Parameters optimizationofinterferometricfiberopticgyroscopefor

1、Parameters optimizationofinterferometricfiberopticgyroscopeforParameters optimization of interferometric ?ber optic gyroscope for improvement of random walk coef?cient degradation in space radiation environmentJing Jin n ,Song LinSchool of Instrument Science and Opto-electronics Engineering,BeiHang

2、University,Beijing 100191,Chinaa r t i c l e i n f oArticle history:Received 17April 2012Received in revised form 5June 2012Accepted 5June 2012Available online 29June 2012Keywords:Fiber optic gyroscope Radiation effectsRandom walk coef?cient Parameter optimizationa b s t r a c tA random walk coef?ci

3、ent (RWC)prediction model of interferometric ?ber optic gyroscope (IFOG)in radiation environment has been developed,combining a radiation-induced attenuation (RIA)model of ?ber and a RWC expression of digital closed-loop IFOG,and veri?ed by the radiation experiments results of two ?ber coils and an

4、experimental the RWC prediction model the effects of source power,?ber length and modulation phase on the RWC of IFOG were investigated in space radiation environments.Based on the prediction model and its parameters analysis,a parameters optimization method was proposed for IFOG design to improve t

5、he RWC degradation in space radiation environments.Finally,the three parameters of the experimental IFOG were redesigned according to the optimization method.&2012Elsevier Ltd.All rights reserved.1.IntroductionRecently,the space industry is increasingly showing a lot of interest in using IFOG becaus

6、e of their high performance,low weight,low power consumption and high reliability 13.However,during their stay in orbit,the IFOG components face a harsh radiative environment of various types.The most important effects of radiation on optical heads include the increase of ?ber attenuation and the fa

7、ll-off of source power and detector responsivity,which would cause RWC degradation and bias drift on IFOG 37.In-orbit calibration can compensate most of the long-term bias drift,but not improve the RWC performance 4,8,9.The RWC degradation must satisfy the requirement for application over the whole

8、mission time.Therefore,RWC prediction in space radiation environment,parameters margin design and vulnerable parts redundancy are indispensable measures to increase IFOG lifetime and reliability 3,4.The main idea of this paper is to propose a parameters optimization method for IFOG design in order t

9、o improve the radiation-induced RWC degradation of IFOG in space.A novel prediction model of RWC was developed to predict measure-ments at a given dose rate,and how the RWC of an IFOG might be affected by radiations at lower dose this prediction model,we analyzed the effects of source power,?ber len

10、gth and modulation phase on the RWC degradation in space radiationenvironment.Based on this analysis,a parameters optimization method was proposed for IFOG design to guarantee the RWC performance during whole space mission.2.RWC prediction modelThe most relevant noise sources affecting optoelectroni

11、c sys-tems performance may be listed as shot noise,source intensity noise,thermal noise in the detector load resistor and dark current noise in detector 10,11.To take an account of these noises,RWC of the digital closed-loop operational IFOG with square wave modulation can be expressed as 1,7,10RWC

12、?l c2p LD ?2e e1tcos f T2I esin f Tte1tcos f T2D v esin f Tt2el d eI sin f Tt4kTR eI sin f T,s e1Twhere k is the Boltzmann constant,T is the absolute temperature,e is the electron charge,D v is the source spectral bandwidth in the frequency domain,l is the wavelength of light,c is the light speed in

13、 vacuum,R is the detector load resistance,I d is the detector dark current,L is the length of ?ber coil,D is the diameter of ?ber coil,f is the modulation phase,and I is the detected photocurrent and can be expressed as I ?Z P o 10?A c teA i tA TL =10,e2Twhere P o is the source power coupled to the

14、optical circuit,Z is the responsivity of the detector,A is the radiation-inducedContents lists available at SciVerse ScienceDirectjournal homepage:Optics and Lasers in Engineering0143-8166/$-see front matter &2012Elsevier Ltd.All rights reserved.nCorresponding author.E-mail address:jinjing (J.Jin).O

15、ptics and Lasers in Engineering 50(2012)15421547attenuation (RIA)of ?ber coil in dB/km,A i is the initial ?ber coil loss in dB/km,and A c includes all the other optical circuit losses due to the ?ber couplers,IOC and splices.The RIA in a ?ber obeys a power law of radiation dose d and radiation dose

16、rate r 5,1214,A ?qr b d f,e3Twhere q ,b and f are constants,d is the radiation dose,and r is the radiation dose rate.By substituting Eqs.(2)and (3)into Eq.(1),a novel RWC prediction model (Eq.(4)can be developed,which describes the effect of IFOG parameters and radiation environ-ment parameters on R

17、WC.RWC ?el c =2p LD T?e2e e1tcos f TT=eZ P o 10?A c teA i tqr b d fTL =10esin f T2Tteee1tcos f T2T=D n esin f T2Ttq te2eI d T=eeZ P o 10?A c teA i tqr b d f TL =10sin f T2Tte4kT T=eR eZ P o 10?A c teA i tqrb d f TL =10sin f T2Te4TThe most signi?cant effect of radiation on RWC is an increase in ?ber

18、coil loss,and the other componentsparameters have no obvious effects on RWC,as in 4,7.Hence,RWC can be predicted by using Eq.(4)after obtaining the ?ber-radiation sensitive parameters f ,q ,and b ?tted to Eq.(3)and the radiation environ-ment parameters r ,d estimated according to orbital altitude,av

19、ailable irradiation time and equivalent aluminum spherical shielding thickness 4,12,15.Two polarization-maintaining (PM)?ber coils were exposed to a g -irradiation source to get the ?ber-radiation sensitive para-meters f ,q ,and b .In the experiment,dose rates were 0.1rad/s and 0.2rad/s,and total do

20、ses were 5krad and 10krad.The experi-mental setup is shown in Fig.1.The ?ber coils losses were ?tted using Eq.(3).The testing and ?tting results of ?ber coils loss are given in Fig.2.At the two dose rates,there is a good agreement between the experimental data and the ?tting results.The equation for

21、 the two curves ?t can be expressed as A ?0:004962r 0:117d0:883e5TAn experimental IFOG was also tested within the g -irradiation source at a dose rate of 0.2rad/s upto a total dose of 10krad.In allthe experiments,we used same kinds of PM ?bers with the absorption coef?cient of 0.6dB/km.The parameter

22、s of the experi-mental IFOG are listed in Table 1.Fig.3gives a comparison between model and experimental RWC for uniform irradiation conditions.With this model Eq.(4),it is possible to predict RWCFig.1.Irradiation test con?guration for two PM ?ber coils and an experimental IFOG.Fig.2.Measured,?tted

23、and extrapolated RIA in the experimental ?bers.Table 1Parameters of experimental IFOG.ParameterValue Z (A/W)0.9A i (dB/km)0.6L (m)535D (mm)60I d (nA)7f (rad)p /2P o (m W)800D v (Hz)6?1012l (nm)1310R (k O )800T (K)296f 0.883b 0.117q0.004962Fig.3.Experimental,modeled and extrapolated RWC of the experi

24、mental IFOG.J.Jin,S.Lin /Optics and Lasers in Engineering 50(2012)154215471543degradation with a precision greater than 4%for an irradiation of 10krad.From one dose rate to another,the model parameters do not vary,con?rming that the extrapolation for various dose rates is possible for ?ber RIA and I

25、FOG RWC,as shown in 12,1618.For a 20year geostationary orbit (GEO)mission,a basic shielding equivalent to 1mm thick Al sphere leads to a total dose of 14krad and a space dose rate of 2.22?10-5rad/s 16,17.These dose and dose rate were input in our two model equations.(3)and (4)with parameters listed

26、in Table 1for a space radiation environment simulation of the experimental IFOG.Extrapolation results of RIA and RWC are presented in Figs.2and 3.3.Analysis of parametersIn a typical IFOG,the shot noise and intensity noise terms are dominant.The most signi?cant expected effect of radiation is an inc

27、rease in shot noise due to a decrease in the transmission of ?ber coil resulting in less power on detector.Intensity noise is independent of source power and ?ber loss but depends on the spectral bandwidth of the source,which is unlikely to change enough to have a signi?cant impact on the intensity

28、noise.Known from Eq.(4),the IFOG RWE is mainly affected by parameters Z ,D v ,D ,l P o ,L ,and f ,in which the source power P o ,the coil length L and the modulation phase f are ?exible to be adjusted during the manufacture of the RWC prediction model Eq.(4)with the parameters in Table 1,we analyzed

29、 and simulated the effects of parameters P o ,L and f on RWC performance to propose a parameters optimization method for improvement of RWC degradation in space radiation environment.Fig.4and Table 2show the dependence of RWC on irradiation dose for ?ve values of source power.The dependence becomes

30、light with increasing source power.As shown in Eq.(4),the increase of RWC due to a growth in the RIA of ?ber can be counteracted by increasing source power.Hence,the RWC degra-dation caused by ?ber RIA can be easily compensated at system level by designing the IFOG with an appropriate source power m

31、argin.The relationship between RWC and radiation dose at ?ve modulation phases is illustrated in Fig.5.For the doses 06krad,624krad and 2428krad,the minimum RWC values appear at the modulation phases of 7p /8rad,6p /8rad and 5p /8rad,respec-tively.The optimal modulation phase minimizing the RWC is g

32、radually close to p /2rad with increasing radiation dose.In Eq.(4),for the modulation phase of p rad the shot noise and theintensity noise terms have the smallest contribution to RWC,and the dark current noise and the thermal noise terms have the smallest impact on RWC for the modulation phase of p

33、/2rad.Therefore,decreasing modulation phase towards p /2rad can minimize the RWC when the dark current noise and the thermal noise prevail over the other noise sources with the increase of ?ber RIA.RWC as a function of irradiation dose for ?ve ?ber coil lengths was simulated.The simulation results a

34、re displayed in Fig.6.For the doses 011krad,1116krad and 1628krad,the mini-mum RWC values appear at the ?ber lengths 2000m,1500mandFig.4.Modeled RWC as a function of radiation dose for ?ve source powers.Table 2Variation in RWC for ?ve source powers during irradiation.Source power (m w)Variation in R

35、WC (o /h 1/2)4000.010028000.0056416000.0032424000.0023632000.00188Fig.5.Modeled RWC as a function of radiation dose for ?ve modulationphases.Fig.6.Modeled RWC as a function of radiation dose for ?ve ?ber coil lengths.J.Jin,S.Lin /Optics and Lasers in Engineering 50(2012)1542154715441000m,respectivel

36、y.The optimal?ber length minimizing the RWC decreases with increasing radiation dose.As illustrated in Eq.(4),the RWC is not only dependent on the noise characteristic but also relevant to the scale factor l c=e2p LDT.The?ber length is inversely proportional to the scale factor,but directly propor-t

37、ional to the shot noise,the dark current noise and the thermal noise.Thereby,the optimal?ber length is shorter,when the three noise terms are dominant with the increase of?ber RIA.4.Parameters optimizationBased on the RWC prediction model and its parameters analysis mentioned in the above paragraphs

38、,an optimization method was developed for the?ber length,source power and modulation phase to improve the RWC degradation in this section.It is the parameters optimization criterion to minimize RWC value in the?nal stage of space mission.4.1.Analytic solution of optimal?ber coil lengthIn Eq.(4),the

39、shot noise related to the?ber coil length plays the most important role to affect the RWC in space radiation environment.To simplify the analysis,the RWC can approxi-mately be expressed,neglecting the intensity noise,the dark current noise and the thermal noise asRWC%l c2p LD?2ee1tcos jTZ P o10-?A c

40、teA itqr b d fTL =10esin fT2se6TAccording to Eq.(6),a new function of?ber coil length L is de?ned asFeLT?L10?A cteA itqr b d fTL =20e7TConsidering the?ber coil length as the only variable in Eq.(6), the RWC obtains a minimum when the value of the function F(L) is maximum.Therefore,the optimal?ber co

41、il length L op can be calculated bydFeLTeL opT?0e8Twhere the result can be presented asL op?8:68A itqr b de9TFor the?ber-radiation sensitive parameters in Table1and the GEO dose rate of2.22?10-5rad/s,the?ber coil losses and optimal ?ber coil lengths were computed by using Eqs.(3)and(9)at?ve radiatio

42、n doses.The results are presented in Table3.4.2.Numerical solution of optimal modulation phaseThe source powers in the range4003200m W,the modulation phases in the range0.4to0.9rad,the optimal?ber lengths and the other IFOG parameters from Table1were input in Eq.(4)for RWC numerical simulation.We ob

43、tained RWC values as a func-tion of the source power and the modulation phase for the GEO dose rate 2.22?10-5rad/s and the?ve doses:4krad,7krad, 14krad,28krad and56krad.The numerical results of RWC for the dose of14krad are presented in Fig.7.The optimal modula-tion phases,corresponding to the sourc

44、e powers of4003200m W, range from1.96to2.43rad at all the?ve doses,as shown in Table3.The RWC numerical simulation results indicate that the optimal modulation phase increases towards p rad with increas-ing source power,and the relationship between optimal modula-tion phase and source power is not d

45、ependent on the radiation dose when the optimal?ber lengths are input in Eq.(4)as simulation parameters.The optimal modulation phases for the ?ve source powers at the radiation doses056krad are listed in Table4.The dependence of optimal modulation phase on source power can be?t to a4order polynomial

46、 equation.(10)using20 source power values in the range from400to3200m W and its corresponding optimal modulation phases.The?tting curve is shown in Fig.8.fop?1:73t6:92?102P o3:46?105P2ot9:55?107P3o1:04?1010P4oe10T4.3.Parameters optimization methodBased on Eqs.(3),(4)and(9),a parameters optimization

47、method was proposed as shown in Fig.9.Max(RWC)is the maximum of RWC during the whole space mission time,and is required to meet the speci?cation for an application.RWC q is the required value of RWC for regular service of an IFOG.Table3Optimal coil lengths and modulation phases for?ve radiation dose

48、s.Radiation dose (Krad)Fiber coilloss(dB/km)Optimal coillength(km)Optimal modulation phase forsource power of4003200m W(rad)4 2.75 3.15 1.962.43 7 4.12 2.1 1.962.43 147.08 1.22 1.962.43 2812.560.69 1.962.43 5622.670.381.962.43Fig.7.Modeled RWC as a function of modulation phase and source power for a

49、 total dose of14krad.Table4Optimal modulation phases for?ve source powers atradiation doses of056krad.Source power(m w)Optimal modulationphase(rad)400 1.96800 2.121600 2.282400 2.363200 2.43J.Jin,S.Lin/Optics and Lasers in Engineering50(2012)154215471545Using the parameters optimization method illus

50、trated in Fig.9,the ?ber length,the modulation phase and the source power of the experimental IFOG were optimized where the space radiation dose rate and the total dose are 2.22?10-5rad/s and 28krad respectively,the initial source power is 800m W,the iterative increment of source power is 20m W and

51、other parameters are listed in Table 1.The optimal ?ber length calculated by using Eq.(9)is 0.69km.Assuming a RWC q of 0.005o /h 1/2,the optimal source power solved by the iterative method is 1020m W with a Max(RWC )of 0.00499o /h 1/ the optimal source power as input of Eq.(10),the optimal modulatio

52、n phase can be calculated,and its result is 2.16rad.The parameters optimization results of the experimental IFOG are listed inTable 5.The RWC extrapolation results for the optimal and unopti-mizable parameters are shown in Fig.10.5.ConclusionBased on an IFOG RWC expression and a comprehensive ?ber R

53、IA model,a novel IFOG RWC prediction model was this prediction model,we have demonstrated that it is possible to predict the degradation caused by radiation on IFOG RWC with at least 10%accuracy.The effects of the source power,the ?ber length and the modulation phase on IFOG RWC were simulated.The s

54、imulation results demonstrate that the depen-dence of RWC on irradiation dose decreases with increasing source power,and shortening ?ber length and decreasing mod-ulation phase towards p /2rad can minimize the RWC with the increase of ?ber RIA.A parameters optimization method to minimize RWC was pro

55、posed and veri?ed.The optimization results indicate that the optimal modulation phase increases towards p rad with increasing the source power;the relationship between optimal modulation phase and source power is not dependent on the radiation dose when the optimal ?ber lengths are input in the prediction model as simulation parameters.AcknowledgmentThis work was supported by the National Natural Science Foundation of China (Grant No.61007040).References1Lefevre HC.The Fiber-Optic Gyroscope.London:Artech House;1993pp.1541.Fig.8.Relationship be