National Aeronautics and Space Administration Offi

NASATechnicalMemorandum4197VideoCameraSystemforLocatingBulletHolesinTargetsataBallisticsRangeA.W.Burner,D.R.Rummler,andW.K.GoadLangleyResearchCenterHampton,VirginiaNationalAeronauticsandSpaceAdministrationOfficeofManagementScientificandTechnica,InformationDivision1991)Tileuseoftrademarksornamesoflnanufacturersillthisreportisforaccuratereportinganddoesnotconstituteallofficialendorsement,eitherexpressedorimplied,ofsuchproductsormanufat'turersbytheNationalAeronauticsandSpaceAdministration.SummaryAsystemconsistingofasinglecharge-coupled-device(CCD)videocamera,computer-controlh_dvideodigitizer,andsoftwaretoautoniatetilemea-surementhasbeendevelopedforlocatingbulletholesintargetsataballisticsrangeattheLangleyRe-searchCenter.Thecamera/digitizersysteniisacrucialcomponentofahighlyinstrunxented,indoor50-mriflerangethatsupportsthedeveloptnentofwind-resistantultramatchammunition.Thesys-temwasdesignedtotakedatarapidly(10secbe-tweenshots)andautomaticallywithlittleoperatorintervention.Thesystemdescription,nmasurementconcept,andprocedurearepresentedalongwithlab-oratorytestsofrepeatabilityandbiaserror.Thelong-term(1-hr)repeatabilityofthesystemwasfoundtobe4pm(onestandarddeviation)attimtarget,andthebiaserrorwasfoundtobelessthan50pro.Ananalysisoftilepotentialerrorsandatech-niqueforcalibrationofthesystemarepresented.IntroductionThepurposeoftheballisticsrangeattheLangleyResearchCenteristosupportthedevelopnlentofwind-resistantultralnatchammunition.Thefacilityconsistsofanindoor50-mrangewithinstrumentedmachinerestsforriflesandbarreledactions.Oneofthecrucialrequirementsoftheinstrmnentationistheautomatedlocationofabulletholeonatargetwithin=i=100pro.Inthepast,theeffectofaballisticvariable,suchasbulletvelocity,onshot-locationprecisionhasbeendeterlnincdbymeasuringthespreadofshotgroupsmanually,whichisnotconducivetothestudyoftileeffects.Therecentavailabilityofrelativelyinexpensivesolid-state,charge-coupled-device(CCD),area-arrayvideocamerasandcomputer-controlledvideoframedigitizershasenabledtheautonmtionofthebullet-hole-locationmeasurement.Theautonmtionofthemeasurenlentwilluniquely,andforthefirsttime,enablethecorrelationofbulletplacementwithmea-suredballisticvariablesandallowcomputerrecon-structionofshotgroups.Thedevelopmentofthepresentsystem,whichusesasinglecameraandob-jectmovenlentconstrainedtoaplane,wasexpeditedbythedevelopmentworkforatwo-camera,three-dimensional(3-D)videophotogranmmtricsystemre-portedinreference1.Itwasdesiredinthedevelopmentoftheauto-matedvideomeasuringsystemtousesoftwarecodethatcanbeeasilymodifiedtointerfacewithotherrequiredinstrumentation,suchaschronographsthatareusedtomeasurebulletvelocities.Inaddition,itwasdesiredtokeepthecodeflexibleenoughthatacasualprogrammer,probablyexperiencedonlyinBASIC,canimplementchangesandadditionstothecodeasthedataacquisitionorreductionproceduresarechanged.SymbolsCDofF&'c,&SXc,,gyc8h_SvX,}\ZX',Y'xc,E,,z,.Xo,_0Xt,,tl!3:pix,./]pixAX,AYAx,Ay0O0Abbreviations:AOIareaofinterestCCDcharge-coupleddeviceealcalibrationhhorizontalrssrootsumsquaresagsagittaofline.mmvverticalimagedistance(canleraconstant),nllndistancefromorigintocamera,mfocallength,ran1radialimagedistance,mmtruescale(toconvertfromimagetoobject)calibratedscalepixelspacing,nuntrueobjectlocation,mmnleasuredobject,location,mmlocationofcameraperspectivecenter,moriginoffsetfortransfornmtion,mmfirst-orderimagecoordinates,mlndistortedimagecoordinates,mmcentroid,pixelsspacingofcalibrationtargetsinobjectplane,mmspacingofcalibrationtargetsinimageplane,mmradialdistortion,mmrotationanglefortrallsformation,degthird-orderradialdistortioncoeffi-cient,nlm-2cameraangletoXY-plane,degMeasurementConceptThemeasurementconceptissimplytousescale,foundbyindependentcalibration,toconvertfrolnimagetoobjectcoordinatesonthepaper-targetob-jectplane.Thisdesiredscaleisequaltotheinverseofthelateralmagnificationcommonlyusedinfirst-orderoptics,anditispositiveforvideoimages.Toavoidbeingstruckbyabullet,thecamerawillbeoffsetfromthenormaltotheobjectplaneandtiltedtocenterthepapertargetinitsfieldofview(fig.1).Thus,thescalewillvaryacrossthefieldofview.Thisistrueevenforaperfectsystemthatobeysthefirst-order(Gaussian)object-imagerelationships.Thisvariationinscale(sometimescalledkeystonedistor-tionforthekeystonelikeimageofarectangularob-ject)isquiteseparatefromtheopticalaberrationofdistortion,whichisalsoduetoavariationinscaleacrosstheimageplane.However,theaberrationofdistortionisnonlinearandcanexistevenwhentheopticalaxisofthecameraisnormaltotileobjectplane.t-4'_'@,,_Paper_targetOoZ(O_JOrigin'J....,___',Objectpoint,/.._,09_._o'&X,Y,0x,_V_rf_PerspectiveOb.eObictycente_planeXc,O,Zc_'°ImageplaneFigure1.Planviewofmeasurementgeometry.Thescalecanbedeterminedastheratioofaknownlengthintheobjectplanetoitslengthintheimageplane.TopartiallycompensatefordifferencesinscalebetweentwoorthogonalaxesonthetiltedobjectplaneaswellasforscalingdifferencesinconvertingpixelstounitsoflengthontheCCDsensor,itwasdecidedtousetwofixedscalesforXandYthataredeterminedbycalibration.Takingthepaper-targetobjecttobeintheX