Feasibility of a heterodyne all-fibreoptical gyroscope

I.P. Giles. Ph.D., C.Eng., M.I.E.E.

Indexing term: Optical fibres

Abstract: The paper discusses the feasibility of a novel heterodyne approach to the design of an all-fibre opticalgyroscope. The IF is produced by source frequency modulation which also serves to reduce the effective sourcecoherence. Such a technique offers distinct advantages in that the optical medium is completely passive, makingit ideal for an all-fibre approach.

1 Introduction

The all-fibre approach to the design of an optical-fibregyroscope has produced laboratory performance suitablefor inertial-grade systems. Limitations are imposed uponthis approach by the 'in-loop' modulator requirements,which generate the required phase modulation by physi-cally stretching the optical fibre. Active optical guides, rea-lisable in integrated optic form, provide a more practicalsolution to phase modulation, but inherent in the use ofsuch components is the optical guide mismatch. Integratedoptics components are more lossy than optical fibre, andhigh-quality single polarisation filters are difficult torealise. Incorporating integrated optic components reducesthe performance to that more applicable to rate gyroscopeapplications. An optical-fibre gyroscope without therequirement of an 'in-loop' modulator would have distinctadvantages and offer the potential of development into ahigh-quality inertial grade system.

This paper describes a heterodyne detection techniqueto measure the rotation-induced phase shift. Developmentof the interferometer leads to a passive optical path detec-tion method in which modulation is applied at the opticalsource and signal processing is performed electronically.Designed to retain the inherent reciprocity of the Sagnacinterferometer, the method is shown to have the potentialof similar sensitivity performance to other designapproaches. Two areas for discussion are raised in thepaper, which have not been completely addressed pre-viously: that of a coherent optical source and reciprocitymeasurements of the electronic processor. Even undersource modulation, the effective coherence length can onlybe reduced to the order of millimetres, giving effectiverotation errors of 10 degrees/h.

A two-channel electronic processor method is used, anda technique to reduce differential electronic drift isdescribed. Limitations to the phase matching stability ofthe electronics is imposed by the normal signal to noisecriteria in the homodyne system.

Conclusions from the discussion are that the all-fibreheterodyne optical gyroscope is a feasible technique withreservations that, for practical high-quality navigationalapplications, further coherent backscatter reduction tech-niques should be incorporated.

2 Initial concept

The concept of the heterodyne optical-fibre gyroscope, firstpublished in 1981 [1], was to overcome some of the funda-

Paper 4138J, (E13), first received 6th June and in revised form 18th July 1985The author is with the Department of Electronic and Electrical Engineering, Uni-versity of Strathclyde, Royal College Building, 204 George Street, Glasgow Gl1XW, United Kingdom

mental problems associated with the basic homodyneoptical-fibre Sagnac interferometer. Heterodyne detectionoffers immunity to baseband noise, insensitivity to sourceintensity fluctuations and possible improvement in signalto noise ratio. Previously suggested techniques [2] wereeither extremely lossy or introduced unacceptable nonreci-procity. This alternative approach was aimed at trans-ferring the rotation-induced optical phase shift to anelectronic phase shift which could be processed by stan-dard electronic techniques. The inherent common-moderejection (reciprocity) of the Sagnac interferometer wasmaintained in this system.

Detection of the rotation-induced phase shift is basedupon using common-path Mach-Zehnder interferometersto detect the phase shift in each direction (Fig. 1). The

D1

polariser

spatialfilter

mirror

BS1 BS2

f | BraggLJcell

BS3

fibre loop

D2Fig. 1 Bulk optics form of heterodyne gyroscope based on a Mach-Zehnder interferometer

Mach-Zehnder is between beamsplitters BS2 and BS3,consisting of a short (~10 cm) reference path with an80 MHz Bragg cell to produce the local oscillator signaland a long (~300 m) fibre sensing path. The laser outputis directed into both ends of the Mach-Zehnder by thebeamsplitter (BS1) and the mirror. Two detectors areplaced at the outputs (Dl, D2) and give an output currentat the IF (80 MHz from the Bragg cell), with a phase equalto the phase difference between the reference path and thefibre sensing path. Provided that the reference path isreciprocal (introduces an identical phase shift in eachdirection), then the phase difference between the two detec-tor outputs is proportional to the rotation rate. Thissystem is inherently reciprocal because the same opticalfrequency propagates in each direction through the sensingcoil, nonreciprocities can only be introduced between thebeamsplitters BS2 and BS3, and the phase information ineach direction is accessible.

Such a system was seen to be an alternative approach tothe standard homodyne detection techniques of the Sagnacinterferometer. Measurements on an experimental systembased on that in Fig. 1 indicated that rotation rate wassensed by the system, but further refinements were necess-ary, in common with the initial homodyne detection

IEE PROCEEDINGS, Vol. 132, Pt. J, No. 5, OCTOBER 1985 265

schemes, to realise and assess the full potential of thesystem. This paper discusses the necessary refinements tothe system, the limitations imposed by the detection tech-nique and possible areas in which such a system has dis-tinct advantages over the more conventional approaches.

3 Source coherence

The optical-fibre gyroscope is a closed-path interferometer,in that the two waves, combined at the detector, have tra-versed identical paths, but in opposite directions. Anyreflections or scatter from the media which is coherentwith the transmitted wave will produce a random error[3]. The waves transmitted in each direction experiencesimilar delay times, even under high rotation rates. Conse-quently, a low temporal coherence source can be used inthe system, which ensures a reduced phase error due tocoherent Rayleigh backscatter. The ideal source for anoptical-fibre gyroscope is a low temporal coherence, highspatial coherence source and many systems use a super-luminescent LED to produce the optical input.

Delay difference between the reference path and thesensing path in the heterodyne gyroscope dictates that along coherence laser source be used. Techniques to reducethe effective coherence of the source were incorporated [4,5] and are analogous to FMCW radar techniques. Thetechnique is fairly simple in concept (Fig. 2), in that the

time

upper

lower

time

Fig. 2 Frequency modulation of optical sourcesa Sawtooth optical frequency modulation indicating delayed (At) versionb Frequency difference between the delayed and undelayed signalsc Spectrum of b

input optical frequency to the Mach-Zehnder interferome-ter is modulated by a sawtooth function. The referencewave has effectively zero time delay and the sensing wave adelay (dependent upon the optical-fibre length); a differ-ence frequency then appears between the two mixed waves,proportional to the time delay. Reflections and scatter,having a different time delay to the transmitted wave,appear at different frequencies. The time delay has, by thismethod, been converted to a frequency shift which can befiltered to give the required output. The detector output isa line spectrum, spaced at a frequency equal to the inverseof the modulation repetition rate (1/T), with an envelope

centred at the difference frequency (A/) between the refer-ence and sensing wave

A/ = - (1)

when/m is the optical frequency deviation, At is the fibretime delay and T is the modulation repetition rate.

In the case of a continuous linear frequency sweep, thegradient of the output spectrum is a single frequency A/,and the coherent backscatter contribution is directly pro-portional to the detector bandwidth. For the practical situ-ation of a repetitive modulation, the coherent backscatternoise will appear at the same frequency as the signal witha level dependent upon the envelope overlap. Taking theideal case when the envelope is a (sin x/x) function, the3 dB points are considered to represent the coherentsection, then the effective coherence length of the sourcecan be shown [6] to be given by

3.8c(2)

Where c is the velocity of light and n is the refractive indexof the core.

To process the output, a single frequency is filtered byeach detector and the phases compared, the effectivecoherence time of the source is approximately the inverseof the maximum frequency deviation of the optical fre-quency. The detected frequency is determined by themodulation repetition rate and can be controlled veryaccurately by a crystal oscillator. Variations in sweep-frequency linearity, however, vary the shape of theenvelope, and consequently the amplitude of the detectedfrequency, but not the phase. Sweep nonlinearity is not adirect problem in detection, but indirectly can cause spec-trum broadening, consequently increasing coherent back-scatter contribution. Fig. 3 indicates the effective coherence

103r

10

I| i o " 2

10,-3

10,-4106 107 10* 109 1010 1011

frequency fm, Hz101 101

Fig. 3input

<£ = •

Effective coherent backscatter length for frequency modulated

3.8c

nfmn

length for varying frequency deviations in eqn. 2. The bulkoptics experimental system operated with a single modeHeNe (0.6328 /an) source which was modulated using aBragg cell [6]. Limitations introduced by spatial modula-tion effects reduced the frequency deviation to 10 MHz, aneffective coherence length of approximately 24 m. A morereasonable approach is to incorporate semiconductor laser

266 IEE PROCEEDINGS, Vol. 132, Pt. J, No. 5, OCTOBER 1985

sources which can be modulated up to frequency devi-ations of 100 GHz giving an effective coherence length of2.4 mm.

The interpretation of the coherence-length effect cannotbe made without investigating the phase errors introducedby the coherent Rayleigh backscatter from the centresection of fibre. The transmitted waves and backscatteradd in amplitude, and vectorial addition describes theeffect (Fig. 4). Rayleigh scatter has a uniform phase dis-tribution and Rayleigh distributed amplitude, which isinversely proportional to the fourth power of the wave-length. 'Worst-case' analysis [3] shows that the maximumphase error is given by

(3)

where PBS is the mean backscatter power from the coher-ent section and PT is the transmitted power.

Fig. 4 shows the worst-case phase error as a function ofcoherence length for several different wavelengths.

10

10'-3

2 .u T 1 0

o

*10"~5

tio"6t io

10'-7

10,-8

10' 10 10"2 10~3 10"* 10" 10'r 6

coherence length, mFig. 4 'Worst case' phase error introduced by coherent backscatterPhase error 4>e = jtx&Twavelength, /im

0.6.330.851.31.5

Rewriting eqn. 3 in terms of coherence length ££, scat-tering coefficient a and fibre trapping factor T

(h ^ (txJZ'T)112 (4)

An order of magnitude reduction in coherence lengthreduces the error by a factor of three and doubling thewavelength reduces the error by a factor of four. Incorpo-rating a long wavelength source with a large frequencymodulation reduces the worst-case phase error from thecoherent backscatter.

Semiconductor lasers offer the possibility of large fre-quency deviations with ease of modulation and compactsize. Typically, linewidths of single longitudinal modelasers are of the order of tens of MHz, which translates toa coherence length of tens of metres. This is shorter thanthe typical path imbalance of the Mach-Zehnder interfer-ometer. Although incorporating a Mach-Zehnder tomeasure the phase variations in each propagation direc-tion, the interferometer is still a Sagnac. Each of theoverall phase shifts for the two sensing waves is identical.The only restriction upon source coherence is that thephotodetector bandwidth is larger than the source line-width. In this situation, the detection process is morecomplex because it is essentially incoherent. To obtainmaximum benefit from the large frequency deviations

obtainable from a semiconductor source, coherenceenhancement techniques may need to be incorporated.

4 Reciprocity

Introducing a difference in frequency between the counter-propagating waves causes a nonreciprocity in the system.Initial considerations were to develop a heterodyne detec-tion technique which was fundamentally reciprocal.Employing frequency modulation techniques maintains thereciprocity [6] because identical frequency waves propa-gate in opposing directions at the same time. Other pos-sible breakdowns in reciprocity must also be considered.

The system is, in essence, a Sagnac interferometer andmust obey the simple minimum-reciprocity rules outlinedfor optical-fibre gyroscopes [7]. This involves detectionfrom the reciprocal port of the beamsplitters whichrequires two additional beamsplitters between BS1, BS2and BS1, BS3 (Fig. 1). This is indicated in the all-fibre form(Fig. 9) by couplers C4 and C5. Quite simply stated, thisensures that all beams have an identical number of trans-missions and reflections from a beamsplitter to avoid errorfrom beamsplitter transfer characteristics.

A single-mode filter is required at the input and outputports of the sensing interferometer [8]. This implies aspatial-mode filter and a polarisation filter at the inputand output of the Mach-Zehnder. Two physically differentmodal filters are required for the heterodyne gyroscope,and the effects on reciprocity must be examined.

The Mach-Zehnder interferometer divides a single waveand compares the phase difference after propagationthrough different paths. The only phase errors which canoccur are between the beam splitting and beam combining.This detection technique relies upon identical phase pathsin each direction through the reference path and thesensing path. Single-mode optical fibres ensure a singlespatial mode during propagation, and spatial filters (singlemode fibre) at the input and output ensure single-modelaunch/detection. In such a system, the reciprocity condi-tion is met in that there is only one spatial mode in eachdirection. Polarisation is a different case; although a singlepolarisation filter can be put at the input and output of theinterferometer, they will each define different polarisationmodes. The fibre is dual polarisation, and, as such, is atwo-moded system. Provided the input and output filtersare purely single mode, i.e. infinite extinction ratio polari-sers, then the system maintains reciprocity. This techniqueis then subject to the same nonideal polarisation filter non-reciprocities as the conventional detection techniques.

Other nonreciprocal effects occur in this type of system,in common with the conventional optical-fibre gyroscopessuch as Kerr effect, magnetic field and thermal gradientnonreciprocities. These can be overcome or reduced usingsimilar techniques.

5 Electronic processing

The phase comparison between the counter-propagatingwaves is not made optically, the phase information istransferred to a lower IF and processed electronicallybefore comparison. This electronic processing system ispart of the detection scheme, and, as such, is subject to thesame reciprocity conditions. The two electronic channelsmust track phase variations to better than the minimumdetectable phase shift, typically 10"7 rads for an inertialnagivation system. In a technique such as this, the elec-tronic reciprocity problem is a major aspect and has beenapproached at an early stage; it is also proving to be an

IEE PROCEEDINGS, Vol. 132, Pt. J, No. 5, OCTOBER 1985 267

important aspect in many other closed-loop optical-fibregyroscope systems.

Each of the detectors (Dl, D2) gives an output currentvarying at the intermediate frequency with a phase shiftdependent upon the optical propagation direction throughthe fibre. The required output information is the phase dif-ference between these two electronic signals. Each channelconsists of amplifiers, mixers, to down convert to a lowersecond IF, and filters and limiters (Fig. 5). Any variations

455 kHznarrowband

D1 limiter mixer filter limiter

poweramplifier

to Bragg \ l Mcell 2

D2

crystalcontrolledlocaloscillator

phasesensitivedetector

limiter mixer 455kHz limiternarrowbandfilter

Fig. 5 Two-channel electronic processing system

in IF or temperature fluctuations produce a phase fluctua-tion between the channels which appears as an error at theoutput. A single-channel detection system must be incor-porated to overcome any fluctuations in electronic phaseshift, and this can be carried out in two ways. Fig. 6 is aschematic diagram of the processing method.

Fig. 6 Electronic reciprocity

a Two-channel switchingb Single-channel switching

The output from the PIN diodes can be considered tobe described by an amplitude A, frequency co, and phase 0.The two outputs are

Ai cos (cot + 0J

A 2 cos (cot + 02)

(5)

(6)

and the required information is (0X — 02). Each of thechannels can be considered to change the amplitude of theinput by a gain factor G, and introduce a phase shift 0.The detector outputs are switched alternately betweenchannels 1 and 2. During the first period, the inputs to thephase sensitive detectors are

(7)

(8)

lctsc sensitive ucicenjis aic

port 1 GXAX cos (cot + 9X + 0X)

port 2 G2 A2 cos (cot + 92 + 02)

producing an output St = G1G2A1A2 cos [(0X — 62) +(0i — $2)]- During the next switching period

port 1 GXA2 cos (cot + 92 + 0 J (9)

port 2 G2 Ax cos (cot + 6X + cj>2) (10)

producing an output

S2 = G,G2AXA2 cos [(0, - 02) - (6, - 02)] (11)

Using a limiter before the phase sensitive detector (Fig. 5)has a twofold effect. First, the amplitude (GiG2A1A2) isimmune to variations in the signal level and gain factor.Secondly, a square-wave input to a mixer with a cosineresponse linearises the output, giving

S2 =

1 - 02) + (0t - 02)]

t - 02) - (9, - 02)]

(12)

(13)

The required output (0X — 02) is a square wave withperiodicity equal to the switching rate, and the unwantedelectronic phase shift appears as an offset of the squarewave (Fig. la).

0

(/3-ct)

0time

08-ty

(/9-e2)

0time

Fig. 7 Phase detector output square-wave with offset

a Two channelb Single channel

The method of Fig. 6b requires only a single channel,and the amplified outputs from the detector are comparedwith an oscillator at the same frequency. In this case, theoutput of the mixer for two square-wave inputs is shownin Fig. 1b.

During the first switching period, the output is

COS (0o ~ 01 - (14)

268

and the second period

Squaring the inputs to the mixer ensures that each of theamplitudes is the same and linearises the phase-outputresponse. The output is then a square wave at the switch-ing rate with amplitude equal to the optical phase differ-ence. A closed-loop technique can be incorporated tomaintain a zero phase offset from the electronic channels.

Introducing a fairly simple electronic switching tech-nique enables reciprocal operation of the electronic chan-nels, an experimental system exhibited noise levels below10 ~6 rad (this was the limit of the measurement system).

There are areas in this processor by which errors can beproduced, in particular, the isolation between the twochannels through the switch. A fraction of the signal fromone channel will contaminate the signal in the other. Eachof the signals in eqns. 7-10 will be slightly modified by a

IEE PROCEEDINGS, Vol. 132, Pt. J, No. 5, OCTOBER 1985

portion from the other channel and become

GXAX cos (cot cj)x) + 3GXA2 cos (cot + 62

G2 A2 cos (cot + 92 + cf)2) + SG2 Ax cos (cot + 6X + <£2)

where (5 <O describes the switch isolation.In this case, the mixer output will consist of cross terms

from each of the input waves. Considering the mixingprocess during each of the switching periods indicates thatthe additional terms affect the DC offset. Decreasing theisolation of the switch (i.e. increasing the value 3) has theeffect of reducing the amplitude of the detected squarewave. The sensitivity of the system is consequently reducedto the limit in which there is zero isolation (Ax = 3AZ) andno square wave is detected.

The only way in which a phase error can be introducedis to affect one signal and not the other, which may occurduring the limiting process, should the limiter produce anamplitude to phase modulation conversion. Careful designreduces this effect to within an acceptable level.

6 All-fibre system

Experimental measurements were taken using a bulk-optics configuration to assess the performance of the elec-tronic processing and the frequency modulation technique.A single mode HeNe laser (0.638 jum) was used and fre-quency modulated over 10 MHz deviation with an exter-nal Bragg cell modulator giving an anticipated effectivecoherence length of ~ 20 m. The sensing coil was 250 m inlength wound on a 30 cm diameter former.

Two main features of the bulk-optics system wereexpected to produce errors: the large coherent backscatterand nonreciprocity in the reference path. This path was afree-space path, and the detected output was highly sus-ceptible to beamsplitter variations. The results are shownin Fig. 8, indicating that the system remains stable over a

4s/divFig. 8 Results from bulk optics experimental rotation sensor indicatingdrift introduced by nonreciprocity

limited period (drifts can be assigned to misalignment ofthe optics) and the noise introduced by the electronics issubstantially less than the optical nonreciprocity. Short-term noise is of the order of 100 degrees/h in 1.25 Hzbandwidth.

An all-fibre version of the sensor is proposed, to over-come the optical nonreciprocities and to offer a systemwhich requires no 'in-loop' modulators and possibly givecertain advantages over other detection methods.

A semiconductor laser is the optical source which canbe modulated, through the bias current, with a sawtoothmodulation, to give between 10 and 100 GHz frequencydeviation.

Laser drift, induced by pulling effects from the radiationtravelling through the interferometer, can be avoided by

ensuring that the laser is switched 'on' for a period equiva-lent to the reference-path delay and 'off' during the returnperiod of the pulse [9]. The sensing path is matched suchthat the pulses are in phase with the reference path. Inaddition to eliminating the requirement for an isolator,this has the added benefit of reducing the optical Kerr-effect-induced nonreciprocity [10]. The entire interferome-ter can be constructed from fibre components (Fig. 9),

D2Fig. 9 Schematic diagram of all-fibre heterodyne rotation sensor

producing a low-loss system without the interface prob-lems associated with the hybrid integrated optics systemswhich require in-loop modulation. The differential delaybetween the reference and sensing paths produces the IF,which is electronically processed as described previously.Optical-fibre polarisers (P) are connected between C 4 , C2

and C 5 , C3 for modal filtering. These can be of thepolished-block type [11] or the differential-loss type [12].

In principle, this heterodyne method of rotation-induced phase offers an optically passive method ofproducing an optical-fibre gyroscope. It has distinctadvantages in that the propagation medium is constantand low-loss components can be constructed with very lowinsertion loss, so that high-quality polarisers can be rea-lised and no modulators are required in the optical path.

7 Performance and feasibility discussion

The proposed all-fibre approach to the heterodyne gyro-scope is certainly very attractive. Predicted componentcosts, however, indicate that the device would probablyhave to perform better than the present developmentsystem aimed at rate gyroscope applications. A practicaldemonstration of the all-fibre system is at present beingpursued, but it is possible to predict from the previous dis-cussion the possible sensitivity of such a system.

Minimum detectable phase difference between twowaves incident upon the detector is determined by therandom nature of the arrival of photons given by aPoisson distribution. The dynamic case is, to order ofmagnitude calculations, the same as the static case inwhich the random phase error is shown to be [13]

for an optical power of 100 /zW and wavelelength 1 fim.Sensitivity of the heterodyne system is, then, similar to

that of the conventional detection systems; however, twomajor areas contribute to large drift errors and these mustbe considered.

Coherent backscatter has always appeared to greatlylimit the potential of the heterodyne detection scheme.Calculations indicate that, even for high frequency devi-ations on the source modulation, an effective coherencelength of the order of millimetres produce effective rota-tion errors of ~ 10 degrees/h. Such levels are unacceptable.

IEE PROCEEDINGS, Vol. 132, Pt. J, No. 5, OCTOBER 1985 269

However, further work investigating the nature of thecoherent backscatter and its phase relationship with thetransmitted radiation indicates that appropriate modula-tion techniques may reduce the backscatter effects byseveral orders of magnitude [14].

The electronic processor is an area in which errors canoccur if careful design is not undertaken. The primarycause of errors is a phase introduced to one wave and notthe other. This only occurs in components through whichthe phase output is amplitude sensitive, such as the lim-iters. Providing these design considerations are met, thesensitivity limiting factor is imposed by the conventionalsignal to noise ratio performance of an RF homodynedetection system.

8 Conclusions

Development of the initial concept of a heterodyne methodto measure rotation-induced optical phase shift, has led tothe possibility of a detection scheme which does notrequire a modulator in the optical path. Distinct advan-tages are gained with the technique, in that an all-fibreapproach to the design can be envisaged with low loss, nomedium mismatch and high-quality optical components.

Sensitivity of detection is comparable with otheroptical-fibre interferometric rotation sensors, and the feasi-bility of this device in a practical system is dependent uponthe application. All-fibre technology is not, at present,applicable to the low-cost requirements of rate gyros. Theheterodyne technique is, therefore, more applicable tohigh-quality inertial-grade systems in which cost is notsuch a limiting factor. The high performance of the systemis limited by coherent backscatter and electronic drift.

In conclusion, this all-fibre heterodyne detection tech-nique is feasible for an optical-fibre gyroscope, but couldseek applications which require inertial grade systems.Two sources of high drift error are present and must bereduced before the full potential of the system can be rea-lised.

9 References

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2 THOMPSON, E., ANDERSON, D., YAO, S., and YOURNANS, B.:'Sagnac fiber-ring interferometer gyro, with electronic phase sensingusing a (GaAl)As laser', Appl. Phys. Lett., 1978, 33, (11), pp. 940-941

3 CUTLER, C.C, NEWTON, S.A., and SHAW, H.J.: 'Limitation ofrotation sensing by scattering', Opt. Lett., 1980, 5, pp. 488-490

4 CULSHAW, B., and GILES, I.P.: 'Frequency modulated heterodyneoptical fibre Sagnac interferometer', IEEE J. Quantum Electron., 1982,QE-18, (4), pp. 690-693

5 GILES, I.P., UTTAM, D., CULSHAW, B., and DA VIES, D.E.N.:'Coherent optical fibre sensors with modulated laser sources', Elec-tron. Lett., 1983, 19, (1), pp. 14-15

6 GILES, I.P.: 'Optical fibre gyroscope systems analysis leading to anovel technique to detection rotation induced optical phase shifts',Ph.D. Thesis, Department of Electronic and Electrical Engineering,University College London, 1983

7 EZEKIEL, S., and ARDITTY, H.J. (Eds): 'Fiber optic rotationsensor. Tutorial review', in 'Fiber optic rotation sensors and relatedtechnologies', Series in Optical Sciences, 32, (Springer-Verlag, 1981),pp. 2-26

8 ULRICH, R., and JOHNSON, M.: 'Fiber-ring interferometer: polari-sation analysis', Opt. Lett., 1979, 4, pp. 152-154

9 GILES, I.P., UTTAM, D , VICKERS, D., and CULSHAW, B.:'Coherent sources in optical fibre gyroscopes', Fibre Optics '84, SPIE468, 1984, pp. 160-166

10 BERGH, R.A., LEFEVRE, H.C., and SHAW, H.J.: 'Compensation ofthe optical Kerr effect in fiber-optic gyroscopes', Opt. Lett., 1982, 7,pp. 282-284

11 BERGH, R.A., DIGONNET, M.J.F., LEFEVRE, H.C., NEWTON,S.A., and SHAW, H.J.: 'Single mode fibre optic components', inEZEKIAL, S., and ARDITTY, H.J, (Eds.): 'Fiber optic rotationsensors and related technologies', Series in Optical Sciences, 32,(Springer Verlag, 1982), pp. 136-143

12 VARNHAM, M , and PAYNE, D.: 'Single polarisation operation inhigh birefringence bow tie fibres', Electron. Lett., 1983, 19, p. 246

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14 GILES, I.P, MACKINTOSH, J., MCMILLAN, J , and CULSHAW,B.: 'Coherence in optical fibre gyroscope', to be presented at Sympo-sium on Optical and electro-optical applied science and engineering,November 1985, Cannes

270 IEE PROCEEDINGS, Vol. 132, Pt. J, No. 5, OCTOBER 1985