Optický systém

IdealeopticalSystem

TheidealopticalSystemISaniMagingSystemtcanProduceaclear, zcelasimilariMageToTheObject.TheBeamsinwhicheachlighTrayoritSextension

lineSallinterSatThesamepointArecalledConcentricBeams.AftertheidentConcentricBeAspasshRoughtheidealopticalSystem, theoutingbeammusthalsobeaconcentricbeam.The IntersectionSectionSidentAnDoutingongOnCentricBeamSIscalledtheObjectPointAndtheimagepoint.TheidealopticalSystemHastheFollowingProperties: ①aferallthelightrayscrossingTheObjectPossThroughtheopticalSystem, theoutinglighTraySareallcrossingtheiMagepointPoint..Viceversa.ThePointATTHTHTHISPAIROFOFObjectImagesCanbeinterChangeDIscAlledTheConjugatepoint.②eachstraightLineonTheObjectSideCoresportStoastraightlineOnTheimagesIdeCalledaConjugateline; ThecorespondingsingurcalledaConjugatesurface.„.④forairairofConjugatePlanesPenPendiculartotheopticaxis, Thelateralmagnificationsconstant.ThetheoryofSusingtheone-on-onEcordencebetweenthetwoObjectsinanideaLopticalSystemscalledgaussaianoptics.ItsfirstClarifiedBegerManscientistc.Gaussinhisworkin1841.Infact, to jeNotrulyidealopticalSystem.TheCoaxialsphericalSystemCanapproxmeetTequirequideaLopticalSystemUnderParaxialConditions.

BasePointAndBasesUrface

NěkolikPairsOfspecialPointSandSurFacestHatdeterTetheConjugationRelationshipBeentheObjectAndiMageofanidealopticalshystem.

Focus afocalplane

ThePontonTheopticaxisTatisconjugatetotheinfinityimagepointIscalledtheObjectFocus (OrthefirstFocus).AsF;thepointontheopticalaxisthatisconjugatetotheinfinityobjectpointiscalledtheimage-sidefocalpoint(orsecondfocalpoint),andisdenotedasF'.TheplanespassingthroughtheFandF′pointsandperpendiculartotheopticalaxisarecalledtheobjectfocalplane(firstfocalplane)andimagefocalplane(secondfocalplane).

PrincipalPointAndPrincipalSurface

ApairofconjugatesUrfacesWithalateralmagnificationEqualTo1IscalledTheprincipalSurface, aIntersectiofThetWoprincipalSurfacesandtheopticalaxisIsCalledMainPoint.AnylightrayemittedfromthefocusoftheobjectF,afterpassingthroughtheopticalsystem,becomesarayparalleltotheopticalaxis.ExtendthepairofconjugatelightraystogettheirintersectionpointM,thisintersectionpointThesetof,constitutesthemainsurfaceoftheobject(thefirstmainsurface),andtheintersectionofthemainsurfaceandtheopticalaxisHiscalledthemainpointoftheobject(thefirstmainpoint).Afterthelightparalleltotheopticalaxisenters,theoutgoinglightintersectsattheimagefocalpointF'.ExtendthepairofconjugatelightraystoobtaintheintersectionpointM'.ThesetofintersectionsconstitutesTheprincipalsurfaceoftheimageside(thesecondprincipalsurface),theintersectionpointH'betweenitandtheopticalaxisiscalledtheprincipalpointoftheimageside(thesecondprincipalpoint).TheTWOPRINCIPALSULSarairofConjugateSurfaces, AthetwoprincipalpointSarairairofConjugatepoints.TheHeightOfanyPairofConjugatePointSothetwomainsUrfacesftheopticalAxiseSqual, athelateralmagnificationIs1.

NodeSandNodalplanes

ApairofconjugatepointswithanangularZvětšeníOf1onteopticalAxiSIsCallEdanode, který sestoupí, žehroughthenodeanisperpenpendiculartotheopticaxis.ThefaceIsCalledThesectionface.

Object-ImageRelationship

Ingaussoptics, theSpecifificopticalSystemIsAbstracteDassystemConsistingofabasePointandaBaseSurface.TheObjectDistance, imagedistanceandFocalLengthArealBaseTontWoMainPointScalculatesaBenchmark.ObjectpointQandobjectfocusFtothemainobjectpointHdistancesandfrespectivelytheobjectdistanceandtheobjectfocallength;theprincipalpointoftheimagesideH'totheimagepointQ'andthefocuspointoftheimagesideF'Thedistancesaretheimagedistances'andtheimagesidefocallengthf'.ThePositionAlRelationshipBetweenTobjectSandImageSisexpressedBefOllowingFormula:

f'/s'+f/s=1

TOTO FORMULAISCALLEDGAUSSIANFORMULA.Thepositionofobjectsandimagescanalsoberepresentedbyxandx'.TherelationshipBetweenthetwois:

xx'=ff'

Tento vzorec se nazývá Newtonův vzorec.

Zvětšení

TheratiooftheConjugatequantityrelatedTotheObjectAndtheimage.ITCanBedIDidedIndothRetypes: Horizontontalmagnification, VerticalZvětšeníAngularZvětšení.

Horizontální zvětšení

Theratiooftheimageheighty'totheobjectheighty,alsoknownastheverticalaxismagnification.βmeans:

β = y '/y = -ns'/n's

wherenandn'aretherefractiveindexoftheobjectspaceandtheimagespace.

Podélné zvětšení

Theratioofthelongitudinaldepthoftheimagealongtheopticalaxistothelongitudinaldepthoftheobjectontheopticalaxis,expressedbyα.Therelationshipbetweenαandβis:

α=β²n'/n

AngularMagnification

Theanglebetweentheemittedlightandtheopticalaxisu'andtheincidentTheratiooftheangleubetweenthelightandtheopticalaxis,expressedbyγ,namely:

γ=u'/u=tanu'/tanu=ny/n'y'

Proto:

n'y'u'=nyu

ThisTheLagrange-Helmholtztheorem.

ThethReemagnificationShavetheFowlowingRelationship:

αγ=β

Clona

AnopticalElementtHatRestrictsthelightBeampassingThroughtheopticalSystem.ItcanbetheframeoftheopticalElement (čočka, zrcadlo atd..) sám, oritcanbeanadditiolalopaquesceswithholes.TheCenterofThediaphragmisusOonTheopticalAxisandPerpendendiculartotheopticaxis.

Každý opticalPartoftheopticalSystemdefinedByitSownlensframetodeFineItslight-Passinghole.Nejvýznamnější, itisaroundhole.Někdy sefixedorvariableDedicatedLightholeSaredDedTothesystem.Mezi všemiThelightholes, OnelightholeMustplayaroleInmitingTheaperTureangleoftheon-AxispointimagingBeam; další vzhled, který je možné.SUCANAPERTUREISCALLEDADIAPHRAGM: TheformerIscAlleDanaperTurediaphragmoraneffectivediaphragm; ThelatIscalledafielddiaphragmmm.AnyopticalSystemMusthaveSuchtwodiaphragms.

Clonadiaphragm

Mezi themultiplediaphragms, thelimitingEfEftecToNtheastheghereatere, to, thediaphragMthatDetermineSthesizeoftheimagingam.TheClonadiaphragmcanblockthelightTheDeviatesFromTheparaxiallightintheBeam, který HasasadiRectimpenMacTonthesHarpness, přesnost, jasce a jasceddepthoftheimage.

BecauSetheimagingBeahoftheon-axispointlimitedbytheaperTurediaphragm, itiseasytoimagiNeThattHellthelightHofThesySmetareimagedTheObjectspaceThroughtheopticalPartsinfrontofit, Theon-AxisobjectjectItisopened..Theimagewiththesmallestangle, ortheimage smallestapertureWHentheObjectisatinfinity, mustbetheaperturestopopopop.TheimageofTheaperturediaphragMintheObjectspaceIscalledtheentrancePupil, aitsopeningangletotheObjectPointhisTheBeaMaperTureangleoftheObjectside.Podobně, TheClonadiaphragmisformedIntoanimageintheimageSpacebytheopticalPartsbehindit, nazývá setheexitpUpil.ItmustalsobeaperTureImagewiththesMallestopeningAngleoftheimagepointOntheaxis, a thisOpeningAngleiStheBeaMofTheimageside.Angleofaperture.ThentrancePupil, aperturestopandexitpupilareconjugovaný.IfthediaphragMaberarationIsnegled, TheentrancePupilightSomentRanceofTheImagingBeamallPointStheObjectlane;.TheLightPossingThroughTheCenterofTheaperTurediaphragmiscalledtHechiefray, a becauseofTheConjugaterationship, italsOpasSestHroughTheCenterofTheenTrancePupilandTentEroftheeXitPupile.Proto itisGenerallySaidtHechiefrayesterTenterLineoftheimagingBeam.

ThePositionOfTheaperTurediaphragMetheopticalSystemSrelatedTomanyFactors.Insomesystémy, následné doporučení.FORMAPLE, TheExitPupiloftHevisualOpticalSystemMustBeloCotOutSidetheeeCeSotHatthepupiloftheeyeCancoinciiDidewitit; inthetelecentricsystem, TheClonastopsHouldbeloCateatthefocalpointOpointOpoint..Inaddition,thepositionoftheaperturestopisalsorelatedtotheaberrationcorrectionandthelateralsizeoftheopticalpartsofthesystem,andshouldbereasonablydeterminedduringdesign.

Membrána pole

ThediaphragMthatDeterMestHerangeofvision.ThefieldDiaphragmcandeterMeTeTeTheSizeofThefieldOfView.ThefieldDiaphragmformedbythefrontopticalSystemscalledtheentrancewindow, aimageformedBerearSystemsCalledTheeXitWindow.

ThefieldDiaphragmisalightholeintheopticalSystemtHatDeterMisinitsisImagingrange.Inystemswithintermediaterealimageplanes (takové, jakskepletescopesAndMicroscopes) asystemswithrealimageplanes (takovéshotograficssystems), thefielddiaphragMisseTontThisimagePlane.TheimageofThefielddiaphragMetheObjectspaceForedBytheopticalPartSinfrontofitiscalledtheentranceWindow.TheangleitopenStotheCenterofTheentrancePipilisthesMallestofallaperTureImages, a thisAngledIscalledTheFieldngAngle.Podobně iMageFormedBetheopticalPartsbehindthefielddiaphragmintheimagespaceIscalledTheeXitWindow.TheenTranceWindow, FielddiaphragMandexitwindowarealsoconjugate.WHEntHefieldDiaphragMisSeTorealImagePlaneortheintermeateRiMagePlane, The AntranceWindowandexitwindowarecoincident s.ISITUACESHETHEETHEREISNORIMAGEORInterMediateRealimagePlane, takové, cosWhentheeyeisobserningThroughhamagnifikující SlassOrgalileoteScope, tedy nadále se systémy.ITSCLEARAPERTUREPLAYSAroleinlitingThefieldOfView.TheClonaofTheTescopeObjecteSiveLenStheFielddiaphragMthatDeterMesterSherofThevibleFieldOfView.Je zřejmé, že TheincidentWindowDoesNotcoincidewiththeObjectPlaneatthistiMistime a thereisnoclearBoundaryofThefieldOfview.

RelativeArture

TheratiooftheobjectivelensdiameterDtothefocallengthfintheimaginginstrument.Thephysicalquantityusedtodescribethelight-gatheringabilityoftheobjectivelens,becausetheluminousfluxdensityontheimagesurfaceisproportionalto(D/f)².ThereciProcaloftherelativeArtureSisCalledTheaperturefactor, orfnumber.ThePhotographicsLensisequippedWithanadjustableDiaphragm (běžně známý astheaperture), který se vyskytl, nakládá se, a proto podává, čímž se podává fondthelinuminousfluxDententephotosensitiveFilm.AserieSoffnumbersAreengravedonthelens.WhentheFnumberisreducedby2^-1/2timesoftheoriginalvalue,theluminousfluxdensitywillincreaseby2times.ThegeneralFnumberseriesvalues​​are

1,1.4,2,2.8,4,5.6,8,11,16,22,...

Thevalues​​oftheabovefilesarecalculatedbythefollowingformula(Roundedup):11

Clonafactor(Fnumber)=(2^1/2)^x

xisapositiveinteger,calledtheindexoftheaperturecoefficient,alsocalledtheAVvalue.IntheaboveF-numberseries,thevalues​​oftheadjacenttwogearsdifferby2times,thecorrespondingluminousfluxdensitydiffersby2times,andtheAVvaluediffersbyonelevel.

Fenomén vinětu

Podrost, thebeamsattheon-axisandoff-axispointsarelimitedbytheaperturediaphragm, a ahavebasicalsthesameBeaMapertureangleanglereangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleangleanglereangleanglereangleangleanglereangleangleanglereanglungungeRningleangluanglereangleangleanglereangleangleanglereanglereanglereanglereanglereanglereanglereanglereanglereanglereanglereanglereanglereanglereanglereanglereanglereangle.IfThefieldOfViewnottoobig, theimagesurfaiLuminanceofTheentirefieldOfViewIsBasBasicallicalform.Inactualualopticalsystems však Theoff-AxispointimagingBeamiSoftenmitedBethelight-PassingholetoropticalParts.Asaresult, TheBeamangleofTheoff-AxispointismisMallerthanthatoftheon-Axispoint.ThisBecausewhentheoff-axispointisAliimagedwithAbeaMofLightThIllsTheentrancePupil, thoselenSesthatarefarfromTheaperSeedToHavearelatiativeLativeLativeLativelatiatiatiatitivellatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiatiameter, additisveryDifficulttocorCorectFortheforthelfull-aperFoff-axisBeambeambeambeambeambeambeambeambeam.Proto inOrderToimproveTheimagingTualityFthe-axispoindThelaterAlsalizeofTheopTopTotParticularlylarge, theSethodofApPoPrailydCorativesCiltEnMetersDiaMetersOftenasedTolimittheoff-AxislightbeaMeach.ThisPhenomenoninwhichthelightBeamfromtheoff-axispointtHilsTheentrancePilisPartiallyinterceptedBySoSopticalPartsandCannotPasstHroughtheopticalSystemsCalledBeamVigNetTing.TheFarthetheoff-axispointisFromTheCthecticaxis, thereSioursheinterceptionPhenomenon (že, vignetting), atheresultisTtheTheimageSurIlluminanceatThePeripHeryofThefieldOfViewIsgreatlyredreduedreduredEdged..Samozřejmě, fastopticalshystemsAlowalowaleanceDegreeofVignigTetTing.

ImagingBeam

TheimagingBeaMofanobjectPointIsAspatialLightconeWithTheObjectPointExandTeentrancePupilaSthebase.AftertheBeAspasshRoughTheopticalSystem, ITSTRUCTURUREWILLCHANGE.Foraxisymmetricopticalsystems(mostsystemsbelongtothiscategory),theon-axispointbeamalwayshassymmetricproperties,buttheoff-axispointbeamlosessymmetryafterpassingthroughthesystem.INorderTofacilitaTeunderStandingofThestructureCtructureofThisBeam, ThePlaneBeaMonthetWoCharacteristicsUsUsUsUsUsuseusedfordscription.

Navržení the-AxisobjectPointTheopticAxisCalledthemeridianPlane.Duetotheaxisymmetricnatureoftheopticalshystem, off-axisobject-boontscAlwaysbetakenthedEdrawingplane, to je, thepaperPlaneisthemeridianplane.TheBeacilyNonthemeridianPlaneIscalledthemeridianbeam.Je zřejmé, že ThechiefrayMustBearayinthemeridianbeam.

TheplaneconturingTHechiefrayandPerpendicularTothemeridianPlaneIscalledtheSagIttalPlane.TheBeacilyNonthesagIttalPlaneIscalledthesagittalbeam.Je zřejmé, že thechiefrayiSiStheInsectiofThemeridianPlaneandthesagittallaplane.SinCetHechiefrayAngesSIRECTIONCTHTEFRAKCE areflectionReflectionSurfaceofTheSystem, ThesagittalplanealsochAngesfaceByfaceInsteadofaunifiedPlane.

DuetotheaxialsymmetryofTheopticalSystem, Theon-AxissspotbeamdoesNeedTobeSeparatedFomThemolecularMidianBeamandthesagitTalBeam, a theoff-axissspotbeammustbesymmethethethemeridianplanelianplan.

Aberace

Theimageformedbythelens (orlensgroup) je bez.BecausetheangleofthelighttedTetheObjectPointHemainaxisoftHelenSistoolarge, Itisfarawayfromtheaxis, orterefraktivnímIndexthelensMaterialChangesWithtHeWavelgentgenthelight.THESIZIZEOBERRATION reflectStheprosandConSofimagingquality.ThereareMainly7Kindsoaberations; formonochromatické světlo, therere5kinds, jmenovitě sféricaaberation, coma, astigmatismus, zakřivení affielddistotretiontretion.Forpolychromaticlight, thereretwokindsofchromaticaaberations, jmenovitě oxialchromaticAberarationAnderverticalchromaticaaberation.Eliminující rerudcingtheseaberrationsasmuchaspossibleisanimportanttaskintheSignOfopticalSystems.

SymetricalCoaxialDrawing

ThePropertiesOfSyMmetricalCoaxial

①Theobjectpointontheopticalaxis,theimagepointisalsoOntheopticalaxis;②Theobjectpointinthesectionpassingtheopticalaxisiscoplanarwiththeimage;③Thepropertiesofanysectionpassingtheopticalaxisarethesame;④Aplaneperpendiculartotheaxishasthesamemagnificationinthesameplane;⑤Knowingthepositionandmagnificationoftwopairsofconjugatesurfaces,orknowingthepositionandmagnificationofapairofconjugatesurfaces,plusthetwopairsofconjugatepointsontheopticalaxis,candeterminetheimagingoftheidealopticalsystem.

ProofBedrawingMethod

①theposition amagnificationOftwopairsOfConjugateSurfacesAre známé.ThePosition amagnificationofTheConjugatesurface, aswellasthePositionSoftHetWopairsOfConjugatePointSontheaxis, AreshownasFollows: