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Externalballistics,Nocontactmeasurement,Electro-opticaltechniques,Positionmeasurement,Speedmeasurement

1Introduction

Thespeedandpositionmeasurementsofprojectilesaretwoimportantitemsinballisticresearch.Todeterminetheseparameterspreciselyoneneedsanaccuratemeasuringsystem.Aconventionalmethod,namelythehangingup（andtakingdown）oftargetdiscs[l],thoughaccurateinpositionmeasuring,istimeconsuming.Ashot-positionindicator（SPI）,describedinReference2,canmeasurethepositionofahighspeedprojectilebyacousticmeasurement.However,theSPIdoesnotprovidethespeedinformation;

neitherdoestheconventionalmethod.Besides,theSPIisusedwithinthelimitsofsupersonicprojectiles.

Tomeasurethespeedandpositionofprojectilesrapidlyandsimultaneously,differentelectro-opticalbasedsystemshavebeenproposed3-5].Thesesystemshavetheabilitytocoverthespeedrangefromsubsonictosupersonic.Onesystem,calledthetargetmeasurementsystem（TMS）[3],usesverticalandhorizontalbanksoflightsourcestoformtwoperpendicularlightgridsthatconstructthetargetarea.Anothersystem,calledtheelectro-opticalprojectileanalyzer[4],usesthesameprincipleasTMS,butsimplifieslightsourceswithfiberopticsbundlesandasinglelightsourceineachlightgrid.Theothersystem,calledtheelectronicyawscreen（EYS）[5],usesasolidstatelaserthatiscollimatedanddirectedtoaone-dimensionalbeamexpandersystemtoformafan-shapedlightscreen.Thislightscreenthenisreflectedbyamirrortoconstructaportionofthetargetarea.Thelightscreenismoreprecisethanthelightgridbecausethereisnodeadzoneinthetargetareaaswiththelightgridsystem.

Fromtheaspectofspeedandpositionmeasurement,wetakeadvantageoftheabovesystemsandproposeanovelsystem;

theelectro-opticaltargetsystem（EOTS）[6].Weuseacylindricalmirrorthatreflectstheincidentlaserbeamintoa90º

fan-shapedlightscreen.Twosuchlightscreensconstructatwo-dimensionalpositioningsystem.Weevenproposeabentcylindricalmirrortogeneratea90º

lightscreenwithafewdegreesextendedinadirectionnormaltothelightscreentoreducethesensitivitytovibrations.

AprototypeEOTS,whosetargetareais1m2andmeasuredspeedrangeisfrom50m/sto1200m/s,hasbeenconstructedandtested.Aspeedrangeofupto5000m/scanalsobeexpectedaccordingtothesimulationresultsfromtheelectroniccircuitusingPSpice[7].Finally,anine-pointtestingresultfroma0.38in.pistolisshowninthispaper.Theresultshowsthatthestandarddeviationofpositionaccuracyislessthan1mm.

2BasicprincipleofEOTS

Fig.1showstheopticalconfigurationofEOTS.AlaserbeamfromaHe-Nelaserisdirectedontoacylindricalmirror.Thereflectedlaserbeamscreateafan-shapedlightscreenandaredirectedontophotodiodesthatareneatlyarrangedintoanL-shapedphotodiodearray.EOTSusestwolasersources,twocylindricalmirrorsandtwophotodiodearrays,whicharearrangedontheoppositesidesoftheEOTSbodytoformtwofan-shapedlightscreens.Eachlightscreeniscombinedwithitsownsignalprocessingcircuittoconstructanopticalgate.Althoughthereisadistancebetweenthetwoparallellightscreens,viewedfromadistancepoint,thesefanbeamsintersectinaregionofspacecalledthetargetarea（Fig.2）.Aprojectilecanbemeasuredonlyifittravelsthroughthistargetarea.

Fig.1OpticalconfigurationofEOTS

Fig.3showstheshotpositionoftheprojectileiscalculated.Thetargetarea,fortheconvenienceofillustration,isasquareofdimensionDoneachside.ThenumberofphotodiodesontheL-shapedphotodiodearrayis2N.Eachphotodiodeisnumberedinorder,asshowninthefigure.Forillustrationclarity,onlythephotodiodearrayandthecylindricalmirrorofthefirstopticalgateareshown.Theprojectileisconsideredtobeincidentnormallytothefirstandtothesecondopticalgateinsequence.Whentheprojectileblocksthelightscreens,therespectivephotodiodeswillbeactivatedbythedisturbance.Inthefirstopticalgate,thelaserbeamfromthecylindricalmirrortoeachphotodiodemakesauniqueanglewiththey-axis.Thisangleismeasuredcounter-clockwisefromtheaxis.Theanglewithrespecttoaphotodiode,numberedn,canbecalculatedas

（1）

and

（2）

Ifcertainphotodiodes,numberedfromjtok,areactivatedbyprojectiles,thentheshot-positionangleδ1,isgivenby

（3）

Fig.2Intersectionsofthetwolightscreensinthetargetarea

Similarly,theshot-positionangleofthesecondopticalgateδ2,measuredclockwisefromtheminusy-axis,isdecided.Afterthetwoangleshavebeenmeasured,the

Fig.3Illustrationofshot-positioncalculation

shotpositionoftheprojectileisdeducedinCartesiancoordinatesas

（4）

（5）

IfSisthedistancebetweenthetwolightscreens,thentheaveragespeedvfortheprojectilepassingthroughthedistanceSisgivenby

（6）

whereTisthetimeintervalfortheprojectiletopassthroughdistanceS.

3ConfigurationofEOTS

3.1OpticalsystemofEOTS

WeuseaHe-Nelaserdirectedontoacylindricalmirrortocreatealightscreen.Therelationamongthelaserbeamdiameterd,thecylindricalmirrordiameterwandthebeamexpandingangleφisshowninFig.4.Thisrelationcanbecalculatedas

（7）

Tocreatealightscreenofwhichφequals90º

theratioofwtodis2.8.BecausetheHe-NelaserbeamhasGaussiandistributionandeachphotodiodeonthephotodiodearrayhasadifferentdistancetothecylindricalmirror,thereceivedlaserpowerateachphotodiodeisnotconstant.ThiswillinfluencethespeedaccuracyofEOTS（seeFig.6andSection4.1）.

3.2Analoguecircuitry

EOTShas2Nanaloguechannelsineachofitstwoopticalgates.Everyanaloguechannelhasthesamestructure.Eachanaloguechannelcontainsaphotodiode,alinearamplifier,aband-passfilterandacomparator.Thelinearamplifieramplifiesthesignalcomingfromthephotodiode.Theband-passfilterfiltersnoisessuchas

Fig.4Laserbeamdirectsonacylindricalmirror

bugsflyingthroughthelightscreenandflickerofotherlightsourcesnearby.ThecomparatorcomparestheoutputV0,comingfromthefilterwithathresholdvoltageVTH.IfV0ishigherthanVTH,thenthecomparatorwillactivateaflip-flop（FF）tochangethestate.

3.3Digitalcircuitry

Fig.5istheblockdiagramofthedigitalsignalprocessingcircuit.InputcomingfromtheanaloguechannelisfedtoarelativeFF.Whentheprojectileblocksthelightscreenofthefirstopticalgate,thestate-changedFFswillmaketheoutputoftheNANDgateU1changestate.TheU1locksallFFsofthefirstopticalgatetoprotectgenuineprojectiledatafromtheinfluenceofshockwavesbehindtheprojectile,andstartsthecounterU5thatoperatesataclockfrequencyof10MHz.Astheprojectileblocksthelightscreenofthesecondopticalgate,thecircuitofthesecondopticalgatefunctionsasthecircuitofthefirstopticalgatedid,butstopsthecounter.Moreover,theNANDgateU2passesaninterruptsignal（INT）tothecentralprocessingunit（CPU）whileU5isbeingstopped.TheCPUthenrecognizestheinterruptrequest,pickstheprojectiledataup,andresetsU5andallFFsforthenextshot,insequence.InFig.5,thecounterrelatesthetimeintervalTineqn.6.Besides,everyphotodiodeisassignedaspecificFFandeveryFFisgivenarelativeaddress.Therefore,theCPUwillbeabletoidentifywhichphotodiodegeneratesthesignal,todecidetheimpactpositionofeqns.1-5,andtocalculatethespeedoftheprojectile.

Fig.5Blockdiagramofdigitalsignalprocessingcircuit

4AccuracyofEOTS

4.1Accuracyofspeedmeasurement

Theaccuracyofprojectilevelocitymeasurementwithsky-screenshasbeendeducedbyHartwig[8]as

（8）

whereparameterswerethesameaseqn.6used.Δv,ΔSandΔTarevaluesofmaximumerrorinv,SandT,respectively.InEOTS,photodiodesaredirectedbynonuniformopticalpower,asdescribedinSection3.1,whichimpliesthatdifferentanaloguechannelswillhavedifferentresponsetimes,asthoughtheyareactivatedinthesameway.Fig.6describesthetypicalinputandoutputwaveformsofananaloguechannelwhenaprojectilepassesthroughthelightscreen.Thedottedlineisthe

Fig.6Typicalinputandoutputwaveformofanaloguechannel

responseoftheweakeropticalinputwithrespecttothesolidline.InthisFigure,theopticalpowerdensitydirectedontothephotodiodeisconsideredtobeconstantalongthex-axis.Referringtothesolidline,theprojectiletouchesthelightscreenatT1andentirelyblockslaserbeamsatT2;

theactivatedphotodiodecurrentIDdropsfromIDHtoIDL.TheoutputvoltageV0oftheanaloguechannelthenrisestoasaturationvoltageVsat.ThecounterisnottriggereduntilV0islargerthanVTH.TheintervalfromT1tothetimethatV0equalsVTHiscalledtheresponsetimetrFromFig.6,wecanrealisethatadifferentinputpowerv