Prototype of interferometric absolute motion sensor

Prototype

of

interferometric

absolute

motion

sensor

C.

Collette

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_F.

_Nassif

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_J.

_Amar

_,

_C.

_Depouhon

_,

_S.-P.

_Gorza

a_{UniversitéLibredeBruxelles,BEAMSDepartment,F.D.Roosevelt50,B-1050Brussels,Belgium} b_{UniversitéLibredeBruxelles,OPERADepartment,F.D.Roosevelt50,B-1050Brussels,Belgium}

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Articlehistory:

Received4November2014

Receivedinrevisedform20January2015 Accepted20January2015

Availableonline29January2015 Keywords: Inertialsensor Accelerometer Seismometer Geophone

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Formanyapplications,thereisanincreasingdemandforlowcost,highresolutioninertialsensors,which arecapableofoperatinginharshenvironments.Basedonrecentdevelopmentsinopticalseismometry, thispaperpresentsanewsmallinterferometricinertialsensorwitharesolutionof3pm/√Hzabove 4Hz.Comparedtomoststate-of-the-artdevices,thisprototypedoesnotcontainanycoil,whichoffers severalimportantadvantages:(i)whenitisusedforactivecontrol,itmagnifiesthecontrolperformances aroundthesensorresonance;(ii)itdecreasesthethermalnoiseinthesuspension(Brownianmotion), (iii)itiscompatiblewithmagneticenvironments(likeparticlecollider);(iv)astheinterferencefringes sweepcontinuouslyacrossthedetector,itallowsarealtimecalibrationoftheparameters,andthusthe calibrationcanbecontinuousmonitoredandupdated.

©2015ElsevierB.V.Allrightsreserved.

1. Introduction

Inertialsensorshavebeenusedformorethanacenturymainly toanswertheneedsofseismology,thesciencewhichstudiesthe propagationof wavesthroughtheEarth.Depending onthe fre-quencyrange of interest,three types of sensorsare commonly usedtomeasureseismicvibrations[1]:seismicaccelerometers, geophonesandbroadbandseismometers.Acomparisonofthese inertialsensorscanbefoundin[2].

Formorethan30years,seismometershavereachedsufficient resolutionanddynamicrangetocaptureseismicsignalsatmost locationoftheEarthsurfaceinabroadfrequencyrange extend-ingtypicallyfrom1minto100Hz(seee.g.[3–6]).However,there isstillacontinuousdemandforhigh-endinstruments,more effi-cient and better adapted to some specific applications. In this respect,recentdevelopmentsinopticaltechnologiesoffer interest-ingperspectivesfornovelinertialsensors.Intheoil/gasandmining industryforinstance,inertialsensorscapableofoperatinginharsh environments(e.g.down-holes,boreholes)areneeded,andoptical seismometerswithoutelectronicsandinsensitivetotemperature and highpressure [7–10]have been developed. In thefield of security,miniatureautonomousopticalinertialsensorshavebeen testedforthedetectionofdetonationarisingfromnucleartests conductedbycountriesengagedinnuclearproliferation[11–13].

∗ Correspondingauthor.Tel.:+3226502840.

E-mailaddress:christophe.collette@ulb.ac.be(C.Collette).

Besidesseismologyandtheaforementionedapplications,there is also a demand for inertial sensors for precision engineering and scientific experimentsrequiring a very stable environment [14]. Typical applications are: (i) Tests and validation of space equipments on vibration-free space simulator. (ii) Isolation of lithographymachinesinthesemiconductorindustry.(iii) Reduc-tionofvibrationsofatomicforcemicroscopes(supportandsample) forincreasingtheirresolution.(iv)Stabilizationand isolationof large instruments dedicated to extreme experimental physics, likegravitationalwaveinterferometricdetectorsorfutureparticle colliders.Inthesesystemstheimmunitytoenvironmental distur-bancesisobtainedbyactivelycancellingthestructuralvibration measuredbyinertialsensors[15].

A few other prototypes of optical inertial sensors and seis-mometers have been developed and reported in theliterature. Theyare based on Fabry-Perot interferometer[22],fiber inter-ferometer[19–21],triangulationsystem[23],fiberBragggrating [24,25], optical encoder [26] or grating sensor [27]. More recently, optical accelerometers have been proposed for mea-suringthemechanical vibrationof gravitationalwave detectors [16–18].

However,tothebestof theauthors’knowledge,there is no commercialseismometercapableoffulfillingtherequirementsfor applicationsin advanced active vibration isolation systems, i.e. small,sub-nanometerresolutionatlow frequency,and compat-ible witha magnetic environment. In this paper, we present a non-magneticOpticalinertialSEnsor(NOSE),whichisbased on ahorizontalpendulumandaMichelsoninterferometer.Itissmall, http://dx.doi.org/10.1016/j.sna.2015.01.019

Fig.1.Picture(a)andschematic(b)oftheprototypeoftheinterferometricinertialsensorNOSE.(A)Singledegreeoffreedomoscillator,(B)interferometricdisplacement sensorand(C)acquisitionprocessingunit.

passive,andmeasuresseismicmotionintheverticaldirection.1_We

willshowthat,besidesthecompatibilitywithmagnetic environ-ment,theabsenceofcoiloffersalsoseveraladvantages.

Thepaperisorganizedasfollows:Thenewsensorispresented inSection2.Section3containsexperimentalvalidations,and Sec-tion4drawstheconclusionsanddirectionsforimprovements. 2. Descriptionoftheopticalinertialsensor

Thesensoriscomposedofthreemainparts(seeFig.1):Asingle degreeoffreedom(d.o.f)oscillator(A),aninterferometric displace-mentsensor(B),andanacquisitionprocessingunit(C).Eachofthe threepartsaredetailedinthefollowingsections.

2.1. Mechanics

Themechanicalpartconsistsofa horizontalpendulum, con-nectedtoarigidframethroughaflexuraljoint,madeofCuBealloy. Aleafspring,madeofthesamealloy,isusedtoadjustthe equilib-riumpositionoftheinertialmassandcompensateforgravity.The oscillatorischaracterizedbyaninertialmassm=0.055kg,a prin-cipalresonancefrequencyω0=6*2rad/s(tunable)andspurious

resonancesabove100Hz.

Usually,andmostspecificallyforgeophones,ahighdampingof theinertialmass,i.e.asmallQfactor,isimposedinordertoincrease thebandwidthofthesensorandreduceitssensitivityto miscali-bration.Acriticaldampingisobtainedbyconnectingaresistorto thesensingcoil.Onthecontrary,ourinertialsensoris character-izedbyahighQfactor(around60)becauseitdoesnotcontainany loadedcoil.Afirstadvantageofthecoil-freeconfigurationisthat thesensoriscompatiblewithmagneticenvironmentslike encoun-teredinproximitytoparticlecolliders.Asecondadvantageisthat thehighQdecreasesthethermalnoiseinthesuspension(Brownian motion)definedas[28]: B(f)=



wherekBistheBoltzmannconstant,T=300Kisthetemperature

andω0istheangularresonancefrequency.

When the inertial sensor is used for active vibration isola-tion,thehighQoffersathirdadvantagebecauseitmagnifiesthe controlperformancearoundthesensor resonance.Asan exam-ple,consider thesingled.o.f. isolator shown in Fig.2(a)where a sensitiveequipment(m) mountedonan activesuspension is represented.The motionx of the equipmentis measured with

1_{Inprinciple,thesensorisalsocapabletomeasureseismicmotioninthe}

hori-zontaldirection.However,thisfeaturehasnotbeeninvestigated.

an inertial sensor. Then, the signal is filtered by a filter H(s), used to generate a feedback force f. Fig. 2(b) shows a typi-caltransmissibility(x/w)ofthesuspensionwhenthecontrolis turned off (solid line), and turned on for two sensors: a geo-phone critically damped (dotted line) and NOSE (dashed line). The same controller H(s) has been used for both sensors. The curveshavebeenobtainedwithanumericalmodeloftheisolator, andthefollowingnumericalvaluesoftheparameters:m=100kg, k=1.6MN/m,c=1200Ns/m.Thefigureshowsthat,forbothsensors, thetransmissibilityhasbeenreducedbythefeedbackoperation inalargebandwidth,extendingfromafractionofthegeophone corner frequency toa multiple of the resonance of the equip-ment.

However,forNOSE,thestrongmechanicalamplificationatthe resonanceimprovessignificantlytheisolationinafrequencyrange aroundthisresonance,whileusingthesamecrossoverfrequencies forbothsensors.Suchfeaturecanbeparticularlyinterestingto can-celnarrowbandexcitations.Moreover,asthephoto-diodessignals amplituderemainsbounded(seeSection2.3),thepeakof perfor-manceisnotlimitedbytheclassicaltrade-offbetweenresolution anddynamicrange.

Ontheotherhand,whenthesensorisnotusedinafeedback loop,thelowdampingoftheinertialmassbecomesadisadvantage becauseitreducesthebandwidthandbecauselargeoscillations oftheinertial massaresuperimposedtotheusefulsignal.Still, theabsenceofcoilremainsinterestingforthecompatibilitywith magneticenvironments.

2.2. Interferometricsensor

Inordertomeasuretherelativedisplacementbetweenthe iner-tialmassandthesupport,wehavedevelopedasensorbasedona Michelsoninterferometer,adaptedtoenablethemeasurementof bothquadraturesofthesignalsasin[7,29].Theopticalschemeis showninFig.3.

ThelasersourceisaHe–Nelaserwithawavelengthof632.8nm. Theinputbeam,linearlypolarizedat45◦,isfirstsplitintwo ortho-gonalbeamsbymeansofa50/50nonpolarizingbeamsplitter(BS). EachbeamisthenreflectedonthemirrorsM1orM2.M1 isfixed

ontheinertialmassandM2ismountedonaminiaturetwod.o.f.

tiltstagetoenablethealignmentoftheinterferometer. Addition-ally,thearmd2containsa/8waveplatetogenerateacircularly

polarizedbeam(itisinanellipticalpolarizationafter1pass,anda circularpolarizationafterdouble-passingthewaveplate).Thetwo beamsarerecombinedinthebeamssplitter(BS).Theverticallyand thehorizontallypolarizedcomponentsoftherecombinedbeamare thenseparatedbyapolarizingbeamsplitter(PBS).Theintensityin thetwobeamsarefinallymeasuredbymeansoftwophotodiodes. Thelasersourceismountedonafourd.o.f.stage(twotranslations andtworotations)toadjustthepositionandtheangleofthebeams

Fig.2.(a)Principleofactivevibrationisolatorusinginertialsensor;(b)simulatedtransmissibility(x/w)ofthenumericalmodeloftheisolatorshownin(a)whenthe controlleristurnedoff,turnedonusingacommercialgeophone,andturnedonusingalowdampedinertialsensorlikeNOSE.

onthephotodiodes.Thelengthofthetwoarms(d1and d2)are

similartominimizetheimpactofthelaserfrequencynoiseonthe measurements[30].NotethattheHe–Nelasercanbereplacedbya pigtailedlaserdiodewithapolarization-maintainingopticalfiber [8]andafibercollimator.

2.3. Acquisitionandprocessing

Thetwophotodiodesignals (PD1and PD2)havethegeneral form:



PD1=a1+b1cos(ϕ0+ϕ)

PD2=a2+b2sin(ϕ)

(2)

wheretheamplitudesa1,a2,b1,b2 dependontheactualsetup

(lossesandbeamsalignment),andϕisthephaseproportionalto therelativedisplacementxofthemirrorM2

ϕ= 4

 x, (3)

beingthewavelengthofthelasersource;andwhereϕ0 takes

intoaccount possibledeviationof thephase delayfrom /4 in theoctaedric waveplate. Fig.4 shows a typicalexample of an experimentalLissajousfigure(bluecurve)obtainedwhenthefirst photodiodesignal(PD1)isplottedagainsttheother(PD2).Note that,inthisexample,thefringevisibilityisnotmaximum.

Fig.3.OpticalschemeoftheinterferometerusedinNOSE. Adaptedfrom[8].

Severalmethodsarereportedintheliteraturetodemodulate thesignalsandextractthephase.In[32],thesineandcosine com-ponentsarenormalized,usingthesignalfromathirdphotodiode. Insomeothertechniques,thesignalsarederivedandrecombined toextractthephase.However,ithasbeenobservedthatthese tech-niquesarequitenoisesensitive,resultinginadecreaseofthesignal tonoiseratio.Inanothertechniquedescribedin[31,33],the param-etersoftheLissajousfigurearefirstcalculatedtotransformthe ellipseinaunitcirclecenteredontheorigin(seeinFig.4,green curve)fromwhichthephasecanreadilybeextracted.This tech-niquehasbeenproventoberobustandwasthenusedtoextract thedisplacementparameterfromtherecordeddata.

Inoperating condition,themass,subjectedtotheexcitation fromthegroundmotion,oscillatescontinuouslyatitsresonance frequency,withanamplitudeproportionaltotheQfactorofthe oscillatortimestheamplitudeofthegroundmotionatthesensor location.AhighQfactor,asforNOSE,leadstoalargemotionofthe inertialmassandresultsinacontinuoussweepingofthe interfer-encefringesacrossthedetector.Thisisafourthadvantageofahigh Qfactor,becauseitallowsarealtimeestimationoftheLissajous fig-ureparameters,andthusanunbiaseddemodulationofthesignals. Anotherassetofthistechnologyisthat,sincetheamplitudeofthe photodiodesignalsisboundedinaninterferometricdisplacement

0 2 4 6 8 10 −2 −1 0 1 2 3 4 5 6 7 [V] [V] PD1 vs. PD2 Reconstructed circle

Fig.4. ExampleofexperimentalLissajousfigure(bluecurve)obtainedwhenthe firstphotodiodesignal(PD1)isplottedagainsttheother(PD2).Unitcirclecentered ontheorigin(green)calculatedusingtheparametersoftheellipseandanalgorithm describedin[31].(Forinterpretationofthereferencestocolorinthisfigurelegend, thereaderisreferredtothewebversionofthearticle.)

Fig.5.ExperimentalamplitudespectrumofthePolytecOFV502(dashedgreenline) comparedtoourprototypeofinertialsensorNOSE(solidblueline).(For interpreta-tionofthereferencestocolorinthisfigurelegend,thereaderisreferredtotheweb versionofthearticle.)

sensor,anequivalentof30bitresolutioncanbeobtainedwithonly a16bitsA/Dconverter.

Thenextsectionpresentstheresultsofthreeexperiments:a validationoftheinterferometricdisplacementsensor(NOSE),an identificationofthedifferentsourcesofnoiseinthesignal,andan experimentalvalidationofNOSEbycomparisonwithacommercial seismometer.

3. Experiments

3.1. Assessmentoftheinterferometer

Asafirststep,wehavemadeanexperimenttoconfirmthatthe displacementmeasuredwithourinterferometerprototype corre-spondstotheactualdisplacementoftheinertialmass.Tothisend, theoutputsignalofNOSEwascomparedtothemeasured displace-mentoftheinertialmassbyacommercialinterferometer(Polytec OFV502).Thelowersideoftheinertialmasswaspointedbyour interferometer,whiletheuppersidewaspointedbythe commer-cialsensor.Theamplitudespectrumofthetwomeasuredsignals areplottedinFig.5.

Itcanbeseenthatbothspectraarenearlyidentical,fromDC toapproximately50Hz.Thetransferfunctionbetweenthe Poly-tecOFV502andourinterferometerisshowninFig.6.Averygood agreementbetweenthetwosensorsisobtainedinthefrequency range0.1–50Hz.Thescalefactorof0.8hasnotbeeninvestigated. Thepeaksinthetransferfunctionaround60Hzandabovehave beenidentifiedtocorrelatewithresonancesofthePolytecOFV502 headholder.

Fig.6. Experimentalamplitudeandphaseofthetransferfunctionbetweenthe Poly-tecOFV502andourprototypeofinertialsensor,pointingtheupperandlowerside oftheinertialmass,respectively.

Fig.7. Experimentalnoisebudgetingoftheinterferometer. 3.2. Noisebudgeting

AnexpectedfeatureoftheNOSEsensorisitsabilitytomeasure lowfrequencyvibrationswithagoodresolution.Inorderto iden-tifythevarioussourcesofnoise,whicharethefactorslimitingthe sensorresolution,wehaveblockedtheinertialmassandrecorded thephotodiodesignalsintheconfigurationslistedbelow(the cor-respondingexperimentalamplitudespectraareplottedinFig.7): • Cableunpluggedfromtherecorder(ADCnoise).

• Voltagesourcealone,whenitsupplies9V(Sourcenoise). • Thevoltagesourcesupplies9Vtothecircuit,butthephotodiode

isnotconnected(Circuitnoise)

• Thevoltagesourcesupplies9Vtothecircuit,thephotodiodeis connected,butthelaserswitchedoff(LaserOFF)

• Thevoltagesourcesupplies9Vtothecircuit,thephotodiodeis connected,andthelaserswitchedon(LaserON)

In our experiment, thesampling frequency is 20kHz. Fig.7 showsthattheresolutionislimitedbyaconstantvoltagenoise above2Hz,andbya1/fcurrentnoisebelow2Hzcomingfromthe laseropticalpowernoise[30].

Thesharppeaksat50Hzandmultiplesof50Hzarerelatedto theelectricalsupplynetwork.Thesepeakscanberemovedbyusing anelectromagneticshieldingofthesensor,andbyusingbatteries tosupplytheoperationalamplifiers.

Fig.8showstheexperimentalamplitudespectrumofthe inter-ferometernoise(bluedashed-dottedline),expressedinphysical unitsof[m/√Hz].Ithasbeenobtainedintwosteps.Inthefirst step,wemanuallyslightlymovedonemirrorinordertoobtainthe

Fig.8.Comparisonofsensorexperimentalresolution:GuralpCMG-6T(blackline, obtainedfromtwosensorssidebysideplacedinaquietenvironment);resolutionof ourNOSEprototype,measuredbyblockingtheinertialmass;estimatedresolution ofNOSE(redline).(Forinterpretationofthereferencestocolorinthisfigurelegend, thereaderisreferredtothewebversionofthearticle.)

Fig.9.Experimentalamplitudeandphaseofthetransferfunctionbetweenthe sig-nalfromacommercialGuralpCMG-6Tcalibratedindisplacementunitsandour prototypeNOSE.

parametersoftheLissajousfigureforthecalibration.Inasecond step,wehaverecordedthesignalwithoutdisturbingthe interfer-ometer,and usedtheparametersfromthefirststeptoexpress thephotodiodesignals assensornoisein displacementunits.It resultsina resolutionof 3pm/√Hz above1Hz,and 20pm/√Hz above0.3Hz.

3.3. Assessmentoftheinertialsensor

Inordertoconfirmthatoursensormeasuresproperlyseismic motion,wemadeathirdexperimentwheretheoutputsignalof ourprototypewascomparedtothereadoutofacommercial seis-mometer(GuralpCMG-6T),locatedbesideoursensor.Fig.9shows theexperimentaltransferfunctionbetweenthesensors(calibrated indisplacementunits),whichcorrespondstothesensitivitycurve ofNOSE,becausetheCMG-6Thasaconstantsensitivityfrom30s to100Hz.

Dividingthe interferometerresolution(Fig.8)by thesensor transferfunction(Fig.9)givestheestimationoftheNOSE reso-lution,alsoshowninFig.8(redcurve).TheresolutionoftheGuralp CMG-6T(measuredinaquietenvironmentwithtwosensorssideby side)isalsoshowninthesamefigureforcomparison.Below50Hz, NOSEresolutionoverpassesGMG-6T,byuptoafactor100around 6Hz,becauseofthemechanicalresonance.Atthatfrequency,NOSE resolutionpeaksat0.1pm/√Hz.

4. Conclusionandfuturework

Wehavepresentedanewsmall,lowcost,non-magnetic opti-calinertialsensor,calledNOSE.Comparedtomoststate-of-the-art commercialinertialsensors,thisprototypedoesnotcontainany coil,resultinginahugeamplificationoftheresponseatthesensor resonance.We haveshownthat,whencombinedtoan interfer-ometricsensor,thisfeatureoffersfourimportantadvantages:(i) whenusedforactivecontrol,itmagnifiesthecontrolperformance aroundthesensorresonance;(ii)thesuspensionhasalow ther-malnoise,(iii)itiscompatiblewithmagneticenvironments(like encounteredinparticlecollider);(iv)itallowsarealtime calibra-tionoftheparameters,andthusanunbiaseddemodulationofthe signaltankstothecontinuoussweepingofthefringesacrossthe detectors.Usinglowcostcomponents,wehavedemonstrateda res-olutionof3pm/√Hzabove4Hz.Theprototypehasbeenvalidated

for funding and supporting this research. We also warmly acknowledgeProf.IulianRomanescuforhishelptoconstructthe mechanicalparts.ManythankstoStefJanssensandKurtArtoosfor theircollaboration,andforlendingtheGuralpseismometers,and toourcolleaguesattheLIGOLaboftheMassachusettsInstituteof Technologyfornumerousinspiringdiscussionsoninterferometric inertialsensors.ThisdocumenthasbeenassignedLIGOLaboratory documentnumberLIGO-P1400115.

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Biographies

ChristopheCollette receivedM.Sc.and Ph.D. degrees inmechanicalengineeringfromtheUniversitéLibrede Bruxellesin2003and2007.Since2014,heisprofessorin theFacultyofEngineeringattheULBandismemberofthe BEAMSdepartment.Hismainresearchinterestsinclude theprecisionandvibrationcontroloflargeinstruments dedicatedtoexperimentalphysics.

FaresNassifreceivedM.S.inMechatronicsand Mechani-calConstructionformUniversiteLibredeBruxelles(ULB) in2012and2014respectively.Hismasterwasfocusedon measuringgroundvibrationsatlowfrequencies.A sen-sorimmunetotilt-to-horizontalcouplingwasstudiedand presented.Alsoasensorfusionexperimentbetweenan inertialsensorandaseismometerinordertoincrease sensingbandwidthwasundertaken.

JulienAmarrecently receivedhis engineeringdegree fromthe Université deTechnologie de Belfort Mont-béliard(UTBM)in2015inFrancebydoingseveralresearch projects,suchastherealizationofanopticalinertial sen-sorattheUniversitylibredeBruxellesandtheconception ofaC++autonomousprogramforaparrotAR.Droneusing OpenCVatWakayamauniversity,Japan.

CélineDepouhon received her M.S. in Mechatronics andMechanicalConstructionfromUniversiteLibrede Bruxelles in2014. Hermasterthesiswas focused on swarm robotics and more specially the distributed control of multi-robot systems. Her research inter-estsincludealsoopticalinertialsensorandMichelson interferometer.

Simon-PierreGorzareceivedhisM.S.andPh.D.degrees inphysicalengineeringfromtheUniversitélibrede Brux-elles(ULB)in2001and2005,respectively.Since2010heis professorintheFacultyofEngineeringattheULBandisa memberoftheOPERA-photonicgroup.Hismainresearch interestsincludespatialandtemporaldynamicsinoptical nonlinearmedia,pulsecharacterizationtechniquesand applicationoflinearandnonlinearopticstobio-imaging andsensors.