Limits of Adaptive Optics for high contrast imagin

arXiv:astro-ph/0505086v229Sep2005LimitsofAdaptiveOpticsforhighcontrastimagingOlivierGuyonSubaruTelescope,650N.A’ohokuPlace,Hilo,96720HI,[e-mail]ffectsofphotonnoise,aliasing,wavefrontchromaticityandscintillationonthepointspreadfunction(PSF)contrastachievablewithgroundbasedadaptiveoptics(AO)areevaluatedfordifferentwavefrontsensingschemes.Ishowthatawavefrontsensor(WFS)basedupontheZernikephasecontrasttechniqueoffersthebestsensitivitytophotonnoiseatallspatialfrequen-cies,whiletheShack-HartmannWFSissignificantlylesssensitive.InAOsystemsperformingwavefrontsensinginthevisibleandscientificimaginginthenear-IR,thePSFcontrastlimitissetbythescintillationchromaticityinducedbyFresnelpropagationthroughtheatmosphere.Ona8mtelescope,thePSFcontrastisthenlimitedto1e-4to1e-5inthecentralarcsecond.Wavefrontsensingandscientificimagingshouldthereforebedoneatthesamewavelength,inwhichcase,onbrightsources,PSFcontrastsbetween1e-6and1e-7canbeachievedwithin1arcsecondona8mtelescopeinoptical/near-IR.Theimpactofatmosphericturbulenceparam-eters(seeing,windspeed,turbulenceprofile)onthePSFcontrastisquantified.Ishowthatafocalplanewavefrontsensingschemeoffersuniqueadvantages,andIdiscusshowtoimplementit.Coronagraphicoptionsarealsobrieflydiscussed.Subjectheadings:instrumentation:adaptiveoptics—instrumentation:interferometers—methods:dataanalysis—techniques:interferometric—techniques:highangularresolution1.IntroductionHighcontrastimagingoftheimmediateen-vironment(withinafewastronomicalunits)ofnearbystarsiscriticaltotheunderstandingoffor-mationandevolutionofplanetarysystems.Theultimategoalofplanetarysystemsstudiesistofindandcharacterizeplanetssimilartoours,inthehopethatwecanfindother“habitable”wordssus-ceptibleofharboringlife.Severalapproachesarecurrentlyunderdevelopmenttoachievethehighlevelofcontrastrequired:•Nullinginterferometryinthemid-IRwitha30mbaselinespaceinterferometer.•Visiblecoronagraphywitha4mto8mspacetelescope.•Largegroundbasedtelescopes(8mto100m)andhighperformanceAOsystemsoptimizedforbrighttargets.Whilethefirst2optionsaretargetingEarth-sizeplanetsaroundnearbystars,thegroundbasedsys-temshavemoremodestinitialgoals:planetsmoremassivethanJupiteroryoungJupitermassplan-ets.Theplanstobuildlarger(30mto100m)tele-scopesandthefastprogressinhigh-performanceAOsystemsandcoronagraphyhoweveropensupthepossibilityofpursuingmoreambitiousgoals.DirectimagingofEarth-sizeplanetsisevencon-sideredfor100mdiametertelescopes(Gilmozzi2004;Hawardenetal.2003).ThecontrastdetectionlimitwithinaPSFissetbyphotonnoiseandspecklenoiseintheimage.Ifonlyphotonnoiseisconsideredthetheoreticalde-tectionlimitforalargetelescope(30mto100m)allowsrelativelyeasydetectionofEarth-sizeplan-etsaroundnearbystars(Angel2003;Hawardenetal.2003).Thishoweverseemstobeaveryopti-misticassumption,ascurrentAOsystemsarealllimitedbyspecklenoise(Racineetal.1999)within1thecentralarcsecond.Thedetectionlimitisthere-forelikelytobedrivenbyhowwellthespeck-lescanbecalibrated/removed.Fastatmosphericspecklesaveragefairlyrapidly,butslower-evolvingspecklesaremoreproblematic.Experienceac-quiredonground-basedtelescopehasshownthatthereisnosuchthingasatrulystaticspeckles,asextremelysmalldriftsinthewavefrontaresuffi-cienttoappreciablychangethespeckle’sintensity:foraspeckleofintensity10−5thecentralstar’sin-tensitytobestabletowithin1%,thecorrespond-ingspatialfrequencywouldneedtobestableto2.510−6wave(4picometersat1.6μm).Innon-coronagraphicimagingwithcurrentAOsystemsonlargetelescopes,thePSFwingsarerelativelysmoothinlongexposures:about10%ofthespecklebackgrounddoesnotaverageatabout1′′(figure1inBoccalettietal.(2003)).ThroughcarefulPSFcalibration,someoftheresidualspecklestructurecanbesubtracted(Rothetal.2001),yieldingapointsourcedetectionlimitmorethan10timesfainterthanthePSFback-groundlevelwithinthecentralarcsecond.Thisfactortendstobecomelargerwithincreasingdis-tancefromthePSFcore,partiallythankstothechromaticelongationofspeckleswhichmakesthePSFsmoother.Differentialimagingtechniquesbasedonspectralpropertiesofthesourcecouldfurtherincreasethisfactorbyupto102forsimul-taneousimagingin2bandsand104forsimultane-ousimagingin3bands(Maroisetal.2000).Tech-niquesusingthecoherencepropertiesofspeckleshavealsobeenproposed(Boccalettietal.1998;Guyon2004).Inthisstudy,performanceofanadaptiveop-ticssystemisquantifiedbytheratiobetweenthelightintensityatthepointofthePSFconsideredandthelightintensityatthePSF’scenter.ThisquantityisreferredtoasthePSFcontrastintherestofthepaper.ThegoalofthisworkistogivelimitsonthisPSFcontrastachievablewithAOsystems,andtoproposesolutionstoreachtheselimits:whichWFStochoose?howtodrivethedeformablemirror(DM)?isacoronagraphnec-essary?ifyes,whichone?Detectionlimitsforfaintcompanionsaresignificantlyhardertopre-dictthanPSFcontrastforthereasonsdetailedabove,andwillnotbecomputedinthispaper.ThePSFcontrastinaphoton-noiselimitedAOsystemisafunctionoftheabilityoftheWFStoaccuratelymeasurethecorrespondingspatialfre-quencyinthepupilplanephase.Analyticalex-pressionsofthefundamentalcontrastlimitsim-posedbyphotonnoiseandchromaticityofthewav