Understanding Focal Length and Field of View | Edmund Optics

By focusing the lens for different working distances (WDs), differently sized field of view (FOV) can be obtained, though the viewing angle is constant. HowmayIhelpyou? Engineersareavailabletoassist. Ouroperatorsarenotavailableatthemoment.Pleaseleaveamessageandwewillcontactyousoon Leaveamessage HappyHolidaysfromEdmundOptics!Pleasenoteourspecialopeninghours.      CHAT    EMAIL Country/Region Wehavesetyourcountry/regiontoUnitedStates Youcanchangethisselectionatanytime,butproductsinyourcart,savedlists,orquotemayberemovediftheyareunavailableinthenewshippingcountry/region. 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Welcome! MyAccount AccessDashboard MyProfile UpdateMyProfile Payment&Shipping AddressBook, TaxCertificates WebOrders ViewPastOrders SavedLists SavedItemsforLater LogOut    Products Capabilities KnowledgeCenter Company ContactUs  MyAccount  Cart   hasbeenaddedtoyourcart. OrderNumberhasbeenaddedtoyourcart. Allitemshavebeenaddedtoyourcart. hasbeenaddedtoyourcomparelist. Productaddedtocart KnowledgeCenter /ApplicationNotes /Imaging /UnderstandingFocalLengthandFieldofView UnderstandingFocalLengthandFieldofView GregoryHollows NicholasJames http://www.edmundoptics.com/knowledge-center/application-notes/imaging/understanding-focal-length-and-field-of-view/ EdmundOpticsInc. http://www.edmundoptics.com UnderstandingFocalLengthandFieldofView ThisisSection1.3 oftheImagingResourceGuide. PreviousSectionNextSection FixedFocalLengthLenses Afixedfocallengthlens,alsoknownasaconventionalorentocentriclens,isalenswithafixedangularfieldofview(AFOV).Byfocusingthelensfordifferentworkingdistances(WDs),differentlysizedfieldofview(FOV)canbeobtained,thoughtheviewingangleisconstant.AFOVistypicallyspecifiedasthefullangle(indegrees)associatedwiththehorizontaldimension(width)ofthesensorthatthelensistobeusedwith. Note:Fixedfocallengthlensesshouldnotbeconfusedwithfixedfocuslenses.Fixedfocallengthlensescanbefocusedfordifferentdistances;fixedfocuslensesareintendedforuseatasingle,specificWD.Examplesoffixedfocuslensesaremanytelecentriclensesandmicroscopeobjectives. ThefocallengthofalensdefinestheAFOV.Foragivensensorsize,theshorterthefocallength,thewidertheAFOV.Additionally,theshorterthefocallengthofthelens,theshorterthedistanceneededtoobtainthesameFOVcomparedtoalongerfocallengthlens.Forasimple,thinconvexlens,thefocallengthisthedistancefromthebacksurfaceofthelenstotheplaneoftheimageformedofanobjectplacedinfinitelyfarinfrontofthelens.Fromthisdefinition,itcanbeshownthattheAFOVofalensisrelatedtothefocallength(Equation1),where$\small{f}$isthefocallengthand$\small{H}$isthesensorsize(Figure1). (1) $$\text{AFOV}=2\times\tan^{-1}{\left(\frac{H}{2f}\right)}$$ Figure1:Foragivensensorsize,H,shorterfocallengthsproducewiderAFOV’s. Ingeneral,however,thefocallengthismeasuredfromtherearprincipalplane,rarelylocatedatthemechanicalbackofanimaginglens;thisisoneofthereasonswhyWDscalculatedusingparaxialequationsareonlyapproximationsandthemechanicaldesignofasystemshouldonlybelaidoutusingdataproducedbycomputersimulationordatatakenfromlensspecificationtables.Paraxialcalculations,asfromlenscalculators,areagoodstartingpointtospeedthelensselectionprocess,butthenumericalvaluesproducedshouldbeusedwithcaution. Whenusingfixedfocallengthlenses,therearethreewaystochangetheFOVofthesystem(cameraandlens).ThefirstandofteneasiestoptionistochangetheWDfromthelenstotheobject;movingthelensfartherawayfromtheobjectplaneincreasestheFOV.Thesecondoptionistoswapoutthelenswithoneofadifferentfocallength.Thethirdoptionistochangethesizeofthesensor;alargersensorwillyieldalargerFOVforthesameWD,asdefinedinEquation1. WhileitmaybeconvenienttohaveaverywideAFOV,therearesomenegativestoconsider.First,thelevelofdistortionthatisassociatedwithsomeshortfocallengthlensescangreatlyinfluencetheactualAFOVandcancausevariationsintheanglewithrespecttoWDduetodistortion.Next,shortfocallengthlensesgenerallystruggletoobtainthehighestlevelofperformancewhencomparedagainstlongerfocallengthoptions(seeBestPractice#3inBestPracticesforBetterImaging).Additionally,shortfocallengthlensescanhavedifficultiescoveringmediumtolargesensorsizes,whichcanlimittheirusability,asdiscussedinRelativeIllumination,Roll-Off,andVignetting. AnotherwaytochangetheFOVofasystemistouseeitheravarifocallensorazoomlens;thesetypesoflensesallowforadjustmentoftheirfocallengthsandthushavevariableAFOV.Varifocalandzoomlensesoftenhavesizeandcostdrawbackscomparedtofixedfocallengthlenses,andoftencannotofferthesamelevelofperformanceasfixedfocallengthlenses. UsingWDandFOVtoDetermineFocalLength Inmanyapplications,therequireddistancefromanobjectandthedesiredFOV(typicallythesizeoftheobjectwithadditionalbufferspace)areknownquantities.ThisinformationcanbeusedtodirectlydeterminetherequiredAFOVviaEquation2.Equation2istheequivalentoffindingthevertexangleofatrianglewithitsheightequaltotheWDanditsbaseequaltothehorizontalFOV,orHFOV,asshowninFigure2.Note:Inpractice,thevertexofthistriangleisrarelylocatedatthemechanicalfrontofthelens,fromwhichWDismeasured,andisonlytobeusedasanapproximationunlesstheentrancepupillocationisknown. (2)\begin{align}\text{AFOV}&=2\times\tan^{-1}\left(\frac{\text{FOV}}{2\,\times\,\text{WD}}\right)\\\\&\text{or}\\\\\text{FOV} &=2\,\times\,\text{WD}\times\tan\left(\frac{\text{AFOV}}{2}\right)\\\end{align} OncetherequiredAFOVhasbeendetermined,thefocallengthcanbeapproximatedusingEquation1andtheproperlenscanbechosenfromalensspecificationtableordatasheetbyfindingtheclosestavailablefocallengthwiththenecessaryAFOVforthesensorbeingused. The14.25°derivedinExample1(seewhiteboxbelow)canbeusedtodeterminethelensthatisneeded,butthesensorsizemustalsobechosen.Asthesensorsizeisincreasedordecreaseditwillchangehowmuchofthelens’simageisutilized;thiswillaltertheAFOVofthesystemandthustheoverallFOV.Thelargerthesensor,thelargertheobtainableAFOVforthesamefocallength.Forexample,a25mmlenscouldbeusedwitha½”(6.4mmhorizontal)sensorora35mmlenscouldbeusedwitha2/3”(8.8mmhorizontal)sensorastheywouldbothapproximatelyproducea14.5°AFOVontheirrespectivesensors.Alternatively,ifthesensorhasalreadybeenchosen,thefocallengthcanbedetermineddirectlyfromtheFOVandWDbysubstitutingEquation1inEquation2,asshowninEquation3. (3)$$f=\frac{\left(H\times\text{WD}\right)}{\text{FOV}}$$ Aspreviouslystated,someamountofflexibilitytothesystem’sWDshouldbefactoredin,astheaboveexamplesareonlyfirst-orderapproximationsandtheyalsodonottakedistortionintoaccount. Figure2:RelationshipbetweenFOV,sensorsize,andWDforagivenAFOV. CalculatingFOVUsingaLenswithaFixedMagnification Generally,lensesthathavefixedmagnificationshavefixedorlimitedWDranges.Whileusingatelecentricorotherfixedmagnificationlenscanbemoreconstraining,astheydonotallowfordifferentFOVsbyvaryingtheWD,thecalculationsforthemareverydirect,asshowninEquation4. (4)$$\text{FOV}=\frac{H}{m}$$ SincethedesiredFOVandsensorareoftenknown,thelensselectionprocesscanbesimplifiedbyusingEquation5. (5)$$m=\frac{H}{\text{FOV}}$$ IftherequiredmagnificationisalreadyknownandtheWDisconstrained,Equation3canberearranged(replacing$\small{\tfrac{H}{\text{FOV}}}$withmagnification)andusedtodetermineanappropriatefixedfocallengthlens,asshowninEquation6. (6)$$m=\frac{f}{\text{WD}}$$ BeawarethatEquation6isanapproximationandwillrapidlydeteriorateformagnificationsgreaterthan0.1orforshortWDs.Formagnificationsbeyond0.1,eitherafixedmagnificationlensorcomputersimulations(e.g.Zemax)withtheappropriatelensmodelshouldbeused.Forthesamereasons,lenscalculatorscommonlyfoundontheinternetshouldonlybeusedforreference.Whenindoubt,consultalensspecificationtable. Note:HorizontalFOVistypicallyusedindiscussionsofFOVasamatterofconvenience,butthesensoraspectratio(ratioofasensor’swidthtoitsheight)mustbetakenintoaccounttoensurethattheentireobjectfitsintotheimagewheretheaspectratioisusedasafraction(e.g.4:3=4/3),Equation7. (7)$$\text{HorizontalFOV}=\text{VerticalFOV}\times\text{AspectRatio}$$ Whilemostsensorsare4:3,5:4and1:1arealsoquitecommon.Thisdistinctioninaspectratioalsoleadstovaryingdimensionsofsensorsofthesamesensorformat.AlloftheequationsusedinthissectioncanalsobeusedforverticalFOVaslongasthesensor’sverticaldimensionissubstitutedinforthehorizontaldimensionspecifiedintheequations. LENSFOCALLENGTHEXAMPLES UsingWDandFOVtoDetermineFocalLength Example1:ForasystemwithadesiredWDof200mmandaFOVof50mm,whatistheAFOV? \begin{align}\text{AFOV}&=2\times\tan^{-1}\left({\frac{50\text{mm}}{2\times200\text{mm}}}\right) \\\text{AFOV}&=14.25°\end{align} CalculatingFOVUsingaLenswithaFixedMagnification Example2:Foranapplicationusinga½”sensor,whichhasahorizontalsensorsizeof6.4mm,ahorizontalFOVof25mmisdesired. \begin{align}m&=\frac{6.4\text{mm}}{25\text{mm}}\\m&=0.256\text{X}\\\end{align} Byreviewingalistoffixedmagnificationortelecentriclenses,apropermagnificationcanbeselected. Note:Asthemagnificationincreases,thesizeoftheFOVwilldecrease;amagnificationthatislowerthanwhatiscalculatedisusuallydesirablesothatthefullFOVcanbevisualized.InthecaseofExample2,a0.25Xlensistheclosestcommonoption,whichyieldsa25.6mmFOVonthesamesensor. PreviousSectionNextSection FeaturedResources  Webinar ChoosingtheRightMachineVisionLensWebinar  TechnicalCalculators ImagingSystemParameterCalculator  TechnicalTool ImagingLensSelector EdmundOptics®Imaging:ManufacturingCapabilities LearnMore   Wasthiscontentusefultoyou? Thankyouforratingthiscontent! RequestanImagingOpticsCatalog Withover800ImagingLensesand40pagesofindepthTechnicalContent,makeEdmundOpticsYourPartnerinImagingOptics. ImagingLenses Telecentric,fixedfocallength,micro-video,fixedmagnification,variablemagnification,orzoomlensesavailable.Highresolutionorlargeformatdesignstocoveryoursensor. FocalLengthCalculator Easeintegrationofsimplelensesintoopticalassembliesbyprovidinglensradii,indexofrefraction,andcenterthickness. 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