Optik
126
(2015)
3420–3423
Contents
lists
available
at
ScienceDirect
Optik
jo
ur
nal
homepage:
www.elsevier.de/ijleo
Systematically
analysis
of
resonant
fiber
optic
gyroscope
Yao-ying
Liu
a
,∗
,
Xiao-wen
Cui
a
,
Jun-bin
Zang
c
,
Zhi-dong
Zhang
a,b
,
Yong-hua
Wang
b
,
Yan-na
Li
b
,
Jun
Liu
a,b
,
Chen-yang
Xue
a,b,∗
a
Science
and
Technology
on
Electronic
Test
&Measurement
Laboratory,
North
University
of
China,
Taiyuan
030051,
China
b
School
of
Instrument
and
Electronics,
North
University
of
China,
Taiyuan
030051,
China
c
North
University
of
China,
Shuozhou
223600,
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
2
July
2014
Accepted
26
July
2015
Keywords:
Resonator
Gyroscope
Sensitivity
Random
walk
a
b
s
t
r
a
c
t
The
research
on
gyroscopes
has
lasted
for
a
long
time,
but
there
is
not
a
thorough
analysis
of
them.
In
this
paper,
a
detailed
theoretical
analysis
of
fiber
ring
gyroscope
and
its
gyroscope
effect
are
presented,
the
performance
characteristics
of
optical
resonator
gyroscope
ranging
from
transmission
function
Tfrr,
Finesse,
Q-factor,
the
gyro
sensitivity,
signal
noise
ratio,
random
walk
to
dynamic
range
are
all
deduced
in
detail.
In
addition,
a
large
number
of
experiments
have
been
done
to
verify
the
deduced
theoretical
results.
The
sensitivity
of
the
fiber
optic
gyroscope
is
analyzed
by
simulating
the
relationship
between
dQ
and
turn
number
of
fiber
ring,
make
the
conclusion
that
with
the
increase
of
turn
number
of
ring,
the
resonance
depth
increased
while
the
dQ
value
decreased,
obtain
a
high
sensitivity
of
0.21
◦
/h,
random
walk
of
0.0035
◦
/
√
h,
and
Q
factor
of
8
×
10
6
.
Moreover,
in
the
digital
frequency
locked
dual
rotation
gyro
experiments,
obvious
step
effect
is
observed.
And
the
experimental
line
of
frequency
difference
is
very
agreement
with
the
theoretical
line.
The
research
provides
a
good
theoretical
and
experimental
basis
for
the
study
of
gyroscopes.
©
2015
Elsevier
GmbH.
All
rights
reserved.
1.
Introduction
The
fiber
ring
resonator
(FRR)
is
the
core
sensing
element
in
a
gyroscope
system,
the
study
of
optical
gyroscopes
was
a
hot
field
in
recent
years,
and
they
have
been
widely
used
in
industry
and
military,
they
were
applied
ranging
from
inertial
navigation
systems
in
aircrafts
and
vessels
to
control,
stabilization
and
posi-
tioning
systems
for
robotics
and
virtual
reality
applications
[1].
The
laser
gyroscopes
produce
two
counter
propagating
beams,
and
their
frequency
difference
is
used
to
measure
the
rotation
speed,
the
sensitivity
is
used
to
measure
the
performance
of
optical
gyro-
scope.
There
has
been
many
elements
influence
the
sensitivity,
such
as
the
quality
factors,
the
diameter
of
ring
resonator,
the
length
of
fiber,
Finesse,
resonance
depth,
the
slope
of
the
resonance
curve
and
so
all.
A
lot
of
scholars
are
in
study
of
the
influence
factors
on
the
sensitivity,
like
Zhejiang
University,
Beijing
University
of
Aero-
nautics
and
Astronautics,
Changchun
University
of
Technology
and
Kanazawa
University.
But
they
all
do
not
have
a
summary
of
the
elements,
so
this
paper
provides
an
in-depth
description.
∗
Corresponding
author
at:
Science
and
Technology
on
Electronic
Test
&Measure-
ment
Laboratory,
North
University
of
China,
Taiyuan
030051,
China.
Tel.:
+86
03513921756.
E-mail
address:
xuechenyang@nuc.edu.cn
(C.-y.
Xue).
2.
Theory
As
shown
in
Fig.
1,
a
schematic
diagram
of
resonated
fiber
optic
gyroscope
is
given
as
follows:
Light
from
laser
S
is
translated
into
isolation
1,
and
divided
to
two
beams
(CW
and
CCW)
by
a
3
dB
coupler
C1.
Then
the
two
beams
transmit
into
isolation
2,
phase
modulator
1
and
isolation
3,
phase
modulator
2,
respectively,
one
of
the
beams
through
circulator
C2
is
coupled
into
fiber
ring
resonator,
and
forming
CCW
wave,
another
beam
through
circulator
C3
is
coupled
into
fiber
ring
resonator,
and
forming
CW
wave.
The
resonance
frequency
of
CW
light
is
detected
by
detector
PD1
through
coupler
C2,
and
the
resonance
frequency
of
CCW
light
is3
detected
by
detector
PD2
through
coupler
C3.
In
order
to
detect
frequency
difference,
the
CCW
light
is
locked
to
laser
through
Lock-in
amplifier
LIA1,
PI
circuit
and
high
voltage
amplifier.
While
the
CW
light
through
Lock-in
amplifier
LIA2
is
detected
as
gyro
signal
f.
Defined
R
is
the
radius
of
the
fiber
ring
resonator,
d
is
the
perime-
ter
of
the
fiber
ring.
L
is
the
length
of
the
fiber
L
=
N
·
2R
=
Nd,
(1)
A
is
the
closed
area
surrounded
by
optical
path,
A
=
N
·
R
2
,
(2)
N
is
the
number
of
the
rings.
http://dx.doi.org/10.1016/j.ijleo.2015.07.162
0030-4026/©
2015
Elsevier
GmbH.
All
rights
reserved.
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