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# Band-Limited Masks and Coronagraphic Imaging of Exoplanets Marc Kuchner - PowerPoint PPT Presentation

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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Coronagraphic Imaging of Exoplanets

Marc Kuchner

Exoplanets and Stellar Astrophysics Laboratory

NASA Goddard Space Flight Center

Krist et al. 2007

Balasubramanian

2008

Krist et al. 2007

Balasubramanian

2008

2008

Entrance Aperturre

M

Lyot Stop

L

F

A

F x A

FA

M

M(F A)

M  (F xA)

L

L(M (F xA))

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 ?

Kuchner 2005

Complete solution:

M(x) = Cj(x-j) + G(x)

j

M(u) du = 0

2)

0

M(u)=0 here

1)

M(u)

1-/2

/2

u

M(u) = Fourier Transform of mask

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

(And Band-Limited)

Notch Filter

Krist et al. 2009

Crepp et al. 2009

Balasubramanian

2008

M(u) du = 0

/2

2)

M(u) u2 du = 0

0

3)

0

For a different, overlapping subset of Notch Filter Masks,

M(u)=0 here

1)

M(u)

1-/2

/2

u

0.8

0.6

0.4

0.2

0.0

Kuchner, Crepp & Ge 2004

Crepp et al. 2006

Transmissivity

0 1 2 3 4 5

distance to optical axis (/D)

4th Order

8th Order

Contrast

Waves (RMS)

Waves (RMS)

Shaklan and Green 2005

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

On HCIT

Kern et al. 2008

Moody et al 2008

Band-limited function

Moody et al 2008

• 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)

Microscope image before

and cleaned in ultrasonic bath

• linear 4th-order

• smooth binary

• IWA = 880 mas

• optimized for Kshort

Crepp et al. 2009, in prep.

Aluminum Fastener

Epsilon Eridani

Calibrator: Delta Eridani

Candidate

Tertiary

• Hide two stars behind

• on formation theories

• compared to single stars

x

x

Crepp et al. 2009, in prep.

~ 230 MJup

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 Stopfor an Occulted Point Source

Using 4l/D wedge occulter

Using 6l/D spot occulter

1/5th root intensity stretches

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

Gl 876b

20 nm RMS wavefront

difference between rolls

Krist et al. 2007

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 eliminateDM effect on some wavelengths

DM

768 nm

800 nm

832 nm

e=0.47

all lsame

±16 l/D

1.00

1.00

1.00

No DMeffect on shortest l

0.00

0.132

1.00

No DMeffect on shortest ls

0.00

0.00

1.00

Planet

Contrasts

Without Coronagraph

With Coronagraph

After PSF Subtraction

Calibrator: Delta Eridani

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

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

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.)

G(u)

u

G(u) = 0

G(u)

u

G(u) du = 0

Bandwidth

0

G(u) u2 du = 0

0

1

cos x

1/2

1/2

1

1

sin2 x = - cos x

2

2

1/2

-1/4

-1/4

Fourier Transforms

multiplication

convolution

-1/4

-1/4

1

1

1-D

sin2 x = - cos x

2

2

2-D

F

F x A

FA

M(F A)

M  (F xA)

L(M (F xA))

(F xA)

1/2

1/4

1/4

=

=

+

=0

+

M  (F xA)

F x A

FA

M(F A)

M  (F xA)

L(M (F xA))

M  (F xA)

x

L(M  (F xA))

= 0

sin2

M(u)

u

Limited

Functions

M(u)

b

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

M(u) du = 0

e.g. HST ACS

Band-

Limited

Functions

M(u)

b

M(u)0 for |u| > b

M(u) du = 0

1

0

M

0 1 2 3 4

/(D)

Kuchner & Kasdin

JPL High Contrast Imaging Testbed

Debes et al. 2004

1.0

0.8

0.6

0.4

0.2

0.0

Transmissivity

0 1 2 3 4 5

distance to optical axis (/D)

1

1

1

1

4

4

4

4

2

-

-

M(x) =

- e2iux + - e-2iux

1/2

1

1

2

4

4

M(x) = - e2iux + - e-2iux

Fourier Transform

1/2

-1/4

-1/4

M(x) = sin2 ux

Fourier Transform

1/2

-1/4

-1/4

1

1

4

4

2

M(x) =

- e2iux + - e-2iux

u < D/

L Lyot stop

L Lyot stop

M(u)

u

M(u) du = 0

Bandwidth

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

calibration pinholes

linear 4th order

1-sinc2 4 /D mask 2.4mm x 8mm

2.054mm x 8mm

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

Coronagraph Schemes: Shaped Pupils

Pupil

PSF

Kasdin, Vanderbei, Spergel et al.

Coronagraph Schemes:

Continuous Pupil Mapping (PIAA)

Guyon, Traub, Vanderbei et al.

^

|M(x)|2

Aperture

A

M

Lyot Stop

L

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)

• linear 4th-order

• IWA = 880 mas

• optimized for Kshort

Aluminum Fastener