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 morepopularity in precise navigation. FOGs outperformmechanical and ring laser gyros as regards their cost,dimensions, power consumption, etc. Kuznetsov Sci�entific Research Institute of Applied Mechanics isinvolved 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 andbetter accuracy, FOG optical components and dataprocessing algorithms should be refined.

All kinds of FOGs employ the same principles toprocess the data coming from the fiber ring interfer�ometer (FRI). These principles differ in the type anddegree of auxiliary phase modulation depending onthe gyro accuracy. FRIs of all types of FOGs have thesame optical scheme and, depending on the gyroaccuracy, different specific designs and sensing coiltechnologies, 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 toimperfections of FRI components and electronic cir�cuit. Degradation of gyro performance under varyingambient temperature, vibration, and radiation effectsalso 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 twofeedback loops. The first feedback loop maintains zerosignal at the output of synchronous detector by simul�taneously applying the digital ramp and electricalphase modulation signal to the electrodes of phasemodulators in the optical IC (OIC). It is done to com�pensate for Sagnac phase shift in the FRI. The secondfeedback loop keeps the amplitude of digital ramp atconstant level, which is required to stabilize the FOGscale factor. Figure 2 presents bias instability recordedfor 12 h (for a FOG with FRI scale factor of18.95 mrad/(deg/s).

The plot shows that bias instability was about0.1 deg/h in the first hour (which is the gyro readinesstime), 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 highaccuracy FOGs, erbium�doped superfluorescent fibersources (SFS’s) are employed [2]. Our team uses theSFS’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 anADC 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 presentedin Fig. 4.

Under temperatures of –40°C to +60°C, SFSpower consumption is max 4 W, and total opticalpower 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 GyrosA. 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 presentsthe 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 aredescribed 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 SFSspectrum (Fig. 4) presents a drawback, reducing theeffective emission bandwidth, and, hence, increasingdepolarization length in linearly birefringent fibers.Among other things, it can result in increased polar�ization error in the FRI, however, its contribution tothe 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

opticalcirculator

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 s10 s100 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 timeafter the cold start, and its accuracy after self�heatingof SFS pump diodes. Variations of SFS power outputwith time are shown in Fig. 5.

Figure 6 demonstrates the variations of SFS centralwavelength and emission bandwidth after the coldstart with constant ambient temperature.

Variations of central wavelength in the first hour arein rough agreement with the exponential law and donot exceed 90 ppm. It provides the scale factor stabilityof 0.009% with constant ambient temperature andcold start. During self�heating, the temperature of cas�ing is also varying under exponential law, therefore,thermal drift coefficient of SFS central wavelength canbe 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 wavelengthalmost 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 ashigh as 0.77 ppm/°C. However, it follows from theabove analysis that instability of SFS central wave�length, even with no thermal correction, is not likelyto extend the FOG readiness time.

Most probably, FOG readiness time is extended dueto variations of SFS power output at its cold start, sincethe period of SFS power output variations (Fig. 5) andFOG warm�up time nearly coincide. Figure 8 shows thetypical drift rate of a FOG with scale factor of18.95 mrad/(deg/s) for 8.5 h in steady�state mode.

Therefore, variations in photodetector temperatureand in SFS power output during self�heating affect theamplitude of the gyro open�loop gyro output.

The rate error is probably generated as follows. Dueto asymmetrical phase modulation parameters andimperfections of phase modulators in the OIC, aresidual 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 ofinterfering 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 ofopen�loop gyro output.

To improve the gyro accuracy, an additional elec�tronic circuit may be employed, which comprises asecond synchronous detector outputting a signal pro�portional to constant optical signal at the photodetec�tor. After the scaling, this signal can be used to stabilizethe amplitude of the open�loop gyro output. Thisprinciple provides stable bias and scale factor even

12.10

12.0612.0512.0412.0312.0212.0112.0011.99

806040200t, min

12.0912.0812.07

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 toself�heating of pump diodes).

1554.95

1554.90

1554.85

1554.80

1554.75

1554.70100806040200 120

Time, min

Cen

tral

wav

elen

gth

, n

m

40.10

40.05

40.00

39.95

39.80

39.75100806040200 120

Time, min

Em

issi

on

ban

dw

idth

, n

m

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 ofelectronic circuit. The intensity of optical signal canbe influenced by vibration, acoustic noise, degradingemission from optical components, and variations inambient temperature. Using an additional electronicchannel 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 fiberis optically isotropic. Majority of available outputoptical 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

1554.31951351006040200 15514512080 165 175 185

Time, min

Cen

tral

wav

elen

gth

,nm

Fig. 7. Variations of SFS central wavelength. For the first 130 min, the central wavelength is changing due to self�heating of pumpdiodes 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

13.1813.1613.1413.12

13.0813.10

8543210 6 7

13.2213.20

37.5537.5037.4537.4037.3537.3037.2537.20

Time, min

1

2

An

gula

r ra

te,

deg

/h

Tem

per

atu

re, °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

5PZ

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 FRIemploys the fibers with the same MFD (except for thefiber of sensing coil).

Fiber of the Sensing Coil

A single�mode fiber Panda characterized by highlinear birefringence is employed in the sensing coil.The birefringence is induced by mechanical stressesgenerated by the stress applying circular rods [5].

The fiber of the sensing coil should feature lowlosses of optical power and low bending losses; itslosses and polarization mode coupling (h) should beweakly dependent on the fiber axial twist. To reducethe 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 fiberwith a W�profile refractive index [6] meets all theserequirements. 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, MFDis (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 thefiber performance (decrease h and depolarizationlength, and reduce the effect of magnetic filed onFOG 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 bedescribed further [7]. However, these fibers could notprovide the desired FOG accuracy due to enhancedRayleigh scattering. Therefore, W�profile Panda fibersare a candidate solution that can improve the FOGparameters.

Polarizing Fiber for Coupling with Optical IC

Use of a polarizing fiber (PZ fiber) at OIC inputreduces the polarizing error in angular rate, which isthe key factor degrading the FRI performance [3, 8].Our team uses segments of PZ fibers 0.5–1.0 m longwith polarization extinction ratio (attenuation ofeither polarization state) of min 30 dB and losses in60 mm�diameter rings of min 0.2 dB [9, 10]. Apartfrom reducing the polarization errors, PZ fiber at OICinput 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 afiber 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 isabout 1.8 μ, the cutoff of the fundamental x�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

25.0 db/D RES: 2.000 nm SENS: MID AVG: 10 SMPL: 1001 (AUTO)

43

2

1

3

4

1300.000 nm 1500.000 nm 40.00 1700.00 nmnm/d

1L1: 1550.0000 nmL2: 1300.0000 nmL3: –66.92 dBmL4: –71.80 dBmL2–L1: –250.0000 nmL4–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 coiledfiber. 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 higherx�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 PZfibers both at OIC input (a fiber with 6–8 μm MFD)and in the sensing coil [11]. It is commonly supposedthat using PZ fibers in the sensing coil is not rational[8]. However, the mathematical simulation suggeststhat PZ fibers in the sensing coil in combination withPZ fibers at OIC input greatly reduce the polarizationerror, 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 ofinput PZ fiber. If the polarization extinction ratio ofthe input PZ fiber is from –30 to –60 dB and of PZfiber in the coil is about 1 dB/m, FOG bias instability,associated with polarization errors, can be decreaseddown to 10–3−10–6 deg/h.

Mounting Fiber

An isotropic fiber with W�profile refractive index isused as a mounting fiber. It should exhibit low trans�mission losses with small bending radii and serve as ahigher�order�mode filter in addition to a segment ofPZ fiber [9]. Figure 12 shows the attenuation of firsthigher mode in a straight fiber SMF�28, in a straightand bent mounting fiber with bending radius of 40 mmand MFD = 10.0 μm. Transmission losses in themounting fiber are within 0.25 dB/km and max0.1 dB/m at 40 mm bending radius.

The plots demonstrate accessible bending lossesand good filtering performance of the mounting fiber,which improves the gyro accuracy. Use of a mountingfiber with MFD of 6.0–8.0 μm instead of 10.0 μm

�

critically reduces the bending losses and enhances thefiltering performance.

Radiation Resistance of Sensing Coil Fiber

Radiation resistance required for space applica�tions can be provided by W�profile fibers with fluoridereflective cladding and undoped pure silica core, or byconventional two�layer fibers with nitrogen�dopedcore [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 thefirst kind, and nitrogen�doped core fibers show a goodradiation response under the second kind [13]. Nitro�gen�doped core fibers exhibit acceptable attenuationlevels under steady�state radiation as well. Therefore,we consider these fibers to be a promising candidatefor use in space FOG applications.

However, the nitrogen�doped core fibers exhibitthe peak of material losses at the wavelength of1.505 μm. Due to the finite spectral width of this peak,it is partly expanded to operating wavelength of1.55 μm. To solve the problem, concentration ofnitrogen in the core should be reduced, which pro�vides improved resistance under steady�state radiationwhile maintaining the required pulsed radiationresponse. In a W�profile fiber [6], a germanate�dopedcore should replaced with a nitrogen�doped one. Fi�gure 13 shows a cross�section of an isotropic W�profilefiber with nitrogen�doped core and fluoride reflectivecladding from Panda fiber preform). Figure 14 pre�sents the spectral losses of this fiber.

A preform for Panda fiber with a nitrogen�dopedcore was manufactured by Faberus JSC, Moscow.From Fig. 14, the losses were 5 dB/km with 1.505 μmwavelength. As to the losses with 1.55 μm wavelength,they did not exceed 1.0 dB/km with SFS excitationusing broadband radiation, despite the peak lossesmentioned above.

The W�profile nitrogen�doped core fiber has a corediameter 2ρ = 8.2 μm, cutoff wavelength λс = 1.36 μm,and MFD = 7.2 μm. The last parameter is in goodagreement with radiation parameters in OIC channelwaveguides. These preforms are suitable for making

300

250

200

150

100

50

01.50 1.584.481.461.441.421.40 1.52 1.54 1.56

straight fiber SMF�28straight W�profile fiberbent W�profile fiber

Wavelength, μm

Att

enu

atio

n o

f th

e fi

rst

hig

her

mo

de,

dB

/m

Fig. 12. Attenuation of the first higher mode in straightsegments of fiber SMF�28 and mounting fiber, and in bentmounting fiber (bending radius is 40 mm). The cutoffwavelength 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 radiationresistant fibers for FOG sensing coils.

To the authors’ opinion, other promising fibersexhibiting good radiation response and low propaga�tion losses (due to the absence of core dopants) arePM and PZ Panda fibers with pure silica cores. Therefractive index profile of the preform cross�section isgiven 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 theprofile. 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�cladstructure 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 silicacore and single broad fluoride�doped cladding as detailedin [14]. Also, the structure with two fluoride claddingsoffers 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 isthat the gyro output is sensitive to varying ambienttemperature, vibration and acoustic noise. The bias iscaused by nonreciprocal phase difference between theinterferometer waves. In the general case, this phasedifference can be presented as follows [15]:

where D is the diameter of the sensing coil, L is thefiber length, n0 is the refractive index of sensing coilfiber, Δn(z, t) is the variation in refractive index of coilfiber in point z at time t, with the dot above denoting

( ) ( )0

0

( ) , 2 ,

L

nt n z t L z dz

LDΔΩ = Δ −∫ �

the time derivative. To compensate the nonreciprocalphase difference in a FRI, a special coiling schemeshould be used, where the parts of fiber equidistantfrom the center are arranged back�to�back, i.e., in thesame conditions. Therefore, the fiber should be woundon the coil in succession from two technologicalspools, each carrying a half fiber length. A dipole anda quadrupole arrangements are known [15, 16]. Out ofthese two, the latter is more effective [15]. However, anarrangement proposed in [17], hereinafter called theimproved quadrupole arrangement, is the most prom�ising. The table summarizes the calculated biases forquadrupole and improved quadrupole arrangements.

However, the quadrupole arrangement is reportedto exhibit bias with axial heating as well [18].

SENSING COIL DESIGN

These special coiling schemes minimize the FOGbias, but are not able to eliminate it completely. There�fore, additional measures are taken, namely, reducingthe rate of coil temperature change using the improvedpackaging of the sensing coil, and quick temperatureequalization throughout its volume. A draft of a coilreflecting 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 thelocal 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 nmL2: 1505.0000 nmL3: –63.44 dBmL4: –65.03 dBmL2–L1: –45.5000 nmL4–L3: –1.59 dB

Fig. 14. Spectral losses in a nitrogen�doped core fiber 1 mlong (curve 1) and 1100 m long (curve 2). The horizontalaxis is the wavelength (nm) with the division value of60 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 Pandapreform.

Table

ArrangementBias 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 highthermal conductivity [19]:

k = l/cρ,where λ, ρ, and c are the thermal conduction, densityand heat capacity. Usually a permalloy shield is used,which simultaneously functions as a magnetic shield.

Next, the layer with low thermal conductivityarranged under the outer shield also serves as a shieldof the other kind: it prevents the thermal waves frompenetrating into the coil, thus reducing the rate oftemperature change throughout the coil volume. As asecond shield, a foamed polyurethane can beemployed, exhibiting low thermal conduction, highheat capacity, and rather high density.

The second shield is followed by a thin copperlayer, which equalizes the temperature throughout thecoil surface by symmetrizing the penetrating heatflows, similarly to the first permalloy shield. Under thecopper layer, the sensing coil is situated.

In using the quadrupole arrangement to minimizethe errors in angular rate, the coil size in axial direc�tion should be increased to accelerate the temperatureequalization in radial direction. This, however,requires a bigger interferometer. From this point ofview, the improved quadrupole arrangement offers afuller use of the coil volume along with reduced ther�mal sensitivity. Since the improved quadrupolearrangement brings no errors under destabilizing fac�tors in radial direction and small errors under destabi�lizing factors in axial direction, the coil may have abigger radial and a smaller axial size. The minimumcoiling diameter is about 25 mm, and therefore, thecoil volume can be effectively used.

Dividing the coil into several coils [20] decreasesthe number of winding layers in each coil, whichimproves the winding quality. The impregnation com�pound applied to the fiber during the coiling shouldhave a low thermal conductivity coefficient and lowadhesion to the fiber protective coating. Low adhesionto the fiber coating and form materials is necessary foreffective suppression of mechanical waves excited byexternal destabilizing factors. In addition, low adhe�sion of the compound makes the fiber refractive indexless dependent on its length under varying tempera�ture. As a thermal conductive compound, silicon withhigh content of aluminum powder can be used, withthe powder increasing the thermal conductivity coeffi�cient and its Young’s modulus. Rather high Young’smodulus enhances the gyro vibration resistance [21].

The volume of the sensing coil is a multicomponentenvironment containing a silica core, polymeric pro�tective coating, and a compound, which can be multi�component as well. The fiber coefficient of thermalconductivity 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 arethe 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 thevolume fractions of silicone and aluminum powder inthe compound. To enhance the thermal conductivityof compound, silicone content should be minimal.

For simplicity, let each fiber segment be of axial sizeL1 and radial size L2. Time of thermal wave relaxation,which characterizes the rate of temperature equaliza�tion throughout the coil volume, can be determined asfollows:

where K is the thermal conductivity coefficient of theenvironment containing the silica core, protectivecoating, and the compound. Therefore, with the con�stant cross�section area S = L1 × L2, Tr can be reducedif the difference between L1 and L2 is maximal (for theimproved 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 throughoutthe 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 temperatureequalization. The stronger is this inequality, the higheris the rate of temperature equalization.

Next, the optimal content of compound in the coilvolume 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 atoroidal structure with rectangular cross�section oflength L1 and width L2. It would seem that to increase

−

= π +r2 1 2 2 2 2

1 2 1 2[ ] [ ( )],T K L L L L

fcompmin

7

654321

Fig. 16. Draft of a FOG sensing coil with two supportforms. 1 – 1st coil form, 2 – 2nd coil form, 3 – copperlayer, 4 – coil fiber, 5 – layer of foamed polyurethane, 6 –outer protective permalloy screen, 7 – outer protectivering.

140



the thermal conductivity of environment, and there�fore, the relaxation time Tr, the content of compoundwith a higher thermal conductivity coefficient shouldbe as great as possible. This, however, increases L1 andL2, 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. Forinstance, with Kf = 0.11, Kcomp = 1.9 (silicone with alu�minum powder), the optimal content of compoundshould 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 thecontrary, the smaller content of compound makessense, as the temperature equalization is scarcely decel�erated, but the interferometer is downsized.

DEAD BAND

Fiber�optic gyros are known to be less sensitive tolow input rates. To improve their sensitivity, additionalphase 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 deadband, and hereinafter we’ll mean it when speaking of adead band.

The dead band can be caused by electrical cross�talk between the input rate signal and the modulationvoltage applied to the phase modulator [1]. Additionalelectronic modulation proposed in [1] reduces thedead band of our gyros tenfold. In FOGs with FRIscale factor of 18.95 mrad/(deg/s) with additionalmodulation applied, the average dead band is varyingfrom 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 OICcan also bring the dead band. The interferometer isformed by back reflected beams in output channelwaveguides of Y�junction divider within the OIC. Twotypes of back reflections are observed here: throughoutthe length of OIC waveguides and from the joints withthe fiber. To compensate the back reflections of thesecond kind, the chip end, where the channelwaveguides are coupled with the fiber, is pitched(skewed) with respect to the chip side surfaces. Thenthe lengths of channel waveguides become different,then the difference should exceed the coherencelength in the waveguides. Then, back reflections fromthe joints bring no spurious effects. However, in ouropinion, the residual effect may be caused by the fol�lowing. The OIC chip is joined to the fiber with a100 μm thick layer of adhesive with a refractive indexbetween the indices of the OIC and the fiber. In thissituation, the wave reflected from the adhesive surfacecloser to the OIC at the joint of the longer waveguidemay become coherent with the wave reflected from theadhesive surface further from the OIC at the joint ofthe shorter waveguide. It should be also probablyremembered that the adhesive is a rather turbid envi�ronment with multiple scattering centers, which alsocontribute to backscattering. Therefore, in the furthercoarse estimation of the backscattering effect on thedead band we won’t account for the SFS coherence.Thus, in this case the effect of the spurious Michelsoninterferometer is determined by the backscatteringfactor 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 determinesthe dead band, Rb is the backscattering factor in theOIC, α is the losses in the coil fiber and in its jointswith the OIC waveguides, θm is the phase difference ofthe Michelson interferometer beams. If θm varies from0 to 2π rad during the reflection and propagation inIOC 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 forIOC backscattering factor Rb = –60 dB. Therefore, itis assumed that the residual part of 0.47 deg/h deadband is induced by the spurious Michelson interfer�ometer, if additional electronic modulation is used. Toachieve a nearly 0.001 deg/h dead band, the IOCbackscattering 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 othertypes of additional electronic modulation, which com�plicate the electronic data processing circuit.

4550

3025201510

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4035

Op

tim

al c

on

ten

t o

f co

mp

ou

nd

, %

Thermal conductivity, min/cm2

Fig. 17. Optimal content of compound in the coil.



To suppress the effect of electrical cross�talk andthe spurious Michelson interferometer, we use thephase modulation voltage of a specific waveform [25].Figure 18a shows a candidate waveform, which sup�presses the dead band. If this kind of modulation isused, no bias appears in the input signal frequencyeven in the presence of the electrical cross�talk andspurious Michelson interferometer.

Figure 18 shows the generation of the open�loopgyro output with the amplitude zeroed at the output ofsynchronous detector using a digital ramp (the firstfeedback 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 secondfeedback loop) (c).

To provide the normal operation of a digital FOGwith two feedback loops using one PLD, phase modu�lation and digital ramp to compensate the Sagnacphase shift are generated simultaneously. To suppressthe dead zone, the additional modulation voltageshould have time�stable parameters. This can beachieved if the peak�to�peak amplitude of the digitalramp differs from 2π rad. Then additional exposure ofphotodetector occurs with duration τ, equal to the coiltransit time. This pulse destabilizes the operation ofelectronic unit for a rather long time.

Next, we focus on the measures suppressing thisspurious effect. The general formula for the radiationpower Pph at the photodetector is given by:

Pph=1/2 × P0{1 + cosΦmcosϕ ± sinΦmsinϕ},where P0 is the radiation power of interfering beamswith account for FRI losses, Φm is the amplitude ofphase modulation, ϕ is the difference between theSagnac phase shift and the ramp�induced phase shiftin normal compensation mode, or variation in thephase difference during the reset. The peak�to�peakamplitude of digital ramp, when there is no spuriouspulse, 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 positivehalf 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 ismeasured, or during the positive half wave as positiverate is measured. With stable phase modulation ±π/2and ±3π/2 rad preventing the spurious optical pulsesat the photodetector, the digital ramp should producea π rad phase difference during the reset. Then, withconsideration for the above�mentioned, the ramp canbe reset at any time. The ramp with a π rad amplitudeis generated using a voltage with successively rising andfalling 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 witha π rad amplitude.

Figure 19 shows an output rate at near�zero inputrates for a FOG using stable phase modulation with3/4 and 5/4π rad amplitude and digital ramp withpeak�to�peak amplitude of π/2 rad.

In the experiment, the input rate was set within therange ±0.25 deg/h by rotating the FOG sensitivity axisin horizon plane with the required accuracy. In eachangular position, for 10 min the FOG output wasrecorded and average rate was calculated and plottedas squares. The dead band was additionally monitored

(a)

3π/2π

π/2

π/2

–π/2

T

12

34

56

78

910 Δ~Φc

1 2 3 4 5 6 7 8 9 10

(b)

(c)

12

34

56

78

910

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 phasemodulators, lower curve – phase difference between theFRI beams, T – period of the open�loop gyro output;(b) generation of open�loop gyro output; (c) generation ofmismatch signal.

142



using the noise psd at each measurement. In the pres�ence of dead band, there should be no noise in FOGoutput, however, the experimental output revealed aconstant noise psd.

DEPTH OF ADDITIONALPHASE 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 thegyro limiting characteristics. The analysis shows thatto 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 toreduce the bias caused by the variations in the constantcomponent of optical power at the photodetector, thisconstant component should be decreased as much aspossible. FOG noise and errors, induced by spuriousintensity modulation in IOC and unstable opticalpower at the photodetector, go down in proportion tocot(Φì/2). Depending on FOG accuracy, auxiliaryphase 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 inIOC channel waveguides can be improved by mini�mum 5 times.

CONCLUSIONS

The paper describes the methods for improving theaccuracy of fiber�optic gyros. To achieve the enhancedaccuracy, the performance of optical components in thegyro fiber ring interferometer is enhanced. Techniquesto extend the performance of erbium�doped fibers,along with new structures of radiation resistant opticalfibers for the sensing coil, polarizing optical fiber joined

to the gyro optical IC, and mounting fiber withenhanced high�order�mode filtering, are detailed. Waysto 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 alsoimproved through auxiliary phase modulation.

ACKNOWLEDGMENTS

We thank our colleagues O.K. Borisov, A.V. Sob�chakov, and N.N. Chanov for their participation inexperiments.

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., and Shaw H.J.,Characteristics of Erbium�Doped Superfluorescent FiberSources 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 FundamentalMode 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

01397431 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 ofFOG 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 ofSagnac 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 PolarizerBased 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 ofPolarization Errors in Fiber Ring Interferometer byPolarizing 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 underIncreased 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 Responsesof Nitrogen�, Germanium�Doped and Pure Silica�Core Optical Fibers, Nucl. Instr. and Methods of PhysicsResearch 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., andSazhin, O.D., Radiation Resistance of Optical Fiberswith Fluorine�Doped Silica Cladding, Proc. SPIE,1994, vol. 2425, pp. 58–62.

15. Mohr, F., Thermooptically Induced Bias Drift in FiberOptical 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 CoilHaving 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 theEffects of Temporal Thermal Gradients in Fiber OpticGyroscope 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 Coilof Fiber Optic Gyro, RF Patent 2295112, 2007.

21. Cordova, A., and Surabian, G., Potted Fiber OpticGyro Sensor Coil for Stringent Vibration and ThermalEnvironments, US Patent 5 546 482, 1996.

22. Lefevre, H.C., Fundamentals of Interferometric FiberOptic Gyroscope, Proc. SPIE, 1996, vol. 2837, pp. 2�16.

23. Chung, J.�Ch., Interferometric Fiber Optic GyroscopeDead 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 DifferenceCompensation in Ring Interferometer of Fiber OpticGyro, RF Patent 2146807, 1998.

26. Pavlath, G.A., Method for Reducing Random Walk inFiber Optic Gyroscopes, US Patent 5 530 545, 1996.

27. Kurbatov, A.M., Method of Data Processing in FiberOptic Gyro, RF Patent 2160886, 1999.

Methods of improving the accuracy of fiber optic gyros

Engineering

Transcript of Methods of improving the accuracy of fiber optic gyros