Chapter 4_ Spatial Resolution and position accuracy .pdf

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1、Chapter4SpatialresolutionandpositionaccuracyPositionaccuracyreferstotheprecisionwithwhichanobjectcanbelocalizedinspace.Spatialresolution,ontheotherhand,isameasurefortheabilitytodistinguishtwoseparatedpoint-likeobjectsfromasingleobject.Thediffractionlimitimpliesthatopticalresolutionisultimatelyl

2、imitedbythewavelengthoflight.Beforetheadventofnear-fieldopticsitwasbelievedthatthediffractionlimitimposesahardboundaryandthatphysicallawsstrictlyprohibitresolutionsignificantlybetterthanλ/2.Itwasfoundthatthislimitisnotasstrictasassumedandthatvarioustricksallowustoaccesstheevanescentmodesofthespat

3、ialspectrum.Inthischapterwewillanalyzethediffractionlimitanddiscusstheprinciplesofdifferentimagingmodeswithresolutionsnearorbeyondthediffractionlimit.4.1ThepointspreadfunctionThepointspreadfunctionisameasureoftheresolvingpowerofanopticalsystem.Thenarrowerthepointspreadfunctionthebettertheresoluti

4、onwillbe.Asthenameimplies,thepointspreadfunctiondefinesthespreadofapointsource.Ifwehavearadiatingpointsourcethentheimageofthatsourcewillappeartohaveafinitesize.Thisbroadeningisadirectconsequenceofspatialfiltering.Apointinspaceischaracterizedbyadeltafunctionwhichhasaninfinitespectrumofspatialfreque

5、n-cieskx,ky.Onthewayofpropagationfromthesourcetotheimage,highfrequencycomponentsarefilteredout.Usually,theentirespectrum(k2+k2)>k2associatedxywiththeevanescentwavesislost.Furthermore,notallplanewavecomponentscanbecollectedwhichleadstoafurtherreductioninbandwidth.Thereducedspectrumisnotabletoacc

6、uratelyreconstructtheoriginalpointsourceandtheimageofthepointwillhaveafinitesize.Thestandardderivationofthepointspreadfunctionis4748CHAPTER4.SPATIALRESOLUTIONANDPOSITIONACCURACYbasedonscalartheoryandtheparaxialapproximation.Thistheoryisinsufficientformanyhighresolutionopticalsystems.Withthesofare

7、stablished‘angularspectrum’frameworkweareinapositiontorigorouslyinvestigateimageformationinanopticalsystem.ConsiderthesituationinFig.4.1whichhasbeenanalyzedbySheppardandWil-son[1]andmorerecentlybyEnderlein[2].Anidealelectromagneticpoint