TELKOM
NIKA
, Vol.12, No
.4, Dece
mbe
r
2014, pp. 81
1~8
1
8
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i4.123
811
Re
cei
v
ed
Jul
y
27, 201
4; Revi
sed O
c
tob
e
r 23, 201
4; Acce
pted No
vem
ber 1
0
, 2014
Resolution Improvement in Fabry-Perot Displacemen
t
Sensor Based on Fringe Counting Method
Nur Izzati Ismail, Nor Hafizah
Ngajiki
n
, No
r Fadzlina Mohd Zaman, Maisarah A
w
ang,
Asrul Izam
Azmi, Nik Noo
r
dini Nik Ab
d. Malik, Norazan M
ohd
Kas
s
im
Lig
h
t
w
ave C
o
mmunicati
on R
e
searc
h
Group
(LCRG)
F
a
cult
y
of Elec
trical Eng
i
ne
eri
ng, Univ
ersiti T
e
kno
l
og
i Mal
a
ysia
813
10 Jo
hor, Mala
ysi
a
, Ph: +
607-5
535
30
2
e-mail: izzati.is
m
ail@fke
g
ra
du
ate.utm.m
y
A
b
st
r
a
ct
T
h
is pap
er pre
s
ents an i
m
pro
v
ed F
r
ing
e
Co
untin
g Metho
d
(F
CM) techniq
ue in ord
e
r to enh
anc
e
the dis
p
lac
e
me
nt resol
u
tion
of a F
abry-Per
o
t Displ
ac
e
m
ent
Sensor (F
PDS)
. A simu
lati
on
mo
de
l of a F
P
DS
base
d
o
n
th
e i
m
pr
ove
d
F
C
M
has
be
en
dev
elo
ped
a
nd s
i
mu
late
d for
na
no
meter
dis
p
la
cement r
ang
e
b
y
usin
g MAT
L
A
B
mathe
m
atic
al s
o
ftw
are. Unlike
co
nve
n
ti
ona
l F
C
M th
at an
aly
z
e
d
th
e
nu
mber
of fri
nges
prod
uced
over
one time per
i
od, the i
m
prov
ed F
C
M ana
ly
z
e
d t
he nu
mb
er of fringes fo
r one lar
gest F
r
ee
Spectral
Ra
ng
e (F
SR). In thi
s
w
o
rk, the i
n
it
ial
le
ngth
of F
abry-Per
o
t Inte
rferometer (F
P
I
) cavity h
a
s b
e
e
n
set at 75
μ
m d
ue to li
mitati
on
of the mach
in
ing pr
ecisi
on e
qui
p
m
ent. F
o
r the disp
lac
e
ment ana
lysis, t
h
e
improve
d
F
C
M
techni
qu
e is
u
s
ed as
an
al
go
rithm. T
h
e
res
e
arch res
u
lts pr
ove th
at this F
P
DS cou
l
d
det
ect
displ
a
ce
ment
at 10
n
m
res
o
l
u
tion
over
a
w
o
rki
ng r
ang
e
of 4
0
n
m
. It
show
ed th
at t
he
improv
ed
F
C
M
techni
qu
e
ma
nag
ed t
o
e
n
h
ance
the
cap
abil
i
ty of
th
e
conv
entio
na
l
F
C
M in
d
e
tecting
na
no
mete
r
displ
a
ce
ment.
Ke
y
w
ords
: frin
ge cou
n
tin
g
method, fabry-
pe
rot displ
a
ce
me
nt sensor, faby
-
perot interfer
o
m
eter
1. Introduc
tion
Displa
ceme
nt as
one
co
mpone
nt in
vibration
can
be dete
c
te
d by a vari
ety of
displ
a
cement
se
nsors
working
ba
sed
o
n
differe
nt
p
r
incipl
es.
T
h
e
s
e se
nsors work ba
sed
on
cap
a
citive, indu
ctive, piezo
e
le
ctric
and mo
st
rece
ntly usin
g optical te
chn
o
logy [1]-[2].
Displa
ceme
nt sen
s
o
r
b
a
sed on
opti
c
al tech
nolo
g
y has
dra
w
n incre
a
si
ng
attention from
manufa
c
turers a
nd
re
se
arche
r
s
sin
c
e it
ca
n give
re
markabl
e p
e
rforman
c
e
s
i
n
high
sen
s
itivity,
lightwei
ght, fast re
sp
on
se
and immu
nity to elec
troma
gnetic inte
rference (EMI) [3
]-[4]. There a
r
e
three types o
f
optical based displ
a
cem
ent sen
s
o
r
s
whi
c
h are Intensity-Ba
se
d
Sensors (IB
S
),
Fabry-P
e
rot I
n
terferomete
r
(FPI), and Fi
ber Br
a
gg G
r
ating (FBG
). Among the
s
e
three metho
d
s,
FPI is mo
re
prefe
rre
d
sin
c
e it p
r
ovide
s
high
disp
la
cement
resolu
tion [5]. This
type of se
nso
r
is
also
calle
d as Fabry-Pe
rot
Displa
ceme
nt Senso
r
(FP
D
S).
In evaluating
the FPDS perfo
rman
ce,
sen
s
or’
s
re
solutio
n
ha
s been an
alyzed. Thi
s
resolution
re
pre
s
ent
s the
small
e
st
chang
e
that can be
d
e
t
e
cted by
th
e
se
nsor. High
displ
a
cement
re
solutio
n
o
f
FPDS all
o
ws the
se
nsor to
dete
c
t
displ
a
cement
ca
used
by
the
moving o
b
je
ct pre
c
isely. In orde
r to
provide FP
DS
with a
high
resol
u
tion, alg
o
rithm
used
to
pro
c
e
ss th
e detecte
d inte
rfere
n
ce sig
n
a
l sho
u
ld be
carefully ch
ose
n
. This i
s
be
cau
s
e t
he
preferred algorithm
will determine the resoluti
on li
mit of the FPDS. Several algorithm
s
have
been
propo
sed for the
past fe
w ye
ars.
Thi
s
in
clud
es wave
numbe
r
sp
a
c
ing
metho
d
[6],
combi
nation
of Fourie
r tra
n
sform meth
od and
mi
nim
u
m
mean sq
uare error est
i
mation
(MM
SE)-
based
sign
al
pro
c
e
s
sing
method [7],
control a
nd
pha
se d
e
mo
dulation te
ch
nique [8], a
n
d
freque
ncy
m
odulate
d
p
h
a
s
e
gen
erated
ca
rri
er
(F
M
P
GC) de
mod
u
lation
sche
me b
a
sed
on
the
arcta
nge
nt (A
rctan
)
alg
o
rit
h
m [9], and Fring
e
Co
unti
ng Metho
d
(FCM
) [10]-[1
2
]. Neverthel
ess,
all the
s
e
met
hod
s h
a
ve th
eir
own
sho
r
tcomin
gs.
The
wave
numb
e
r sp
aci
ng
met
hod
mana
ge
d to
achi
eve re
so
lution abo
ut 16 nm b
u
t requires
accu
rate data
an
alysis
on th
e waven
u
mb
er
spa
c
in
g. Oth
e
r m
e
thod
s
such
a
s
Fo
urie
r tra
n
sfo
r
m m
e
thod
and
M
M
SE-ba
sed
signal p
r
o
c
e
ssing
method, the
control and
pha
se dem
o
dulation
te
ch
nique, an
d the FMPG
C-Arctan te
chni
que
contri
bute ve
ry high re
sol
u
tion, up to sub nan
omet
e
r
displ
a
ceme
nt resol
u
tion.
However, these
techni
que
s n
eed a
compl
e
x data p
r
o
c
essing. In
co
ntrast, F
C
M t
e
ch
niqu
e offers an
algo
rithm
with less
co
mplex data
pro
c
e
ssi
ng i
n
displ
a
cem
ent dete
c
tion
. Despite the
simpli
city of the
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
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TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 811
– 818
812
system, this tech
niqu
e is limited to disp
lacem
ent det
e
ction up to
micromete
r
range only. It is
only po
ssibl
e
to rea
c
h n
anomete
r
di
splacement d
e
tection
with
some
modif
i
cation in
F
C
M
techni
que [1
3]-[14]. Therefore, in this pape
r,
a new frin
ge co
unting me
ch
anism
ha
s b
een
develop
ed in
orde
r to en
ha
nce the FP
DS resol
u
tion
and called a
s
the improve
d
FCM techniq
ue.
This te
chni
qu
e is di
scusse
d in detail
s
in
the
followin
g
se
ction. The
develope
d
F
P
DS ba
sed o
n
the improve
d
FCM si
mula
tion model i
s
analyze
d
in
terms of n
u
m
ber
of fring
e
for a
spe
c
i
f
ic
displ
a
cement
.
2. Working P
r
inciple of F
P
DS
FPI is a pa
ssive optical
stru
cture that
used m
u
ltip
le-be
a
m inte
rferen
ce in a
cavity
b
e
t
w
e
e
n
tw
o s
e
mi r
e
flec
tive
s
u
r
f
ac
es [1
5
]. T
h
is FPI configu
r
ation is u
s
e
d
for nan
om
eter
displ
a
cement
detection in
this proj
ect.
Figur
e 1
sh
ows the FP
DS co
nfigura
t
ion in detect
i
ng
displ
a
cement
. Refere
nce b
eam in this fi
gure i
s
the
re
flection from f
i
ber-air inte
rf
ace at the fro
n
t
of the cavity while
se
nsin
g
beam i
s
the
reflectio
n
of fiber-air i
n
terfa
c
e at the
ba
ck of the
cavity.
Mirro
r M
2
that attached t
o
the moving obje
c
t will
move backward and al
so forwa
r
d, h
ence
cha
nge
s the
length of F
P
I cavity,
d
. This chan
g
e
s lea
d
to significa
n
t alteration of ph
ase
differen
c
e (
φ
) between
ref
e
ren
c
e reflect
i
on and sen
s
i
n
g refle
c
tion in FPDS operation as state
d
in (3). Th
ese
two beam
s
sign
al interfe
r
e with ea
ch
other a
nd re
sulted in the variation
s
of F
P
I
interferen
ce signal a
s
pre
s
ented in (1
).
Figure 1. FPDS Con
c
e
p
t in Displa
ceme
nt Sensing
Acco
rdi
ng to the multi-be
a
m
interferen
ce prin
ciple, t
he no
rmali
z
e
d
tran
sfer fu
nction of
the refle
c
ted
interferen
ce
spectrum at wavelength
λ
i
s
given by th
e well
-known
Airy function
. It
can b
e
expre
s
sed a
s
belo
w
[16].
(1)
Whe
r
e
(2)
and ph
ase differen
c
e,
(3)
R
is
reflec
tivity of the mirror,
n
is
refrac
tive index of the FP
c
a
vit
y
,
d
is le
ngth
of FPI
cavity, and
λ
is light cente
r
wavelength i
n
vacuum. By
utilizing (1),
the displa
ce
ment of the M
2
can b
e
dete
c
ted from the reflected inte
rferen
ce
spe
c
trum.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
9
30
Res
o
lution Improv
ement in Fabry
-
P
e
rot
Displac
e
ment Sens
or (FP
D
S) .... (Nur Izz
a
ti Is
mail)
813
3. FPDS Bas
e
d on the Im
prov
ed FCM Techniqu
e
3.1. FPDS Simulation Mo
del
As afo
r
e
m
entione
d, th
e imp
r
oved
FCM i
s
dev
elope
d
to
e
n
han
c
e
re
so
lution of
conve
n
tional
FCM for nanom
eter range di
spla
ce
me
nt dete
c
tion. In order to eval
uate
perfo
rman
ce
of the
ne
w i
m
prove
d
m
e
thod, a
simul
a
tion
m
o
del
based on
eq
uation
s (1-3)
is
develop
ed u
s
ing MATLA
B
mathematical software.
Several important pa
ra
meters in FPDS
stru
cture are
analyzed in 2
-
dime
nsi
onal
analysi
s
whi
c
h are length
of the FPI cavity and mirror
reflec
tivity.
Figure 2
sho
w
s the ill
ust
r
ation of th
e d
e
velope
d FP
DS mo
del. T
he initial
len
g
t
h of FPI
c
a
vity,
d
o
is chosen to be a
t
75 µm due to limitation in
pre
c
isi
o
n ma
chini
ng eq
uip
m
ent. Length
of
FPI cavity is increa
sed
by nanom
eter v
a
riation
fo
r e
a
ch
simul
a
tio
n
. Hen
c
e, th
e length of F
P
I
cavity
unde
rg
oes a
continu
ous ch
ang
e with
a certai
n
displ
a
cemen
t,
D,
thus resulting in a new
d
.
This
displa
ce
ment vari
atio
n an
alysi
s
is
need
ed in
o
r
der to
obtai
n
displ
a
cement
re
solutio
n
of
the
sen
s
o
r
. The o
t
her pa
ramet
e
rs involve
d
in this simul
a
tion are a
s
tab
u
lated in Tabl
e 1.
Figure 2. Modelling of FP
DS in MATLA
B
Software
Table 1. FPDS Simulation
Parameters
Values
Initial length of FPI cavity
,
d
0
75
µm
Mirrors reflectivity,
R
98%
Refractive index
of FP cavity
,
n
1.0
Light incident angle at M
1
0°
3.2. The Improv
ed FCM Technique
Based
on
F
C
M te
chni
qu
e, a la
rge
nu
mber of
cou
n
ted
frin
ge
s prod
uced will
improve
resolution
of the FPDS. T
h
erefo
r
e, this
pape
r p
r
e
s
en
ts an im
prove
d
fring
e
count
ing meth
od th
at
con
s
id
ers tot
a
l num
be
r of
fringe
s in
the
larg
est
FS
R
instea
d of
on
e time p
e
ri
od
in
conve
n
tio
n
al
FCM. Pro
c
e
s
s step
s for b
o
t
h countin
g method
s are
ill
ustrate
d
in flow ch
art
s
in Figure 3.
In this work, the simul
a
ted light sou
r
ce is
ran
g
ing fro
m
600 nm to 1700 nm wavelength.
Acco
rdi
ngly, the large
s
t F
S
R is exa
m
in
ed within thi
s
wavelen
g
th
rang
e. Witho
u
t displ
a
ce
m
ent
(
D
=
0 n
m
), t
he la
rge
s
t FS
R i
s
fou
nd to
be 2
00
nm a
s
sh
own in
Fig
u
re
4. Thi
s
F
S
R value
will
be
used in the proposed
algorithm.
Varying the di
splacement val
ue
w
ill varies the FSR range,
thus
will ch
ange th
e numbe
r of fringe
s p
r
od
uced.
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ISSN: 16
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TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 811
– 818
814
(a)
Conventional FCM Technique
(b) Imp
r
oved
FCM Te
ch
niq
u
e
Figure 3. Pro
c
e
ss Step
s of
the Conventi
onal FCM an
d the Improve
d
FCM Te
ch
n
i
que
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
9
30
Res
o
lution Improv
ement in Fabry
-
P
e
rot
Displac
e
ment Sens
or (FP
D
S) .... (Nur Izz
a
ti Is
mail)
815
Figure 4. Rel
a
tive Output Intensity of
FPDS in Wavele
ngth Dom
a
in
Rep
r
e
s
entati
o
n
(
d
0
= 7
5
µm)
Fring
e
calculation in both
FCM te
chni
q
ues
i
s
d
one i
n
time dom
ai
n analy
s
is.
Hence, the
optical
sp
ect
r
um n
eed
s t
o
be tra
n
sfo
r
med i
n
to
time dom
ain
rep
r
e
s
entatio
n. The follo
wing
equatio
ns a
r
e
used fo
r the tran
sform
a
tion
process.
Operating fre
quen
cy, f
m
=
(4)
Sampling fre
quen
cy, f
s
= 2 f
m
(5)
Time,
(6)
Whe
r
e
c
is sp
eed of light,
λ
is operating
wavele
ngth a
nd
L
is len
g
th
of the signal.
As stated b
e
fore, the conv
entional F
C
M
techni
q
ue a
n
alyze
s
nu
m
ber of frin
ges for one
time pe
riod. I
n
contrast, th
e imp
r
oved
F
C
M
co
unts
th
e nu
mbe
r
of f
r
inge
s
exists
within th
e la
rgest
F
S
R
.
F
i
gu
r
e
5
sh
ow
s th
e fr
in
g
e
pa
tte
rn
s
o
b
t
ain
ed
by usi
ng th
e
co
nvention
a
l
FCM
an
d t
h
e
improve
d
FCM techni
que.
The imp
r
ov
ed FCM tech
nique
pro
d
u
c
ed 33 fri
nge
s for the la
rg
est
FSR while th
e co
nvention
a
l FCM
prod
uce
d
only
25
fringe
s for on
e time pe
rio
d
.
Highe
r
cou
n
t
ed
numbe
r of fringe
s re
sulted
in a better re
solutio
n
of FPDS.
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ISSN: 16
93-6
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TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 811
– 818
816
(a)
Conve
n
tio
nal FCM T
e
chniqu
e
(b) Imp
r
oved
FCM Te
ch
niq
u
e
Figure 5. Rel
a
tive Output Intensity of FPDS
in Time Domain Repr
es
entation for Both
Tech
niqu
es (
d
0
= 75 µm)
4. Results a
nd Discu
ssi
on
In this sectio
n, relation
shi
p
between th
e num
b
e
r
of fringe
s an
d d
i
spla
cem
e
nt
of FPDS
based on the
improved F
C
M techniqu
e is presente
d
.
This rel
a
tionship provid
es informatio
n on
the displ
a
ce
ment re
soluti
on and
wo
rki
ng ra
nge of
t
he develo
ped
FPDS simul
a
tion model. G
r
aph
depi
cted in F
i
gure
6(a) illu
strate
s that n
u
mbe
r
of
frin
ges
are va
rie
d
acco
rdin
g to the value
of
displ
a
cement
. Numbe
r
of f
r
inge
s d
e
cre
a
se
stea
dily starting
from
75 µm to 75.
04 µm len
g
th
of
FPI cavity. Beyond
75.04
µm, the nu
m
ber
of frin
ge
s sta
r
ts to
in
crease a
gain
d
ue to i
n
cohe
ren
t
sup
e
rp
ositio
n
[17]. This pa
ttern sho
w
s that
the
devel
oped
FPDS
ba
sed
on the
improved F
C
M
techni
que i
s
able to dete
c
t
the displ
a
ce
ment up to 4
0
nm. The relation
ship b
e
twee
n the le
ngth
of FPI cavity
and the di
spl
a
cem
ent is ill
ustrate
d
in
Fi
gure 6
(
b
)
. Th
e FPDS re
sol
u
tion is ide
n
tified
as 10 nm
sin
c
e the num
be
r of cou
n
ted fringe
s le
ss th
an this value i
s
not linea
r in
pattern.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Res
o
lution Improv
ement in Fabry
-
P
e
rot
Displac
e
ment Sens
or (FP
D
S) .... (Nur Izz
a
ti Is
mail)
817
(a)
(b)
Figure 6. (a)
Cou
n
ted Nu
mber of FP Interfere
n
ce Fri
nge
s for a Sp
ecific L
ength
of FPI Cavity
and (b
) Detected Displa
ce
ment for a Sp
ecific L
ength
of FPI Cavity
5. Conclusio
n
FPDS ba
se
d
on the im
prov
ed F
C
M te
ch
nique i
s
d
e
ve
loped
and
prese
n
ted in thi
s
pa
pe
r.
Analytical mo
del of FPDS is sim
u
lated b
y
using
initial
length of the
FPI cavity of 75 µm. Fro
m
the sim
u
latio
n
, FPDS
with
a di
spla
cem
ent re
sol
u
tion
of 10
nm a
n
d
wo
rking
ra
n
ge of 4
0
nm
are
reali
z
ed
with the used of the improve
d
FCM te
chniq
ue. These re
sults a
r
e obt
ained for 75
µm
initial length
of FPI cavity
with a light source
rangi
n
g
from 60
0 n
m
to 1700 n
m
wavele
ngt
h. The
prop
osed FP
DS config
urat
ion is targete
d
for app
lications that re
qui
re a nano
met
e
r displa
cem
ent
detectio
n
su
ch a
s
mi
croscope, tele
scop
e, and
al
so
di
sk sli
d
e
r
. Th
e
appli
c
atio
n o
f
this FP
DS
can
be exten
ded
to many
othe
r a
ppli
c
ation
s
sin
c
e
it
offers the immuni
zation to EMI, lightweight and
als
o
ease of implementation.
Referen
ces
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u
rasi
ya
H.
Rece
nt T
r
ends of Meas
urem
ent a
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e
ve
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br
ation S
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ors.
Internati
ona
l
Journ
a
l of Co
mputer Scie
nce I
ssues (IJCSI).
201
2;
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[2]
Santoso
D
R
.
A Simp
le I
n
strumentati
o
n
S
yst
e
m
fo
r La
rge Stru
ctu
r
e Vi
b
r
a
t
i
o
n Mon
i
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. Ind
ones
ia
n
Journ
a
l Of Elektrical Eng
i
ne
e
r
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10; 8(3)
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25
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75.01
75.02
75.03
75.04
75.05
75.06
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Interference
Fringes
Length of FPI Cavity
(µm)
0
10
20
30
40
50
60
75
75.01
75.02
75.03
75.04
75.05
75.06
Displacement (nm)
Length of
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ISSN: 16
93-6
930
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