The ex tra curvature and airspace are used to control higherorder spherical aberration and sphe rochromatism However the ray angles of incidence in the airspace between the two elements can become very large making the alignment tolerances of the tw ID: 79813
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DesignForms31AirspacedDoublets ThespeedofaFraunhofercanbeincreasedto5byseparatingthece-mentedsurfacetocreateanairspaceddoublet.Theex-tracurvatureandairspaceareusedtocontrolhigher-ordersphericalaberrationandsphe-rochromatism.However,therayanglesofincidenceintheairspacebetweenthetwoelementscanbecomeverylarge,makingthealignmenttolerancesofthetwoelementsverytight.AsecondtypeofairspaceddoubletisaGaussdou-,whichhasmuchsteepercurvesandsignicantlylargerhigher-orderaberrations.Asaresult,Gaussdou-bletsarenotasfastasFraunhoferdoubletsandareoftenfoundinstop-symmetricanastigmaticlenses. Twoseparatedpositiveandneg-ativeelements(orgroupsofele-ments)witharelativelylargeairgapbetweenthemisknownasa.Althoughtheperformanceofasimpletwo-elementdialyteisusuallyinsufcient(primarilyduetoitsinabilitytocor-rectlateralcolor),itisthebasisformore-complex(positive/negative)andreversetelephototive/positive)multi-elementdesigns.Schupmannlensisaspecialairspaceddoubletthatiscorrectedforprimarycolorbutusesthesamematerialinbothelements.Becausethelenshasavirtualimage,itisseldomusedalonebutratherisoftenpartofmore-complexlenssystems. FieldGuidetoLensDesign 32DesignFormsCookeTriplet Cooketripletisthesimplestde-signformwithenoughdegreesoffreedomtocorrectallrst-andthird-orderaberrationsandholdrst-orderimagingconstraintssuchasEFLandBFL.Theoutertwoelementsarepos-itivecrowns,andthemiddleelementisanegativeintwiththeaperturestoplocatedoneithersideofthemiddleelement.Thesymmetryofthedesignhelpscontrolcoma,distortion,andlateralcolor.Becauseitisonlycorrectedtothirdorder,theCooketripletislimitedbyhigher-orderaberrationsandisthuscapableofrelativelyslowaper-tures(/6)andmoderateelds(10–15deg).Upto50%vignettingmaybeneededinsystemswithlargerelds.TheCooketripletisthemostbasicformofan.Strictlyspeaking,thetermanastigmatmeans“freeofastigmatism;”however,itisalsousedtodescribeopticalsystemswithreducedastigmatismandrelativelyatelds.Inthesedesigns,theeldisattenedbyseparatingpositiveandnegativepoweralongtheopticalaxis(betweensurfaces,elements,orevenmulti-elementgroupsofcomponents).PLANmicroscopeobjectivesusethisprincipaltoattentheeldcurvature.photographicobjectivedesignformsarederivedfromtheCooketripletbyorotherwisemodifyingelementsofthebasictriplet.Forexample,intheTessarlens,thelastelementofaCooketripletiscompoundedintoadoublet. Thisdesignallowsforspeedsupto/4and/orlargereldsofviewthantheba-sictripletwithreducedvi-gnetting. FieldGuidetoLensDesign DesignForms33DoubleGauss doubleGauss)isapowerfulanastigmatdesignformusedinawiderangeofapplications,includingxed-focuscameraobjectives,projectionlenses,andhigh-resolutionmicroscopeobjectives.Theclassicsix-elementdesignisnearlysymmetricaboutthestop(reducingcoma,distortion,andlateralcolor),withouterpositivesingletsandinnercementedthick-meniscusdoublets(tominimizePetzval).Astigmatismiscontrolledbyadjustingthedistanceoftheelementsfromthestop,asthisseparationhaslittleeffectontheotheraberrations.Designimprovementstothebasicformhavebeenstudiedextensivelyintheliterature;allowingthesystemtodepartfromsymmetryand/oraddingelements(bysplittingorcompounding)allowsonetoachievespeedsupto/1orFFOVslargerthan50deg. Fastanastigmatswithsmalleldstendtohaverelativelyshortvertexlengths,whereasslow-speedwide-anglelensestendtohavelongervertexlengths.InCooketripletsthevertexlengthcanbecontrolledbyglasschoice(particularlythedifferenceinbetweenpositiveandnegativeelements). Manyotherlensformsusestopsymmetryandpowerseparationtoachievewideeldsofview.Thesimplestisthe;twoidenticalmeniscuselementssymmetricaboutthestopachievinganimpressive135-degFFOV.Petzvalisreducedbytheseparationofpositiveandnegativepowerintheelementsthemselveswhere eachelementhasapositiveandanegativesurfacewithradiidifferingbylessthan7%.However,Hypergonsareslow(/20)asthereisnoremainingdegreeoffreedomtocorrectthesphericalaberration.More-complexdesigns(e.g.,Topogon,and)addelementstoincreasetheirspeed. FieldGuidetoLensDesign 34DesignFormsPetzvalLens PetzvalPetzvalportraitlensisadesignformusefulforhigh-speedapplicationsthatrequirehigh-qualityimagingoverrelativelysmallelds(e.g.,aerialreconnaissance).Originallydesignedforindoorphotography,Petzvallensesareanorderofmagnitudefasterthanlandscapelenses.ThePetzvallensisthebasisofmanymicroscopeobjectiveswhereaplanaticelementsareaddedtotheshortconjugateforincreasedNA. Unlikemanyoftheotherba-sicdesignforms,thePetzvallenshasverylittlesymme-try.Thebasiclayoutusestwoseparated,positivelypoweredachromatswiththestopatornearthefrontlens.Negativeastigmatismfromtherstdoubletisbalancedwithposi-tiveastigmatismfromtheseconddoublet.Becausetherearenolensgroupswithnetnegativepower,thedesignformisfundamentallylimitedbyPetzval,restrictingitseldsize.Decreasingtheairspacebetweenthetwodou-bletscanhelpreducethePetzvalattheexpenseofin-creasedastigmatism.GiventhefocallengthofaPetzvallens,therst-orderthinlenslayoutcanbecalculatedasfollows:Frontelementfocallength:2Rearelementfocallength:Elementseparation:Backfocallength:ImprovementstothebasicPetzvallensincludeaddingastrongnegativeeldlensneartheimageplanetocorrectPetzvalandincreaseitseld(althoughthissignicantly decreasestheworkingdistance).ThePetzvallensisalsothebasedesignformofmanyextremelyfast(/1)lenses,includingveryhigh-speed,6–8-elementPetzvalprojectionlenses FieldGuidetoLensDesign