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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]

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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. 2009

Krist et al. 2007

Balasubramanian

2008


Krist et al. 2007

Krist et al. 2007

Balasubramanian

2008



A

Entrance Aperturre

M

Image Mask

Lyot Stop

L



Incoming field

F

A

F x A

FA

M

M(F A)

M  (F xA)

L

L(M (F xA))


Try to solve this in 1-D given:

A

L

1/2

1/2-/2

Set F=1 to represent on-axis light.

What can M be such that L (M A)=0 ?


Not physical

Notch Filter Masks

Kuchner 2005

Complete solution:

M(x) = Cj(x-j) + G(x)

j


/2

M(u) du = 0

2)

0

Notch Filter Masks

M(u)=0 here

1)

M(u)

1-/2

/2

u

M(u) = Fourier Transform of mask


/2

M(u) du = 0

2)

0

For a subset of Notch Filter Masks,

M(u)=0 here and also here

1)

M(u)

1-/2

/2

u

We call these masks Band-Limited Masks.


Notch Filter

(And Band-Limited)

Notch Filter

Krist et al. 2009

Crepp et al. 2009

Balasubramanian

2008


/2

M(u) du = 0

/2

2)

M(u) u2 du = 0

0

3)

0

We call these masks Eighth-Order Masks.

For a different, overlapping subset of Notch Filter Masks,

M(u)=0 here

1)

M(u)

1-/2

/2

u


1.0

0.8

0.6

0.4

0.2

0.0

Kuchner, Crepp & Ge 2004

Eighth Order Mask

Crepp et al. 2006

1 - sinc2 Mask

Transmissivity

Eighth Order Mask

0 1 2 3 4 5

distance to optical axis (/D)


Aberration Sensitivity

4th Order

8th Order

Contrast

Waves (RMS)

Waves (RMS)

Shaklan and Green 2005


Hcit results with band limited masks
HCIT RESULTS WITH BAND LIMITED MASKS

Variable thickness nickel masks on a glass substrate

1-D sinc2 profile

Central wavelength 800 nm

Electric Field Conjugation algorithms for single and dual DM control

Trauger & Traub 2007

Contrast Achieved:

6e-10 @ 4l/D with 10% bandpass

1.2e-9 @ 3 l/D with 10% bandpass

2.7e-9 @ 3 l/D with 20% bandpass


Contrast

On HCIT

Kern et al. 2008


Nickel Mask

Moody et al 2008


Hybrid Mask: Nickel + Dielectric

Band-limited function

Moody et al 2008


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)

Mask Design

Microscope image before

mask was cut from substrate

and cleaned in ultrasonic bath

  • linear 4th-order

  • smooth binary

  • IWA = 880 mas

  • optimized for Kshort

Crepp et al. 2009, in prep.

Aluminum Fastener


After PSF Subtraction

Epsilon Eridani

Calibrator: Delta Eridani


High contrast imaging of binaries
High-Contrast Imaging of Binaries

Candidate

Tertiary

  • Hide two stars behind

  • mask simultaneously

  • Place additional constrains

  • on formation theories

  • compared to single stars

x

x

Crepp et al. 2009, in prep.

~ 230 MJup


Nircam occulter layout

HWHMc = 0.58”

(4l/D @ 4.6 mm)

HWHMc = 0.27”

(4l/D @ 2.1 mm)

Planet

Imaging

@ 2.4-5.0 μm

Planet

Imaging

@ 2.1 μm

NIRCam Occulter Layout

5” x 5” ND Square

(OD = 3)

20 arcsec

60 mm

12 mm

HWHM = 0.40”

(6l/D @ 2.1 mm)

HWHM = 0.64”

(6l/D @ 3.35 mm)

HWHM = 0.82”

(6l/D @ 4.3 mm)

Disk

Imaging

@ 4.3 μm

Disk

Imaging

@ 3.4 μm

Disk

Imaging

@ 2.1 μm


Pupil intensity at lyot stop for an occulted point source
Pupil Intensity at Lyot Stopfor an Occulted Point Source

Using 4l/D wedge occulter

Using 6l/D spot occulter

1/5th root intensity stretches


Nircam lyot stops mask openings white superposed on pupil
NIRCam Lyot StopsMask Openings (white) Superposed on Pupil

Lyot stop for

6l/D spot occulters

Lyot stop for

4l/D wedge occulters

Effective Throughput = 19%

Stops are metal coatings on the pupil wedges


NIRCAM Predicted Contrast

Gl 876b

20 nm RMS wavefront

difference between rolls

Krist et al. 2007



F460m contrast
F460M Contrast

Coronagraph

4l/D Sinc2 Wedge

Coronagraph

6l/D Sombrero2 Spot

No Coronagraph

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

Kern et al. 2009

Use Lyot stop to eliminateDM effect on some wavelengths

DM

768 nm

800 nm

832 nm

e=0.47

all lsame

±16 l/D

4 radP-V

1.00

1.00

1.00

No DMeffect on shortest l

105 radP-V

0.00

0.132

1.00

No DMeffect on shortest ls

106 radP-V

0.00

0.00

1.00




Without with the coronagraph
Without & With the Coronagraph

Without Coronagraph

With Coronagraph


Epsilon Eridani

After PSF Subtraction

Calibrator: Delta Eridani


/2

M(u) du = 0

2)

0

For a different, overlapping subset of Notch Filter Masks,

M(u)=0 here

1)

M(u)

1-/2

/2

u

/2

M(u) u2 du = 0

3)

0

We call these masks Eighth-Order Masks.


/2

M(u) du = 0

2)

0

M(u) = constant translates into two requirements on M(u) :

M(u)=0 here

1)

M(u)

1-/2

/2

u

We call masks that meet these criteria Notch Filter Masks.


What can M be such that L (M A)=0 ?

Define M(u): d/du M(u) = M(u)

Then the above equation has the

following solution:

M(u) = M(u+1) for /2 < u < 1- /2


For example, take M(u) = constant.

(There are other possibilities but they

are all unpleasantly chromatic,

like Fresnel lenses.)


Notch Filter Functions

G(u)

u

G(u) = 0


Eighth Order

Notch Filter Image Masks

G(u)

u

G(u) du = 0

Bandwidth

0

G(u) u2 du = 0

0


1

1

cos x

1/2

1/2

1

1

sin2 x = - cos x

2

2

1/2

-1/4

-1/4

Fourier Transforms


Fourier Transforms

multiplication

convolution



1/2

-1/4

-1/4

Simplest Possible Band-Limited Mask

1

1

1-D

sin2 x = - cos x

2

2

2-D


On-axis point source

F

F x A

FA

M(F A)

M  (F xA)

L(M (F xA))


M

(F xA)

1/2

1/4

1/4

=

=

+

=0

+

M  (F xA)


F

F x A

FA

M(F A)

M  (F xA)

L(M (F xA))


L

M  (F xA)

x

L(M  (F xA))

= 0



sin2

M(u)

u


Band-

Limited

Functions

M(u)

b

M(u)=0 for |u| > b

M(u) du = 0


Classical Lyot Coronagraph

e.g. HST ACS

Band-

Limited

Functions

M(u)

b

M(u)0 for |u| > b

M(u) du = 0


Useful Band-Limited Functions

1

0

M

0 1 2 3 4

/(D)

Kuchner & Kasdin


Band-limited masks in the

JPL High Contrast Imaging Testbed


Kuchner & Spergel 2003

Debes et al. 2004

Binary Band-Limited Masks


Kuchner, Crepp & Ge 2004

1.0

0.8

0.6

0.4

0.2

0.0

1 - sinc2 Mask

Transmissivity

Eighth Order Mask

0 1 2 3 4 5

distance to optical axis (/D)


1

1

1

1

1

4

4

4

4

2

-

-

M(x) =

- e2iux + - e-2iux

1/2


1

1

1

2

4

4

M(x) = - e2iux + - e-2iux

Fourier Transform

Mask

1/2

-1/4

-1/4


M(x) = sin2 ux

Fourier Transform

Mask

1/2

-1/4

-1/4


1

1

1

4

4

2

M(x) =

- e2iux + - e-2iux

u < D/


A entrance aperture

M image mask

L Lyot stop


A entrance aperture

M image mask

L Lyot stop


Band-limited Image Masks

M(u)

u

M(u) du = 0

Bandwidth


Microscope Photos of Newly Completed JPL Binary Masks

linear 8th order 3/D mask 2.4mm x 8mm

calibration pinholes

linear 4th order

1-sinc2 4 /D mask 2.4mm x 8mm

linear 8th order optimized mask

2.054mm x 8mm

linear 8th order 4 /D mask 2.4mm x 8mm


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 2004

^

|M(x)|2

Eighth Order Mask

1 - sinc2 Mask


Entrance

Aperture

A

Image Mask

M

Lyot Stop

L



Crepp et al. 2009, in prep.

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)

  • linear 4th-order

  • IWA = 880 mas

  • optimized for Kshort

Aluminum Fastener


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