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1、A.N.SimonovandM.C.RombachVol.27,No.12/December2010/J.Opt.Soc.Am.A2563Asymptoticbehaviorofthespatialfrequencyresponseofanopticalsystemwithdefocusandsphericalaberration1,*andMichielC.Rombach2AlekseyN.Simonov1A.V.Schendelplein137,2624CVDelft,TheNetherland
2、s2Overaseweg9,4836BABreda,TheNetherlands*Correspondingauthor:A.N.Simonov@gmail.comReceivedJune1,2010;revisedOctober9,2010;acceptedOctober9,2010;postedOctober11,2010(Doc.ID129392);publishedNovember10,2010Asymptoticexpressionsarederivedforthetwo-dimensio
3、nalincoherentopticaltransferfunction(OTF)ofanopticalsystemwithdefocusandsphericalaberration.Thetwo-dimensionalstationaryphasemethodisusedtoevaluatetheaberratedOTFatlargeandmoderatelylargedefocusandsphericalaberration.Forsmallaber-rations,theOTFisapprox
4、imatedbyapowerseriesintheaberrationcoefÞcients.Anaccurateapproximation(inelementaryfunctions)totheOTFisobtainedforadefocusedopticalsystemwithacircularpupil.Weex-perimentallydemonstratethevalidityoftheOTFapproximationsinsharp-focusimagerestorationfromtw
5、odefocusedimages.Adigitalfocusingmethodispresented.©2010OpticalSocietyofAmericaOCIScodes:110.4850,110.0110,000.3860.1.INTRODUCTIONphasedistortions[12].ToextendouranalysistothecaseofsmallaberrationsweapproximatetheOTFbyapowerTheopticaltransferfunction(O
6、TF)isaquantitativemea-seriesintheaberrationcoefÞcients.Theapproximatesureoftheimagingqualityofanopticalsystem[1Ð3].Themethodsareillustratedbyapplicationtoanopticalsys-OTFdescribesthespatialfrequencyresponseofanopti-temwithacircularpupilinthepresenceofd
7、efocusandcalsystemandcanbeusedtoassessthefocusingandim-sphericalaberration,butcanbegeneralizedtoothersitu-agingpropertiesofthesysteminthepresenceofaberra-ations.tions.DetailedknowledgeoftheaberratedOTFcouldbeadvantageousforaccurateimagereconstruction[3
8、,4];however,asconcludedin[5],themodelaccuracyshouldbeconsistentwiththeimagequalityrequirementsinthe2.GENERALIZEDPUPILFUNCTIONANDpresenceofnoise.THEOTFInmostcases,theaberratedOTFcanbefoundonlynu-Weconsiderimagingofaplanarobject,inspatial
