astronomical observing techniques lecture 6: everything you...

AstronomicalObservingTechniques

Lecture6:EverythingYouAlwaysWantedtoKnowAboutOpAcs

ChristophU.Kellerkeller@strw.leidenuniv.nl

Outline1.  GeometricalOp<cs

– WavesandRays–  ImagesandPupils– Aberra<ons

2.  PhysicalOp<cs– Diffrac<on– TransferFunc<ons–  ImageMetrics

3.  HighContrastImaging

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SphericalandPlaneWaves•  lightsource:collec<onofsourcesofsphericalwaves

•  astronomicalsources:almostexclusivelyincoherent

•  lasers,masers:coherentsources

•  sphericalwaveorigina<ngatverylargedistancecanbeapproximatedbyplanewave

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IdealOpAcs

•  idealop<cs:sphericalwavesfromanypointinobjectspaceare•  imagedintopointsinimagespace•  correspondingpointsarecalledconjugatepoints•  focalpoint:centerofconvergingordivergingsphericalwavefront•  objectspaceandimagespacearereversible7-3-2016 Astronomical Observing Techniques 2016: Optics 4

IdealOpAcalSystem

idealop<calsystemtransformsplanewavefrontintospherical,convergingwavefront

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AzimuthalSymmetry

•  mostop<calsystemsareazimuthallysymmetric•  axisofsymmetryisop<calaxis

Optical Axis

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LocallyFlatWavefronts

•  raysnormaltolocalwave(loca<onsofconstantphase)

•  localwavearoundraysisassumedtobeplanewave7-3-2016 Astronomical Observing Techniques 2016: Optics 7

Rays

•  geomtricalop<csworkswithraysonly•  raysreflectedandrefractedaccordingtoFresnelequ.•  phaseisneglected(incoherentsum)7-3-2016 Astronomical Observing Techniques 2016: Optics 8

FiniteObjectDistance

•  objectmayalsobeatfinitedistance•  alsoinastronomy:reimagingwithininstrumentsandtelescopes

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GeometricalOpAcsExample:SPEX

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SPEXonNASAER-2plane

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picture by Ken Ulbrich, NASA

•  Aperturestop:determinesdiameteroflightconefromaxialpointonobject.

•  Fieldstop:determinesthefieldofviewofthesystem.

ApertureandFieldStops

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Images

•  everyobjectpointcomestofocusinimageplane•  lightinimagepointcomesfromallpupilposi<ons•  objectinforma<onencodedinposi<on,notangle

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Pupils

•  allobjectraysaresmearedoutovercompleteaperture•  lightinonepupilpointcomesfromdifferentobjectposi<ons

•  objectinforma<onisencodedinangle,notinposi<on

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Speedofop<calsystemdescribedbynumericalaperture(NA)orFnumber:

NA)(21 and sinNA =≡⋅=

DfFn θ

f

DΘ

•  fastop<cs(largeNA)•  slowop<cs(smallNA)

n

Speed/F-Number/NumericalAperture

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AberraAonsAberra<onsaredeparturesoftheperformanceofanop<calsystemfromtheidealop<calsystem.1.  On-axisaberra<ons:aberra<onsthatcanbeseen

everywhereintheimage,alsoontheop<calaxis(centeroftheimage)

2.  Off-axisaberra<ons:aberra<onsthatareabsentontheop<calaxis(centeroftheimage)a)  Aberra<onsthatdegradetheimageb)  Aberra<onsthataltertheimageposi<on

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•  ReferencesphereSwithradiusRforoff-axispointP’andaberratedwavefrontW

•  “Aberrated”rayfromobjectintersectsimageplaneatP”

•  Rayaberra<onisP’P”

•  Waveaberra<onisn·QQ ( )

rrW

nRri

i ∂∂=SmallFOV,radiallysymmetricwavefrontW(r)

WaveandRayAberraAons

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22

NA1

22 ⎟

⎠⎞⎜

⎝⎛== λλδ F

defocusedimage

Usuallyreferstoop<calpathdifferenceofλ/4.

Depthoffocus:

focusedimage

Defocus(OutofFocus)

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Raysfurtherfromtheop<calaxishaveadifferentfocalpointthanraysclosertotheop<calaxis.

SphericalAberraAon

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Made with Touch Optical Design

HubbleTrouble

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•  Nullcorrectorformeasuringmirrorshapewasincorrectlyassembled(onelensmisplacedby1.3mm).

•  Amanagementproblem:Mirrormanufacturerhadanalyzedsurfacewithothernullcorrectors,whichindicatedtheproblem,buttestresultswereignoredbecausetheywerebelievedtobelessaccurate.

•  Nullcorrectorcancelsnon-sphericalpor<onofasphericmirrorfigure.WhencorrectmirrorisviewedfrompointA,combina<onlookspreciselyspherical.

HSTPrimaryMirrorSphericalAberraAon

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ComaVaria<onofmagnifica<onacrossentrancepupil.Pointsourceswillshowacometarytail.Comaisaninherentpropertyoftelescopesusingparabolicmirrors.

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Fromoff-axispointAlensdoesnotappearsymmetricalbutshortenedinplaneofincidence(tangen<alplane).Emergentwavewillhaveasmallerradiusofcurvaturefortangen<alplanethanforplanenormaltoit(sagifalplane)andformanimageclosertothelens.

AsAgmaAsm

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Onlyobjectsclosetoop<calaxiswillbeinfocusonflatimageplane.Off-axisobjectswillhavedifferentfocalpoints.

FieldCurvature

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DistorAon

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Straightlineonskybecomescurvedlineinfocalplanebecausemagnifica<ondependsondistancetoop<calaxis.1.  Outerpartshavelargermagnifica<onàpincushion2.  Outerpartshavesmallermagnifica<on àbarrel

AberraAonsSummary

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Refrac<veindexvaria<onwithwavelengthn(λ)resultsinfocallengthoflensf(λ)todependonwavelength;differentwavelengthshavedifferentfoci

ChromaAcAberraAon

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Fresneldiffrac<on=near-fielddiffrac<on:Whenawavepassesthroughanapertureanddiffractsinthenearfielditcausestheobserveddiffrac<onpaferntodifferinsizeandshapefordifferentdistances.ForFraunhoferdiffrac<onatinfinity(far-field)thewavebecomesplanar.

1

1

2

2

<<⋅

=

≥⋅

=

λ

λ

drF

drFFresnel:

Fraunhofer:F=Fresnelnumber,r=aperturesizeandd=distancetoscreen

FresnelandFraunhoferDiffracAon

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FraunhoferDiffracAon•  ElectricfieldinimageplaneisFouriertransformofelectricfieldinaperture

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E x, y, z( ) = A u,v( )eiϕ u ,v( )e− i2π

λzxu+yv( )

dudv∫∫

Whenthecircularpupilisilluminatedbyapointsourcethentheresul<ngPSFisdescribedbya1storderBesselfunc<on:ThisisalsocalledtheAiryfunc<on.Theradiusofthefirstdarkring(minimum)isat:

Point Spread Function (1)

( ) ( ) 2

0

011 / 2

/ 22⎟⎟⎠

⎞⎜⎜⎝

⎛=

λθπλθπθ

rrJI

DfrFr λαλ 22.1or 22.1 1

11 ===

ThePSFisojensimplycharacterizedbythehalfpowerbeamwidth(HPBW)orfullwidthhalfmaximum(FWHM)inangularunits.

cωθ 2

1=Δ

AccordingtotheNyquist-ShannonsamplingtheoremI(Θ)(oritsFWHM)shallbesampledwitharateofatleast:

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PointSpreadFuncAons

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OpAcal/ModulaAonTransferFuncAonRayleighcriterion:twosourcescanberesolvedifthepeakofthesecondsourceisnocloserthanthe1stdarkAiryringofthefirstsource.

Abefermeasureoftheresolu<onthatthesystemiscapableofistheop<caltransferfunc<on(OTF):

Dλ22.1sin =Θ

(a) Input (b) output

( ) ( )minmax

minmax

0

re whe,IIIIC

CfCfMTF

+−==

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OpAcal/ModulaAonTransferFuncAon(2)Op<calTransferFunc<on(OTF)describesspa<alsignalvaria<onasafunc<onofspa<alfrequency.Withspa<alfrequencies(ξ,η)Modula<onTransferFunc<on(MTF)describesitsmagnitude,andthePhaseTransferFunc<on(PTF)thephase.

( ) ( ) ( )( ) ( )( ) ( )ηξπληξ

ηξηξηξηξηξ

,2,

,,,,,

iePTF

OTFMTFPTFMTFOTF

−=

=⋅=

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•  Strehlra<oisconvenientmeasureofop<calquality.•  Strehlra<o(SR)isra<oofobservedpeakintensityofPSFcomparedtotheore<calmaximumpeakintensityofpointsourceseenwithperfectimagingsystem

•  Withwavenumberk=2π/λ,RMSwavefronterrorω

•  Examples:•  SR>80%considereddiffrac<on-limitedàWFE~λ/14•  typicaladap<veop<cssystemdeliversSR~10-80%•  seeing-limitedPSFon8mtelescopehasaSR~0.1-0.01%

22122

ωω keSR k −≈= −

StrehlRaAo

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Q: What is the maximum concentration of light within a small area? The fraction of the total PSF intensity within a certain radius is given by the encircled energy (EE):

Encircled Energy

( ) ⎟⎠⎞⎜

⎝⎛−⎟

⎠⎞⎜

⎝⎛−=

FrJ

FrJrEE

λπ

λπ 2

1201

Note that the EE depends strongly on the central obscuration ε of the telescope:

F is the f/# number

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SPHEREatVLT

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AdapAveOpAcs(lecture13)

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Student-BuiltLeidenAO

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Coronagraph

•  goal:minimizediffractedlightclosetostar•  canintroduceop<csinpupiland/orfocalplanes

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ApodizingPupilPhaseCoronagraph

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Gilles Otten Frans Snik Matt Kenworthy Christoph Keller UofA MagAO team NCSU OLEG group

simulation on-sky close binary companion

360°vAPPon-skyatMagAO

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theory on-sky

Otten et al. 2015

gvAPPonMagAO/Clio2

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