Methods of improving the accuracy of fiber optic gyros

ISSN 2075 1087, Gyroscopy and Navigation, 2012, Vol. 3, No. 2, pp. 132–143. © Pleiades Publishing, Ltd., 2012.
132
INTRODUCTION
Fiber optic gyros (FOGs) gain more and more
popularity in precise navigation. FOGs outperform
mechanical and ring laser gyros as regards their cost,
dimensions, power consumption, etc. Kuznetsov Sci
entific Research Institute of Applied Mechanics is
involved in development of a range of FOGs for vari
ous applications. The gyros under development fea
ture drift rate of 0.5 to 0.01 deg/h and scale factor sta
bility of 0.1% to 0.01%. To achieve 0.001 deg/h and
better accuracy, FOG optical components and data
processing algorithms should be refined.
All kinds of FOGs employ the same principles to
process the data coming from the fiber ring interfer
ometer (FRI). These principles differ in the type and
degree of auxiliary phase modulation depending on
the gyro accuracy. FRIs of all types of FOGs have the
same optical scheme and, depending on the gyro
accuracy, different specific designs and sensing coil
technologies, and type and length of fibers.
FOG developers face a number of technical prob
lems, which constrain the gyro limiting characteris
tics, such as readiness time, dead band, and bias due to
imperfections of FRI components and electronic cir
cuit. Degradation of gyro performance under varying
ambient temperature, vibration, and radiation effects
also presents a problem.
Figure 1 shows the FOG block diagram.
The FRI data are processed using the so called dig
ital serrodyne [1]. The electronic unit comprises two
feedback loops. The first feedback loop maintains zero
signal at the output of synchronous detector by simul
taneously applying the digital ramp and electrical
phase modulation signal to the electrodes of phase
modulators in the optical IC (OIC). It is done to com
pensate for Sagnac phase shift in the FRI. The second
feedback loop keeps the amplitude of digital ramp at
constant level, which is required to stabilize the FOG
scale factor. Figure 2 presents bias instability recorded
for 12 h (for a FOG with FRI scale factor of
18.95 mrad/(deg/s).
The plot shows that bias instability was about
0.1 deg/h in the first hour (which is the gyro readiness
time), and then it did not exceed 0.02 deg/h.
READINESS TIME
Gyro readiness times can grow due to the perfor
mance of light sources used. In medium and high
accuracy FOGs, erbium doped superfluorescent fiber
sources (SFS’s) are employed [2]. Our team uses the
SFS’s produced by IRE Polus Research and Techni
cal Company, Fryazino, Russia. These SFS’s are com
monly packaged with an AP, at the output of which an
ADC is installed providing communication with a DP.
Figure 3 shows the block diagram of FOG compo
nents that are packaged with the SFS.
Typical radiation spectrum of an SFS is presented
in Fig. 4.
Under temperatures of –40°C to +60°C, SFS
power consumption is max 4 W, and total optical
power output of four channels is 52 mW.
SFS advantages include high power output, depo
larized output radiation, high thermal stability of cen
tral wavelength, and broad emission bandwidth. The
Methods of Improving the Accuracy of Fiber Optic Gyros
A. M. Kurbatov and R. A. Kurbatov
Federal State Unitary Enterprise Center for Ground Based Space Infrastructure,
Kuznetsov Scientific Research Institute of Applied Mechanics, Moscow, Russia
Received July 25, 2011
Abstract—The paper considers the key problems, which limit the accuracy of fiber optic gyros, and presents
the methods to solve them.
DOI: 10.1134/S2075108712020071
1 2
3
4
5
SFS
AP
DP
FRI
Interface device
Fig. 1. FOG block diagram: 1–erbium doped superlumi
niscent fiber source with low temporal coherence (SFS),
2–fiber ring interferometer (FRI), 3–analog processor
(AP), 4–digital processor (DP), 5–interface device.

GYROSCOPY AND NAVIGATION Vol. 3 No. 2 2012
METHODS OF IMPROVING THE ACCURACY 133
central wavelength and emission bandwidth are
described by the following equations:
( ) ( )
( ) ( ) ( )22
,
,
d S d S
d S d S
λ = λλ λ λ λ
⎡ ⎤Δλ = λλ λ λ λ − λ⎣ ⎦
∫ ∫
∫ ∫
where S(λ) is the emission psd. However, a dip in SFS
spectrum (Fig. 4) presents a drawback, reducing the
effective emission bandwidth, and, hence, increasing
depolarization length in linearly birefringent fibers.
Among other things, it can result in increased polar
ization error in the FRI, however, its contribution to
the error is insignificant [3].
Fig. 2. Bias instability for 12 hours after FOG cold start. Warm up period is about 1 hour. Averaging times are 1, 10, and 100 s.
1
2 3
4
SFS
AP
optical
circulator
FRI
Fig. 3. Packaged FOG components: 1–SFS, 2–AP, 3–PIN photodiode, 4–optical circulator or fiber triple ported coupler.
–10.6
–20.6
–30.6
–40.6
–50.6
–60.6
5.0 dB/C RES: 0.020 nm SENS: MID AVG: 1 SMPL: 20001 (AUTO)
1600.000nm 8.00 nm/D1560.000 nm1520.000 nm
REF
001 002
dBm
Fig. 4. SFS typical radiation spectrum. The vertical axis is the power level in dBm, the horizontal axis is the wavelength in nm.
1.0
0.5
0
–0.5
–1.0
1 s
10 s
100 s
0 1 2 3 4 5 6 7 8 9 10 11 12
Time (hours)

134
A.M. KURBATOV, R.A. KURBATOV
Therefore, stability of SFS power output and cen
tral wavelength can determine the gyro warm up time
after the cold start, and its accuracy after self heating
of SFS pump diodes. Variations of SFS power output
with time are shown in Fig. 5.
Figure 6 demonstrates the variations of SFS central
wavelength and emission bandwidth after the cold
start with constant ambient temperature.
Variations of central wavelength in the first hour are
in rough agreement with the exponential law and do
not exceed 90 ppm. It provides the scale factor stability
of 0.009% with constant ambient temperature and
cold start. During self heating, the temperature of cas
ing is also varying under exponential law, therefore,
thermal drift coefficient of SFS central wavelength can
be found, which is 7.7 ppm/°C.
Figure 7 presents variations of SFS central wave
length at temperature rise by 20°C after the gyro self
heating within 130 min (see Fig. 6).
The plot demonstrates that the central wavelength
almost linearly depends on ambient temperature,
which makes it possible to increase the scale factor sta
bility by more than an order of magnitude using ther
mal correction of SFS central wavelength. Therefore,
thermal correction provides the scale factor stability as
high as 0.77 ppm/°C. However, it follows from the
above analysis that instability of SFS central wave
length, even with no thermal correction, is not likely
to extend the FOG readiness time.
Most probably, FOG readiness time is extended due
to variations of SFS power output at its cold start, since
the period of SFS power output variations (Fig. 5) and
FOG warm up time nearly coincide. Figure 8 shows the
typical drift rate of a FOG with scale factor of
18.95 mrad/(deg/s) for 8.5 h in steady state mode.
Therefore, variations in photodetector temperature
and in SFS power output during self heating affect the
amplitude of the gyro open loop gyro output.
The rate error is probably generated as follows. Due
to asymmetrical phase modulation parameters and
imperfections of phase modulators in the OIC, a
residual spurious signal Δ, caused merely by imperfec
tions of electronics, occurs at the output of synchro
nous detector. Then, during FOG closed loop opera
tion, the error is proportional to
ϕs – ϕk = (Δ/P0ηpG0sinΦm),
where ϕs is the Sagnac phase shift, P0 is the power of
interfering beams on photodetector, ηp is the sensitiv
ity of photodetector, G0 is the gain of electronic circuit,
Φm is the amplitude of auxiliary phase modulation, ϕk
is the phase shift induced by the digital ramp [4].
Therefore, the rate error depends on the amplitude of
open loop gyro output.
To improve the gyro accuracy, an additional elec
tronic circuit may be employed, which comprises a
second synchronous detector outputting a signal pro
portional to constant optical signal at the photodetec
tor. After the scaling, this signal can be used to stabilize
the amplitude of the open loop gyro output. This
principle provides stable bias and scale factor even
12.10
12.06
12.05
12.04
12.03
12.02
12.01
12.00
11.99
806040200
t, min
12.09
12.08
12.07
P,mW P(t), SFS
Fig. 5. Variations of SFS power output after the cold start
(temperature of SFS casing is increased by 12°C due to
self heating of pump diodes).
1554.95
1554.90
1554.85
1554.80
1554.75
1554.70
100806040200 120
Time, min
Centralwavelength,nm
40.10
40.05
40.00
39.95
39.80
39.75
100806040200 120
Time, min
Emissionbandwidth,nm
39.90
39.85
Fig. 6. Variations of SFS central wavelength and emission bandwidth after the cold start.

with varying intensity of optical signal and gain of
electronic circuit. The intensity of optical signal can
be influenced by vibration, acoustic noise, degrading
emission from optical components, and variations in
ambient temperature. Using an additional electronic
channel improves the gyro overall performance,
including the warm up time after the start.
FIBER RING INTERFEROMETER (FRI)
FRI block diagram is presented in Fig. 9.
The fiber of the sensing coil and input PZ fiber fea
ture high linear birefringence, and the mounting fiber
is optically isotropic. Majority of available output
optical fibers of SFS’s, photodetectors, circulators,
and triple ported fiber couplers have a mode field
1555.0
1554.9
1554.8
1554.7
1554.6
1554.5
1554.4
1554.3
1951351006040200 15514512080 165 175 185
Time, min
Centralwavelength,nm
Fig. 7. Variations of SFS central wavelength. For the first 130 min, the central wavelength is changing due to self heating of pump
diodes under constant ambient temperature (see Fig. 6, left), since the 131st min, the central wavelength is changing due to ambi
ent temperature rise by 20°C.
37.6013.24
13.18
13.16
13.14
13.12
13.08
13.10
8543210 6 7
13.22
13.20
37.55
37.50
37.45
37.40
37.35
37.30
37.25
37.20
Time, min
1
2
Angularrate,deg/h
Temperature,°C
Fig. 8. Typical drift rate (curve 1, left vertical axis) and photodetector temperature curve (curve 2, right vertical axis) in steady
state mode for 8.5 h.
1
2 3 4
5
PZ
Fig. 9. FRI block diagram. 1–mounting fiber, 2–polarizing fiber (PZ fiber), 3–optical IC, 4–sensing coil, 5–fiber welding point.

136
diameter (MFD) of approximately 10.0 μm, and FRI
employs the fibers with the same MFD (except for the
fiber of sensing coil).
Fiber of the Sensing Coil
A single mode fiber Panda characterized by high
linear birefringence is employed in the sensing coil.
The birefringence is induced by mechanical stresses
generated by the stress applying circular rods [5].
The fiber of the sensing coil should feature low
losses of optical power and low bending losses; its
losses and polarization mode coupling (h) should be
weakly dependent on the fiber axial twist. To reduce
the FOG bias under the effect of magnetic field (Fara
day effect), the fiber should be highly linearly birefrin
gent and highly resistant to axial twist. A Panda fiber
with a W profile refractive index [6] meets all these
requirements. Low losses and stability of h are main
tained during the fiber bending and axial twist by con
fining the fundamental mode in the core. Then, MFD
is (0.8–0.9) × 2Rc, where Rc is the core radius.
The W profile Panda fibers have a germanate
doped core, fluorine doped inner cladding, borosili
cate stress applying rods, and silica outer cladding [6].
The Panda fibers feature the losses of 0.35–
0.8 dB/km, typical h of (1.0–0.5) × 10–5 1/m and bire
fringence B = (3.5–6.2) × 10–4. To further improve the
fiber performance (decrease h and depolarization
length, and reduce the effect of magnetic filed on
FOG output), birefringence should be increased.
Microstructured fibers with air core, having tem
perature insensitive refractive index of core material,
were proposed for reducing the Shupe effect to be
described further [7]. However, these fibers could not
provide the desired FOG accuracy due to enhanced
Rayleigh scattering. Therefore, W profile Panda fibers
are a candidate solution that can improve the FOG
parameters.
Polarizing Fiber for Coupling with Optical IC
Use of a polarizing fiber (PZ fiber) at OIC input
reduces the polarizing error in angular rate, which is
the key factor degrading the FRI performance [3, 8].
Our team uses segments of PZ fibers 0.5–1.0 m long
with polarization extinction ratio (attenuation of
either polarization state) of min 30 dB and losses in
60 mm diameter rings of min 0.2 dB [9, 10]. Apart
from reducing the polarization errors, PZ fiber at OIC
input functions as a high order mode filter.
Figure 10 presents a photo of a Panda fiber.
Figure 11 shows the spectral losses of fundamental
polarization modes in a straight fiber 1 m long and in a
fiber arranged in 60 mm diameter rings.
The fiber parameters are as follows: MFD is 10.0 μm,
the cutoff of the fundamental х polarization mode is
about1.8μ,thecutoffofthefundamentalx polarization
Fig. 10. Cross section of PZ fiber at the input of FRI opti
cal IC.
–50.8
–60.8
–70.8
–80.8
–90.8
–100.8
2
5.0 db/D RES: 2.000 nm SENS: MID AVG: 10 SMPL: 1001 (AUTO)
4
3
2
1
3
4
1300.000 nm 1500.000 nm 40.00 1700.00 nmnm/d
1
L1: 1550.0000 nm
L2: 1300.0000 nm
L3: –66.92 dBm
L4: –71.80 dBm
L2–L1: –250.0000 nm
L4–L3: –4.88 dB
Fig. 11. Spectral losses of fundamental polarization modes in a PZ fiber 1 m long: 1 and 2⎯in a straight fiber, 3 and 4⎯in a coiled
fiber. The horizontal axis is the wavelength (nm) with division value of 40 nm, the vertical axis is the power level (dBm).

mode is about 1.4 μm, and the cutoff of the first higher
x mode is about 0.95 μm. Therefore, with a wave
length of about 1.55 μm, we observe a single polariza
tion, single mode operation with extensive suppres
sion of the spurious polarization y mode (dichroism)
and of the first higher x mode.
For high precision gyros, it is proposed to use PZ
fibers both at OIC input (a fiber with 6–8 μm MFD)
and in the sensing coil [11]. It is commonly supposed
that using PZ fibers in the sensing coil is not rational
[8]. However, the mathematical simulation suggests
that PZ fibers in the sensing coil in combination with
PZ fibers at OIC input greatly reduce the polarization
error, if the following condition is met:
αL 1,
where α is the attenuation factor of the fundamental y
polarization mode in the coil fiber, L is the length of
input PZ fiber. If the polarization extinction ratio of
the input PZ fiber is from –30 to –60 dB and of PZ
fiber in the coil is about 1 dB/m, FOG bias instability,
associated with polarization errors, can be decreased
down to 10–3
−10–6
deg/h.
Mounting Fiber
An isotropic fiber with W profile refractive index is
used as a mounting fiber. It should exhibit low trans
mission losses with small bending radii and serve as a
higher order mode filter in addition to a segment of
PZ fiber [9]. Figure 12 shows the attenuation of first
higher mode in a straight fiber SMF 28, in a straight
and bent mounting fiber with bending radius of 40 mm
and MFD = 10.0 μm. Transmission losses in the
mounting fiber are within 0.25 dB/km and max
0.1 dB/m at 40 mm bending radius.
The plots demonstrate accessible bending losses
and good filtering performance of the mounting fiber,
which improves the gyro accuracy. Use of a mounting
fiber with MFD of 6.0–8.0 μm instead of 10.0 μm
ӷ
critically reduces the bending losses and enhances the
filtering performance.
Radiation Resistance of Sensing Coil Fiber
Radiation resistance required for space applica
tions can be provided by W profile fibers with fluoride
reflective cladding and undoped pure silica core, or by
conventional two layer fibers with nitrogen doped
core [12].
There are two opposite kinds of space radiation:
low level steady state radiation and pulsed radiation.
Pure silica core fibers are the most resistant under the
first kind, and nitrogen doped core fibers show a good
radiation response under the second kind [13]. Nitro
gen doped core fibers exhibit acceptable attenuation
levels under steady state radiation as well. Therefore,
we consider these fibers to be a promising candidate
for use in space FOG applications.
However, the nitrogen doped core fibers exhibit
the peak of material losses at the wavelength of
1.505 μm. Due to the finite spectral width of this peak,
it is partly expanded to operating wavelength of
1.55 μm. To solve the problem, concentration of
nitrogen in the core should be reduced, which pro
vides improved resistance under steady state radiation
while maintaining the required pulsed radiation
response. In a W profile fiber [6], a germanate doped
core should replaced with a nitrogen doped one. Fi
gure 13 shows a cross section of an isotropic W profile
fiber with nitrogen doped core and fluoride reflective
cladding from Panda fiber preform). Figure 14 pre
sents the spectral losses of this fiber.
A preform for Panda fiber with a nitrogen doped
core was manufactured by Faberus JSC, Moscow.
From Fig. 14, the losses were 5 dB/km with 1.505 μm
wavelength. As to the losses with 1.55 μm wavelength,
they did not exceed 1.0 dB/km with SFS excitation
using broadband radiation, despite the peak losses
mentioned above.
The W profile nitrogen doped core fiber has a core
diameter 2ρ = 8.2 μm, cutoff wavelength λс = 1.36 μm,
and MFD = 7.2 μm. The last parameter is in good
agreement with radiation parameters in OIC channel
waveguides. These preforms are suitable for making
300
250
200
150
100
50
0
1.50 1.584.481.461.441.421.40 1.52 1.54 1.56
straight fiber SMF 28
straight W profile fiber
bent W profile fiber
Wavelength, μm
Attenuationofthefirst
highermode,dB/m
Fig. 12. Attenuation of the first higher mode in straight
segments of fiber SMF 28 and mounting fiber, and in bent
mounting fiber (bending radius is 40 mm). The cutoff
wavelength of the first higher mode is 1.35 µm and MFD =
10.0 µm.
Fig. 13. Cross section of a nitrogen doped core fiber.

138
polarization maintaining and polarizing radiation
resistant fibers for FOG sensing coils.
To the authors’ opinion, other promising fibers
exhibiting good radiation response and low propaga
tion losses (due to the absence of core dopants) are
PM and PZ Panda fibers with pure silica cores. The
refractive index profile of the preform cross section is
given in Fig. 15.
The preform has a pure silica core (2ρ diameter),
two depressed inner fluoride claddings (diameters 2τ1
and 2τ2), and an outer silica cladding (diameter 2ρ0).
Figure 15 illustrates the geometrical parameters of the
profile. For low bending losses, the following require
ments are to be met: 2τ1 = (1.5–2.0)ρ, 2τ2 ≥ 6.5ρ.
According to the simulation results, this triple clad
structure with a narrow outer cladding [2τ1 = (1.5–
1.7)ρ] will provide improved higher order mode filter
ing as compared to a traditional fiber with a pure silica
coreandsinglebroadfluoride dopedcladdingasdetailed
in [14]. Also, the structure with two fluoride claddings
offers significant dichroism, which is, to our opinion,
barely possible in a traditional pure silica core fiber.
SHUPE EFFECT
One of the key problems associated with FOGs is
that the gyro output is sensitive to varying ambient
temperature, vibration and acoustic noise. The bias is
caused by nonreciprocal phase difference between the
interferometer waves. In the general case, this phase
difference can be presented as follows [15]:
where D is the diameter of the sensing coil, L is the
fiber length, n0 is the refractive index of sensing coil
fiber, Δn(z, t) is the variation in refractive index of coil
fiber in point z at time t, with the dot above denoting
( )( )0
0
( ) , 2 ,
L
n
t n z t L z dz
LD
ΔΩ = Δ −∫
the time derivative. To compensate the nonreciprocal
phase difference in a FRI, a special coiling scheme
should be used, where the parts of fiber equidistant
from the center are arranged back to back, i.e., in the
same conditions. Therefore, the fiber should be wound
on the coil in succession from two technological
spools, each carrying a half fiber length. A dipole and
a quadrupole arrangements are known [15, 16]. Out of
these two, the latter is more effective [15]. However, an
arrangement proposed in [17], hereinafter called the
improved quadrupole arrangement, is the most prom
ising. The table summarizes the calculated biases for
quadrupole and improved quadrupole arrangements.
However, the quadrupole arrangement is reported
to exhibit bias with axial heating as well [18].
SENSING COIL DESIGN
These special coiling schemes minimize the FOG
bias, but are not able to eliminate it completely. There
fore, additional measures are taken, namely, reducing
the rate of coil temperature change using the improved
packaging of the sensing coil, and quick temperature
equalization throughout its volume. A draft of a coil
reflecting this design philosophy is illustrated in Fig. 16.
The first (outer) shield is used to equalize the tem
perature throughout the coil surface by smoothing the
local heat sources, which break the symmetry of heat
–53.2
–63.2
–73.2
–83.2
–93.2
–103.2
dBm
5.0 db/D RES: 1.000 nm SENS: MID AVG: 1 SMPL: 3001 (AUTO)
1100.000 nm 1400.000 nm 60.00 nm/D 1700.000 nm
1
2
2 1L1: 1550.5000 nm
L2: 1505.0000 nm
L3: –63.44 dBm
L4: –65.03 dBm
L2–L1: –45.5000 nm
L4–L3: –1.59 dB
Fig. 14. Spectral losses in a nitrogen doped core fiber 1 m
long (curve 1) and 1100 m long (curve 2). The horizontal
axis is the wavelength (nm) with the division value of
60 nm, the vertical axis is the power level (dBm).
2ρ
2τ1
2τ2
2ρ0
n(r)
Δn2
–
Δn1
–
Fig. 15. Refractive index profile of pure silica core Panda
preform.
Table
Arrangement
Bias in deg/h
with radial heating
at 1°C/min rate
Bias in deg/h
with axial heating
at 1°C/min rate
Quadrupole 0.7 0.0
Improved
quadrupole
0.0 0.04

flows. The shield is made of a material with a high
thermal conductivity [19]:
k = l/cρ,
where λ, ρ, and c are the thermal conduction, density
and heat capacity. Usually a permalloy shield is used,
which simultaneously functions as a magnetic shield.
Next, the layer with low thermal conductivity
arranged under the outer shield also serves as a shield
of the other kind: it prevents the thermal waves from
penetrating into the coil, thus reducing the rate of
temperature change throughout the coil volume. As a
second shield, a foamed polyurethane can be
employed, exhibiting low thermal conduction, high
heat capacity, and rather high density.
The second shield is followed by a thin copper
layer, which equalizes the temperature throughout the
coil surface by symmetrizing the penetrating heat
flows, similarly to the first permalloy shield. Under the
copper layer, the sensing coil is situated.
In using the quadrupole arrangement to minimize
the errors in angular rate, the coil size in axial direc
tion should be increased to accelerate the temperature
equalization in radial direction. This, however,
requires a bigger interferometer. From this point of
view, the improved quadrupole arrangement offers a
fuller use of the coil volume along with reduced ther
mal sensitivity. Since the improved quadrupole
arrangement brings no errors under destabilizing fac
tors in radial direction and small errors under destabi
lizing factors in axial direction, the coil may have a
bigger radial and a smaller axial size. The minimum
coiling diameter is about 25 mm, and therefore, the
coil volume can be effectively used.
Dividing the coil into several coils [20] decreases
the number of winding layers in each coil, which
improves the winding quality. The impregnation com
pound applied to the fiber during the coiling should
have a low thermal conductivity coefficient and low
adhesion to the fiber protective coating. Low adhesion
to the fiber coating and form materials is necessary for
effective suppression of mechanical waves excited by
external destabilizing factors. In addition, low adhe
sion of the compound makes the fiber refractive index
less dependent on its length under varying tempera
ture. As a thermal conductive compound, silicon with
high content of aluminum powder can be used, with
the powder increasing the thermal conductivity coeffi
cient and its Young’s modulus. Rather high Young’s
modulus enhances the gyro vibration resistance [21].
The volume of the sensing coil is a multicomponent
environment containing a silica core, polymeric pro
tective coating, and a compound, which can be multi
component as well. The fiber coefficient of thermal
conductivity can be formulated as
Kfiber ≈ Kcore(1 – fcore) + Kcoatfcoat,
where Kcore, Kcoat are the thermal conductivity coeffi
cients of the core and protective coating, fcore, fcoat are
the volume fractions of silica core and protective coat
ing in the fiber. Thermal conductivity of a silicone com
pound containing aluminum powder can be given by
Kcomp ≈ Ksil(1 – fsil) + Kapfap,
where Ksil, Kap are the thermal conductivity coeffi
cients of silicone and aluminum powder, fsil, fap are the
volume fractions of silicone and aluminum powder in
the compound. To enhance the thermal conductivity
of compound, silicone content should be minimal.
For simplicity, let each fiber segment be of axial size
L1 and radial size L2. Time of thermal wave relaxation,
which characterizes the rate of temperature equaliza
tion throughout the coil volume, can be determined as
follows:
where K is the thermal conductivity coefficient of the
environment containing the silica core, protective
coating, and the compound. Therefore, with the con
stant cross section area S = L1 × L2, Tr can be reduced
if the difference between L1 and L2 is maximal (for the
improved quadrupole arrangement, L1 < L2). Thus,
dividing the coil into N coils using the central mem
brane in each coil gives 2N segments of coiled fiber,
then the rate of temperature equalization throughout
the coil volume is increased by 4N2
times, as the relax
ation time depends on cross section area. Then,
selecting L2 > L1 yields even higher rate of temperature
equalization. The stronger is this inequality, the higher
is the rate of temperature equalization.
Next, the optimal content of compound in the coil
volume should be determined. The thermal conduc
tivity of the environment depends on the fiber com
pound ratio. Then the following formula is true:
K ≈ Kf(1 – fcomp) + Kcompfcomp,
where fcomp is the compound content in the coil vol
ume. From the general considerations, minimum
content of compound in total volume is = 0.215.
Consider a fiber of some length coiled to form a
toroidal structure with rectangular cross section of
length L1 and width L2. It would seem that to increase
−
= π +r
2 1 2 2 2 2
1 2 1 2[ ] [ ( )],T K L L L L
fcomp
min
7
654321
Fig. 16. Draft of a FOG sensing coil with two support
forms. 1 – 1st coil form, 2 – 2nd coil form, 3 – copper
layer, 4 – coil fiber, 5 – layer of foamed polyurethane, 6 –
outer protective permalloy screen, 7 – outer protective
ring.

140
the thermal conductivity of environment, and there
fore, the relaxation time Tr, the content of compound
with a higher thermal conductivity coefficient should
be as great as possible. This, however, increases L1 and
L2, which extends Tr. In this case, the following con
dition for the compound content is optimal:
0.215 ≤ fcomp ≤ (Kcomp – 2Kf)/2(Kcomp – Kf).
Figure 17 shows how the optimal content of com
pound in the coil depends on the coefficient К. For
instance, with Kf = 0.11, Kcomp = 1.9 (silicone with alu
minum powder), the optimal content of compound
should be fcomp = 0.47.
A greater content of compound is not reasonable,
since it barely accelerates the temperature equalization,
but enlarges the interferometer, thus degrading the per
formance of FOG based navigation systems. On the
contrary, the smaller content of compound makes
sense, as the temperature equalization is scarcely decel
erated, but the interferometer is downsized.
DEAD BAND
Fiber optic gyros are known to be less sensitive to
low input rates. To improve their sensitivity, additional
phase modulation is used [22].
The dead band appearing even under phase modu
lation arises from the imperfections of optic and elec
tronic components. It is a so called residual dead
band, and hereinafter we’ll mean it when speaking of a
dead band.
The dead band can be caused by electrical cross
talk between the input rate signal and the modulation
voltage applied to the phase modulator [1]. Additional
electronic modulation proposed in [1] reduces the
dead band of our gyros tenfold. In FOGs with FRI
scale factor of 18.95 mrad/(deg/s) with additional
modulation applied, the average dead band is varying
from 0.3 to 0.5 deg/h and is not eliminated if the mod
ulation amplitude is further increased.
A spurious Michelson interferometer in the OIC
can also bring the dead band. The interferometer is
formed by back reflected beams in output channel
waveguides of Y junction divider within the OIC. Two
types of back reflections are observed here: throughout
the length of OIC waveguides and from the joints with
the fiber. To compensate the back reflections of the
second kind, the chip end, where the channel
waveguides are coupled with the fiber, is pitched
(skewed) with respect to the chip side surfaces. Then
the lengths of channel waveguides become different,
then the difference should exceed the coherence
length in the waveguides. Then, back reflections from
the joints bring no spurious effects. However, in our
opinion, the residual effect may be caused by the fol
lowing. The OIC chip is joined to the fiber with a
100 μm thick layer of adhesive with a refractive index
between the indices of the OIC and the fiber. In this
situation, the wave reflected from the adhesive surface
closer to the OIC at the joint of the longer waveguide
may become coherent with the wave reflected from the
adhesive surface further from the OIC at the joint of
the shorter waveguide. It should be also probably
remembered that the adhesive is a rather turbid envi
ronment with multiple scattering centers, which also
contribute to backscattering. Therefore, in the further
coarse estimation of the backscattering effect on the
dead band we won’t account for the SFS coherence.
Thus, in this case the effect of the spurious Michelson
interferometer is determined by the backscattering
factor Rb. Further, this mechanism is detailed.
The dead band caused by the Michelson interfer
ometer, with any amplitude of phase modulation Φm,
is given by:
P0sin ΦmsinΔΨdb = P0αRb(cosθm– sinΦmsinθm),
where ΔΨdb is the phase difference, which determines
the dead band, Rb is the backscattering factor in the
OIC, α is the losses in the coil fiber and in its joints
with the OIC waveguides, θm is the phase difference of
the Michelson interferometer beams. If θm varies from
0 to 2π rad during the reflection and propagation in
IOC waveguides, the dead band is calculated as fol
lows:
ΔΩdb = [λc/4πRL][4αRb]deg/h.
With α = 0.625, Φm = π/2 rad, FRI scale factor =
18.95 mrad/(deg/s), the dead band is 0.47 deg/h for
IOC backscattering factor Rb = –60 dB. Therefore, it
is assumed that the residual part of 0.47 deg/h dead
band is induced by the spurious Michelson interfer
ometer, if additional electronic modulation is used. To
achieve a nearly 0.001 deg/h dead band, the IOC
backscattering factor should be as high as about 87 dB,
which is barely possible in practice.
Several methods to suppress the dead band were pro
posed [23, 24]. It is a common practice to apply other
types of additional electronic modulation, which com
plicate the electronic data processing circuit.
45
50
30
25
20
15
10
5
0 5.04.03.02.01.00.5 4.53.52.51.5
40
35
Optimalcontentofcompound,%
Thermal conductivity, min/cm2
Fig. 17. Optimal content of compound in the coil.

To suppress the effect of electrical cross talk and
the spurious Michelson interferometer, we use the
phase modulation voltage of a specific waveform [25].
Figure 18a shows a candidate waveform, which sup
presses the dead band. If this kind of modulation is
used, no bias appears in the input signal frequency
even in the presence of the electrical cross talk and
spurious Michelson interferometer.
Figure 18 shows the generation of the open loop
gyro output with the amplitude zeroed at the output of
synchronous detector using a digital ramp (the first
feedback loop) (b), and the generation of varying half
wave voltage of IOC phase modulators (mismatch sig
nal) used to stabilize the gyro scale factor (the second
feedback loop) (c).
To provide the normal operation of a digital FOG
with two feedback loops using one PLD, phase modu
lation and digital ramp to compensate the Sagnac
phase shift are generated simultaneously. To suppress
the dead zone, the additional modulation voltage
should have time stable parameters. This can be
achieved if the peak to peak amplitude of the digital
ramp differs from 2π rad. Then additional exposure of
photodetector occurs with duration τ, equal to the coil
transit time. This pulse destabilizes the operation of
electronic unit for a rather long time.
Next, we focus on the measures suppressing this
spurious effect. The general formula for the radiation
power Pph at the photodetector is given by:
Pph=1/2 × P0{1 + cosΦmcosϕ ± sinΦmsinϕ},
where P0 is the radiation power of interfering beams
with account for FRI losses, Φm is the amplitude of
phase modulation, ϕ is the difference between the
Sagnac phase shift and the ramp induced phase shift
in normal compensation mode, or variation in the
phase difference during the reset. The peak to peak
amplitude of digital ramp, when there is no spurious
pulse, is as follows:
ϕpp = 2(π – Φm).
There is no spurious pulse, if the reset occurs dur
ing the negative half wave of the open loop gyro out
put as positive rate is measured, or during the positive
half wave as negative rate is measured. Another condi
tion is that
ϕpp = 2Φm,
then the reset should occur during the negative half
wave of the open loop gyro output as negative rate is
measured, or during the positive half wave as positive
rate is measured. With stable phase modulation ±π/2
and ±3π/2 rad preventing the spurious optical pulses
at the photodetector, the digital ramp should produce
a π rad phase difference during the reset. Then, with
consideration for the above mentioned, the ramp can
be reset at any time. The ramp with a π rad amplitude
is generated using a voltage with successively rising and
falling edges [20], but with π/2 rad voltage amplitude.
When the polarity of electrodes is inverted during min
imum or maximum ramp it is equivalent to a usual dig
ital ramp containing either rising or falling edges with
a π rad amplitude.
Figure 19 shows an output rate at near zero input
rates for a FOG using stable phase modulation with
3/4 and 5/4π rad amplitude and digital ramp with
peak to peak amplitude of π/2 rad.
In the experiment, the input rate was set within the
range ±0.25 deg/h by rotating the FOG sensitivity axis
in horizon plane with the required accuracy. In each
angular position, for 10 min the FOG output was
recorded and average rate was calculated and plotted
as squares. The dead band was additionally monitored
(a)
3π/2
π
π/2
π/2
–π/2
T
1
2
3
4
5
6
7
8
9
10 Δ~Φc
1 2 3 4 5 6 7 8 9 10
(b)
(c)
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9 10
Fig. 18. (a) Phase modulation. Upper curve – phase mod
ulation voltage applied to the electrodes of IOC phase
modulators, lower curve – phase difference between the
FRI beams, T – period of the open loop gyro output;
(b) generation of open loop gyro output; (c) generation of
mismatch signal.

142
using the noise psd at each measurement. In the pres
ence of dead band, there should be no noise in FOG
output, however, the experimental output revealed a
constant noise psd.
DEPTH OF ADDITIONAL
PHASE MODULATION
In the FOG under consideration, we use an auxil
iary phase modulation with a (π ± Δ) rad amplitude,
where Δ = π/2n
, n = 1, 2, 3, …. The amplitude of aux
iliary modulation is a critical factor in achieving the
gyro limiting characteristics. The analysis shows that
to reduce the noise [26], to suppress the spurious mis
match signal (scale factor instability) induced by spu
rious intensity modulation in the IOC [27], and to
reduce the bias caused by the variations in the constant
component of optical power at the photodetector, this
constant component should be decreased as much as
possible. FOG noise and errors, induced by spurious
intensity modulation in IOC and unstable optical
power at the photodetector, go down in proportion to
cot(Φì/2). Depending on FOG accuracy, auxiliary
phase modulation with amplitudes Φì = [(2n
± 1)/2n
] ×
π rad, where n = (1–4) is applied. For example, if Δ =
π/8 rad, the optical noise and the scale factor instabil
ity associated with spurious intensity modulation in
IOC channel waveguides can be improved by mini
mum 5 times.
CONCLUSIONS
The paper describes the methods for improving the
accuracy of fiber optic gyros. To achieve the enhanced
accuracy, the performance of optical components in the
gyro fiber ring interferometer is enhanced. Techniques
to extend the performance of erbium doped fibers,
along with new structures of radiation resistant optical
fibers for the sensing coil, polarizing optical fiber joined
to the gyro optical IC, and mounting fiber with
enhanced high order mode filtering, are detailed. Ways
to suppress the thermally induced bias using the opti
mized sensing coil are covered. A dead band suppres
sion approach using the phase modulation of interfer
ometer beams is proposed. FOG accuracy is also
improved through auxiliary phase modulation.
ACKNOWLEDGMENTS
We thank our colleagues O.K. Borisov, A.V. Sob
chakov, and N.N. Chanov for their participation in
experiments.
REFERENCES
1. Pavlath, G.A., Closed loop Fiber Optic Gyros, Proc.
SPIE, 1996. vol. 2837, pp. 46–60.
2. Wysocki,P.F.,Digonnet,M.J.F.,Kim,B.Y.,andShawH.J.,
Characteristics of Erbium Doped Superfluorescent Fiber
Sources for Interferometric Sensor Applications, J. Light
wave Technology, 1994. vol. LT 12, no. 1, ðp. 550–567.
3. Burns, W. K., Chin Lin, Ch., and Moeller, R., Fiber
Optic Gyroscopes with Broad Band Sources, J. Light
wave Technology, 1983, vol. LT 1, no. 1, ðp. 98–105.
4. Song, N., Zhang, Ch., and Du, X., Analysis of Vibra
tion Error in Fiber Optic Gyroscope, Proc. SPIE, 2002,
vol. 4920, pp. 115–121.
5. Noda, J., Okamoto, K., and Sasaki, Y., Polarization
Maintaining Fibers and Their Applications, J. Light
wave Technology, 1986, vol. LT 4, no. 8, ðp. 1071–
1089.
6. Kurbatov, A.M. and Kurbatov, R.A., New Optical W
Fiber Panda for Fiber Optic Gyroscope Sensitive Coil,
Technical Physics Letters, 2010, vol. 36, no. 9, pp. 789–
791.
7. Dangui, V., Kim. H., Digonnet, M., and Kino, G.,
Phase Sensitivity to Temperature of the Fundamental
Mode in Air Guiding Photonic Bandgap Fibers,
Optics Express, 2005, vol. 13, no. 18, pp. 6669–6684.
–0.10
–0.15
–0.05
0.25
0.20
0.15
0.10
0.05
0
1397431 2 1110865 12
–0.20
–0.25
Fig. 19. FOG output at low input rates. Output rates (deg/h) are plotted on the vertical axis, the numbers of angular position of
FOG sensitivity axis, corresponding to the input range ±0.25 deg/h (1 through 13) are plotted on the horizontal axis.

8. Andronova, I.A. and Malykin, G.B., Physical Issues of
Sagnac Fiber Optics, Uspekhi Fizicheskikh Nauk, 2002,
vol. 172, no. 8, pp. 849–873.
9. Kurbatov, A.M., Single Mode Optic Fiber for Polariz
ing Mode Filter, RF Patent 2040493, 1995.
10. Kurbatov, A.M. and Kurbatov, R.A., Fiber Polarizer
Based on W Lightguide Panda, Technical Physics Let
ters, 2011, vol. 37, no. 7, pp. 626–629.
11. Kurbatov, A.M. and Kurbatov, R.A., Suppression of
Polarization Errors in Fiber Ring Interferometer by
Polarizing Fibers, Technical Physics Letters, 2011,
vol. 37, no. 5, pp. 397–400.
12. Tomashuk, A.L., Golant, K.M., and Zabezhailov, M.O.,
Development of Optic Fibers for Application under
Increased Readiation,Volokonno Opticheskie Tekhnologii,
Materialy i Ustroistva, 2001, no. 4, pp. 52–65.
13. Girard, S., Keurinck, J., Boukenter, A., Meunier, J. P.,
Ouerdane, Y., Azas, B., Charre, P., and Vié, M.,
Gamma Rays and Pulsed X Ray Radiation Responses
of Nitrogen , Germanium Doped and Pure Silica
Core Optical Fibers, Nucl. Instr. and Methods of Physics
Research B, 2004, no. 215, pp. 187–195.
14. Dianov, E.M, Golant K.M., Khrapko, R.R.,
Mashinsky, V.M., Neustruev, V.B., Guryanov, A.N.,
Gusovsky, D.D., Miroshnichenko, S.I., and
Sazhin, O.D., Radiation Resistance of Optical Fibers
with Fluorine Doped Silica Cladding, Proc. SPIE,
1994, vol. 2425, pp. 58–62.
15. Mohr, F., Thermooptically Induced Bias Drift in Fiber
Optical Sagnac Interferometers, J. Lightwave Technol
ogy, 1996, vol. LT 14, no. 1, pp. 27–41.
16. Frigo, N.J., Compensation of Linear Sources of Non
reciprocity in Sagnac Interferometers, Proc. SPIE.
1983, vol. 412, pp. 268 271.
17. Malvern, A., Optical Fiber Gyroscope Sensing Coil
Having a Reduced Sensitivity to Temperature Varia
tions Occurring Therein, US Patent 5 465 150, 1995.
18. Sawyer, J., Ruffin, P., and Sung, C., Investigation of the
Effects of Temporal Thermal Gradients in Fiber Optic
Gyroscope Sensing Coils, Part 2, Opt. Eng., 1997,
vol. 36, p. 29.
19. Lykov, A.V., Teoriya Teploprovodnosti (Theory of Ther
mal Conductivity), Moscow: Vysshaya Shkola, 1967.
20. Kurbatov, A.M., A Method of Winding the Sensing Coil
of Fiber Optic Gyro, RF Patent 2295112, 2007.
21. Cordova, A., and Surabian, G., Potted Fiber Optic
Gyro Sensor Coil for Stringent Vibration and Thermal
Environments, US Patent 5 546 482, 1996.
22. Lefevre, H.C., Fundamentals of Interferometric Fiber
Optic Gyroscope, Proc. SPIE, 1996, vol. 2837, pp. 2 16.
23. Chung, J. Ch., Interferometric Fiber Optic Gyroscope
Dead Band Suppression, Applied Physics Express, 2008.
no. 7, p. 072501 1.
24. Sanders, D., Dankwort, R., Strandjort, L., and Bergh, R.,
Fiber Optic Gyroscope with Dead Band Error Reduc
tion, US Patent 5 999 304, 1999.
25. Kurbatov, À.Ì., Method of Sagnac Phase Difference
Compensation in Ring Interferometer of Fiber Optic
Gyro, RF Patent 2146807, 1998.
26. Pavlath, G.A., Method for Reducing Random Walk in
Fiber Optic Gyroscopes, US Patent 5 530 545, 1996.
27. Kurbatov, A.M., Method of Data Processing in Fiber
Optic Gyro, RF Patent 2160886, 1999.

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