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Band-Limited Masks and Coronagraphic Imaging of Exoplanets Marc Kuchner Exoplanets and Stellar Astrophysics Laboratory NASA Goddard Space Flight Center

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水星 Mercury [water star] 金星 Venus [metal star] + 明星 [bright star] 地球 Earth [Earth globe] 火星 Mars [fire star] 木星 Jupiter [wood star] 土星 Saturn [earth (soil) star] 天王星 Uranus [heaven-king (Uranus) star] 海王星 Neptune [sea-king (Neptune) star] 冥王星 Pluto [netherworld-king (Pluto)

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Crepp et al. 2009 Krist et al. 2007 Balasubramanian 2008

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Krist et al. 2007 Balasubramanian 2008

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Balasubramanian 2008

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L Lyot Stop MImage Mask A Entrance Aperturre

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Martinez 2009

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L L(M (F x A)) M (F x A) M M(F A) F AF A A F x A Incoming field F

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Try to solve this in 1-D given: A 1/2 L 1/2- /2 What can M be such that L (M A)=0 ? Set F=1 to represent on-axis light.

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Complete solution: M(x) = C j (x-j) + G(x) Notch Filter MasksNot physical Kuchner 2005 j

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Notch Filter Masks /2 u M(u)=0 here 1- /2 1) M(u) M(u) du = 0 /2 0 2) M(u) = Fourier Transform of mask

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We call these masks Band-Limited Masks. For a subset of Notch Filter Masks, /2 u M(u)=0 here and also here 1- /2 1) M(u) M(u) du = 0 /2 0 2)

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Crepp et al. 2009 Balasubramanian 2008 Notch Filter (And Band-Limited) Krist et al. 2009

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For a different, overlapping subset of Notch Filter Masks, We call these masks Eighth-Order Masks. M(u) u 2 du = 0 /2 0 3) /2 u M(u)=0 here 1- /2 1) M(u) M(u) du = 0 /2 0 2)

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Transmissivity distance to optical axis ( / D) 1 - sinc 2 Mask 1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 Eighth Order Mask Crepp et al. 2006 Kuchner, Crepp & Ge 2004 Eighth Order Mask

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Shaklan and Green 2005 Aberration Sensitivity 4th Order 8th Order Waves (RMS) Contrast

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HCIT RESULTS WITH BAND LIMITED MASKS –Variable thickness nickel masks on a glass substrate –1-D sinc 2 profile –Central wavelength 800 nm –Electric Field Conjugation algorithms for single and dual DM control Contrast Achieved : 6e-10 @ 4 /D with 10% bandpass 1.2e-9 @ 3 /D with 10% bandpass 2.7e-9 @ 3 /D with 20% bandpass Trauger & Traub 2007

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Kern et al. 2008 Contrast On HCIT

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Nickel Mask Moody et al 2008

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Hybrid Mask: Nickel + Dielectric Band-limited function

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First On-sky Demonstration of a Band-limited Mask NGS AO at Palomar 200-inch Installed in PHARO Use well-corrected subaperture to achieve ExAO Strehl ratios with current DM (Serabyn et al. 2007) Crepp et al. 2009, in prep. Mask Design linear 4 th -order smooth binary IWA = 880 mas optimized for K short Aluminum Fastener Microscope image before mask was cut from substrate and cleaned in ultrasonic bath

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Epsilon Eridani After PSF Subtraction Calibrator: Delta Eridani

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High-Contrast Imaging of Binaries Candidate Tertiary x x Hide two stars behind mask simultaneously Place additional constrains on formation theories compared to single stars ~ 230 M Jup Crepp et al. 2009, in prep.

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NIRCam Occulter Layout 60 mm HWHM = 0.40” (6 /D @ 2.1 m) HWHM = 0.64” (6 /D @ 3.35 m) HWHM = 0.82” (6 /D @ 4.3 m) 20 arcsec 5” x 5” ND Square (OD = 3) Disk Imaging @ 2.1 μm Disk Imaging @ 3.4 μm Disk Imaging @ 4.3 μm HWHM c = 0.27” (4 /D @ 2.1 m) Planet Imaging @ 2.1 μm HWHM c = 0.58” (4 /D @ 4.6 m) Planet Imaging @ 2.4-5.0 μm 12 mm

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Pupil Intensity at Lyot Stop for an Occulted Point Source Using 6 /D spot occulter Using 4 /D wedge occulter 1/5 th root intensity stretches

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NIRCam Lyot Stops Mask Openings (white) Superposed on Pupil Lyot stop for 6 /D spot occulters Lyot stop for 4 /D wedge occulters Effective Throughput = 19% Stops are metal coatings on the pupil wedges

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Gl 876b NIRCAM Predicted Contrast Krist et al. 2007 20 nm RMS wavefront difference between rolls

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Levine et al. 2009

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F460M Contrast No Coronagraph Coronagraph 4 /D Sinc 2 Wedge Coronagraph 6 /D Sombrero 2 Spot Raw Image Roll Subtraction 131 nm RMS wavefront error at occulter 40 nm RMS wavefront change between rolls

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Use Lyot stop to eliminate DM effect on some wavelengths =0.47 768 nm800 nm832 nm 1.00 all same 0.000.13 2 1.00 0.00 1.00 4 rad P-V 10 5 rad P-V 10 6 rad P-V No DM effect on shortest No DM effect on shortest s ±16 /D DM Kern et al. 2009

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Imaging Known RV Planets

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Achievable Contrast for a M0V Star at 4 pc (F460M) Planet Contrasts

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Without & With the Coronagraph Without Coronagraph With Coronagraph

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Epsilon Eridani After PSF Subtraction Calibrator: Delta Eridani

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We call these masks Eighth-Order Masks. /2 u M(u)=0 here 1- /2 1) M(u) M(u) du = 0 /2 0 2) For a different, overlapping subset of Notch Filter Masks, M(u) u 2 du = 0 /2 0 3)

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We call masks that meet these criteria Notch Filter Masks. /2 u M(u)=0 here 1- /2 1) M(u) M(u) du = 0 /2 0 2) M (u) = constant translates into two requirements on M(u) :

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What can M be such that L (M A)=0 ? Then the above equation has the following solution: M (u) = M (u+1) for /2 < u < 1- /2 Define M (u): d/du M (u) = M(u)

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For example, take M (u) = constant. (There are other possibilities but they are all unpleasantly chromatic, like Fresnel lenses.)

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Notch Filter Functions u G(u) G(u) = 0

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Notch Filter Image Masks u G(u) Bandwidth G(u) du = 0 0 G(u) u 2 du = 0 0 Eighth Order

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Fourier Transforms 1 cos x 1/2 -1/4 1/2 1 sin 2 x = - cos x 1 2 1 2

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Fourier Transforms multiplication convolution

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1/2 -1/4 sin 2 x = - cos x 1 2 1 2 Simplest Possible Band-Limited Mask 1-D 2-D

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F F x A M (F x A) L(M (F x A)) M(F A) F AF A On-axis point source

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+ + = = M (F x A) =0 (F x A) M 1/2 1/4

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F F x A M (F x A) L(M (F x A)) M(F A) F AF A

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= 0 L(M (F x A)) L x M (F x A)

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Lyot Stop

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sin 2 u M(u)

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b M(u)=0 for |u| > b M(u) du = 0 Band- Limited Functions

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b M(u) M(u) 0 for |u| > b M(u) du = 0 Classical Lyot Coronagraph e.g. HST ACS Band- Limited Functions

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0 1 2 3 4 /( D) M Useful Band-Limited Functions Kuchner & Kasdin 1010

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Band-limited masks in the JPL High Contrast Imaging Testbed

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Kuchner & Spergel 2003 Debes et al. 2004 Binary Band-Limited Masks

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Kuchner, Crepp & Ge 2004 Transmissivity distance to optical axis ( / D) 1 - sinc 2 Mask 1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 Eighth Order Mask

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M(x) = - e 2 iux + - e -2 iux 1 4 1 4 1 4 - 1 4 - 1/2 1 2

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M(x) = - e 2 iux + - e -2 iux Fourier Transform 1/2 -1/4 Mask 1 2 1 4 1 4

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M(x) = sin 2 ux Fourier Transform 1/2 -1/4 Mask

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M(x) = - e 2 iux + - e -2 iux u < D/ 1 4 1 4 1 2

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M image mask L Lyot stop A entrance aperture

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M image mask L Lyot stop A entrance aperture

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Band-limited Image Masks u M(u) Bandwidth M(u) du = 0

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linear 8th order 3 /D mask 2.4mm x 8mm linear 8th order 4 /D mask 2.4mm x 8mm linear 8th order optimized mask 2.054mm x 8mm calibration pinholes linear 4th order 1-sinc2 4 /D mask 2.4mm x 8mm Microscope Photos of Newly Completed JPL Binary Masks

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Other Competitive Coronagraph Schemes: Shaped Pupils Pupil PSF Kasdin, Vanderbei, Spergel et al.

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Other Competitive Coronagraph Schemes: Continuous Pupil Mapping (PIAA) Guyon, Traub, Vanderbei et al.

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Kuchner, Crepp & Ge 2004 1 - sinc 2 Mask Eighth Order Mask |M(x)| 2 ^

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Entrance Aperture A Image Mask M Lyot Stop L

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Band-Limited masks in the JPL testbed Trauger et al. 2005

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First On-sky Demonstration of a Band-limited Mask NGS AO at Palomar 200-inch Installed in PHARO Use well-corrected subaperture to achieve ExAO Strehl ratios with current DM (Serabyn et al. 2007) Crepp et al. 2009, in prep. linear 4 th -order IWA = 880 mas optimized for K short Aluminum Fastener

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