CODEVIntroductorySeminar:Day1

“Optics101”

DigitalCameraDesignStudy3280EastFoothillBoulevardPasadena,California91107USA(626)795-9101Fax(626)795-0184e-mail:service@WorldWideWeb:Section1

Optics101

(onaBudget)Goalsand“NotGoals”Goals:BriefoverviewofbasicimagingconceptsIntroducesomelingooflensdesignersProvideresourcesforquickreferenceorfurtherstudyNotGoals:DerivationofequationsExplainallthereistoknowaboutopticaldesignExplainhowCODEVworksSignConventionsDistances:positivetoright

Curvatures:positiveifcenterofcurvatureliestorightofvertex

Angles:positivemeasuredcounterclockwise

Heights:positiveabovetheaxist>0t<0

VCc=1/r<0

VCc=1/r>0q>0q<0LightfromPhysics102Lighttravelsinstraightlines(homogeneousmedia)Snell’sLaw:nsinq

=n’sinq’Paraxialapproximation:Smallangles:sinq~tanq~q;andcosq~1OpticalsurfacesrepresentedbytangentplaneatvertexignoresagincomputingrayheightthicknessisalwayscenterthicknessPowerofasphericalrefractingsurface:

1/f=f

=(n’-n)*cUsefulfortracingraysquicklyanddevelopingaberrationtheoryCardinalPoints6importantpointsalongtheaxisofanopticalsystem2focalpoints(frontandback):

inputlightparalleltotheaxiscrossestheaxisatfocalpointsFandF’2principalpoints(primaryandsecondary):

extendlinesalonginputrayandexitingfocalray;wheretheyintersectdefinesprincipal“planes”whichintersecttheaxisattheprincipalpoints2nodalpoints(firstandsecond):raysaimedatthefirstappeartoemergefromthesecondatthesameangle.“first”pointsdefinedbyparallelraysenteringfromtheright;“second”pointsdefinedbyparallelraysenteringfromtheleftCardinalPointsIllustratedEffectiveFocalLength(EFL)=distancefromprincipalpointtofocalpointP1F1F2EFLEFLApertureStopAperturestop:determineshowmuchlightentersthesystem2specialraysMarginalray:fromon-axisobjectpointthroughtheedgeofthestopChiefray:frommaximumextentofobjectthroughthecenterofthestopApertureStopChiefrayMarginalrayPupilsandtheApertureStopPupilsEntrancepupil:imageofaperturestopviewedfromobjectspaceExitpupil:imageofaperturestopviewedfromimagespaceEntrancepupillocationExitpupillocationEntrancepupildiameter(EPD)ApertureStopSpecifyingtheApertureEPD=EntrancepupildiameterNAO=Numericalapertureinobjectspace(finiteobject)NA=Numericalapertureinimagespacef/#=EFL/EPDNote:someNAOsystemswillnotfillaphysicalaperturestop(commoninphotonicssystems.)Youstillmustspecifyastopsurface.SpecifyingthePupilObjectHH'ImageTHIS0LEntrancepupilEPDqNAO=nsinqq=tan-1(EPD/2L)NA=NAO/RED=n'sinq'FNO=1/(2NA)q'RED=–H'/HInfiniteobject:?/#=EFL/EPDNAOnotvalidSameTriplet,Differentf/#’sf/3f/4f/8“Faster”“Slower”FieldDefinitionFielddefinitiondescribeshowmuchoftheobjectyouimage.Specifyobjectangle,objectheight(finiteobject),imageheight.ObjectImageObjectheight(YOB)Objectangle(YAN)Imageheight(YIM)EntrancepupilLYOB

=-YIM/REDYOB

=-L*tan(YAN)AberrationsPerfectimaging:pointonobjectmapstopointontheimage,forallpointsonobjectandallraysthroughtheaperturestop.Aberrations:deviationsfromthis“1storder”aberrations:Defocus:wrongimagelocationTilt:wrongimageorientationThird-OrderAberrationsSpherical:focallengthfvarieswithapertureheightonlyaberrationon-axisComa:magnificationvarieswithapertureraysthroughedgeofaperturehitimageatdifferentheightthanraysthroughcenterofapertureAstigmatism:sagittal(x-axis)andtangential(y-axis)rayfanshavedifferentfoci.Fieldcurvature:planarobjectformscurvedimagedependsonindexoflensesandtheirpowerDistortion:imagemagnificationdependsonimageheightimageismisshapen,butfocusisn’tchangedRayAberrationCurvesVerticalaxis:distanceonimageplanebetweenchiefrayandcurrentrayHorizontalaxis:relativeheightofrayinaperturestop(orentrance/exitpupil)Chiefrayy(r=1)y(r=-0.75)ImageplaneAperturestopr=1r=-0.75yzRayAberrationCurves(cont.)RelativeAperture

r01-110Rayerror(mm)-0.75y(r=1)y(r=-0.75)Tangential(y-fan)Sagittal(x-fan)RelativeAperture

rRayerror(mm)ChromaticAberrationIndexisfunctionofwavelength:n=n(l)Abbenumberdescribesthedispersion:Vd

=(nd–1)/(nF–nc)

ld=587.6nm(yellow)

lF=486.1nm(blue)

lc=656.3nm(red)SmallVd(Vd~20-50):verydispersive,colorsspreadalotLargeVd(Vd~55-90):lessdispersionRaysandWavesRaysarenormaltowavefrontWavesdiffractataperturesandcaninterfereRayscanimageperfectly;wavescan’tduetodiffractionataperturesApointimagestoAirydiskDiffraction-limitedspotsize(diameter)=2.44l

f/#(microns)2.44

l

f/#IntensityatimageplaneModulationTransferFunction(MTF)Startwithblackandwhitebars(orsinusoid)withspecifiedfrequency.Frequencyin“l(fā)ines/mm”,where“l(fā)ines”=“l(fā)inepairs”(1blackline+1whiteline)=cycleModulation=contrastImax=maximumintensityImin=minimumintensityforobject,contrast=1(pureblackandwhite)MTFMTFSpatialFrequency(cycles/mm)YXTS(R)Object:10IntensityalongimagesliceObject:1010Image1:Image1PositionImage2Image2:MTFdependsontargetorientation:(directionofvariationofintensity)S=Sagittal(a.k.a.R=Radial)orT=TangentialMTF(cont.)Imageisnotperfect;contrastdropsdueto:AberrationDiffractionVignettingVarieswith:fieldpointconsideredorientati