astronomical observing techniques lecture 6: everything you...

AstronomicalObservingTechniques

Lecture6:EverythingYouAlwaysWantedtoKnowAboutOpAcs

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Outline1.  GeometricalOp<cs

– WavesandRays–  ImagesandPupils– Aberra<ons

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

3.  HighContrastImaging

7-3-2016 Astronomical Observing Techniques 2016: Optics 2

SphericalandPlaneWaves•  lightsource:collec<onofsourcesofsphericalwaves

•  astronomicalsources:almostexclusivelyincoherent

•  lasers,masers:coherentsources

•  sphericalwaveorigina<ngatverylargedistancecanbeapproximatedbyplanewave


IdealOpAcs

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

IdealOpAcalSystem

idealop<calsystemtransformsplanewavefrontintospherical,convergingwavefront


AzimuthalSymmetry

•  mostop<calsystemsareazimuthallysymmetric•  axisofsymmetryisop<calaxis

Optical Axis


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


GeometricalOpAcsExample:SPEX


SPEXonNASAER-2plane


picture by Ken Ulbrich, NASA

•  Aperturestop:determinesdiameteroflightconefromaxialpointonobject.

•  Fieldstop:determinesthefieldofviewofthesystem.

ApertureandFieldStops


Images

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


Pupils

•  allobjectraysaresmearedoutovercompleteaperture•  lightinonepupilpointcomesfromdifferentobjectposi<ons

•  objectinforma<onisencodedinangle,notinposi<on


Speedofop<calsystemdescribedbynumericalaperture(NA)orFnumber:

NA)(21 and sinNA =≡⋅=

DfFn θ

f

DΘ

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

n

Speed/F-Number/NumericalAperture


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


•  ReferencesphereSwithradiusRforoff-axispointP’andaberratedwavefrontW

•  “Aberrated”rayfromobjectintersectsimageplaneatP”

•  Rayaberra<onisP’P”

•  Waveaberra<onisn·QQ ( )

rrW

nRri

i ∂∂=SmallFOV,radiallysymmetricwavefrontW(r)

WaveandRayAberraAons


22

NA1

22 ⎟

⎠⎞⎜

⎝⎛== λλδ F

defocusedimage

Usuallyreferstoop<calpathdifferenceofλ/4.

Depthoffocus:

focusedimage

Defocus(OutofFocus)


Raysfurtherfromtheop<calaxishaveadifferentfocalpointthanraysclosertotheop<calaxis.

SphericalAberraAon


Made with Touch Optical Design

HubbleTrouble


•  Nullcorrectorformeasuringmirrorshapewasincorrectlyassembled(onelensmisplacedby1.3mm).

•  Amanagementproblem:Mirrormanufacturerhadanalyzedsurfacewithothernullcorrectors,whichindicatedtheproblem,buttestresultswereignoredbecausetheywerebelievedtobelessaccurate.

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

HSTPrimaryMirrorSphericalAberraAon


ComaVaria<onofmagnifica<onacrossentrancepupil.Pointsourceswillshowacometarytail.Comaisaninherentpropertyoftelescopesusingparabolicmirrors.


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

AsAgmaAsm


Onlyobjectsclosetoop<calaxiswillbeinfocusonflatimageplane.Off-axisobjectswillhavedifferentfocalpoints.

FieldCurvature


DistorAon


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

AberraAonsSummary


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

ChromaAcAberraAon


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


FraunhoferDiffracAon•  ElectricfieldinimageplaneisFouriertransformofelectricfieldinaperture


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:


PointSpreadFuncAons


OpAcal/ModulaAonTransferFuncAonRayleighcriterion:twosourcescanberesolvedifthepeakofthesecondsourceisnocloserthanthe1stdarkAiryringofthefirstsource.

Abefermeasureoftheresolu<onthatthesystemiscapableofistheop<caltransferfunc<on(OTF):

Dλ22.1sin =Θ

(a) Input (b) output

( ) ( )minmax

minmax

0

re whe,IIIIC

CfCfMTF

+−==


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

−=

=⋅=


•  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


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


SPHEREatVLT


AdapAveOpAcs(lecture13)


Student-BuiltLeidenAO


Coronagraph

•  goal:minimizediffractedlightclosetostar•  canintroduceop<csinpupiland/orfocalplanes


ApodizingPupilPhaseCoronagraph


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

simulation on-sky close binary companion

360°vAPPon-skyatMagAO


theory on-sky

Otten et al. 2015

gvAPPonMagAO/Clio2


astronomical observing techniques lecture 6: everything you...

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