像素尺寸和光学元件

PixelSizesandOptics

Understandingtheinterplaybetweencamerasensorsandimaginglensesisavitalpartofdesigningandimplementingamachinevisionsystem.Theoptimizationofthisrelationshipisoftenoverlooked,andtheimpactthatitcanhaveontheoverallresolutionofthesystemislarge.Animproperlypairedcamera/lenscombinationcouldleadtowastedmoneyontheimagingsystem.Unfortunately,determiningwhichlensandcameratouseinanyapplicationisnotalwaysaneasytask:morecamerasensors(andasadirectresult,morelenses)continuetobedesignedandmanufacturedtotakeadvantageofnewmanufacturingcapabilitiesanddriveperformanceup.Thesenewsensorspresentanumberofchallengesforlensestoovercome,andmakethecorrectcameratolenspairinglessobvious.

Thefirstchallengeisthatpixelscontinuetogetsmaller.Whilesmallerpixelstypicallymeanhighersystem-levelresolution,thisisnotalwaysthecaseoncetheopticsutilizedaretakenintoaccount.Inaperfectworld,withnodiffractionoropticalerrorsinasystem,resolutionwouldbebasedsimplyuponthesizeofapixelandthesizeoftheobjectthatisbeingviewed(seeourapplicationnoteObjectSpaceResolutionforfurtherexplanation).Tobrieflysummarize,aspixelsizedecreases,theresolutionincreases.Thisincreaseoccursassmallerobjectscanbefitontosmallerpixelsandstillbeabletoresolvethespacingbetweentheobjects,evenasthatspacingdecreases.Thisisanoversimplifiedmodelofhowacamerasensordetectsobjects,nottakingnoiseorotherparametersintoaccount.

Lensesalsohaveresolutionspecifications,butthebasicsarenotquiteaseasytounderstandassensorssincethereisnothingquiteasconcreteasapixel.However,therearetwofactorsthatultimatelydeterminethecontrastreproduction(modulationtransferfunction,orMTF)ofaparticularobjectfeatureontoapixelwhenimagedthroughalens:diffractionandaberrationalcontent.Diffractionwilloccuranytimelightpassesthroughanaperture,causingcontrastreduction(moredetailsinourapplicationnoteLimitationsonResolutionandContrast:TheAiryDisk).Aberrationsareerrorsthatoccurineveryimaginglensthateitherblurormisplaceimageinformationdependingonthetypeofaberration(moreinformationonindividualopticalaberrationscanbefoundinourapplicationnoteHowAberrationsAffectMachineVisionLenses.Withafastlens(≤f/4),opticalaberrationsaremostoftenthecauseforasystemdepartingfrom“perfect”aswouldbedictatedbythediffractionlimit;inmostcases,lensessimplydonotfunctionattheirtheoreticalcutofffrequency(ξCutoff),asdictatedbyEquation1.

Torelatethisequationbacktoacamerasensor,asthefrequencyofpixelsincreases(pixelsizegoesdown),contrastgoesdown-everylenswillalwaysfollowthistrend.However,thisdoesnotaccountfortherealworldhardwareperformanceofalens.Howtightlyalensistolerancedandmanufacturedwillalsohaveanimpactontheaberrationalcontentofalensandthereal-worldperformancewilldifferfromthenominal,as-designedperformance.Itcanbedifficulttoapproximatehowarealworldlenswillperformbasedonnominaldata,buttestsinalabcanhelpdetermineifaparticularlensandcamerasensorarecompatible.

OnewaytounderstandhowalenswillperformwithacertainsensoristotestitsresolutionwithaUSAF1951bartarget.Bartargetsarebetterfordetermininglens/sensorcompatibilitythanstartargets,astheirfeatureslineupbetterwithsquare(andrectangular)pixels.Thefollowingexamplesshowtestimagestakenwiththesamehighresolution50mmfocallengthlensandthesamelightingconditionsonthreedifferentcamerasensors.Eachimageisthencomparedtothelens’snominal,on-axisMTFcurve(bluecurve).Onlytheon-axiscurveisusedinthiscasebecausetheregionofinterestwherecontrastwasmeasuredonlycoveredasmallportionofthecenterofthesensor.Figure1showstheperformanceofthe50mmlenswhenpairedwitha1/2.5”ONSemiconductorMT9P031with2.2mpixels,whenatamagnificationof0.177X.UsingEquation1fromourapplicationnoteResolution,thesensor’sNyquistresolutionis227.7lp/mm,meaningthatthesmallestobjectthatthesystemcouldtheoreticallyimagewhenatamagnificationof0.177Xis12.4m(usinganalternateformofEquation7fromourapplicationnoteResolution).

Keepinmindthatthesecalculationshavenocontrastvalueassociatedwiththem.TheleftsideofFigure1showstheimagesoftwoelementsonaUSAF1951target;thetopimageshowstwopixelsperfeature,andthebottomimageshowsonepixelperfeature.AttheNyquistfrequencyofthesensor(227lp/mm),thesystemimagesthetargetwith8.8%contrast,whichisbelowtherecommended20%minimumcontrastforareliableimagingsystem.Notethatbyincreasingthefeaturesizebyafactoroftwoto24.8μm,thecontrastisincreasedbynearlyafactorofthree.Inapracticalsense,theimagingsystemwouldbemuchmorereliableathalftheNyquistfrequency.

Figure1:Comparisonnominallensperformancevs.real-worldperformanceforahighresolution50mmlensontheONSemiconductorMT9P031with2.2mpixels.TheredlineshowstheNyquistlimitofthesensorandtheyellowlineshowshalfoftheNyquistlimit.

Theconclusionthattheimagingsystemcouldnotreliablyimageanobjectfeaturethatis12.4minsizeisindirectoppositiontowhattheequationsinourapplicationnoteResolutionshow,asmathematicallytheobjectsfallwithinthecapabilitiesofthesystem.Thiscontradictionhighlightsthatfirstordercalculationsandapproximationsarenotenoughtodeterminewhetherornotanimagingsystemcanachieveaparticularresolution.Additionally,aNyquistfrequencycalculationisnotasolidmetriconwhichtolaythefoundationoftheresolutioncapabilitiesofasystem,and首ldonlybeusedasaguidelineofthelimitationsthatasystemwillhave.Acontrastof8.8%istoolowtobeconsideredaccuratesinceminorfluctuationsinconditionscouldeasilydrivecontrastdowntounresolvablelevels.

Figures2and3showsimilarimagestothoseinFigure1thoughthesensorsusedweretheSonyICX655(3.45mpixels)andONSemiconductorKAI-4021(7.4mpixels).Thetopimagesineachfigureshowtwopixelsperfeatureandthebottomimagesshowonepixelperfeature.ThemajordifferencebetweenthethreeFiguresisthatalloftheimagecontrastsforFigures2and3areabove20%,meaning(atfirstglance)thattheywouldbereliableatresolvingfeaturesofthatsize.Ofcourse,theminimumsizedobjectstheycanresolvearelargerwhencomparedtothe2.2mpixelsinFigure1.However,imagingattheNyquistfrequencyisstillill-advisedasslightmovementsintheobjectcouldshiftthedesiredfeaturebetweentwopixels,makingtheobjectunresolvable.Notethatasthepixelsizesincreasefrom2.2m,to3.45m,to7.4m,therespectiveincreasesincontrastfromonepixelperfeaturetotwopixelsperfeaturearelessimpactful.OntheICX655(3.45mpixels),thecontrastchangesbyjustunderafactorof2;thiseffectisfurtherdiminishedwiththeKAI-4021(7.4mpixels).

Figure2:Comparisonnominallensperformancevs.real-worldperformanceforahighresolution50mmlensontheSonyICX655with3.45mpixels.ThedarkbluelineshowstheNyquistlimitofthesensor,andthelightbluelineshowshalfoftheNyquistlimit.

Figure3:Comparisonnominallensperformancevs.real-worldperformanceforahighresolution50mmlensontheONSemiconductorKAI-4021with7.4mpixels.ThedarkgreenlineshowstheNyquistlimitofthesensor,andthelightgreenlineshowshalfoftheNyquistlimit.

AnimportantdiscrepancyinFigures1,2,and3isthedifferencebetweenthenominallensMTFandthereal-worldcontrastinanactualimage.TheMTFcurveofthelensontherightsideofFigure1showsthatthelens首ldachieveapproximately24%contrastatthefrequencyof227lp/mm,whenthecontrastvalueproducedwas8.8%.Therearetwomaincontributorstothisdifference:sensorMTFandlenstolerances.MostsensorcompaniesdonotpublishMTFcurvesfortheirsensors,buttheyhavethesamegeneralshapethatthelenshas.Sincesystem-levelMTFisaproductoftheMTFsofallofthecomponentsofasystem,thelensandthesensorMTFsmustbemultipliedtogethertoprovideamoreaccurateconclusionoftheoverallresolutioncapabilitiesofasystem.Asmentionedabove,atolerancedMTFofalensisalsoadeparturefromthenominal.Allofthesefactorscombinetochangetheexpectedresolutionofasystem,andonitsown,alensMTFcurveisnotanaccuraterepresentationofsystem-levelresolution.

AsseenintheimagesinFigure4,thebestsystem-levelcontrastisintheimagestakenwiththelargerpixels.Asthepixelsizedecreases,thecontrastdropsconsiderably.Agoodbestpracticeistouse20%asaminimumcontrastinamachinevisionsystem,asanycontrastvaluebelowthatistoosusceptibletofluctuationsinnoisecomingfromtemperaturevariationsorcrosstalkinillumination.Theimagetakenwiththe50mmlensandthe2.2mpixelinFigure1hasacontrastof8.8%andistoolowtorelyontheimagedataforobjectfeaturesizescorrespondingtothe2.2mpixelsizebecausethelensisonthebrinkofbecomingthelimitingfactorinthesystem.Sensorswithpixelsmuchsmallerthan2.2mcertainlyexistandarequitepopular,butmuchbelowthatsizebecomesnearlyimpossibleforopticstoresolvedowntotheindividualpixellevel.ThismeansthattheequationsdescribedinourapplicationnoteResolutionbecomefunctionallymeaninglessforhelpingtodeterminesystem-levelresolution,andimagessimilartothosetakenintheaforementionedfigureswouldbeimpossibletocapture.However,thesetinypixelsstillhaveause-justbecauseopticscannotresolvetheentirepixeldoesnotrenderthemuseless.Forcertainalgorithms,suchasblobanalysisoropticalcharacterrecognition(OCR),itislessaboutwhetherthelenscanactuallyresolvedowntotheindividualpixellevelandmoreabouthowmanypixelscanbeplacedoveraparticularfeature.Withsmallerpixelssubpixelinterpolationcanbeavoided,whichwilladdtotheaccuracyofanymeasurementdonewithit.Additionally,thereislessofapenaltyintermsofresolutionlosswhenswitchingtoacolorcamerawithaBayerpatternfilter.

Figure4:Imagestakenwiththesamelensandlightingconditionsonthreedifferentcamerasensorswiththreedifferentpixelsizes.Thetopimagesaretakenwithfourpixelsperfeature,andthebottomimagesaretakenwithtwopixelsperfeature.

Anotherimportantpointtorememberisthatjumpingfromonepixelperfeaturetotwopixelsperfeaturegivesasubstantialamountofcontrastback,particularlyonthesmallerpixels.Althouyhalvingthefrequency,theminimumresolvableobjecteffectivelydoublesinsize.Ifitisabsolutelynecessarytoviewdowntothesinglepixellevel,itisoftenbettertodoubletheoptics’magnificationandhalvethefieldofview.Thiswillcausethefeaturesizetocovertwiceasmanypixelsandthecontrastwillbemuchhigher.Thedownsidetothissolutionisthatlessoftheoverallfieldwillbevisible.Fromtheimagesensorperspective,thebestthingtodoistomaintainthepixelsizeanddoubletheformatsizeoftheimagesensor.Forexample,animagingsystemwitha1Xmagnificationusinga”sensorwitha2.2mpixelwillhavethesamefieldofviewandspatialresolutionasa2Xmagnificationsystemusinga1”sensorwitha2.2mpixel,butwiththe2Xsystem,thecontrastistheoreticallydoubled.

Unfortunately,doub领thesensorsizecreatesadditionalproblemsforlenses.Oneofthemajorcostdriversofanimaginglensistheformatsizeforwhichitwasdesigned.Designinganobjectivelensforalargerformatsensortakesmoreindividualopticalcomponents;thosecomponentsneedtobelargerandthetolerancingofthesystemneedstobetighter.Continuingfromtheexampleabove,alensdesignedfora1”sensormaycostfivetimesasmuchasalensdesignedfora”sensor,evenifitcannothitthesamepixellimitedresolutionspecifications.

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