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

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)

Crepp et al Krist et al Balasubramanian 2008

Krist et al Balasubramanian 2008

Balasubramanian 2008

L Lyot Stop MImage Mask A Entrance Aperturre

Martinez 2009

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

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.

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

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

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)

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

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)

Transmissivity distance to optical axis ( /  D) 1 - sinc 2 Mask Eighth Order Mask Crepp et al Kuchner, Crepp & Ge 2004 Eighth Order Mask

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

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 : 4 /D with 10% bandpass 3 /D with 10% bandpass 3 /D with 20% bandpass Trauger & Traub 2007

Kern et al Contrast On HCIT

Nickel Mask Moody et al 2008

Hybrid Mask: Nickel + Dielectric Band-limited function

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

Epsilon Eridani After PSF Subtraction Calibrator: Delta Eridani

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.

NIRCam Occulter Layout 60 mm HWHM = 0.40” (6 2.1  m) HWHM = 0.64” (  m) HWHM = 0.82” (6 4.3  m) 20 arcsec 5” x 5” ND Square (OD = 3) Disk 2.1 μm Disk 3.4 μm Disk 4.3 μm HWHM c = 0.27” (4 2.1  m) Planet 2.1 μm HWHM c = 0.58” (4 4.6  m) Planet μm 12 mm

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

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

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

Levine et al. 2009

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

Use Lyot stop to eliminate DM effect on some wavelengths  = nm800 nm832 nm 1.00 all same 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

Imaging Known RV Planets

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

Without & With the Coronagraph Without Coronagraph With Coronagraph

Epsilon Eridani After PSF Subtraction Calibrator: Delta Eridani

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)

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) :

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)

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

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

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

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

Fourier Transforms multiplication convolution 



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

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

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

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

= 0 L(M  (F x A)) L x M  (F x A)

Lyot Stop

sin 2 u M(u)

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

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

/(  D) M Useful Band-Limited Functions Kuchner & Kasdin 1010

Band-limited masks in the JPL High Contrast Imaging Testbed

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

Kuchner, Crepp & Ge 2004 Transmissivity distance to optical axis ( /  D) 1 - sinc 2 Mask Eighth Order Mask

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

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

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

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

M image mask L Lyot stop A entrance aperture

M image mask L Lyot stop A entrance aperture

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

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

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

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

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

Entrance Aperture A Image Mask M Lyot Stop L

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

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