如何测量调制传递函数How to Measure Modulation Transfer Function.docx

如何测量调制传递函数How to Measure Modulation Transfer Function.docx

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如何测量调制传递函数HowtoMeasureModulationTransferFunction

HowtoMeasureModulationTransferFunction

HowtoMeasureModulationTransferFunction

（1）

Inasimplewording,themodulationtransferfunctionorMTFisameasureofthespatialresolutionofanimagingcomponent. Thelattercanbeanimagesensor,alens,amirrororthecompletecamera. Intechnicalterms,theMTFisthemagnitudeoftheopticaltransferfunction,beingtheFouriertransformoftheresponsetoapointillumination.

TheMTFisnotreallythemosteasiestmeasurementthatcanbedoneonanimagingsystem. VariousmethodscanbeusedtocharacterizetheMTF,suchasthe“slitimage”,the“knifeedge”,the“laser-speckletechnique”and“imagingofsine-wavepatterns”. Itshouldbenotedthatallmethodlisted,exceptthe“laser-speckletechnique,measuretheMTFofthecompleteimagingsystem:

allpartsoftheimagingsystemareincluded,suchaslens,filters（ifanypresent）,coverglassandimagesensor. Eventheeffectoftheprocessingofthesensor’ssignalcanhaveaninfluenceontheMTF,andwillbeincludeinthemeasurement.

InthisfirstMTF-blogthemeasurementofthemodulationtransferfunctionbasedonimagingwithasine-wavepatternwillbediscussed. ItshouldbenotedthatinthiscasededicatedtestchartsareusedtomeasuretheMTF,butthepatternonthechartshouldsinusoidallychangebetweendarkpartsandlightparts. Inthecaseasquare-wavepatternisused,nottheMTFbuttheCTF（=ContrastTransferFunction）willbemeasured. Andthevaluesobtained fortheCTFwillbelargerthantheonesobtainedfortheMTF.

ThemethoddescribedhereisbasedontheworkofAnkeNeumann,writtendowninherMScthesis“VerfahrenzurAufloesungsmessungdigitalerKameras”,June2003. Thebasicideaistouseasingletestchartwithaco-calledSiemens-star. AnexampleofsuchatestchartisillustratedinFigure1.

Figure1:

Outputimageofthecamera-under-testobservingtheSiemensstar.

（Withoutgoingfurtherintodetail,thetestchartcontainsmorestructuresthanusedinthereportedmeasurementperformedfortheMTF.） TheheartofthetestchartistheSiemensstarwith72“spokes”. Ascanbeseenthedistancebetweentheblackandwhitestructuresonthechartisbecominglargerifonemovesawayfromthecenterofthechart. Inotherwords,thespatialfrequencyofthesinusoidalpatternisbecominglowerattheoutsideoftheSiemensstar,andisbecominghigherclosertothecenteroftheSiemensstar. AroundthecenteroftheSiemensstar,thespatialfrequencyofthesinusoidalpatterniseventoohightoberesolvedbythecamera-under-testandaliasingshowsup. InthecenteroftheSiemensstarasmallcircleisincludedwith2whiteandtwoblackquarters. Thesearegoingtoplayaveryimportantroleinthemeasurements.

Themeasurementproceduregoesasfollows:

1.FocustheimageoftheSiemensstar,placedinfrontofthecamera,asgoodaspossibleontheimager. TrytobringtheSiemensstarascloseaspossibletotheedges（topandbottom）oftheimager,

2.Shootanimageofthetestchart（intheexampledescribedhere,50imagesweretakenandaveragedtolimitthetemporalnoise）.

Inprinciple,thesetwostepsisalloneneedstobeabletomeasure/calculatetheMTF. Buttoobtainahigheraccuracyofthemeasurements,thefollowingadditionalstepsmightberequired:

1.Camerascanoperatewithorwithoutaparticularoffsetcorrected/addedtotheoutputsignal. Forthatreasonitmightbewisetotakeadarkreferenceframetomeasuretheoffsetanddarksignal（includingitsnon-uniformities）forlatercorrection. Intheexperimentsdiscussedhere,50darkframesweretakenandaveragedtominimizethetemporalnoise.

2.ThedatausedinthemeasurementiscomingfromarelativelylargeareaofthesensorandisrelyingonanuniformilluminationofthecompleteSiemensstar. Moreover,thecameraisusingalensandonehastotakeintoaccountthelensvignettingorintensityfall-offtowardsthecornersofthesensor. Forthatreasonaflat-fieldingoperationmightbeneeded:

takeanimageofauniformtesttarget,andusethedataobtainedtocreateapixelgainmap. Intheexperimentsdiscussedher,50flatfieldimagesweretakenandaveragedtominimizethetemporalnoise.

3.ThecameraundertestinthisdiscussiondeliversRAWdata,withoutanyprocessing. Ifthatwasnotthecaseitwouldhavebeenworthwhiletocheckthelinearityofthecamera（e.g.useofagammacorrection）bymeansofthegreysquarespresentonthetestchartaswell.

TakenalltogetherthetotalmeasurementsequenceoftheMTFcharacterizationisthencomposedof:

1.Shoot50imagesofthefocusedtestchart,andcalculatetheaverage. Theresultiscalled:

 Image_MTF,

2.Shoot50flatfieldimageswiththesameilluminationasusedtoshoottheimagesofthefocusedtestchart,andcalculatetheaverageimageofallflatfieldimages.Theresultiscalled:

Image_light,

3.Shoot50imagesindark,andcalculatetheaverageimageofalldarkimage. Theresultiscalled Image_dark,

4.Both Image_MTF and Image_light arecorrectedfortheiroffsetanddarknon-uniformitiesbysubtracting Image_dark,

5.Theobtainedcorrection（Image_light – Image_dark） willbeusedtocreateagainmapforeachpixel,called Image_gain,

6.Theobtainedcorrection（Image_MTF – Image_dark）willbecorrectedagainforanynon-uniformitiesinpixelillumination,basedon Image_gain.

Ifthissequenceisfollowed,animageliketheoneshowninFigure1canbeobtained.

1.Nextthepixelcoordinatesofthecenterofthetestchartneedtobefound. Thiscanbedonemanuallyorautomatically. Thelatterisdoneinthiswork,basedonthepresenceofthe4quadrantsinthecenterofthetestchart.

2.Oncethecentroidofthetestchartisknown,severalconcentriccirclesaredrawnwiththecentroidofthetestchartastheircommoncenter. AnexampleoftheseconcentriccirclesontopofthetestchartisshowninFigure2.

Figure2:

Siemens starwithconcentriccircles（showningreen）,withtheircenterscoincideswiththecentroidofthetestchart（redcross）.

1.Aftercreatingthecircles,thesensoroutputvaluesofthevariouspixelslyingonthesecirclesarechecked. Oneverycirclethepixelvalueschangeaccordingtoasinewave,ofwhichthefrequencyisknown（72completecyclesofthesinewaveanditradius,innumberofpixels,canbecalculated）. Foreachofthecircles,atheoreticalsinewavecanbefittedthroughthemeasureddata. Consequentlyforeachcircleaparametercanbefoundthatcorrespondstotheamplitudeofthefittedsinewave.

2.InprincipletheMTFcurvecouldbeconstructed,theonlymissinglinkisthevalueoftheMTFforverylowfrequenciesclosetoDC. Thisvaluecanbefoundasthedifferencebetweenthewhitevaluesandblackvaluesofthefourquadrantsrightinthemiddleofthetestchart.

3.NormalizingtheobtaineddatacompletestheMTFcurve:

thecalculatedamplitudesofthesinewavesarenormalizedwiththesignalsofthefourquadrantsinthemiddleofthechart,thefrequenciesofthesinewavesarenormalizedtothesamplingfrequencyoftheimager（6mmpixelpitch）.

TheoutcomeofthecompleteexerciseisshowninFigure3.

 Figure3:

ModulationTransferFunctionofthecamera-under-test.

AsindicatedinFigure3,theMTFmeasurementisdonewithwhitelightcreatedby3colourLEDarrays（wavelengths470nm,525nm,630nm）. Ascanbeseenfromthecurve,thecamerahasarelativelowMTF,around8%atNyquistfrequency（fN）. IntheoryanimagerwithalargefillfactorcanhaveanMTFvalueof60%atfN. Butthiscameraisperformingfarawayfromthistheoreticalvalue. Butoneshouldnotforget,thisMTFmeasurementdoesincludeALLcomponentsintheimagingsystem,notjustthesensor!

NowthattheMTFmeasurementmethodisexplained,inthenextblogsmoreMTFresultswillbeshownandcompared.

Albert,20-02-2014.

HowtoMeasureModulationTransferFunction

（2）

Inthepreviousblog,themeasurementoftheModulationTransferFunctionbymeansoftheSiemensstarwasexplained. Inthisblog,thismethodwillbeappliedtocheckouttheeffectofthelensF-numberontheMTF.

InFigure1theresultoftheMTFmeasurementisshown.

Figure1:

ModulationTransferFunctionfortwosettingsofthelensF-number.

ItisquitenicetoseetheinfluenceoftheF-number:

∙alowF-numberisreferringtoalargelensopening（=alotoflightgoestothesensor,ashortexposuretimeisneeded）,andinthatcasetheincominglightisreachingthesensorwithalargechief-rayangle（=deviationfromthenormal）,

∙alargeF-numberisreferringtoasmalllensopening（=muchlesslightgoestothesensor,alongexposuretimeisneeded）,andinthatcasetheincominglightisreachingthesensorwithasmallchief-rayangle（=almostperpendiculartothesensor）.

Lightthatisperpendicularlyreachingthesensorwillsufferlessfromopticalcross-talkincomparisontolightthatisreachingthesensorunderacertainangleandisdeviatingmorefromthenormal. More（optical）cross-talkdoesresultinlesscontrastbetweenneighbouringpixels,thusloweringtheMTFforlargerspatialfrequencies. AndthiseffectisobservedinFigure1!

NexttimesomethingaboutcolourandMTF.

Albert,25-03-2014.

HowtoMeasureModulationTransferFunction（3）

AnewmeasurementresultintheMTF-seriesisshowninthisblog:

theMTFofamonochromesensor,butnolongerwithwhitelightinput,butwithred,greenandbluelight. Someinterestingobservationscanbereported.

InFigure1,theresultsoftheMTFmeasurement areshown.

Figure1:

Modulation