IPv6 The Big Move: Transition and Coexistent Frenil V. Dand.
High-contrast Imaging: Below the Diffraction Limit with ...kjens/exoplanets_2_poster.pdf · to...
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How do we detect companions? PSF reconstruction High-contrast Imaging: Below the Diffraction Limit with Kernel Phase Jens Kammerer, Mike Ireland & Frantz Martinache RESEARCH SCHOOL OF ASTRONOMY & ASTROPHYSICS We extract kernel phases, which are interferometric measureables independent of pupil plane phase noise to second order, from archival NACO mid-infrared cube mode data. Since high Strehl is essential for this technique we perform lucky imaging first and calibrate our measureables (which are often dominated by systematic errors) against those of well-known point sources. Finally, we fit analytical models directly to the kernel phases. We demonstrate the direct detection of a low-contrast companion below the classical diffraction- limit and the capabilities towards smaller separations and contrasts. What is the kernel phase technique? How do we extract the kernel phases? Sparse aperture masking: • Look at Fourier transform of detector image • Fourier plane phase can be split into eigenphase and kernel phase (~ closure phase) • Kernel phase is independent of pupil plane phase noise (which is dominated by phase pistons on each hole, see eigenphase) to second order [1] Full pupil kernel phase imaging: • Assume that full pupil is highly redundant array of individual sub-apertures (left panel) • No transmission losses and Nyquist or better Fourier plane sampling (right panel) • In high-Strehl regime, there is a linear relationship Φ= $% + Φ )*+,-. between Fourier plane phase Φ and pupil plane phase , where $% is determined by pupil model [2] VLT pupil model (left panel) and its Fourier plane coverage (right panel). The axes represent size in meters. Full pupil kernel phase imaging: • Multiplication with left kernel of $% yields Φ = $% + Φ )*+,-. = Φ )*+,-. • Hence, in high-Strehl regime, kernel phase Φ is independent of noise in pupil plane phase • Such noise can originate from atmospheric seeing or optical aberrations in instrument itself Keck JHKs-band multicolor image of HR 8799 after ADI post-processing revealing the sub-stellar companions HR 8799 b/c/d. The innermost 10-15 / are dominated by speckles which are caused by pupil plane phase noise and form the limit for classical high- contrast imaging (from Marois et al. 2008 [3]). Fully automatic data cleaning pipeline: • Detector linearization, bias/flat/background/jitter subtraction • Read-noise estimation from bias frames • Bad pixel correction/cosmic ray rejection using Fourier techniques • Lucky imaging to pick high-Strehl frames • Final contrast of individual frames ~500:1 and final contrast of median frame over full data cubes >1000:1 Cross-section of the PSF of HIP 11484 before (upper left panel) and after application of our reconstruction algorithm (upper right panel). The x-axes represent pixels and the y-axes represent detector counts. The PSF core is saturated and therefore marked as bad pixels (lower left panel) and our iterative reconstruction algorithm also identifies additional bad pixels based on their Fourier power (lower right panel). • Reconstruction of saturated point spread functions (PSFs) from the PSF wings by minimizing the Fourier power outside the region of support permitted by the pupil geometry • This is important for Fourier plane imaging techniques because saturated pixels cause Fourier plane phase noise Fourier plane phase and kernel phase extraction: • Fourier plane phase Φ is obtained by analytical Fourier transform of each individual cube mode frame • Kernel phase KΦ is obtained by matrix multiplication for each individual cube mode frame, then a covariance weighted mean kernel phase is computed for each data cube (see figure to the left) Median of raw data cube (left panel) of HIP 50156, median of bias/flat/background subtracted data cube (middle panel) and median of data cube after subtracting the median cleaned data cube of a jittered image (right panel). Fourier plane phase (upper right panel) and covariance between the 192 kernel phases extracted from the data of HIP 50156 (lower left panel). The median Fourier plane phases (over all frames of a data cube) at the Fourier plane positions of our pupil model are shown in the lower right panel (blue curve), but the maximum (green curve) and minimum (orange curve) reveal spikes which ramp up to pi. This must be prevented by improving the pupil model and is work in progress! Model fitting: • Fit analytical binary model % + 5 $578(: ;< =>: ?@A B) directly to kernel phases by multiplying model phases with left kernel of $% , where and represent Fourier plane coordinates normalized by observing wavelength • First perform grid search for fixed small contrast (e.g. 5 / % = 0.001), then optimize contrast for best fit grid position in order to find prior for least squares fit • Least squares fit optimizes separation, position angle and contrast simultaneously Measured kernel phases of HIP 50156 and model kernel phases for a grid search fit (upper left panel) and a least squares fit (upper right panel). The lower right panel gives the chi 2 if varying separation, position angle or contrast around the best fit from the least squares routine and illustrates that it found the minimum. Data calibration: • Kernel phases are independent of pupil plan phase noise to second order, but are still affected by systematics at third order in phase [4] • Subtracting off kernel phases of well-known point sources is essential in high-contrast regime • We use Karhunen-Loeve projection →− ∑ < | > R STUV , where follows from eigendecomposition of covariance matrix of calibrator kernel phases • This allows us to get rid of statistically most significant calibrator kernel phases Measured kernel phases of HIP 50156 (src), measured mean kernel phases of three different calibrator stars (cal) and Karhunen-Loeve projected (i.e. calibrated) kernel phases of HIP 50156 (src_poise). This will only become relevant in the high- contrast regime. Companion with separation = 74 mas (~0.75 /), position angle = 63 deg and raw contrast = 0.22 sep = 74 mas pa = 63 deg con = 0.22 74-20 mas 63-20 deg 0.22-0.1 74+20 mas 63+20 deg 0.22+0.1 Bowler et al. 2015 report companion at ~90 mas, 1.8 mag Ks- band contrast, substantial orbital motion [5] References: [1] Ireland 2016, ASSL, 439, 43I; [2] Martinache 2010, ApJ, 724, 464M; [3] Marois et al. 2008, Sci, 322, 1348M [4] Ireland 2013, MNRAS, 433, 1718I; [5] Bowler et al. 2015, ApJS, 216, 7B
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Howdowedetectcompanions? PSFreconstruction
High-contrast Imaging:Below the Diffraction Limit with Kernel Phase
Jens Kammerer, Mike Ireland & Frantz Martinache
RESEARCH SCHOOL OFASTRONOMY & ASTROPHYSICS
We extract kernel phases, which are interferometric measureables independent of pupil plane phase noise to second order, from archivalNACO mid-infrared cube mode data. Since high Strehl is essential for this technique we perform lucky imaging first and calibrate ourmeasureables (which are often dominated by systematic errors) against those of well-known point sources. Finally, we fit analyticalmodels directly to the kernel phases. We demonstrate the direct detection of a low-contrast companion below the classical diffraction-limit and the capabilities towards smaller separations and contrasts.
Whatisthekernelphasetechnique?
Howdoweextractthekernelphases?
Sparseaperturemasking:• LookatFouriertransformofdetectorimage• Fourierplanephasecanbesplitinto
eigenphase andkernelphase(~closurephase)• Kernelphaseisindependentofpupilplane
phasenoise(whichisdominatedbyphasepistonsoneachhole,seeeigenphase)tosecondorder[1]
Fullpupilkernelphaseimaging:• Assumethatfullpupilishighlyredundantarray
ofindividualsub-apertures(leftpanel)• NotransmissionlossesandNyquistorbetter
Fourierplanesampling(rightpanel)• Inhigh-Strehl regime,thereisalinear
relationshipΦ = 𝑅$%𝐴𝜑 +Φ)*+,-. betweenFourierplanephaseΦ andpupilplanephase𝜑,where𝑅$%𝐴 isdeterminedbypupilmodel[2]
VLT pupil model (left panel) and its Fourier planecoverage (right panel). The axes represent size inmeters.
Fullpupilkernelphaseimaging:• Multiplicationwithleftkernel𝐾 of𝑅$%𝐴 yields
𝐾Φ = 𝐾𝑅$%𝐴𝜑 + 𝐾Φ)*+,-. = 𝐾Φ)*+,-.• Hence,inhigh-Strehl regime,kernelphase𝐾Φ
isindependentofnoiseinpupilplanephase𝜑• Suchnoisecanoriginatefromatmospheric
seeingoropticalaberrationsininstrumentitself
Keck JHKs-band multicolorimage of HR 8799 after ADIpost-processing revealingthe sub-stellar companionsHR 8799 b/c/d. Theinnermost 10-15 𝜆/𝐷 aredominated by speckleswhich are caused by pupilplane phase noise and formthe limit for classical high-contrast imaging (fromMarois et al. 2008 [3]).
Fullyautomaticdatacleaningpipeline:• Detectorlinearization,bias/flat/background/jittersubtraction• Read-noiseestimationfrombiasframes• Badpixelcorrection/cosmicrayrejectionusingFouriertechniques• Luckyimagingtopickhigh-Strehl frames• Finalcontrastofindividualframes~500:1andfinalcontrastofmedian
frameoverfulldatacubes>1000:1
Cross-section of the PSF of HIP 11484 before (upper left panel) andafter application of our reconstruction algorithm (upper rightpanel). The x-axes represent pixels and the y-axes representdetector counts. The PSF core is saturated and therefore marked asbad pixels (lower left panel) and our iterative reconstructionalgorithm also identifies additional bad pixels based on their Fourierpower (lower right panel).
• Reconstructionofsaturatedpointspreadfunctions(PSFs)fromthePSFwingsbyminimizingtheFourierpoweroutsidetheregionofsupportpermittedbythepupilgeometry
• ThisisimportantforFourierplaneimagingtechniquesbecausesaturatedpixelscauseFourierplanephasenoise
Fourierplanephaseandkernelphaseextraction:• FourierplanephaseΦ isobtainedbyanalyticalFourier
transformofeachindividualcubemodeframe• KernelphaseKΦ isobtainedbymatrixmultiplication
foreachindividualcubemodeframe,thenacovarianceweightedmeankernelphaseiscomputedforeachdatacube(seefiguretotheleft)
Median of raw data cube (left panel) of HIP 50156, median ofbias/flat/background subtracted data cube (middle panel) and median ofdata cube after subtracting the median cleaned data cube of a jitteredimage (right panel).
Fourier plane phase (upper rightpanel) and covariance betweenthe 192 kernel phases extractedfrom the data of HIP 50156 (lowerleft panel). The median Fourierplane phases (over all frames of adata cube) at the Fourier planepositions of our pupil model areshown in the lower right panel(blue curve), but the maximum(green curve) and minimum(orange curve) reveal spikes whichramp up to pi. This must beprevented by improving the pupilmodel and is work in progress!
Modelfitting:• Fitanalyticalbinarymodel𝑙% + 𝑙5𝑒$578(:;<=>:?@AB) directly
tokernelphasesbymultiplyingmodelphaseswithleftkernel𝐾 of𝑅$%𝐴,where𝑈 and𝑉 representFourierplanecoordinatesnormalizedbyobservingwavelength
• Firstperformgridsearchforfixedsmallcontrast(e.g.𝑙5/𝑙% =0.001),thenoptimizecontrastforbestfitgridpositioninordertofindpriorforleastsquaresfit
• Leastsquaresfitoptimizesseparation,positionangleandcontrastsimultaneously
Measured kernel phases of HIP 50156 and model kernel phasesfor a grid search fit (upper left panel) and a least squares fit (upperright panel). The lower right panel gives the chi2 if varyingseparation, position angle or contrast around the best fit from theleast squares routine and illustrates that it found the minimum.
Datacalibration:• Kernelphasesareindependentofpupilplanphasenoiseto
secondorder,butarestillaffectedbysystematicsatthirdorderinphase[4]
• Subtractingoffkernelphasesofwell-knownpointsourcesisessentialinhigh-contrastregime
• WeuseKarhunen-Loeve projection𝑇 → 𝑇 −∑ < 𝑇|𝑍 > 𝑍�RSTUV ,where𝑍 followsfrom
eigendecomposition ofcovariancematrixofcalibratorkernelphases
• Thisallowsustogetridofstatisticallymostsignificantcalibratorkernelphases
Measured kernel phases of HIP 50156 (src), measured meankernel phases of three different calibrator stars (cal) andKarhunen-Loeve projected (i.e. calibrated) kernel phases of HIP50156 (src_poise). This will only become relevant in the high-contrast regime.
Companionwithseparation=74mas(~0.75𝜆/𝐷),
positionangle=63deg andrawcontrast=0.22
sep =74maspa=63degcon=0.22
74-20mas63-20deg0.22-0.1
74+20mas63+20deg0.22+0.1
Bowleretal.2015reportcompanionat~90mas,1.8magKs-bandcontrast,substantialorbitalmotion[5]
References: [1] Ireland 2016, ASSL, 439, 43I; [2] Martinache 2010,ApJ, 724, 464M; [3] Marois et al. 2008, Sci, 322, 1348M [4] Ireland2013, MNRAS, 433, 1718I; [5] Bowler et al. 2015, ApJS, 216, 7B
