应用光学2011春(第八章(2次6课时)).ppt

1、2020/6/15,1,第八章光学系统成像质量评价,2020/6/15,2,实际光学系统都有一定大小的相对孔径合视场，远远超出近轴区所限定的范围。,8-1概述,与近轴区成像比较必然在成像位置和像的大小方面存在一定的差异，被称为像差,指在光学系统中由透镜材料的特性或折射（或反射）表面的几何形状引起实际像与理想像的偏差。,2020/6/15,3,Thegaussianformulasdevelopedandusedintheprecedingchaptersgive,therefore,onlyanidealizedaccountoftheimagesproducedwithlensesofwid

2、eaperture.,Whenraytracingisappliedtoobjectpointsfartherandfartherofftheaxis,theobservedimagedefectsbecomemoreandmorepronounced.,2020/6/15,4,ExpansionOfTheSine.First-OrderTheory,Inordertoformulateasatisfactorytheoryoflensaberrations,itsconvenienttostartwiththecorrectandpreciseray-tracingformulasandto

3、expandthesinesofeachangleintoapowerseries,Maclaurinstheorem,2020/6/15,5,Forsmallanglesthisisarapidlyconvergingseries.Forparaxialrays,wemay,toafirstapproximation,neglectalltermsbeyondthefirst,Whenissmall,theotherangles,andarealsosmall,providedtherayliesclosetotheaxis.,so,2020/6/15,6,Allanglescanbeeli

4、minated.Thefinalequationobtainedbythesesubstitutionsisnoneotherthanthegaussianformula,Theequationandothersdevelopedfromitformthebasisofwhatisusuallycalledfirst-ordertheory,2020/6/15,7,Thejustificationforwriting,etc,forallsmallangles,2020/6/15,8,2020/6/15,9,Ifalensweretobefreeofalldefectsinisabilityt

5、oformimages,allfiveofthesesumswouldhavetoequalzero.,Noopticalsystemcanbemadetosatisfyalltheseconditionsatonce.,Itiscustomarytotreateachsumseparately,andthevanishingofcertainonescorrespondstotheabsenceofcertainaberrations,2020/6/15,10,IfforagivenaxialobjectpointtheSeidelsum,thereisnosphericalaberrati

6、onsatthecorrespondingimagepoint.Ifbothand,thesystemwillalsobefreeofcoma(彗差).Ifinadditiontoand,thesumsandaswell,theimageswillbefreeofastigmatism（象散）andcurvatureoffield（象场弯曲）.Iffinallycouldbemadetovanish,therewouldbenodistortion（畸变）oftheimage.,Theseaberrationsarealsoknownasthefivemonochromaticaberrati

7、onsbecausetheyexistforanyspecifiedcolorandrefractiveindex.,2020/6/15,11,像差的大小反映了光学系统质量的优劣,几何像差主要有七种：,单色光像差有五种：球差彗差(正弦差)像散场曲畸变,复色光像差有两种：轴向像差(位置色差)垂轴像差(倍率色差),2020/6/15,12,在实际光学系统中，各种像差是同时存在的。,这些像差影响光学系统成像的清晰度、相似性和色彩逼真度等，降低了成像质量。,1、球差：,球面像差的简称,2020/6/15,13,SphericalAberrationofaSingleSurface,Ablurringo

8、ftheimagethatoccursuponrefractionbysphericalsurfaces,2020/6/15,14,Thedistanceisameasureofthelongitudinalsphericalaberration,Ameasureofthedeviationsfromfirst-ordertheory,Itsmagnitudevarieswiththepositionoftheobjectpointandforanyfixedpointisapproximatelyproportionalto,thesquareoftheradiusofthezoneonth

9、erefractingsurfacethroughwhichtherayspass,2020/6/15,15,Iftheobjectpointisatinfinitysothattheincidentraysareparalleltotheaxis,2020/6/15,16,Againthemagnitudeoftheaberrationisproportionalto,thesquareoftheheightoftherayabovetheaxis,2020/6/15,17,SphericalAberrationofaThinLens,Theexistenceofsphericalaberr

10、ationforasinglesphericalsurfaceindicatesthatitmayalsooccurincombinationsofsuchsurfaces,e.g.,inathinlens,Itisusualforcomparisonpurposestodeterminethesphericalaberrationforparallelincidentlight,Theparaxialfocalpoint,2020/6/15,18,Illustratesthedifferencebetweenlongitudinalsphericalaberration,abbreviate

11、dLong.SA,andlateralsphericalaberration,abbreviatedLat.SA,2020/6/15,19,Agraphshowingthisvariationoffocallengthwithzoneradius,Forsmallh,thecurveapproximatesaparabola,Sincethemarginalraysintersecttheaxistotheleftoftheparaxialfocalpoint,thesphericalaberrationissaidtobepositive,2020/6/15,20,Asimilarcurve

12、,drawnforatypicaldoubleconcavelensofnearlythesamedimensions,Bendingtotheright,thislensissaidtohavenegativesphericalaberration,2020/6/15,21,Aseriesofpositivelensesofthesamediameterandparaxialfocallengthbutofdifferentshape,2020/6/15,22,Thealterationofshaperepresentedinthisseriesisknownasbendingthelens

13、.,Eachlensislabeledbyanumberqcalleditsshapefactor,配曲调整,2020/6/15,23,e.g.ifthetworadiiofaconvergingmeniscuslensareandithasashaperfactor,2020/6/15,哈工大光电测控技术与装备研究所,24,Theusualreasonforconsideringthebendingofalensistofindthatshapeforwhichthesphericalaberrationisaminimum,Theleastsphericalaberration,2020/

14、6/15,25,Theamountofthisaberrationfortherayhavingh=1.0cmisshownforthesameseriesoflensesbythecurvesofFigure,Overtherangefromaboutq=+0.4cmtoq=+1.0cmthesphericalaberrationisclosetoaminimum,butitgoestozeroatnopoint,2020/6/15,26,Weseethereforethatbychoosingtheproperradiiforthetwosurfacesofalensthespherica

15、laberrationcanbereducedtoaminimumbutcannotbemadetovanishcompletely,Withsphericalsurfacesthemarginalraysaredeviatedthroughtoolargeanangle,Anequaldivisionofrefractionwillyieldthesmallestsphericalaberration,2020/6/15,27,2020/6/15,28,z位于近轴像点距边缘像点3/4处,球差图形,2020/6/15,30,2020/6/15,31,2020/6/15,32,Resultsof

16、Third-OrderTheory,Forathinlenswehavethereasonablysimpleformula,where,2020/6/15,哈工大光电测控技术与装备研究所,33,Thenumericalresultsofthird-ordertheory,2020/6/15,34,Fifth-OrderSphericalAberration,Thethird-orderequationshowsthatsphericalaberrationshouldbeproportionalto,Neverthelessaccuratemeasurementsshowthatforlar

17、gerhdeparturesfromproportionalitytodooccurandthatsphericalaberrationismorecloselyrepresentedbyanequationoftheform,Thethird-ordereffect,Thefifth-ordereffect,aandbareconstants,2020/6/15,35,Thefirstrowgivesthethird-ordercorrectionsandthesecondrowthefifth-ordercorrections,a=0.11356andb=0.00174,2020/6/15

18、,36,Thenegligiblecontributionofthefifth-ordercorrectionatsmallvaluesofh,2020/6/15,37,Ifonlythethird-orderaberrationwerepresentinalens,itwouldbepossibletocombineapositiveandanegativelenshavingequalaberrationstoobtainacombinationcorrectedforallzones,Becausetheactuallywouldhavedifferentamountsoffifth-o

19、rderaberration,however,suchacombinationcanbecorrectedforonezoneonly,2020/6/15,38,Itspositioncorrespondstothatofthecircleofleastconfusion,2020/6/15,39,Letaandbrepresenttheconstantsforathin-lensdoublet,Ifthecombinationistobecorrectedatthemargin,i.e.forarayattheheight,or:,2020/6/15,40,Weobtain:,isfixed

20、,hmaytakeanyvaluebetween0and,2020/6/15,41,Wedifferentiatewithrespecttohandequatetozero,Weobtain,Astheradiusofthezoneatwhichtheaberrationreachesamaximum,Inlensdesignsphericalaberrationisalwaysinvestigatedbytracingaraythroughthecombinationforthezoneofradius0.707hm,2020/6/15,42,Becausetheprimarymirrori

21、stooflat,raysfromtheouteredgesmetatapoint38mmbeyondthepointwhereinnerraysconverge.,2020/6/15,43,对应孔径角Umax入射光线的高度hmax被称为全孔径（边光球差）,若h/hmax=0.7，则称为0.7孔径或0.7带光（带光球差）,对应孔径角U入射光线的高度h,球差与孔径之间的关系,2020/6/15,44,球差是轴上点唯一的单色像差,可在沿轴方向和垂轴方向来度量分别称为轴向球差和垂轴球差。,轴向球差又称为纵向球差,它是沿光轴方向度量的球差，用符号L表示,垂轴球差是过近轴光线像点A的垂轴平面内度量的球差

22、。用符号T表示,它表示由轴向球差引起的弥散圆的半径,T=LtanU,2020/6/15,45,对于单透镜来说，U越大则球差值越大,单透镜自身不能校正球差,2020/6/15,46,单正透镜会产生负值球差，也被称为球差校正不足或欠校正,单负透镜会产生正值球差，也被称为球差校正过头或过校正,如果将正负透镜组合起来，能否使球差得到校正？,这种组合光组被称为消球差光组,2020/6/15,47,光学系统中对某一给定孔径的光线达到L=0的系统称为消球差系统,单透镜的球差与焦距、相对孔径、透镜的形状及折射率有关。,对于给定孔径焦距和折射率的透镜，通过改变其形状可使球差达到最小。,2020/6/15,48,

23、大孔径产生的球差,2020/6/15,49,加发散透镜消除球差,2020/6/15,50,球差,2020/6/15,51,球差,2020/6/15,52,2、彗差,了解成像光束光线的全貌：子午平面和弧矢平面,由轴外物点和光轴所确定的平面称为子午平面,子午平面内的光束称子午光束,过主光线且与子午平面垂直的平面称为弧矢平面,弧矢平面内的光束称弧矢光束,2020/6/15,53,彗差是轴外物点发出宽光束通过光学系统后，并不会聚一点，相对于主光线而是呈彗星状图形的一种失对称的像差,彗差通常用子午面上和弧矢面上对称于主光线的各对光线，经系统后的交点相对于主光线的偏离来度量，分别称为子午彗差和弧矢彗差,子

24、午彗差指子午光线对度量的彗差,子午光线对交点离开主光线的垂直距离KT用来表示此光线对交点偏离主光线的程度,2020/6/15,54,弧矢彗差指对弧矢光线度量的彗差,弧矢光线对交点离开主光线的垂直距离Ks用来表示此光线对交点偏离主光线的程度,2020/6/15,55,折射后的成像光束与主光束OBY失去了对称性,在折射前主光线是光束的轴线，折射后主光线就不再是光束轴线,不同孔径的光线在像平面上形成半径不同的相互错开的圆斑,2020/6/15,56,距离主光线向点越远，形成的圆斑直径越大,这些圆斑相互叠加的结果就形成了带有彗星形状的光斑,光斑的头部（尖端）较亮，至尾部亮度逐渐减弱，称为彗星像差，简称

25、彗差,2020/6/15,57,Thesecondofthemonochromaticaberrationofthird-ordertheoryiscalledcoma,Itappearsthatthemagnificationisdifferentfordifferentpartsofthelens.,2020/6/15,58,Itsoriginslieinthefactthattheprincipal“planes”canactuallybetreatedasplanesonlyintheparaxialregion.,Theeffectivefocallengths,andtherefo

26、rethetransversemagnifications,willdifferforraystraversingoffaxisregionsofthelens.,2020/6/15,59,彗差的形状有两种：,彗星像斑的尖端指向视场中心的称为正彗差,彗星像斑的尖端指向视场边缘的称为负彗差,由于彗差没有对称轴只能垂直度量，所以它是垂轴像差的一种,彗差对成像的影响：,像的清晰度，使成像的质量降低,2020/6/15,60,Ifthemagnificationfortheouterraysthroughalensisgreaterthanthatforthecentralrays,thecomais

27、saidtobepositive,whileifthereverseistrue,thecomaissaidtobenegative,2020/6/15,61,Positivecoma(photobyE.H.),2020/6/15,62,Severalskewraysaredrawnfromanextra-axialobjectpointSinfollowingfiguretoillustratetheformationofthegeometricalcomaticimageofapoint.,2020/6/15,63,Tangentialcoma切向,Sagittalcoma弧矢,2020/

28、6/15,64,Tangentialcoma切向,Sagittalcoma弧矢,2020/6/15,65,入瞳,像面,2020/6/15,66,2020/6/15,67,Thefactthatthelinerepresentingcomacrossesthezeroaxisindicatesthatasinglelenscanbemadethatisentirelyfreeofthisaberration,2020/6/15,68,Theshapefactorq=0.800fornocomaissoneartheshapefactorq=0.714forminimumsphericalaber

29、rationthatasinglelensdesignedforwillhavepracticallytheminimumamountofsphericalaberration,2020/6/15,69,Iftheshapeandpositionfactorsofasinglelensobeythisrelation,thelensiscoma-free,Adoubletdesignedtocorrectforsphericalaberrationcanatthesametimebecorrectedforcoma,2020/6/15,70,Thecomacone,justliketheGau

30、ssianimagepoint,isanoversimplification.Theimagepointisreallyanimagedisk-ringsystem,andthecomaconeisactuallyacomplicatedasymmetricaldiffractionpattern.Themorecomathereis,themoretheconedepartsfromtheAirypatternintoanelongatedstructureofblotchesandarcs.,2020/6/15,71,彗差对于大孔径系统和望远系统影响较大,彗差的大小与光束宽度、物体的大小、

31、光阑位置、光组内部结构（折射率、曲率、孔径）有关,对于某些小视场大孔径的系统（如显微镜），常用“正弦差”来描述小视场的彗差特性。,正弦差等于彗差与像高的比值，用符号SC表示,2020/6/15,72,2020/6/15,73,彗差,2020/6/15,74,彗差,2020/6/15,75,62.51,2020/6/15,76,3、像散,轴外点细光束成像，将会产生像散和场曲它们是互相关联的像差,轴外物点用光束成像时形成两条相互垂直且相隔一定距离的短线像的一种非对称性像差被称为像散,Astigmatism,whenanobjectpointliesanappreciabledistancefrom

32、theopticalaxis,theincidentconeofrayswillstrikethelensasymmetrically,givingrisetoathirdprimaryaberration.,Theconfigurationofanoblique,parallelraybundlewillbedifferentinthemeridional(子午)andsagittal(弧矢)planes.Asaresult,thefocallengthsintheseplaneswillbedifferentaswell.,Thefocallengthdifferencedependsef

33、fectivelyonthepowerofthelensandtheangleatwhichtheraysareinclined.,Thecrosssectionofthebeamasitleavesthelensisinitiallycircular,butitgraduallybecomesellipticalwiththemajoraxisinthesagittalplane,untilatthetangentialormeridionalfocusFT,theellipsedegeneratesintoaline.Beyondthispoint,thebeamscrosssection

34、rapidlyopensoutuntilitisagaincircular.Atthatlocation,theimageisacircularblurknownasthecircleofleastconfusion.,Acomputer-generateddiagramshowingthedistributionoflight.,IftheobjectisaspokedwheelinaplaneperpendiculartotheaxiswithitscenteratM,IfthepositionoftheTandSimagesaredeterminedforawidefieldofdist

35、antobjectpoints,theirlociwillformparaboloidalsurfaces,AstigmatismissaidtobepositivewhentheTsurfaceliestotheleftofS,Foraconcavemirror,thesagittalsurfaceisaplanecoincidingwiththeparaxialfocalplane,Theastigmaticimagedistancesforasinglerefractingsurface,andaretheanglesofincidenceandrefractionofthechiefr

36、ay,rtheradiusofcurvature,stheobjectdistance,andandtheTandSimagedistances,thelatterbeingmeasuredalongthechiefray.,Forasphericalmirrortheseequationsreduceto,and,Forathinlensinairwithanaperturestopatthelens,thepositionofthetangentialandsagittalimages:,Theangelistheangleofobliquityoftheincidentchiefrays

37、,andtheangleofthisraywithinthelens,Therefore:,Althoughacontactdoubletcomposedofonepositiveandonenegativelensshowsconsiderableastigmatism,theintroductionofanotherelementconsistingofastoporalenscanbemadetogreatlyreduceit,freeofastigmatism,thesingleparaboloidalsurfaceP,overwhichpointimagesareformed,isc

38、alledthePetzvalsurface,2020/6/15,87,由子午光束所形成的像是一条垂直子午面的短线t称为子午焦线,由弧矢光束所形成的像是一条垂直弧矢面的短线s称为弧矢焦线,2020/6/15,88,这两条短线不相交但相互垂直且隔一定距离,两条短线间沿光轴方向的距离即表示像散的大小,用符号Xts表示Xts=Xt-Xs,2020/6/15,89,这种即非对称又不会聚于一点的细光束称为像散光束,这两条短线（焦线）光能量最为集中，它们是轴外点的像,2020/6/15,90,如果轴外物点是“十”字形图案,Bt与Bs是B点通过光学系统形成的子午像点与弧矢像点，沿光轴之间的距离BtBs是光学

39、系统的像散,2020/6/15,91,当光学系统的子午像点比弧矢像点更远离高斯像面，即ltls，像散Xts为负值，反之，像散为正值,像散是物点远离光轴时的像差，且随视场的增大而迅速增大,4、场曲,场曲是像场弯曲的简称。,场曲是物平面形成曲面像的一种像差,CurvatureOfField,TheimagesfallonthecurvedPetzvalsurfacewherethetangentialandsagittalsurfacescometogether,Eventhoughastigmatismiscorrectedforsuchasystem,thefocalsurfaceiscurv

40、ed,TheratioofthedistancesPTandPSis3:1,IfascreenisplacedatacompromisepositionA,theimagesovertheentirefieldwillbeinreasonablygoodfocus,Inthiscaseascreenplacedattheparaxialfocuswillshowconsiderableblurringatthefieldedges,Typicalcurvesforthecameraobjectivecalledananastigmat,Experiencehasshownthatthebest

41、stateofcorrectionisobtainedbymakingthecrossoverpoint,calledthenode,occuratarelativelyshortdistanceinfrontofthefocalplane,2020/6/15,97,若光学系统存在像散，则实际像面还受像散的影响而形成子午像面和弧矢像面,场曲需要以子午场曲和弧矢场曲来表征,（1）子午场曲,用细光束子午场曲和宽光束子午场曲来度量,2020/6/15,98,子午细光束焦点相对于理想像面的偏离称为细光束子午场曲，用符号xt表示,2020/6/15,99,子午宽光束焦点相对于理想像面的偏离称为宽光束子午

42、场曲，用符号XT表示,2020/6/15,100,细光束子午场曲与宽光束子午场曲之差为轴外点子午球差,（2）弧矢场曲,用细光束弧矢场曲和宽光束弧矢场曲来度量,2020/6/15,101,弧矢细光束焦点相对于理想像面的偏离称为细光束弧矢场曲，用符号xs表示,2020/6/15,102,弧矢宽光束焦点相对于理想像面的偏离称为宽光束弧矢场曲，用符号XS表示,2020/6/15,103,当光学系统不存在像散（即子午像与弧矢像重合）时，垂直于光轴的一个物平面经实际光学系统后所得到的像面也不一定于理想像面重合,细光束弧矢场曲与宽光束弧矢场曲之差为轴外点弧矢球差,就形成一个曲面（纯场曲）,像散和场曲既有区别

43、又有联系,有像散必然存在场曲，但场曲存在是不一定有像散,2020/6/15,104,光学系统存在场曲时，不能使一个较大的平面物体上的各点同时在同一像面上成清晰像,若按视场中心调焦，中心清晰，边缘则模糊,若按视场边缘调焦，边缘清晰，中心则模糊,5、畸变,畸变是垂轴（横向）放大率随视场的增大而变化，所引起一种失去物像相似的像差,Distortion,EvenifanopticalsystemweredesignedsothatthefirstfourSeidelsumswerezero,itcouldbeaffectedbythefifthaberrationknownasdistortion,T

44、obefreeofdistortionasystemmusthaveuniformlateralmagnificationoveritsentirefield,Apinholecamera,(b):theundistortedimageofanobjectconsistingofarectangularwiremesh,(c):barreldistortion,whichariseswhenthemagnificationdecreasestowardtheedgeofthefield,(d):pincushiondistortion,correspondingtoagreatermagnif

45、icationattheborders,Asinglethinlensispracticallyfreeofdistortionforallobjectdistances.Itcannotbefreeofalltheotheraberrationsatthesametime,Ifastopisplacedatthelens,thereisnodistortion,Thissystemsuffersfrombarreldistortion,Pincushiondistortion,Thesystemisfreefromdistortionforunitmagnification,Withothe

46、rmagnifications,however,thelensesmustbecorrectedforsphericalaberrationwithrespecttotheentranceandexitpupils.,2020/6/15,112,畸变的存在使轴外直线成为曲线像,枕形畸变（正畸变）：垂轴放大率随视场角的增大而增大的畸变,桶形畸变（负畸变）：垂轴放大率随视场角的增大而减小的畸变,2020/6/15,113,视场的畸变用符号q表示,式中,实际放大率可以用实际主光线与高斯像面的交点高度yz与物高y之比表示,y为理想像高,2020/6/15,114,称为相对畸变,光学系统的线畸变,必须注

47、意：,1、畸变与其它像差不同，它仅由主光线的光路决定,2、畸变的存在仅引起像的变形，但不影响成像的清晰度,2020/6/15,115,有些场合，如果畸变的数值很小，是可以允许的,但有些场合，畸变是非常有害的,如：计量仪器中的投影物镜、航空测量物镜等（影响其测量精度）,结构完全对称的光学系统，以-1倍的放大率成像，所有垂轴像差都能自动消除,畸变是一种垂轴向差，也能消除,2020/6/15,116,单个薄透镜或薄透镜组的主面与孔径光阑重合时也不会产生畸变,因为主光线通过透镜的主点并沿理想方向出射的原因,当光阑位于单透镜组之前或之后即产生畸变，符号相反,表明垂轴像差与光阑位置的依赖关系,2020/6

48、/15,117,正畸变,负畸变,Suchacorrectedlenssystemiscalledanorthoscopicdoublet,orrapidrectilinearlens,Summarizingverybrieflythevariousmethodsofcorrectingforaberration:,Sphericalaberrationandcomacanbecorrectedbyusingacontactdoubletofthepropershape,Astigmatismandcurvatureoffieldrequirefortheircorrectiontheuseof

49、severalseparatedcomponents,Distortioncanbeminimizedbytheproperplacementofastop,2020/6/15,119,6、色差,色差分为：位置色差和倍率色差,（1）位置色差（轴向色差、纵向色差）,白光是由各种不同波长的单色光所组成的,复色光成像时，由于不同色光而引起的像差称为色差,白色光中波长愈短折射率愈大,2020/6/15,120,由薄透镜的焦距公式可知，同一薄透镜对不同色光有不同的焦距,一定物距l成像时，因各色光的焦距不同所得到的像距l也不同,按色光的波长由短到长，其相应的像点离透镜有近到远地排列在光轴上，这种现象称为位

50、置色差,2020/6/15,121,位置色差定义为：,2020/6/15,122,称为色差校正不足,称为色差校正过渡,若AF和AC重合，则,称为光学系统对F光（兰）和C光（红）消色差,消色差系统是指对两种色光消轴向（位置）色差的系统,2020/6/15,123,位置色差不同于球差，它在近轴区就产生,细光束成像也不能获得白光的清晰像,因为位置色差会严重影响成像质量（可能比球差严重）,因此用白光成像的光学系统都必须校正位置色差,孔径不同，白光将会有不同的位置色差,2020/6/15,124,位置色差的性质类似于球差,光学系统只能对一个孔径的光线进行校正色差,一般情况下对0.7孔径的光线校正位置色差

51、,随着接收器的不同，应取接近接收器有效波段边缘的波长进行校色差,2020/6/15,125,（2）倍率色差（垂轴色差）,光学材料对不同色光的折射率不同，对于光学系统对不同色光就有不同的焦距,不同色光的焦距不等时，其放大率也不等,就有不同的像高，这就是倍率色差,2020/6/15,126,B,B,A,A,BF,BD,BC,BF,BD,BC,yzc,yzD,yzF,yzF,yzD,yzc,2020/6/15,127,上图的叠加结果使像的边缘呈现彩色,光学系统的倍率色差是以两种色光的主光线在高斯像面上的交点高度之差来度量的,影响成像清晰度,128,像质评价的其它方法,评价一个光学系统的像质优劣的根据

52、是物空间一点发出的光能量在像空间的分布状况。按几何光学的观点来看，光学系统成像的理想状况是在像空间光能量集中在一个几何点上，实际像差使能量分散。几何光学认为光学系统能分辨无限细小的物体结构，而实际情况与此不符。这表明用几何光学方法不能描述能量分布问题，即光学系统成像质量评价不能单纯依靠几何光学的方法来解决。多年来，人们提出多种像质评价方法，如斯特列尔准则（中心点亮度）、瑞利判据、分辨率、点列图、光学传递函数等。以上几种光学系统像质评价方法，其依据都是以直接或间接地分析光学系统对点物所成的像点源响应（又称点扩散函数）在空域和频域中的特性作为评价标准的。所不同的是，各种方法依据点源响应的特点，从几个不同角度反映了光学系统的成像性质