to (khere,
+ 1/4)p;
here, k is an integer. Due to space limitations, the center distance D takes the value 1275 µm
an integer.
Due
to space
limitations,
center distance
D takes
the value
1275the
µmvalue
(namely,
4).
here,
k is an
integer.
Due
to space the
limitations,
the center
distance
D takes
1275k =µm
(namely, k = 4). The center of a low reflective is set as a starting point. The two received optical
The center
a low
a startingispoint.
two received
power
signals
are,
(namely,
k of
= 4).
Thereflective
center ofisa set
lowasreflective
set asThe
a starting
point. optical
The two
received
optical
power signals are, respectively, obtained and normalized, and the curve of lateral displacement and
respectively,
obtained
and normalized,
andand
thenormalized,
curve of lateral
and optical
power can
be
power
signals
are, respectively,
obtained
anddisplacement
the curve of lateral
displacement
and
optical power can be fitted, as shown in Figure 5. The optical power signals vary like a sinusoid,
fitted, as
shown
in be
Figure
5. The
opticalinpower
likepower
a sinusoid,
with
thelike
cycle
the
optical
power
can
fitted,
as shown
Figuresignals
5. Thevary
optical
signals
vary
a being
sinusoid,
with the cycle being the same as the pitch of RGP, 300 µm. From Figure 5, the signals from two
same
as
the
pitch
of
RGP,
300
µm.
From
Figure
5,
the
signals
from
two
receiving
fibers
have
a
phase
with the cycle being the same as the pitch of RGP, 300 µm. From Figure 5, the signals from two
receiving fibers ˝have a phase difference of 90°, which can be used to realize the subdivision and
differencefibers
of 90 have
, which
can bedifference
used to realize
subdivision
and discerning
direction
in order
to
receiving
a phase
of 90°,the
which
can be used
to realize the
subdivision
and
discerning direction in order to improve measurement system performance.
improve measurement
systemtoperformance.
discerning
direction in order
improve measurement system performance.
Figure 5. Simulation on relationship between received optical power and lateral displacement.
Figure 5. Simulation on relationship between received optical power and lateral displacement.
Figure 5. Simulation on relationship between received optical power and lateral displacement.
Sensors 2016, 16, 808
6 of 15
Sensors 2016, 16, 808
6 of 15
4. Signal Subdivision and Error Analysis
4. Signal When
Subdivision
and Error
the measured
objectAnalysis
moves, the reflecting grating and the optical fiber probe start relative
motion at the same time, and the receiving optical fiber will receive a periodic signal modulated
When the measured object moves, the reflecting grating and the optical fiber probe start
by the reflecting grating. As shown in Figure 6, the measured displacement can be obtained by the
relative motion at the same time, and the receiving optical fiber will receive a periodic signal
computational expression x = N¨ p = 3p, with the period number N = 3 and the resolution p (namely
modulated
by grating
the reflecting
grating. As
in Figure
6, the
measured
displacement
can be
the known
pitch). Assuming
that shown
the subdivision
number
is 10,
then the resolution
increase
obtained
thetimes
computational
expression
= N·p = 3p,xwith
period
number
Ncotangent
= 3 and the
of upby
to 10
can be achieved,
and thexdisplacement
= 30τ.the
Here
the tangent
and
Sensors
2016,
16,
808
6 of 15
resolution
p (namely
the
grating
pitch). Assuming
that the
subdivision
is 10,
functions
were used
to known
realize signal
subdivision
for the modulated
intensity
from thenumber
RGP, which
canthen
the resolution
increase
of up(7)toand
10 shown
times in
can
be achieved,
and the displacement x = 30τ. Here the
be expressed
as Equation
Figure
7.
4.
Signal
Subdivision
and
Error
Analysis
tangent and cotangent functions were
$ used to realize signal subdivision for the modulated intensity
& |u1 | “ | Asinθ | “ |tanθ| , |u1 | ď |u2 |
from When
the RGP,
can beobject
expressed
(7) andgrating
shown and
in Figure
7.
Acosθreflecting
thewhich
measured
the optical
fiber probe
| Equation
|u2 as
|the
|
w “ moves,
(7)start
| Acosθ |
|u2 |
%
“
“
|cotθ|
|
ą
|u
|
,
|u
relative motion at the same time, and
receiving
optical
2 will receive a periodic signal
1 fiber
|u1 | the
| Asinθ
|
modulated
by
the
reflecting
grating.
As
shown
in
Figure
6,
the
measured displacement can be
Errors analysis of subdivision signals for displacement measurement is carried out for the
obtained
by the
computational
expression
N·pamplitude
= 3p, with
the period
number
N harmonic
= 3 and the
following
aspects:
(a) the DC signal
error Ud ; x(b)= the
variation
coefficient
ε; (c) the
resolution
p (namely
known
grating pitch).
the subdivision
is 10, then
component
Ah ; andthe
(d) the
non-orthogonal
phaseAssuming
error δ. For that
example,
the change in number
the fiber-grating
the resolution
increaseabove
of up
to cause
10 times
can be achieved,
and
thedegree.
displacement
x = 30τ.curves
Here the
distance discussed
may
the amplitude
variation to
some
The subdivision
andand
signal
subdivision
processing
given
in Figures
8 and
9, and thefor
error
shown
in
tangent
cotangent
functions
wereare
used
to realize
signal
subdivision
theanalysis
modulated
intensity
1 [36].which can be expressed as Equation (7) and shown in Figure 7.
fromTable
the RGP,
Figure 6. Schematic diagram of signal subdivision in displacement measurement.
 u1
A sin 

 tan  ,

A cos
 u2
w
 u 2  A cos  cot  ,
 u1
A sin 

u1  u 2
(7)
u1  u 2
Figure
6. Schematic
diagram
displacement
measurement.
Figure
6. Schematic
diagramofofsignal
signal subdivision
subdivision inindisplacement
measurement.
 u1
A sin 

 tan  ,

A cos
 u2
w
 u 2  A cos  cot  ,
 u1
A sin 

u1  u 2
(7)
u1  u 2
Figure
7. Ideal
subdivision
curve
andcotangent
cotangent
functions.
Figure
7. Ideal
subdivision
curvebased
based on
on tangent
tangent and
functions.
Errors analysis of subdivision signals for displacement measurement is carried out for the
following aspects: (a) the DC signal error Ud; (b) the amplitude variation coefficient ε; (c) the
harmonic component Ah; and (d) the non-orthogonal phase error δ. For example, the change in the
fiber-grating distance discussed above may cause the amplitude variation to some degree. The
subdivision curves and signal subdivision processing are given in Figures 8 and 9, and the error
analysis shown in
Table7. 1Ideal
[36].subdivision curve based on tangent and cotangent functions.
Figure
Sensors 2016, 16, 808
7 of 15
Sensors 2016, 16, 808
Sensors 2016, 16, 808
7 of 15
7 of 15
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
Figure
analysis
of subdivision
signals.
(a) Error
DC the
signal;
error from
the signal
Figure 8.8.Error
Error
analysis
of subdivision
signals.
(a) from
Errorthe
from
DC(b)
signal;
(b) error
from
Figure
8.
Error
analysis
of
subdivision
signals.
(a)
Error
from
the
DC
signal;
(b)
error
from
the signal
amplitude
error from(c)the
harmonic
component;
(d) error from
the signal variation;
amplitude(c)variation;
error
from the
harmonicand
component;
and the
(d) non-orthogonal
error from the
amplitude variation; (c) error from the harmonic component; and (d) error from the non-orthogonal
phase.
non-orthogonal phase.
phase.
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
Figure 9. Signal subdivision processings. (a) Original signal (above) and tangent subdivision signal
Figure 9.
9. (b)
Signal
subdivision
processings.
(a)signal
Original
signal
(above)
and tangent
tangent
subdivision
signal
(below);
filtered
signal processings.
by FIR; (c)(a)
bysignal
noise(above)
processing;
and subdivision
(d) displacement
Figure
Signal
subdivision
Original
and
signal
(below); (b)
(b)filtered
filtered
signal
by
(c)bysignal
by noise and
processing;
and (d) measurements
displacement
measurements
with signal
de-noising
process.
(below);
by FIR;
(c)FIR;
signal
noise processing;
(d) displacement
measurements
with
de-noising
process.
with de-noising process.
Sensors 2016, 16, 808
8 of 15
Table 1. Error analysis for signal subdivision (subdivision 100).
Sensors 2016, 16, 808
Parameter Index8 of 15
Ensuring Measures for
Accumulation Quantitative
Before Noise
After Noise
Requirements
Interval
Precision Subdivision
Processing
Processing
Table 1. Error analysis for signal subdivision (subdivision 100).
Error Type
DC
signal
Error
Type
Accumulation
π/4
Interval
DC signal
π/4
Ud < 3.68%
π/2
ε < ±11.8%
Amplitudes variation
Amplitudes
variation
Harmonic component
Harmonic
component
π/2
Non-orthogonal
phase
ε < ˘11.8%
Ah < 0.038A
π
Ah < 0.038A
π
Non-orthogonal phase
Quantitative
Ud < 3.68%
Requirements
Original signals are
Ensuring
Measures
for
subtracted
from
Precision
Subdivision
average
value
Original
signals
are subtracted
signal
peak-to-peak
from averageare
value
amplitudes
used to
signal peak-to-peak
correct theamplitudes
error
are used to correct the error
FIR low-pass filtering
FIR
low-pass filtering
Calculation
of phase
δ < 0.0133π Calculation
difference
based
on the
of phase
difference
position
of signal
peak
based
on the
position
π
π
δ < 0.0133π
Parameter Index
Ud =Noise
0.0304A
After
Processing
Processing
U
d = 0.1373A
Before
Noise
Ud = 0.1373A
Ud = 0.0304A
ε = 0.1884A
ε = 0.0086A
ε = 0.1884A
Ah = 0.0523A
Ah = 0.0523A
δ = 0.0741π
δ = 0.0741π
ε = 0.0086A
Ah = 0.0351A
Ah = 0.0351A
δ = 0.0286π
δ = 0.0286π
of signal peak
5. Experimental Results and Discussion
5. Experimental Results and Discussion
5.1. Self-Made Fiber Optic Grating Ruler and Signal Processing
5.1. Self-Made Fiber Optic Grating Ruler and Signal Processing
A fiber optic grating ruler was set up based on the homemade RGP, as shown in Figure 10.
A fiber optic grating ruler was set up based on the homemade RGP, as shown in Figure 10. The
The RGP
is made up of a printed circuit board (PCB), using gilded and striped pads as high reflective
RGP is made up of a printed circuit board (PCB), using gilded and striped pads as high reflective
areas,areas,
the the
for low
areas.areas.
The measuring
probe,probe,
including
emitting
and receiving
thesubstrate
the substrate
forreflective
low reflective
The measuring
including
emitting
and
fibers,receiving
spring groove,
and
guiding
ball
bearings,
can
move
laterally
above
the
RGP.
fibers, spring groove, and guiding ball bearings, can move laterally above the RGP.
(a)
(b)
(c)
(d)
Figure 10. Fiber optic grating ruler. (a) Overall composition chart; (b) measuring probe; (c) overall
Figure
10. Fiber optic grating ruler. (a) Overall composition chart; (b) measuring probe; (c) overall
ruler appearance and measuring probe; and (d) engineering drawings (left) and physical appearance
ruler (right)
appearance
of RGP.and measuring probe; and (d) engineering drawings (left) and physical appearance
(right) of RGP.
5.2. Displacement Measurement Experiments
5.2. Displacement
Measurement Experiments
To verify the effectiveness of the proposed method, an experimental platform was set up, as
shown
in Figure
11. Some system
parameters,
as thean
signal
to noise ratio
(SNR), sensitivity,
To
verify
the effectiveness
of the
proposedsuch
method,
experimental
platform
was set up, as
and
resolution,
have
close
relationship
to
the
grating
parameters.
For
comparison,
three kinds
of
shown in Figure 11. Some system parameters, such as the signal to noise ratio (SNR),
sensitivity,
RGPs with different grating pitches of 12 mil (304.8 µm), 20 mil (508 µm), and 30 mil (762 µm), were
and resolution, have close relationship to the grating parameters. For comparison, three kinds of
fabricated. In order to simplify the analysis, the highly-reflective area width p1 is set equal to p2. A
RGPs with different grating pitches of 12 mil (304.8 µm), 20 mil (508 µm), and 30 mil (762 µm), were
Sensors 2016, 16, 808
9 of 15
fabricated. In order to simplify the analysis, the highly-reflective area width p1 is set equal to p2 .
Sensors 2016,glass
16, 808 fiber is adopted as the emitting fiber (M15L02, Thorlabs, Newton, NJ, USA),
9 of 15 and
A multimode
plastic fibers as the receiving fibers (HFBR-RNS001Z, AVAGO, San Jose, CA, USA). A fiber-coupled
multimode glass fiber is adopted as the emitting fiber (M15L02, Thorlabs, Newton, NJ, USA), and
high-power LED is selected as the light source (M660F1, Thorlabs, central wavelength 660 nm, FWHM
plastic fibers as the receiving fibers (HFBR-RNS001Z, AVAGO, San Jose, CA, USA). A fiber-coupled
20 nm).
A dual-channel
power meter
used
(PM320E,
Thorlabs)
and,
correspondingly,
twonm,
optical
high-power
LED is selected
as the is
light
source
(M660F1,
Thorlabs,
central
wavelength 660
power
sensors
(S150C,power
Thorlabs).
the process
of Thorlabs)
the experiment,
the measurand
moves
FWHM
20 are
nm).adopted
A dual-channel
meter In
is used
(PM320E,
and, correspondingly,
two
according
to
following
five
stages:
A-keep
static
for
5
s;
B-move
forward
for
3.125
mm
at
a
speed
optical power sensors are adopted (S150C, Thorlabs). In the process of the experiment, the of
movesforward
according
following
five
stages: of
A-keep
forD-keep
5 s; B-move
for
312.5measurand
µm/s; C-move
forto9.375
mm at
a speed
937.5 static
µm/s;
static forward
for 3 s; E-move
3.125 mm
at a speed
of a312.5
µm/s;
C-move
forward
mmstages,
at a speed
937.5 µm/s;
D-keep
backward
for 12.5
mm at
speed
of 625
µm/s.
Afterfor
the9.375
above
the of
measured
object
returns
3 s;position
E-move with
backward
for 12.5
mm at aofspeed
of 625
µm/s. After
the
back static
to its for
initial
the total
movement
25 mm.
Generally,
therethe
areabove
somestages,
measurement
objectasreturns
back to its
initial position
with the
totalofmovement
of 25
mm. Generally,
errormeasured
factors, such
transmission
clearance
and losing
steps
the stepper
motor;
therefore, the
there are some measurement error factors, such as transmission clearance and losing steps of the
above-mentioned motion processes are monitored by a laser displacement sensor (LDS, LK-G400,
stepper motor; therefore, the above-mentioned motion processes are monitored by a laser
LK-G3001, KEYENCE, Osaka, Japan) synchronously. The comparative data by the RFODS (single
displacement sensor (LDS, LK-G400, LK-G3001, KEYENCE, Osaka, Japan) synchronously. The
channel)
and LDSdata
areby
shown
in Figure
12.channel) and LDS are shown in Figure 12.
comparative
the RFODS
(single
Figure 11. Experimental platform for lateral displacement measurement.
Figure 11. Experimental platform for lateral displacement measurement.
Figure 12 indicates that the output voltage matches the displacement data well. The velocity of
the measured
object can
obtained
processing
either the
the displacement
displacement data
LDS
or velocity
the
Figure
12 indicates
thatbethe
outputbyvoltage
matches
datafrom
well.
The
output
voltage
data
from
RFODS.
The
relative
measurement
error
was
computed,
for
example,
of the measured object can be obtained by processing either the displacement data from LDSinor the
stage
B, where
thefrom
velocities
fromThe
the LDS
and RFODS
are 314.4error
µm/swas
and 313.7
µm/s, respectively,
output
voltage
data
RFODS.
relative
measurement
computed,
for example, in
and the relative error is about −0.223%. The measurement errors comparison under different pitches
stage B, where the velocities from the LDS and RFODS are 314.4 µm/s and 313.7 µm/s, respectively,
and different stages are listed in Table 2.
and the relative error is about ´0.223%. The measurement errors comparison under different pitches
and different
stages
are listed
Table 2. error between proposed method and LDS (1 mil = 25.4 µm).
Table
2. Comparison
of in
measurement
Stage 1
Stage 2
Stage 3
Stage 1
Stage B
Stage 2
Stage C
Stage
3
Stage E
Stage
Stage BB
Stage C
Stage C
Stage E
Stage E
Stage
Stage BB
Stage C
Stage C
Stage E
Stage E
Stage B
Stage C
Stage E
Table 2. Comparison of
measurement
betweenbyproposed
andMeasurement
LDS (1 mil =Error
25.4 µm).
Velocity
by LDS error
VL Velocity
R
RFODS Vmethod
Relative
Pitch
Pitch
12 mil
12 mil
20 mil
20 mil
30 mil
30 mil
(µm·s−1)
315.8
Velocity
by LDS V L
(µm¨
936.0s´1 )
−626.9
315.8
315.6
936.0
933.4
´626.9
−628.2
315.6
314.4
933.4
935.9
´628.2
−627.6
314.4
935.9
´627.6
(µm·s−1)
316.9
Velocity
by RFODS V R
(µm¨ s´1 )
937.8
−627.6
316.9
315.9
937.8
933.6
´627.6
−628.9
315.9
313.7
933.6
938.7
´628.9
−625.6
313.7
938.7
´625.6
(VR − VL)/VL
0.348%
Relative
Measurement Error
(V R ´ V L )/V L
0.192%
0.111%
0.095%0.348%
0.192%
0.021%
0.111%
0.111%
0.095%
−0.223%
0.021%
0.299%
0.111%
−0.319%
´0.223%
0.299%
´0.319%
10.5, 6.3, and 4.2 cycles for RGP pitches of 12 mil, 20 mil, and 30 mil, respectively, and their relative
errors are about 2.4%. However, smaller pitch is easier to be influenced by the machining process.
As shown in Figure 13, in stages A and D, the measured object remains static, so the output voltage
can be treated theoretically as noise signals of the RFODS. Then, the signal to noise ratios under
different
Sensors
2016,pitches
16, 808 can be calculated and listed in Table 3. We can see that the pitch is generally
10 of 15
inversely related to the SNR.
(a)
(b)
Figure 12. Comparisons between proposed RFODS (RGP pitch = 30 mil) and LDS. (a) Output voltage
Figure 12. Comparisons between proposed RFODS (RGP pitch = 30 mil) and LDS. (a) Output voltage
verse displacement; and (b) displacement from the RFODS and LDS.
verse displacement; and (b) displacement from the RFODS and LDS.
Table 3. SNR with different grating pitches (1 mil = 25.4 µm).
The whole output from RFODS under different pitches are given in Figure 13, which shows that
Pitch changes
(mil) with
P-P of
Noise
Signal
(V)For example,
P-P of Effective
Signal
SNR
the signal cycle
the
grating
pitch.
the actual
cycles(V)
in stage
B are 10.5, 6.3,
and 4.2 cycles for
RGP
pitches
of
12
mil,
20
mil,
and
30
mil,
respectively,
and
their
relative
12
0.050
1.191
21.655 errors are
about 2.4%. However, smaller pitch is easier to be influenced by the machining process. As shown in
20
0.026
1.709
65.731
Figure 13, in stages A and D, the measured object remains static, so the output voltage can be treated
2.885ratios under different
137.381pitches can
theoretically as30
noise signals of the 0.021
RFODS. Then, the signal to noise
be calculated and listed in Table 3. We can see that the pitch is generally inversely related to the SNR.
Table 3. SNR with different grating pitches (1 mil = 25.4 µm).
Pitch (mil)
P-P of Noise Signal (V)
P-P of Effective Signal (V)
SNR
12
20
30
0.050
0.026
0.021
1.191
1.709
2.885
21.655
65.731
137.381
Sensors 2016, 16, 808
11 of 15
Sensors 2016, 16, 808
11 of 15
Sensors 2016, 16, 808
11 of 15
Figure 13. Comparisons of the output voltages under different RGP pitches.
Figure 13. Comparisons of the output voltages under different RGP pitches.
In addition,Figure
as shown
in Figure of14,
twovoltages
receiving
fibers
collect
two
light signals, whose
13. Comparisons
thethe
output
under
different
RGP
pitches.
phase
difference
is
approximately
equal
to
90°.
Based
on
phase
difference,
the measurement
In addition, as shown in Figure 14, the two receiving fibers collect two light signals,
whose phase
˝
resolution
could be
improved
to to
about
µm
with
400-fold
subdivision.
When
RGP resolution
moves
In is
addition,
as shown
in Figure
the
twoon
receiving
fibers
collectthe
two
lightthe
signals,
whose
difference
approximately
equal
9014,.0.76
Based
phase
difference,
measurement
forward,
the
phase
of
signal
1
is
behind
that
of
signal
2,
and
vice
versa,
then
the
function
of
phase
difference
is
approximately
equal
to
90°.
Based
on
phase
difference,
the
measurement
could be improved to about 0.76 µm with 400-fold subdivision. When the RGP moves forward,
discerning could
direction
can be realized
practically.
Moreover,
the subdivision.
exit peak and
valley
errors
mainly
resolution
be
improved
to
about
0.76
µm
with
400-fold
When
the
RGP
moves
the phase of signal 1 is behind that of signal 2, and vice versa, then the function of discerning
caused bythethephase
reflectivity
inhomogeneity
of the
lead then
to the
forward,
of signal
1 is behind that
of RGP,
signal which
2, andwould
vice versa,
thereduction
function of
direction can be realized practically. Moreover, the exit peak and valley errors mainly caused by the
measurement
accuracy
Throughpractically.
high-precision
fabrication
processes
and valley
assurance
measures,
discerning
direction
can[34].
be realized
Moreover,
the exit
peak and
errors
mainly
reflectivity inhomogeneity of the RGP, which would lead to the reduction of measurement accuracy [34].
the measurement
accuracy could
be improved
caused
by the reflectivity
inhomogeneity
of accordingly.
the RGP, which would lead to the reduction of
Through
high-precision
processes
and assurance
accuracy
measurement
accuracyfabrication
[34]. Through
high-precision
fabricationmeasures,
processes the
and measurement
assurance measures,
could
improved accordingly.
thebe
measurement
accuracy could be improved accordingly.
Figure 14. Two receiving fiber signals with phase difference.
5.3. Large Range Measurement
Figure Experiments
14. Two receiving fiber signals with phase difference.
Figure 14. Two receiving fiber signals with phase difference.
It can be known from the system structure and operating principle that the measurement range
5.3. Large Range Measurement Experiments
is
related
to the
length of the
RGP, and a large range measurement could be obtained with a long
5.3. Large Range
Measurement
Experiments
RGP.ItIncan
these
experiments,
RGP
length
takes the
value
of 300 principle
mm, and that
the grating
pitch distance
of
be known
from the
system
structure
and
operating
the measurement
range
Itrelated
can be
known
from
the
system
structure
and
operating
principle
thatbethe
measurement
range is
12
mil.
The
lengths
of the
emitting
receiving
fibers
are
both 40
m.
is
to
the length
of
the
RGP,fiber
andand
a large
range
measurement
could
obtained
with a long
related
toInthe
length
of the RGP,
and
a large
range
measurement
begrating
obtained
with
a longofRGP.
RGP.
these
experiments,
RGP
length
takes
the value
of 300 mm,could
and the
pitch
distance
12 mil.
The lengths RGP
of thelength
emitting
fiberthe
and
receiving
fibers
both
m.
In these
experiments,
takes
value
of 300
mm,are
and
the40grating
pitch distance of 12 mil.
The lengths of the emitting fiber and receiving fibers are both 40 m.
Sensors 2016, 16, 808
12 of 15
Sensors 2016, 16, 808
12 of 15
In order
order to
to investigate
investigate the
the system
system accuracy,
accuracy, the
In
the measured
measured object
object moves
moves by
by the
the following
following stages:
stages:
(a)-move
forward
for
50
mm
at
a
speed
of
2
mm/s;
(b)-move
forward
for
150
mm
at
a
speed
(a)-move forward for 50 mm at a speed of 2 mm/s; (b)-move forward for 150 mm at a speed of
of 66 mm/s;
mm/s;
and (c)-move
(c)-move backward
backward for
for 200
200 mm
mm at
at aa speed
Thetotal
totalmeasurement
measurementrange
rangeisis400
400mm.
mm.
and
speed of
of 44 mm/s.
mm/s. The
Figure
15
has
shown
the
accuracy
errors
between
the
proposed
RFODS
and
commercial
LDS
under
Figure 15 has shown the accuracy errors between the proposed RFODS and commercial LDS under
different velocities
movement
time
to 10
in seach
stage.stage.
The peak-peak
accuracy
errors
different
velocitiesfrom
fromthe
theinitial
initial
movement
time
to s10
in each
The peak-peak
accuracy
are ˘0.0205
mm, ˘0.0393
mm, mm,
˘0.0303
mmmm
in (a),
respectively.
It isItobvious
thatthat
the
errors
are ±0.0205
mm, ±0.0393
±0.0303
in (b),
(a), (c)
(b),stages,
(c) stages,
respectively.
is obvious
measurement
system
could
maintain
its
accuracy
well
over
a
large
measurement
range.
the measurement system could maintain its accuracy well over a large measurement range.
Figure
Figure 15.
15. Accuracy
Accuracy error
error between
between the
the proposed
proposed RFODS
RFODS and
and LDS
LDS under
under different
different velocities.
velocities.
5.4. Temperature Test
5.4. Temperature Test
Due to the capability of remote measurement by optical fiber, only the fiber probe is needed to
Due to the capability of remote measurement by optical fiber, only the fiber probe is needed to be
be put near the measurand; the other components could be placed in a favorable environment away
put near the measurand; the other components could be placed in a favorable environment away from
from the measurand. Therefore, the proposed RFODS has the capability to work in some harsh
the measurand. Therefore, the proposed RFODS has the capability to work in some harsh conditions,
conditions, such as high to low temperature. To obtain system performance in high to low
such as high to low temperature. To obtain system performance in high to low temperature working
temperature working environments, an incubator is used to set up the experimental platform. As
environments, an incubator is used to set up the experimental platform. As shown in Figure 16, the
shown in Figure 16, the measurand, fiber probe, RGP, and stages are placed inside the incubator,
measurand, fiber probe, RGP, and stages are placed inside the incubator, while the other modules
while the other modules are put outside. In the experimental process, the incubator temperature
are put outside. In the experimental process, the incubator temperature change from ´20 to 80 ˝ C by
change from
−20 to 80 °C by every 10 °C. At each temperature, the measurand moves forward for
every 10 ˝ C. At each temperature, the measurand moves forward for 20 mm at a speed of 625 µm/s
20 mm at a speed of 625 µm/s three times. At the same time the light signals are acquired by the
three times. At the same time the light signals are acquired by the device outside the incubator.
device outside the incubator. The movement velocities under different temperatures can be
The movement velocities under different temperatures can be obtained, as shown in Table 4, where V 1 ,
obtained, as shown in Table 4, where V1, V2, and V3 are the velocities for each time, respectively.˝The
V 2 , and V 3 are the velocities for each time, respectively. The average velocity of three times at 20 C is
average velocity of three times at 20 °C is treated as the nominal value. Accordingly, the relative
treated as the nominal value. Accordingly, the relative errors α1 , α2 , and α3 could also be computed
errors α1, α2, and α3 could also be computed and shown in Table 4.
and shown in Table 4.
It can be seen that the proposed RFODS works well in the temperature range from −20 to 80 °C,
and the relative error is less than ±0.5%. When the temperature is higher than 80 °C, the system
performance is influenced by softening and deformation of the fibers. With glass or special optical
fibers, the measurement system has the potential to work at higher temperature.
Sensors 2016, 16, 808
13 of 15
Sensors 2016, 16, 808
13 of 15
(a)
(b)
Figure 16. Experimental system for temperature test. (a) Overall system appearance; and (b) system
Figure 16. Experimental system for temperature test. (a) Overall system appearance; and (b) system
architecture
architecture schematic.
schematic.
Table 4. Analysis of measurement error between proposed RFODS and LDS.
Table 4. Analysis of measurement error between proposed RFODS and LDS.
Temperature (°C)
˝
Temperature
−20 ( C)
V1 (µm/s)
V 1 (µm/s)
622.2
V2 (µm/s)
V 2 621.9
(µm/s)
´20
−10
´100
0
10
10
2020
3030
4040
50
50
60
7060
8070
622.2
622.8
622.8
623.4
623.4
623.8
623.8
623.7
623.7
624.3
624.3
624.3
624.3
625.5
625.5
622.2
622.2
625.1
625.1
624.5
621.9
623.3
623.3
623.7
623.7
622.7
622.7
622.7
622.7
624.0
624.0
625.8
625.8
626.3
626.3
623.9
623.9
624.7
624.7
625.5
80
624.5
625.5
V3 (µm/s)
V 3621.8
(µm/s)
621.8
623.2
623.2
624.6
624.6
623.4
623.4
623.7
623.7
624.3
624.3
625.3
625.3
625.4
625.4
624.6
624.6
625.3
625.3
625.3
625.3
α1
α1
−0.188%
´0.188%
−0.091%
´0.091%
0.005%
0.005%
0.069%
0.069%
0.053%
0.053%
0.149%
0.149%
0.149%
0.149%
0.342%
0.342%
´0.188%
−0.188%
0.278%
0.278%
0.181%
0.181%
α2
α3
α2
α3
−0.236%
−0.252%
´0.236% −0.027%
´0.252%
−0.011%
´0.011%
´0.027%
0.053%
0.197%
0.053%
0.197%
−0.107%
0.005%
´0.107%
0.005%
−0.107%
´0.107% 0.053%
0.053%
0.101%
0.149%
0.101%
0.149%
0.390%
0.310%
0.390%
0.310%
0.470%
0.326%
0.470%
0.326%
0.085%
0.197%
0.085%
0.197%
0.213%
0.310%
0.213%
0.310%
0.342%
0.310%
0.342%
0.310%
It can be seen that the proposed RFODS works well in the temperature range from ´20 to 80 ˝ C,
6. Conclusions
and the relative error is less than ˘0.5%. When the temperature is higher than 80 ˝ C, the system
performance
is influenced
by softening
and deformation
of the fibers.
With
or special system
optical
In this paper,
we demonstrate
an optical
fiber measurement
method
andglass
experimental
fibers,
the measurement
has athe
potentialgrating
to workpanel.
at higher
temperature.
for
lateral
displacement system
based on
reflective
Through
theoretical derivation, the
optimized distance between the emitting fiber ends and the reflective grating panel is obtained. By
6. Conclusions
means
of modeling and simulation, the efficiency parameters are verified, and the relationship
between
thepaper,
displacement
and the
optical
power ismethod
summarized.
Experiments
under
In this
we demonstrate
an received
optical fiber
measurement
and experimental
system
for
different
grating
pitches
indicate
that
the
proposed
method
can
achieve
a
long-distance
lateral displacement based on a reflective grating panel. Through theoretical derivation, the optimized
measurement,
especially
for applications
harsh
working grating
environments
with
high temperatures.
distance between
the emitting
fiber ends in
and
the reflective
panel is
obtained.
By means of
Moreover,
utilizing
the
two
receiving
fiber
signals
with
phase
difference,
discerning
direction
modeling and simulation, the efficiency parameters are verified, and the relationship betweenand
the
subdivision
be received
realized. optical
If larger
multiples
of subdivision
are applied,
and
the reflective
displacementcould
and the
power
is summarized.
Experiments
under
different
grating
grating
fabricated
is potential
to reduce
system uncertainties
and
greatly
pitches panel
indicate
that the precisely,
proposed there
method
can achieve
a long-distance
measurement,
especially
improve
the
measurement
accuracy.
for applications in harsh working environments with high temperatures. Moreover, utilizing the
two receiving fiber signals with phase difference, discerning direction and subdivision could be realized.
Acknowledgments: This research is supported by the State Key Laboratory of Precision Measurement
If larger multiples of subdivision are applied, and the reflective grating panel fabricated precisely,
Technology and Instruments, the National Natural Science Foundation of China (Grant No. 51275259 and
there is potential to reduce system uncertainties and greatly improve the measurement accuracy.
No. 61362035) and the National Important Scientific Instrument Development Program of China (Grant No.
2011YQ030134).
Acknowledgments: This research is supported by the State Key Laboratory of Precision Measurement Technology
and Instruments,
the National
Science Foundation
of China measurement
(Grant No. 51275259
andZhaohui
No. 61362035)
and
Author
Contributions:
YuheNatural
Li developed
the displacement
method;
Hu was
the National Important Scientific Instrument Development Program of China (Grant No. 2011YQ030134).
responsible for the design and simulation of optical path; Kaisen Guan and Yanxiang Chen carried out the
Author Contributions:
Yuhe Li developed
the displacement
method;
Hu was
responsible
intensity
calculation; Zhaohui
Hu involved
in fabricatingmeasurement
the reflective
gratingZhaohui
panel and
seting
up the
for
the
design
and
simulation
of
optical
path;
Kaisen
Guan
and
Yanxiang
Chen
carried
out
the
intensity
calculation;
measurement system; Yuhe Li and Kaisen Guan participated in the experiments and the most of result
analysis.
Zhaohui Hu involved in fabricating the reflective grating panel and seting up the measurement system; Yuhe Li
All authors wrote the paper together.
Conflicts of Interest: The authors declare no conflict of interest.
Sensors 2016, 16, 808
14 of 15
and Kaisen Guan participated in the experiments and the most of result analysis. All authors wrote the
paper together.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
Andrew, J.F. A review of nanometer resolution position sensors: Operation and performance. Sens. Actuators
A Phys. 2013, 190, 106–126.
Li, H.; Ren, L.; Jia, Z.; Yi, T.; Li, D. State-of-the-art in structural health monitoring of large and complex civil
infrastructures. J. Civ. Struct. Health Monit. 2015. [CrossRef]
Poeggel, S.; Tosi, D.; Duraibabu, D.; Leen, G.; McGrath, D.; Lewis, E. Optical Fibre Pressure Sensors in
Medical Applications. Sensors 2015, 15, 17115–17148. [CrossRef] [PubMed]
Baxter, L.K. Capacitive Sensors: Design and Applications; IEEE Press: New York, NY, USA, 1997.
Guo, T.; Wang, S.; Dorantes-Gonzalez, D.J.; Chen, J.; Fu, X.; Hu, X. Development of a hybrid atomic force
microscopic measurement system combined with white light scanning interferometry. Sensors 2011, 12,
175–188. [CrossRef] [PubMed]
Fericean, S.; Droxler, R. New noncontacting inductive analog proximity and inductive linear displacement
sensors for industrial automation. IEEE Sens. J. 2007, 7, 1538–1545. [CrossRef]
Nabavi, M.R.; Nihtianov, S.N. Design strategies for eddy-current displacement sensor systems: Review and
recommendations. IEEE Sens. J. 2012, 12, 3346–3355. [CrossRef]
Proksch, R.; Cleveland, J.; Bocek, D. Linear Variable Differential Transformers for High Precision Position
Measurements. U.S. Patent 7262592, 28 August 2007.
FASTRACK. High-Accuracy Linear Encoder Scale System. Data Sheet l-9517-9356-01-b. Available online:
www.renishaw.com (accessed on 20 February 2016).
Lee, J.; Chen, H.; Hsu, C.; Wu, C. Optical heterodyne grating interferometry for displacement measurement
with subnanometric resolution. Sens. Actuators A Phys. 2007, 137, 185–191. [CrossRef]
Moro, E.A.; Todd, M.D.; Puckett, A.D. Using a validated transmission model for the optimization of bundled
fiber optic displacement sensors. Appl. Opt. 2011, 50, 6526–6535. [CrossRef] [PubMed]
Cusano, A.; Cutolo, A.; Giordano, M. Fiber Bragg gratings evanescent wave sensors: A view back and recent
advancements. Sensors 2008, 21, 113–152.
Ma, Y.; Wang, C.; Yang, Y. High resolution and wide scale fiber Bragg grating sensor interrogation system.
Opt. Laser Technol. 2013, 50, 107–111. [CrossRef]
Ho, S.C.M.; Ren, L.; Li, H.; Song, G. Dynamic fiber Bragg grating sensing method. Smart Mater. Struct. 2016,
25, 025028. [CrossRef]
Chang, Y.; Yen, C.; Wu, Y.; Cheng, H. Using a Fiber Loop and Fiber Bragg Grating as a Fiber Optic Sensor to
Simultaneously Measure Temperature and Displacement. Sensors 2013, 13, 6542–6551. [CrossRef] [PubMed]
Zhang, Q.; Ianno, N.; Han, M. Fiber-Optic Refractometer Based on an Etched High-Q π-Phase-Shifted
Fiber-Bragg-Grating. Sensors 2013, 13, 8827–8834. [CrossRef] [PubMed]
Kampmann, P.; Kirchner, F. Integration of Fiber-Optic Sensor Arrays into a Multi-Modal Tactile Sensor
Processing System for Robotic End-Effectors. Sensors 2014, 14, 6854–6876. [CrossRef] [PubMed]
Allen, G.; Sun, K.; Byer, R. Fiber-coupled, Littrow-grating cavity displacement sensor. Opt. Lett. 2010, 35,
1260–1262. [CrossRef] [PubMed]
Harun, S.W.; Yasin, M.; Ahmad, H. Micro-displacement sensor with multimode fused coupler and concave
mirror. Laser Phys. 2011, 21, 729–732. [CrossRef]
Golnabi, H. Design and operation of different optical fiber sensors for displacement measurements.
Rev. Sci. Instrum. 1999, 70, 2875–2879. [CrossRef]
Hu, X.; Li, Y.; Chen, Y. Transmissive fiber optical displacement sensor using cutting plate. Microw. Opt.
Technol. Lett. 2012, 54, 446–448. [CrossRef]
Yasin, M.; Harun, S.W.; Fawzi, W.A. Lateral and axial displacements measurement using fiber optic sensor
based on beam-through technique. Microw. Opt. Technol. Lett. 2009, 51, 2038–2040. [CrossRef]
Golnabi, H.; Azimi, P. Design and operation of a double-fiber displacement sensor. Opt. Commun. 2008, 281,
614–620. [CrossRef]
Sensors 2016, 16, 808
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
15 of 15
Shen, W.; Wu, X.; Meng, H. Long distance fiber-optic displacement sensor based on fiber collimator.
Rev. Sci. Instrum. 2010, 81. [CrossRef] [PubMed]
Choi, S.; Kim, Y.; Song, M.; Pan, J. A Self-Referencing Intensity-Based Fiber Optic Sensor with Multipoint
Sensing Characteristics. Sensors 2014, 14, 12803–12815. [CrossRef] [PubMed]
Martinez-Rios, A.; Monzon-Hernandez, D.; Torres-Gomez, I.; Salceda-Delgado, G. An Intrinsic Fiber-Optic
Single Loop Micro-Displacement Sensor. Sensors 2012, 12, 415–428. [CrossRef] [PubMed]
Zawawi, M.A.; O’Keeffe, S.; Lewis, E. Plastic optical fibre sensor for spine bending monitoring with power
fluctuation compensation. Sensors 2013, 13, 14466–14483. [CrossRef] [PubMed]
Harun, S.W.; Yang, H.Z.; Arof, H.; Ahmad, H. Theoretical and experimental studies on coupler base fiber
optic displacement sensor with concave mirror. Optik 2012, 123, 2105–2108. [CrossRef]
Pinto, A.M.R.; Baptista, J.M.; Santos, J.L.; Lopez-Amo, M.; Frazão, O. Micro-displacement sensor based on a
hollow-core photonic crystal fiber. Sensors 2012, 12, 17497–17503. [CrossRef] [PubMed]
Islam, M.; Ali, M.; Lai, M.; Lim, K.; Ahmad, H. Chronology of Fabry-Perot Interferometer Fiber-Optic Sensors
and Their Applications: A Review. Sensors 2014, 14, 7451–7488. [CrossRef] [PubMed]
Yang, H.Z.; Harun, S.W.; Arof, H.; Ahmad, H. Environment-independent liquid level sensing based on
fiber-optic displacement sensors. Microw. Opt. Technol. Lett. 2011, 53, 2451–2453. [CrossRef]
Rahman, H.A.; Rahim, H.R.A.; Harun, S.W. Detection of stain formation on teeth by oral antiseptic solution
using fiber optic displacement sensor. Opt. Laser Technol. 2013, 45, 336–341. [CrossRef]
Lee, Y.; Kim, Y.; Kim, C. Fiber optic displacement sensor with a large extendable measurement range while
maintaining equally high sensitivity, linearity, and accuracy. Rev. Sci. Instrum. 2012, 83, 045002. [CrossRef]
[PubMed]
Birch, K.P. Optical fringe subdivision with nanometric accuracy. Precis. Eng. 1990, 12, 195–198. [CrossRef]
Libo, Y.; Jian, P. Analysis of the compensation mechanism of a fiber-optic displacement sensor. Sens. Actuators
A Phys. 1993, 36, 177–182. [CrossRef]
Chen, Y. Reflective Grating Panel Based Fiber Optic Displacement Measurement System and Experiments.
Master’s Thesis, Tsinghua University, Beijing, China, 30 May 2014.
© 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/).