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High-Contrast Imaging with a Band-Limited Coronagraphic Mask

Permanent Link: http://ufdc.ufl.edu/UFE0022673/00001

Material Information

Title: High-Contrast Imaging with a Band-Limited Coronagraphic Mask
Physical Description: 1 online resource (159 p.)
Language: english
Creator: Crepp, Justin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: brown, contrast, coronagraph, direct, dwarf, imaging, mask, planet
Astronomy -- Dissertations, Academic -- UF
Genre: Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We present a comprehensive study of the band-limited coronagraphic mask. Emphasis is placed on its ability to detect faint substellar companions when operating in concert with a high-actuator-density deformable mirror. Both space and ground-based applications are considered. It is shown that a new kind of band-limited mask, the 'eighth-order' mask, can remove diffracted starlight while providing more resistance to tip/tilt errors and low-order aberrations as compared to other designs. This feature also naturally translates to an improved resistance to the finite size of stars. Our numerical simulations indicate that a TPF-C-like instrument equipped with an eighth-order mask can, in addition to achieving its baseline goal of characterizing 'Earth-like' planets orbiting main-sequence stars, also address fundamental questions regarding planet formation and evolution by targeting nearby evolved stars. We show that such observations can probe the exoplanet population near the high-mass-end of the spectral-sequence and also possibly constrain the timescale for the development of life. We next make a comparative study of the performance of various coronagraphic masks when in the presence of atmospheric turbulence. It is shown that there are several guidelines for deciding the design of a ground-based image-plane occulter: (i) to justify the use of a band-limited mask, the on-sky Strehl ratio delivered by the adaptive optics system must exceed $\approx 0.88 \: S_{qs}$, where $S_{qs}$ is the intrinsic (quasi-static) Strehl ratio provided by the instrument; (ii) one should never build a Gaussian coronagraphic mask; and (iii) the use of higher-order band-limited masks, such as the eighth-order mask, is relegated to situations where quasi-static residual starlight cannot be sufficiently removed from the search area with speckle-nulling hardware. These results are independent of the telescope entrance aperture geometry. We then built the first series of eighth-order band-limited masks using electron-beam lithography and test their performance in the lab. Our experiments show that eighth-order masks follow the theoretical predictions for resistance to tip/tilt and focus alignment errors and can generate contrast levels of $2\times10^{-6}$ at $3 \:\lambda / D$ in a system with $\approx1$ nm of rms wavefront error over the surface of critical optics. This work culminates with the design and fabrication of the first band-limited mask for on-sky observations: a demonstration that also constitutes the first tests of a leading TPF-C design candidate using 'extreme' AO. Contrast levels sufficient to detect brown dwarfs over a wide range of ages are generated at projected separations $\gtrsim 100$ AU for the stars: HIP 72567, HIP 83389, and HD 102195, a.k.a. ET-1. The sensitivity is limited by non-common-path errors and AO lag-time for the fainter targets. Taking advantage of the mask's linear geometry, we also conducted the first high-contrast imaging observations of visual binary stars by suppressing both sources simultaneously to search for faint tertiary companions.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Justin Crepp.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Ge, Jian.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022673:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022673/00001

Material Information

Title: High-Contrast Imaging with a Band-Limited Coronagraphic Mask
Physical Description: 1 online resource (159 p.)
Language: english
Creator: Crepp, Justin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: brown, contrast, coronagraph, direct, dwarf, imaging, mask, planet
Astronomy -- Dissertations, Academic -- UF
Genre: Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We present a comprehensive study of the band-limited coronagraphic mask. Emphasis is placed on its ability to detect faint substellar companions when operating in concert with a high-actuator-density deformable mirror. Both space and ground-based applications are considered. It is shown that a new kind of band-limited mask, the 'eighth-order' mask, can remove diffracted starlight while providing more resistance to tip/tilt errors and low-order aberrations as compared to other designs. This feature also naturally translates to an improved resistance to the finite size of stars. Our numerical simulations indicate that a TPF-C-like instrument equipped with an eighth-order mask can, in addition to achieving its baseline goal of characterizing 'Earth-like' planets orbiting main-sequence stars, also address fundamental questions regarding planet formation and evolution by targeting nearby evolved stars. We show that such observations can probe the exoplanet population near the high-mass-end of the spectral-sequence and also possibly constrain the timescale for the development of life. We next make a comparative study of the performance of various coronagraphic masks when in the presence of atmospheric turbulence. It is shown that there are several guidelines for deciding the design of a ground-based image-plane occulter: (i) to justify the use of a band-limited mask, the on-sky Strehl ratio delivered by the adaptive optics system must exceed $\approx 0.88 \: S_{qs}$, where $S_{qs}$ is the intrinsic (quasi-static) Strehl ratio provided by the instrument; (ii) one should never build a Gaussian coronagraphic mask; and (iii) the use of higher-order band-limited masks, such as the eighth-order mask, is relegated to situations where quasi-static residual starlight cannot be sufficiently removed from the search area with speckle-nulling hardware. These results are independent of the telescope entrance aperture geometry. We then built the first series of eighth-order band-limited masks using electron-beam lithography and test their performance in the lab. Our experiments show that eighth-order masks follow the theoretical predictions for resistance to tip/tilt and focus alignment errors and can generate contrast levels of $2\times10^{-6}$ at $3 \:\lambda / D$ in a system with $\approx1$ nm of rms wavefront error over the surface of critical optics. This work culminates with the design and fabrication of the first band-limited mask for on-sky observations: a demonstration that also constitutes the first tests of a leading TPF-C design candidate using 'extreme' AO. Contrast levels sufficient to detect brown dwarfs over a wide range of ages are generated at projected separations $\gtrsim 100$ AU for the stars: HIP 72567, HIP 83389, and HD 102195, a.k.a. ET-1. The sensitivity is limited by non-common-path errors and AO lag-time for the fainter targets. Taking advantage of the mask's linear geometry, we also conducted the first high-contrast imaging observations of visual binary stars by suppressing both sources simultaneously to search for faint tertiary companions.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Justin Crepp.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Ge, Jian.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022673:00001


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HIGH-CONTRAST IMAGING WITH A BAND-LIMITED CORONAGRAPHIC MASK


By

JUSTIN ROBERT CREPP



















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2008
































2008 Justin Robert Crepp



































For Aaron. I can't wait to meet you!









ACKNOWLEDGMENTS

I am grateful for the support and kindness of many people over the past several years

who have helped me throughout graduate school and with life in general.

I thank Mom, Dad, Adam, & Kristina for your continued love and support it has

been difficult to be so far away for so long; Larry & Gay Slozat, for the great C'!i 1-1i11 1 -

parties, your help with our first home, and, most importantly, allowing me to whisk your

daughter away to Florida; Lori, Tim, & Jaxon, for giving me a place to sleep before and

after observing runs; Brian Sands, for the late-night physics conversations, get-rich-quick

schemes, and teaching me the art of your great patience (of which I am still learning);

Andrew Vanden Heuvel, for your contagious enthusiasm, being my partner in crime our

first two years in Florida, and conquering Rome with me in a single div,; Matthew Turk,

for sharing with me your mad-scientist-like computer skills, dining with Judy and I at IP

and Herwig's before becoming a vegetarian, and giving me a place to stay during post-doc

interviews; Anthony, Craig, Curtis, Dave, Ji, Jorge, Mark, and PC, for keeping me

involved in athletics because of you, my sanity is, I think, still intact; Knicole and Paola

for keeping me company in the office while working into the wee hours of the morning;

Dimitri for your famous "Late Night Cookie Time" and trivia; Sun Mi, for your karaoke

skills, love of Indian food, and multiple birthd-ia parties (per year); Leah, for giving me

a lift to and from the Gainesville airport at a moment's notice; Kelly Bradley, for hiring

me at the Athletic Tutoring Center; C! ,i lotte Dare, for hiring me as the billiards leisure

course instructor; Pam Fitzgerald, for keeping me involved in public outreach with the

local grade schools; Steamers, for serving such delectable dishes, and, to a lesser extent,

the Krishna folks.

I thank Darren Williams, my undergraduate advisor, Blair Tuttle, and the other

professors at Penn State Behrend for preparing me for graduate school and showing

me the importance of balance in life; Jian Ge, my graduate thesis advisor, for setting a

good example of work-ethic, improving my proposal writing skills, p ,iing my fees every









semester, and supporting the many high-contrast imaging projects; Marc Kuchner, for

inventing the band-limited mask and being my external mentor; Eugene Serabyn, for

giving us access to the relay optics and serving as PI for observations at Palomar; Joe

Carson, for taking care of the politics to install a coronagraphic mask in PHARO; Kent

Wallace, Rick Burruss, and Jeff Hickey for your help on the mountain at Palomar we

will get flex-cam working 'ii. '1 i,, I promise; Bo and Xiaoke, for your help in the lab;

Suvrath, for your leadership, knowledge of the literature, and our frequent pizza runs to

Cloudcroft; Ji Wang, aka "King Lucky", for reconstructing wavefronts, calculating Strehl

ratios, and your optimism towards our projects; Julian, for bringing your consistency

to the radial velocity team and reminding me when the space shuttle would next be

launched; Scott and PC for the many fun observing runs and stimulating scientific and

nonscientific conversations; Audrey Simmons, for pl1 iring chess, basketball, piano, cards,

frisbee, pool, and backgammon with the ET observers to help pass the time at Sloan; all

members of the ET radial velocity team for your hard work; Jeff Julian, for letting me

borrow your tools; and Margaret, for conversations in a different bandpass.

Thanks also go to my PhD thesis committee, Jian Ge, Steve Eikenberry, Eric Ford,

Katia Matcheva, and C'!i i Telesco, which is comprised of world-class instrument

builders and experts in planetary science.

I acknowledge support from the Sigma Xi for two grants in aid of research, the SPIE

for a scholarship, and the Advanced Research Projects Agency for a grant to work on

technologies associated with the Terrestrial Planet Finder (TPF) mission.

Finally, this work would not have been possible without the support of my beautiful

and loving wife Amy. You have sacrificed so much to be with me in Florida. Thank you

for your encouragement and patience, for accommodating my awkward work schedule, and

for entertaining me with stories from Westwood Middle School. I love you.









TABLE OF CONTENTS


page


ACKNOW LEDGMENTS .................................

LIST O F TABLES . . . . . . . . . .

LIST OF FIGURES . . . . . . . . .

LIST OF SYM BOLS .. .. .. ... .. .. .. .. ... .. .. .. .. ... .. .. .

A B ST R A C T . . . . . . . . . .

CHAPTER

1 INTRODUCTION TO HIGH-CONTRAST IMAGING ..............

1.1 Background Information ............................
1.2 Essential Concepts . . . . . . . .
1.2.1 Faint Com panions ... .. .. .. ... .. .. .. .. ... .. .. .
1.2.1.1 Visible wavelengths ......................
1.2.1.2 Mid-infrared wavelengths ..................
1.2.1.3 Near-infrared wavelengths ..................
1.2.2 Diffraction M management ........................
1.2.3 Speckle Form ation . . . . . . .
1.3 The Lyot Coronagraph . . . . . . . .

2 THE BAND-LIMITED MASK . . . . . . .


Basic Principle . .
Eighth-Order Masks . .
Higher Spatial-Frequencies .
2.3.1 Binary Masks . .
2.3.2 Sampled Graded Masks


3 PROSPECTS FOR SPACE OBSERVATIONS .

3.1 Introduction: Quasi-Static Wavefront Errors anc
3.2 Targeting Evolved Stars . . . .
3.2.1 M otivation . . . . .
3.2.2 Extended Sources . . . .
3.2.2.1 Imaging terrestrial planets .
3.2.2.2 Imaging Jovian planets . .
3.2.3 Numerical Simulations . . .
3.2.4 Contrast vs. Angular Size . .
3.2.5 PSF Role-Subtraction . . .
3.3 Conclusions . . . . .


"The Dark










4 PROSPECTS FOR GROUND-BASED OBSERVATIONS


4.1 Introduction . . . . . . . . .
4.2 Model of Atmosphere & Wavefront Correction ................
4.3 Comparative Lyot Coronagraphy .......................
4.3.1 Hard-Edge vs. Apodized Image Masks ................
4.3.2 Gaussian vs. Band-Limited Masks . . . . .
4.3.3 Tip/Tilt and Low-order Aberrations . . . . .
4.4 C conclusions . . . . . . . . .

5 LABORATORY TESTS . . . . . . . .

5.1 Mask Design and Fabrication . . . . . .....
5.2 Experimental Setup . . . . . . . .....
5.3 R results . . . . . . . . . .
5.3.1 (C! i i ..i Transmission and Relative Intensities . . ..
5.3.2 Contrast Measurements . . . . . .....
5.3.3 Tip/Tilt and Focus Sensitivity . . . . .....
5.4 Summary & Concluding Remarks . . . . . .....

6 A BAND-LIMITED MASK FOR P.H.A.R.O. . . . . .....

6.1 Relay Optics . . . . . . . . ......
6.2 Design & Fabrication . . . . . . . .....
6.2.1 Binary Image Mask . . . . . . .....
6.2.2 Aluminum Fastener & Lyot Stop . . . . .....
6.3 White Light Tests . . . . . . . ......
6.4 On-Sky Demonstration . . . . . . ......
6.4.1 Data Acquisition & Reduction . . . . .....
6.4.2 HIP 72567 . . . . . . . .....
6.4.3 H IP : . . . . . . . .
6.4.4 HD 102195, a.k.a. ET-1 . . . . . .....

7 MINI-PILOT-SURVEY FOR LOW-MASS CIRCUMBINARY COMPANIONS .


7.1 Motivation . . . .
7.2 Target Selection . . .
7.3 Tertiary Companion Sensitivity .
7.3.1 HIP 88637 . . .
7.3.2 HIP 82510 . . .
7.3.3 HIP S 1. . . ...
7.3.4 HIP 66458 . . .
7.3.5 HIP 76952 . . .
7.3.6 HIP 82898 . . .
7.4 Discussion . . . .


8 AFTERWORD: PROJECT CONCLUSIONS & LONG-TERM PROSPECTS


87
90
93
93
93
96
100

102

102
106
107
109
111
114
115
116
120
123


.....................
.....................









REFEREN CES . . . . . . . . . 148

BIOGRAPHICAL SKETCH ................................ 159




















































8










LIST OF TABLES


Tabl

1-1

1-2

2-1

3-1

3-2

5-1

6-1

6-2

6-3

7-1

7-2

7-3

7-4

7-5

7-6


b


e

Comparison chart of planet detection techniques Fe

Direct imaging tradeoffs with bandpass . ..

Sampled eighth-order mask parameters . ..

Physical parameters for a Centauri . . .

High-contrast images of stars with large angular diam

Mask design parameters for lab experiments . .

Physical parameters for HIP 72567. . . .

Physical parameters for HIP : :1.. . .......

Physical parameters for ET-1. . . . .

Physical parameters for HIP 88637. . . .

Physical parameters for HIP 82510 . . .

Physical parameters for HIP 88964. . . .

Physical parameters for HIP 66458. . . .

Physical parameters for HIP 76952. . . .

Physical parameters for HIP 82898. . . .


page

ruary 2008 . . 17

. . . . 2 7

. . . . 4 5

. . . . 6 0

vters. . . .. 63

. . . . 9 0

. . . . 117

. . . . 12 1

. . . . 12 3

. . . . 3 0

. . . . 3 2

. . . . 3 5

. . . . 3 8

. . . . 3 9

. . . . 3 9


e









LIST OF FIGURES


Figure page

1-1 Number of planets orbiting other stars . . . . . 18

1-2 SAO model of the solar system as seen from 10 pes . . . ... 22

1-3 Contrast vs. wavelength for various ages and masses . . . 25

1-4 First images of candidate extrasolar planets . . . . . 26

1-5 The Airy pattern (must be removed) . . . . . . 28

1-6 Phase conjugation with a DM . . . . . . 30

1-7 Monochromatic speckles from a laboratory experiment ... . . 31

1-8 Optical layout of a transmissive Lyot coronagraph ..... . . 34

2-1 Convolution of the telescope entrance aperture with a coronagraphic mask 36

2-2 Eighth-order BLM functions described by Equation 2-6 for n 1 5.. . 38

2-3 Eighth-order BLM functions described by Equation 2-7 for m = 1, I = 2 5. .. 39

2-4 Intensity transmissions for various BLM's. . . . . . 39

2-5 An example of the sampling function for an m = 1, I = 3 mask . . 43

2-6 Simulated pictures of an m = 1, I = 3 eighth-order sampled binary mask . 43

2-7 Simulated pictures of an m = 1, 1= 3 eighth-order sampled graded mask . 46

3-1 Simulated deformable mirror surface and resulting dark hole. . . 50

3-2 Boston Micromachines 12x12 deformable mirror. . . . . 50

3-3 Inner and outer-edge of the habitable zone for nearby stars. . . 55

3-4 TPF-C stellar angular diameter sensitivity for an 8m telescope. . ... 62

3-5 PSF role-subtraction . . . . . . . . 64

4-1 Intensity transmission profiles for each radial image mask. . . . 82

4-2 Coronagraph simulations with perfect incident wavefronts . . . 83

4-3 Contrast curves for the hard-edge, Gaussian, and 4th-order BLM's . ... 84

4-4 Contrast versus wavefront correction . . . . . . 85

4-5 Contrast versus Lyot stop throughput . . . . . . 85










4-6 Contrast versus systematic tilt . ....

5-1 Linear binary notch filter image masks .

5-2 Laboratory images of the simulated star. .

5-3 Telescope PSF, coronagraph PSF, and Chi'ai,,i.

5-4 Experimental 3 a detection limits. . ...


transm


Coronagraph sensitivities to tilt and focus. . .

Lyot pupil plane experimental images . ...

Layout of relay optics. . . . . .

Image of subaperture pupil. . . . .

Anticipated Strehl as function of Fried parameter. .

The PHARO near-IR camera. . . . .

Coronagraphic mask for PHARO. . . .

Available slot in PHARO slit wheel. . .....

Aluminum fastener. . . . . .

Lyot stop installed in PHARO. . . .

White light tests: mask alignment, PSF, and Lyot pu


5-5

5-6

6-1

6-2

6-3

6-4

6-5

6-6

6-7

6-8

6-9

6-10

6-11

6-12

6-13

6-14

6-15

6-16

6-17

6-18

6-19

6-20


Experimental contrast using the PALAO internal whit

Flat-field image showing relay optics vignetting elemer

Calibration image of HIP 72567. . . .

Fully processed coronagraphic images of HIP 72567. .


. . . . 8 6

. . . . 8 8

. . . . 9 2

mission. . . 94

. . . . 9 5

. . . . 9 7

. . . . 9 9

. . . . 1. 04

. . . . 0 5

. . . . 0 5

. . . . 1. 06

. . . . 1. 09

. . . . 110

. . . . 110

. . . . 111

il im age. . .. 112

e light source. . .. 113

its. ... . . 116

. . . . 117

. . . . 118


HIP 72567 coronagraph sensitivity above and below mask in magnitudes .

HIP 72567 coronagraph sensitivity in Jupiter masses as a function of age. .

Fully processed coronagraphic images of HIP . . . ....

HIP s : -' i coronagraph sensitivity above and below mask in magnitudes .

HIP s ; ;-' I coronagraph sensitivity in Jupiter masses as a function of age. .

Fully processed coronagraphic images of ET-1. . . . . .....

ET-1 coronagraph sensitivity above and below mask in magnitudes. . .


119

119

121

122

122

124

124


p









ET-1 coronagraph sensitivity in Jupiter masses as a function of age. .

Qualitative images comparing circular to linear masks with binary stars.

Calibration and coronagraph images of HIP 88637. . . .

HIP 88637 coronagraph sensitivity in magnitudes. . . . .

HIP 88637 coronagraph sensitivity in Jupiter masses for an age of 100 M)


. 125

. 127

. 131

. 131

rs. 132


7-5 Calibration images of HIP 82510 in April 2007 and May 2008 .

7-6 Coronagraph images of HIP 82510 in April 2007 and M ,- 2008. .

7-7 HIP 82510 coronagraph sensitivity in magnitudes in 2007 and 2008..


HIP 82510 coronagraph sensitivity in Jupiter masses in 2007 and 2008. . .

Calibration and coronagraph images of HIP S . . . . .

HIP 88964 coronagraph sensitivity in magnitudes. . . . . .

HIP 88964 coronagraph sensitivity in Jupiter masses for various ages. . .

Coronagraph images of HIP 66458 showing off-axis sources. . . .

HIP 66458 coronagraph sensitivity in magnitudes. . . . . .

HIP 66458 coronagraph sensitivity in Jupiter masses for various ages. . .

Calibration and coronagraph images of HIP 76952. .... . . .

HIP 76952 coronagraph sensitivity in magnitudes. . . . . .

HIP 76952 coronagraph sensitivity in Jupiter masses for various ages. . .

Calibration and coronagraphic images of HIP 82898 . . . ..

HIP 82898 coronagraph sensitivity above and below mask in magnitudes.....

HIP 82898 coronagraph sensitivity in Jupiter masses for an age of 5 Gyrs .


133

133

134

134

136

136

137

138

138

139

140

140

141


8-1 Contrast predictions using the PALM-3k AO system in the J-band . ..


6-21

7-1

7-2

7-3

7-4


7-8

7-9

7-10

7-11

7-12

7-13

7-14

7-15

7-16

7-17

7-18

7-19

7-20


J'









LIST OF SYMBOLS AND ABBREVIATIONS

BLM band-limited mask

DH dark hole

DM deformable mirror

FOV field of view

GPI Gemini Planet Imager

IWA inner-working-angle

JPL Jet Propulsion Laboratory

PALAO PALomar Adaptive Optics system

PHARO Palomar High Angular Resolution Observer

PSF point-spread function

RV radial velocity

SETI Search for ExtraTerrestrial Intelligence

SIM Space Interferometry Mission

SPHERE Spectro-Polarimetric High-contrast Exoplanet REsearch instrument

TPF-C The Terrestrial Planet Finder Coronagraph

TPF-I The Terrestrial Planet Finder Interferometer

WFE wavefront error









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

HIGH-CONTRAST IMAGING WITH A BAND-LIMITED CORONAGRAPHIC MASK

By

Justin Robert Crepp

August 2008

C'!: iw: Jian Ge
Major: A-ii iv

We present a comprehensive study of the band-limited coronagraphic mask. Emphasis

is placed on its ability to detect faint substellar companions when operating in concert

with a high-actuator-density deformable mirror. Both space and ground-based applications

are considered.

It is shown that a new kind of band-limited mask, the i;!li !I-order" mask, can

remove diffracted starlight while providing more resistance to tip/tilt errors and low-order

aberrations as compared to other designs. This feature also naturally translates to an

improved resistance to the finite size of stars. Our numerical simulations indicate that a

TPF-C-like instrument equipped with an eighth-order mask can, in addition to achieving

its baseline goal of characterizing "Earth-like" planets orbiting main-sequence stars, also

address fundamental questions regarding planet formation and evolution by targeting

nearby evolved stars. We show that such observations can probe the exoplanet population

near the high-mass-end of the spectral-sequence and also possibly constrain the timescale

for the development of life.

We next make a comparative study of the performance of various coronagraphic

masks when in the presence of atmospheric turbulence. It is shown that there are several

guidelines for deciding the design of a ground-based image-plane occulter: (i) to justify the

use of a band-limited mask, the on-sky Strehl ratio delivered by the adaptive optics system

must exceed a 0.88 Sqs, where Sqs is the intrinsic (quasi-static) Strehl ratio provided by









the instrument; (ii) one should never build a Gaussian coronagraphic mask; and (iii) the

use of higher-order band-limited masks, such as the eighth-order mask, is relegated to

situations where quasi-static residual starlight cannot be sufficiently removed from the

search area with speckle-nulling hardware. These results are independent of the telescope

entrance aperture geometry.

We then built the first series of eighth-order band-limited masks using electron-beam

lithography and test their performance in the lab. Our experiments show that eighth-order

masks follow the theoretical predictions for resistance to tip/tilt and focus alignment

errors and can generate contrast levels of 2 x 10-6 at 3 A/D in a system with t 1 nm of

rms wavefront error over the surface of critical optics.

This work culminates with the design and fabrication of the first band-limited mask

for on-sky observations a demonstration that also constitutes the first tests of a leading

TPF-C design candidate using "extreme" AO. Contrast levels sufficient to detect brown

dwarfs over a wide range of ages are generated at projected separations > 100 AU for the

stars: HIP 72567, HIP S : -', and HD 102195, a.k.a. ET-1. The sensitivity is limited by

non-common-path errors and AO lag-time for the fainter targets.

Taking advantage of the mask's linear geometry, we also conducted the first

high-contrast imaging observations of visual binary stars by suppressing both sources

simultaneously to search for faint tertiary companions.









CHAPTER 1
INTRODUCTION TO HIGH-CONTRAST IMAGING

1.1 Background Information

High-contrast imaging is a technique whereby astronomers attempt to detect and

characterize faint objects that are located in the immediate vicinity of a bright source.

Applications include searching for debris disks, brown dwarf companions, and planets

orbiting nearby stars. Extragalactic studies, such as observations close to the nucleus of an

active galaxy, are also possible.

The first demonstration of high-contrast imaging technology took place in the late

1930s when Bernard Lyot built an instrument to block light from the disk of the Sun

in order to study its peripheries. He was particularly interested in the solar corona and

planned to conduct extensive observations whenever desired, instead of waiting for the

infrequent occurrence of an eclipse. His invention, which now bares the name: the Lyot

coronagraph (1.3), has become an indispensable tool in the field. It can be found at

most ground-based observatories. Moreover, the Hubble Space Telescope (HST) has a

coronagraphic operating mode (Krist 2007), the James Webb Space Telescope (JWST) will

be equipped with coronagraphic starlight suppression hardware (Clampin 2007), and one

of the Terrestrial Planet Finder (TPF) missions (3) will likely utilize some variation of

Lyot's original concept to generate unprecedented sensitivity (Shaklan & Levine 2007).

Modern high-contrast imaging is motivated primarily by extrasolar planet research.

To date, nearly 300 planets have been detected orbiting other stars (http://exoplanet.eu/;

http://exoplanets.org/); however, the vast i i, ii ly were discovered using indirect

techniques. Radial velocity (RV) (\! ,ircy & Butler 2000), transit photometry (C'!i rbonneau

et al. 2000), gravitational microlensing (Gaudi et al. 2008), astrometry (Benedict et al.

2006), and pulsar timing (Wolszczan & Frail 1992) each rely upon measurements of the

star but not the planet itself. The evidence is often a periodic signal superposed onto

the star's signature (e.g., its relative position in the sky, brightness, location of spectral









lines) and is compelling enough to infer the existence of a companion.1 Such observations,

however, often leave important physical characteristics, such as mass, radius, effective

temperature, and chemical composition poorly constrained (Table 1-1). Direct imaging is

an intuitive alternative that yields explicit photometric and spectroscopic information. In

this regard, it represents the future of exoplanetary science.

Table 1-1. Comparison chart of planet detection techniques February 2008
RV Transits Astrometry Lensing Pulsar Timing Imaging
Mass ~ / ~ / ~ /
Radius x / x x x /
Tff x x x x ./
Composition x ~ x x x /
Orbit" proj. / proj. proj. proj. proj.
Obser. Biasb age, P P P P neutron stars P
Efficiency > 1P > 2P > 1P hours > 1P hours'
Detections 221 36" 1t 6 5 1
x no information; ~ = weak constraint; / = strong constraint
-'\ .-I techniques provide information only on the projected orbit (proj.). The inclination of a
transiting planet is approximately 900.
bAll approaches, including pulsar timing, have an intrinsic observational bias to the orbital pe-
riod, P. The bias is most severe with transit photometry.
cThe members of entire planetary systems can, in principle, be detected and characterized simul-
taneously via direct imaging.
'w\. re than one-third were originally detected with RV and later found to eclipse the star.
eHST astrometric measurements have confirmed the RV planet c Eridani b (Benedict et al.
2006), and shown another candidate, HD 33636 b, to be a low-mass star (Bean et al. 2007).


All such techniques are naturally most sensitive to companions with substantive

mass. For instance, Jupiter (Mjup ~ 332MEarth) serves as a convenient fiducial for the

bulk of discoveries listed above. There is even a class of short-period planets known as

"hot-Jupiters" whose existence has revealed that planets can migrate during the latter

stages of formation (Lin et al. 1996). However, to address other questions regarding the

origin and structure of planetary systems, it is necessary to detect lower-mass bodies, of



1 A planet orbiting a white dwarf has even been discovered using stellar oscillation
(pulsation) timing (\!ll! i!!y et al. 2008).










order Neptune and smaller, by refining these methods and building instruments for space.

Current data (Fig. 1 1) and the leading formation theory of "core-accretion" (Pollack

et al. 1996) s---:.- -1 that low-mass planets may indeed be common (Ida & Lin 2004).



120
125-



100



75
65


50

27
19
25
010


0 5 10 15
Mass / M
Jup

Figure 1-1. Number of planets detected orbiting other stars as a function of mass (data
from the Exoplanet Encyclopedia, Schneider, J. March 7, 2008). Evidence
for a paucity of brown-dwarfs is clear, given the current sensitivity, ~ 1 m/s, of
RV instruments (\! ,rcy & Butler 2000). The prospects for an abundance of
low-mass planets are promising.


One of astronomy's principle goals in the next century is to detect a terrestrial planet

orbiting in the habitable zone (Kasting et al. 1993) of a nearby star. The space missions

COROT (transit photometry launched December 2006), Kepler (transit photometry

- scheduled launch 2009), and SIM (astrometry launch date uncertain) will each be

sensitive to rocky worlds located at orbital distances where water can persist in the liquid

phase. Their observations will place the first constraints on the population statistics

of planets with potentially hospitable environments. However, only a direct imaging









instrument will be able to unambiguously detect atmospheric biomarkers, such as H20,

CO2, 02, 03, CH4, and N20, which are indicative of life (Kaltenegger et al. 2007).

NASA has therefore proposed two additional missions, a series of Terrestrial Planet

Finders, that will obtain spectra of "Earth-like" exoplanets (should they exist). The

first instrument, TPF-C, will utilize a coronagraph and single-dish telescope operating

at visible wavelengths to collect reflected light (3), while the second, TPF-I, will

complement these observations at mid-IR wavelengths, with a long-baseline interferometer.

The TPF-C will be launched before TPF-I, even though the difference in brightness

between a star and planet is more favorable in the infrared (1.2.1). This decision is

based on the fact that coronagraphic technologies, such as those described in this thesis,

are maturing rapidly (see also http://www.lyot2007.org/), while interferometric-nulling

technologies (Wallace et al. 2000), such as precision formation flying2 which is required

to achieve the necessary spatial resolution are more risky and difficult to demonstrate

pre-launch. (Nevertheless, ESA has elected to move straight to the interferometric

approach with the Darwin mission (Fridlund 2004).)

There are several prospective designs for the TPF-C. One of the most promising

candidates utilizes a band-limited mask: an occulter that resides in the focal plane of the

Lyot coronagraph and controls diffraction by manipulating the amplitude of starlight.

The band-limited mask provides numerous benefits for high-contrast iin .-,.i such as

deep suppression of starlight over a broad bandpass, high off-axis transmission, close

inner-working-angle, resistance to low-order aberrations, resistance to finite stellar size,

and flexibility in design and manufacturing. It also requires a minimal number of optics



2 SIM will have a 9m baseline and employ rigid-body beam-combination. The TPF-I
calls for multiple baselines exceeding 100m. The positioning of optics, for both missions,
must be controlled to a level of order the coherence length of light, A2/AA.









to implement, which limits the number of scattering surfaces and allows for a compact

instrument. These advantages also translate to ground-based observations.

The following work describes the band-limited mask (2) and its performance

in numerical simulations (with respect to both space (3) and ground-based (4)

observations) and lab experiments (5), as well as on-sky tests using an "extreme"

adaptive optics system (6) and coronagraphic observations of visual binary stars (7).

The remainder of this chapter outlines the various goals and challenges of high-contrast

imaging in general and introduces the Lyot coronagraph. The discussion assumes single

main-sequence stars as the .1- i|, .1~i J1 targets of interest, unless otherwise stated.

1.2 Essential Concepts

Contrast, C, is defined as the relative brightness between a companion and its host,

IAmax -Amax
C = Bcompanion(A) dA /m Bstar(A) dA < (tt)


where Amin and Amax indicate the bandpass. Its value depends strongly on the mass

ratio and system age, and can change by several orders of magnitude when observations

are conducted in visible versus mid-infrared wavelengths. Direct detection requires

that instruments generate sensitivities comparable to C at a given angular separation,

otherwise companions will remain hidden beneath stellar residuals.

"His;h -contrast imaging, as is often written in the literature (even though Equ. 1-1 is

the conventional definition), is difficult because optical phenomena that are commonplace

and unavoidable, such as diffraction or reflection from a mirror, scatter a large amount

of starlight into the search area. Moreover, the pattern, or frequency spectrum, of noise

is structured such that contamination increases for regions closer to the star, making

detection a considerable challenge. The degree of difficulty depends on the type of

companion since the formation mechanisms, which govern the mass and characteristic

orbital separation, of terrestrial planets, giant planets, and brown dwarfs, fundamentally

differ.









1.2.1 Faint Companions

1.2.1.1 Visible wavelengths

In reflected light, the relative brightness can be calculated from the system geometry.

Consider a companion with radius Rp placed at a distance dp from its star. The

approximate monochromatic contrast is given by the fraction of starlight intercepted

by the companion's surface,

C c (1-2)
4wd / 2'
where c is an order unity factor that takes into account reflection efficiency effects, such as

albedo and orbital phase.

The canonical example is that of an Earth-like planet, Rp = 6400 km, located in the

habitable zone, dp = 1 AU. Using e 0.4, Equ. 1-2 yields C w 4 x 10-10. More careful

calculations, that include spectral features and a reasonable bandpass, find C w 2 x 10-10

(Des Marais et al. 2002), as is nominally quoted.

Measurement of any quantity to an accuracy of 1 part in 1010 requires compensation

for a variety of subtle effects. A comparison to experimental results for the values of

fundamental physical constants places the number into context: the mass of the electron,

Boltzmann's constant, Newton's gravitational constant, Planck's constant, and the

elementary charge have relative uncertainties of 4.9 x 10-8, 1.7 x 10-6, 1.0 x 10-4, 5.0 x 10-8,

2.5 x 10-8 respectively (National Institute of Standards http://www.nist.gov/). One of

the most important and reliably measured quantities, the fine structure constant, a, has a

relative uncertainty of 6.8 x 10-10. Its value was most recently determined by comparing

the results from a one-electron quantum cyclotron to a QED calculation involving 891

eighth-order Feynman diagrams (Gabrielse et al. 2006). The analogy is not without flaw,

but rightfully conveys the message that imaging an Earth-like exoplanet is non-trivial.

Jupiter would be the easiest planet to detect if the solar system were targeted by a distant

observer, but it is still a factor of 109 times fainter than the Sun in the visible (Fig. 1-2).










SAO Solar System Model at 10 PC


10-6 -

10-7

10-18

10-9



10-10

10-11

10- 12



10-13
10-14

10-15

10-16


10-18

i0-19

10-2o
0.1


Figure 1-2.


X (im)

Smithsonian Astrophysical Observatory code model of the solar system as seen
from 10 pcs (from Des Marais et al. (2002)). Contrast is found by comparing
the stellar flux to planet flux in a particular wavelength range, where 'J' is
Jupiter, 'V' is Venus, 'E' is Earth, \!' is Mars, and 'Z' is the zodiacal dust
cloud. Important trade-offs exist between required sensitivity, spatial
resolution, atmospheric correction, and background noise when considering the
bandpass of observations.


Instruments must generate these contrast levels at angular separations smaller than

1" (4.8 microradians) since the closest stars are several parsecs away. These considerations

essentially preclude ground-based imaging detections of planets at short wavelengths due

to the blurring effects of the atmosphere (see 4), even in the foreseeable future. Only

the TPF-C (3) or similar space-mission can begin to access this observational parameter

space.


1 10


100









1.2.1.2 Mid-infrared wavelengths

The sensitivities required in the mid-IR are more reasonable, since the blackbody

radiation of a cool companion, Teff < 800 K, peaks where the Rayleigh-Jeans tail of

the (presumably much hotter) star declines. For instance, the contrast of the Earth-Sun

system at A = 10 pm is "only" 10-6 (Fig. 1-2). Recent lab demonstrations have achieved

comparable sensitivities, C = 6 x 10-5, at close separations using a TPF-I candidate design

(Labadie et al. 2007).

A number of ground-based instruments operate in this spectral range. They are

diffraction limited and some are even equipped with a coronagraph (Telesco et al. 1998;

Telesco 2007; Kasper et al. 2007). Nevertheless, exoplanets have yet to be discovered in

the mid-IR because bright thermal emission from the sky can only be subtracted out to

one part in t 105 at the photon noise limit, e.g., when short exposures are taken in an

attempt to i i.... the thermal pattern before substantial fluctuations occur. The sky is

roughly as bright as a 6th magnitude star in the L-band (Phillips et al. 1999) and brighter

in M and N.

Companions such as 2MASS1207, GQ Lupi, and AB Pic, whose near-IR images are

shown in the next section, may be just bright enough to outshine this sea of thermal noise

(Telesco et al. 2008, in prep.). M and N-band photometry can place tight constraints on

their effective temperature and mass. However, only the youngest and most massive

Jovian planets with large orbital separations will satisfy the detection criterion to

circumvent these fundamental limitations. Ground-based imaging at infrared wavelengths

longwards of A m 5 pm can thus p1l i only a minor role in extrasolar planet direct imaging

detection in the near-term. The study of brown dwarfs, however, is not preclusive.

Current space missions, such as Spitzer (Fazio et al. 2004), do not have the requisite

spatial resolution, which is an issue even for 8-10m telescopes. Instead, TPF-I and Darwin

will exploit the advantages of the mid-IR using interferometry. As with SIM and TPF-C,

their funds are limited and schedules currently uncertain.









For information regarding mid-IR circumstellar debris disk in .-ii.- which has

important implications for planet formation, see the PhD thesis of Margaret Moerchen

2008.

1.2.1.3 Near-infrared wavelengths

Most ground-based efforts have focused on near-IR observations. There are two

particularly compelling reasons: (i) the J, H, & K bands, corresponding to Acentrai w 1.25,

1.65, 2.20 pm respectively, offer a practical compromise between the competing effects of

star-to-planet brightness, spatial resolution, atmospheric correction, and sky background

noise; and (ii) atmospheric models predict that young, massive exoplanets, which have a

high internal luminosity, preferentially release energy in these bands (Fig. 1-3).

Contrast levels of order 10-8 are required to detect 100 Myr old Jovian planets

(Burrows et al. 2004; Marley et al. 2007), but many stellar clusters, associations, and

moving groups are younger and host brighter, more easily detectable companions (see

L6pez-Santiago et al. (2006) for an excellent reference). For instance, the expected

J-band contrast of a 1Mj1p planet orbiting a KOV star at 5 Myrs and 50 Myrs is about

1.2 x 10-5 and 3.3 x 10-7 respectively (Baraffe et al. 2003; Girardi et al. 2002). The

only remaining complication is that young stars tend to be relatively distant, and large

aperture telescopes cannot achieve the necessary atmospheric correction (1.2.3) without

"extreme" adaptive optics (AO) systems (4), which do not yet exist.

The next generation of high-contrast instruments, namely GPI (\! ,. inIosh et al.

2006a) and SPHERE (Dohlen et al. 2006), which will begin operations within the next

three-four years, will feature high-actuator-density deformable mirrors (3, 4) and

coronagraphs coupled to integral field units (\IcElwain et al. 2007). Near-IR sensitivities

of ~ 10-7 at ~0.2" are anticipated. This is sufficient to directly detect self-luminous

Jovian planets.

Current AO-coronagraph instruments have generated contrast levels of order 10-4 at

0.5" 1.0" separations, with final effective sensitivities of t 10-5 following post-processing





















-6





-8





-10




-12





-14




-16





-4





-6




-8





-10




-12





-14




-16


05 06 070809 1


2
Wavelength [microns]


3 4 5 6


4 5 6


Figure 1-3. Atmospheric model predictions of contrast vs. wavelength for various ages

(top) and masses (bottom) of Jovian exoplanets (from Burrows et al. (2004)).


06 07 0809 1 2
Wavelength [microns]










(Lafreniere et al. (2007); Nielsen et al. (2008)). They have placed tight constraints on the

population statistics of brown dwarfs (13MAjp < M < 80MJup) orbiting single stars at

intermediate to large (> 10 AU) separations (Carson et al. 2006; Metchev & Hillenbrand

2004) and have produced the first images of candidate planetary mass companions.

VLT-NaCo K-band


GO Lup A


b




N
EJ


0.3 arc sec


*


k N


S IDI RedLICH011





A



B (22 degrees)

0 B (0 degrees)


Figure 1-4. The first images of candidate extrasolar planets: (upper-left) 2MASS1207 from
C'!i mvin et al. (2005a), (upper-middle) GQ Lupi from Neuhauser et al. (2005),
(upper-right) AB Pic from C'!, mvin et al. (2005b), (lower-left) SCR 1845 from
Biller et al. (2006), and (lower-right) UScoCTIO from B.'i -, et al. (2008).


1.2.2 Diffraction Management

Diffraction sets the angular scale for which high-contrast imaging instruments can

operate. The inner-working-angle (hereafter, IWA) is the closest distance that reasonable

sensitivities can be generated. Coronagraphs can typically access regions several A/D away

from the star. At smaller scales, the light from low-order diffraction and phase aberration

modes (see 1.2.3) is too intense and cannot be properly managed without simultaneously

attenuating the companion.









Table 1-2. Direct imaging tradeoffs with bandpass
Visible Near-IR Mid-IR
bandpass (pm) 0.5 0.8 1.0 2.5 5 20
IWA" (mas) 62 193 387, 773, 1547
contrast needed < 10-9 < 10-7 < 10-5
AO correction not feasible "extreme" AO low-order AO
active opticsb precision < 1 A precision < 1 nm low-order correction
sky background negligible manageable limiting
(exo)zodiacal light faint moderate bright
terrestrial space space space
Jovian space ground / space spacec
"Inner-working-angle (IWA) is defined here as 3 A~ax/D, where D = 8 m. The mid-IR
IWA's are for Amax 5, 10, and 20 pm respectively.
bCorrection of quasi-static wavefront errors (3). Values are quoted for space applications.
cGround-based imaging in the mid-IR can potentially access the youngest and most massive
exoplanets that have large (> 15 AU) orbital separations.

A slice of the Airy pattern is shown in Fig. 1-5. It is clearly not an optimal direct

imaging point-spread function (hereafter, PSF): the contrast at 3 A/D is 1.4 x 10t-.

A coronagraph can suppress the Airy pattern while efficiently passing off-axis light.

Entrance apertures with central obstructions and support structures complicate the issue

by requiring more restrictive stops to block diffraction, resulting in throughput losses. For

this reason, the baseline design for TPF-C incorporates an off-axis primary mirror (Ford

et al. 2006). ('!i Ipter 6 describes a ground-based approach involving a clear aperture.

Interferometers can create a PSF consisting of very deep nulls by changing the

phase of light in one or more arms. This circumvents the problem of building occulting

spots that have a physical size of several diffraction widths3 and results in an improved

IWA (a 0.5 A/d, where d is the baseline). However, the total search area decreases as a

result of alternating bright and dark fringes (planets can only be found in the dark ones),

requiring instrument rotations and hence losses in duty-cycle efficiency. This fundamental



3 Another option is to change the shape of the entrance aperture. The -!i iped-pupil"
coronagraph (Kasdin et al. 2003) is a former TPF-C design candidate at least in this
author's opinion. It requires that too much throughput be sacrificed to be viable.










Airy Pattern


10-2

4-3 PSF "wings"

S10-4
0
C)

10-6



108
0 2 4 6 8 10
angular separation (X / D)

Figure 1-5. Diffraction-limited point-spread-function from an unobstructed circular
aperture. The contrast is insufficient to detect extrasolar planets.


tradeoff is a result of interference, which forms the basis for diffraction. The mathematics

for understanding coronagraphy (1.3) are similar to high-contrast interferometry; in

cor(ii ii' ., however, the multiple (virtual) dishes can overlap.

1.2.3 Speckle Formation

Wavefront errors transfer energy from the PSF-core to a halo of 'speckles' surrounding

the source. They arise from non-uniformities in the optical path length (phase errors)

and transmission (amplitude errors). Active optics, such as deformable mirrors or light

modulators, can be used to compensate for these effects over low spatial frequencies that

are commensurate with the search area.

Phase errors result from temperature fluctuations in the atmosphere (which lead

to changes in the index of refraction) and the surface roughness of optical components.

Atmospheric phase errors change on a millisecond timescale and have a larger amplitude

than the systematics produced by telescope and instrument optics. Left uncorrected, both

sources can limit sensitivities at the 10-3 level.









Amplitude errors result from deviations in the throughput of parcels of air and

reflectivity of optics. They are, however, much less problematic than phase errors and can

be categorized as a < 10-7 effect, provided the system is free of large dust particles. For

example, the baseline GPI strategy is to correct for phase errors only (Bruce Macintosh,

private communication), in order to maximize search area (see 3).

Wavefront errors manifest as speckles in the image plane. One can gain an intuition

for their formation from the following example. Consider a complex field passing through

a one-dimensional telescope entrance aperture given by A(u) where u is the physical

coordinate and has units of D/A. Assume that the phase aberration, Q(u), consists of a

single sine-wave ripple of frequency f cycles per aperture and amplitude a in radians. The

electric field in the pupil plane is:

E(u) = A(u) ei(u) (1-3)

where A(u) is a top-hat function,

( 1 where Ju < /2(14)

0 elsewhere.

For small aberrations (a << 1) we can expand the exponential and keep the first term,
e&P(u) 1 + i a sin(27rfu). In the Fraunhofer or far-field diffraction regime (Hecht & Z i I-

1974), the electric field in the image plane is found by taking a Fourier transform, FT{...}:

E(x) FT{E(u)5)

= FT{A(u)} (6(x) a/2 [6(x + f) 6(x )])

where the hat, -, denotes an image plane quantity, is the convolution operator, and x

corresponds to an angle with units A/D.

We now let FT{A(u)} = A(x), which is simply the diffraction-limited PSF, and

recognize that it is copied at the location of the three delta functions, x = 0, x = -f, and











x = +f, but with a different weighting,


E(x) = A(x) a/2 A(x + f) + a/2 A(x f). (1-6)


An ideal coronagraph will remove the zero-frequency component, A(x), but cannot

eliminate the other two terms, otherwise the companion would be attenuated. Thus, a

sine-wave phase ripple creates two peaks of light, or speckles, at locations in the image

plane that correspond to the spatial frequency f. This forms the basis for understanding

high-contrast imaging wavefront aberration theory, since any general wavefront shape

can be constructed from of a series of sines and cosines. A deformable mirror (DM) can

suppress speckles by reshaping the phase of starlight (Fig. 1-6).


Sine-wave Phase Ripple
2.5, ,

2.0
f = 3 cycles / aperture
1 .5 ,, I

1.0 -- -

0.5-
0Aperture Stop


a -0.5
DM Surface
-1.0 -

-1.5

-2.0

-2.5 ------
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
u (DI X)

Figure 1-6. Cartoon of a single frequency 1 nm peak-to-trough phase error across the
telescope entrance aperture and a 19 actuator DM for conjugation. The f = 3
sine-wave aberration would normally create 2 speckles at 3 A/D in the image
plane. Instead, the phase errors are suppressed to a level given by how well the
DM can match the in-coming wavefront shape (fitting-errors). The DM surface
need only be half the wavefront phase height due to the reflection. The light is
then sent to the coronagraph.












-6.5




-7.5

-8

-8.5

-9

Figure 1-7. Monochromatic speckles at the detector of a lab experiment using a Lyot
coronagraph. The contrast is of order 10-6 (5) as is indicated by the intensity
gi ilv- J. shown to the right.


Notice also that the speckle intensity, |E'|2 (1-6), scales as a2. This relation has been

verified with numerical simulations in 3. Phase errors of order 1 nm limit contrast at the

, 10-' level at the coronagraph IWA in the visible. Therefore, to detect an Earth-like

planet, the phase of light must be controlled to better than a 1/ lO3 nm, or a 0.6 Bohr

radii, over the spatial frequencies of interest.

The phase amplitudes, a(f), form a frequency spectrum (3) that dictates the

spatial distribution of power or energy in the image. The power-spectra of atmospheric

aberrations differ from that of lenses and mirrors, but both can be reasonably well-modeled

with a monotonically decreasing power-law or broken power-law in f. In other words,

more stellar residuals are located close to the optical axis than further away.

Figure 1-7 shows quasi-static speckles from a lab experiment using a coronagraph

(Crepp et al. 2006). The contrast is limited at the 10-6 level at the IWA, implying that

wavefront phase errors are several nanometers in size. This was verified explicitly with

profilometer measurements of the surface of the most critical optic.

Image quality is often characterized by the Strehl ratio, S, which is defined as,

measured peak intensity of source
theoretical max peak intensity of source)
theoretical max peak intensity of source









A Strehl of 0.6 indicates that the atmosphere or instrument optics have scattered ~ !ii' .

of the PSF core energy. Much of that light lands in the search area.

The Strehl ratio can be related to the rms wavefront error by the Marichal formula,


S e"-s (1-8)


where arms is the root-mean-square wavefront error in radians. If we substitute for arms

the previous result that the wavefront must be controlled to better than 1/ \o3 nm at

A 650 nm in order to generate 10-10 contrast, we find that S = 0.99999990656. Hence,

ground-based imaging of terrestrial planets at visible wavelengths is impractical (see also

Guyon (2005) for other reasons).

At near-IR wavelengths, the Strehl ratio of 8-O1m telescopes is often less than 10' .

without wavefront correction. With current adaptive optics (AO) technology, Strehl ratios

of a .!I', are possible. This value is still insufficient and serves as the motivation for the

development of "extreme" AO and the work done in '!i ipter 6.

1.3 The Lyot Coronagraph

There are many kinds of coronagraphs. They can be roughly categorized into two

groups: interferometricc' coronagraphs and modifications of the Lyot coronagraph. Most

designs fall into the latter category, although there still exists an impressively large

diversity amongst individual approaches. Guyon et al. (2006) have compiled a list of

coronagraphic concepts that can, in principle, achieve 10-10 contrast at 5 A/D the

so-called "Coronagraph Tree of Life". Their abbreviated names are: the AIC, CPAIC,

VNC, PSC, CPA, PPA, PIAAC, PIZZA, APLC, APLCN, BLM4, BLM8, PM, 4QPM,

APKC, OVCm, AGPMC, and ODC.

Guyon et al. (2006) have also compared their performance on an equal footing using

a 'useful throughput' metric. In the ideal case, the OVC Optical Vortex (\! Iwet et al.

2007), PIAAC Phase Induced Amplitude Apodization (Guyon 2003), BLM4 4th-order

Band-limited Mask (Kuchner & Traub 2002), and BLM8 8th-order Band-limited Mask









(Kuchner, Crepp, & Ge 2005) coronagraphs yield the best results. The differences between

their individual benefits are: the OVC and PIAAC have sharper PSF's, better IWA's, and

higher throughput than the BLM4 and BLM8, and can therefore detect more targets per

time, but are -.i<,'.. ,,i1;./i more susceptible to low-order optical aberrations (2,4, 5) and

finite stellar size (3). These practical tradeoffs (which are studied in this work), along

with chromaticity considerations, will determine the design of the TPF-C (see also Cash

(2006) and 3). The BLM4 and BLM8 are unique amongst this elite list in that they are

also useful from the ground (4, 6, 7). They, along with the optical vortex (phase) mask,

are located in the image plane of the Lyot coronagraph, which is described below. The

BLM4 and BLM8 are described in detail in 2.

The Lyot coronagraph (Lyot 1939) controls diffraction with a combination of an

image mask and aperture stop. The mask and stop work together to suppress light from a

source that is aligned to the optical axis. Light emanating from an off-axis source, such as

a debris disk or substellar companion, enters the coronagraph at a small angle and suffers

minimal attenuation. The result is a gain in the relative number of photons received from

faint objects located in close angular proximity to the star. A well-calibrated coronagraph

operates like a high-pass filter and can improve sensitivities by many orders of magnitude.

Figure 1-8 depicts a transmissive design without wavefront control.

The first-order diffraction theory for light propagation through the Lyot coronagraph

is as follows: The electric-field at the entrance aperture is given by,


E (u, v) Eou, v) A (u, v), (1-9)


where Eo is the complex field and u, v are pupil plane quantities. For simplicity, we

assume here that no aberrations are present and set E = 1. We also neglect telescope

obstructions so that A(u, v) is just a circle or two-dimensional top-hat function.
















Entrance Aperture Lyot Stop

Figure 1-8. Optical layout of a transmissive Lyot coronagraph. The design is similar to a
spectrograph, except there is a mask and stop instead of a slit and grating.


Light entering the coronagraph is focused onto an occulting mask in the first image

plane. The electric-field is then,


E(x,y) A(x,y)M(x,y), (1-10)


where M(x, y) is the mask amplitude transmission profile. The mask intensity transmission

is IM(x,y) 2 and, typically, M(x 0, y= 0) 0.

The electric field at the subsequent pupil plane is found by taking another Fourier

transform,

ELyot(U, v) A(u, v) M(u, v). (1- 11)

This equation is the key to understanding Lyot coronagraphy. The field at the Lyot stop

is the convolution of the entrance aperture with the mask spatial frequency function. In

order to generate dynamic range, the light pattern must be faint near the center of the

pupil and bright near the edges. This way the Lyot stop can effectively remove starlight

while allowing most of the off-axis light to reach the detector.

The field at the detector is,


Efina = L(x, y) A(x, y) M(x, y), (1-12)


where L(u, v) L(x, y) is the Lyot stop. The intensity is Efial 2. Images of the field at

various locations along the path are shown in 4.









CHAPTER 2
THE BAND-LIMITED MASK

2.1 Basic Principle

The band-limited mask is an occulter located in the image plane of the Lyot

coronagraph (Kuchner & Traub 2002). It diffracts starlight into spatially succinct

regions that follow the contour of the telescope entrance aperture. The combination of

a band-limited mask and appropriately shaped Lyot stop can ,..-/pl./. l,/ remove the

on-axis light from an optical system when it is free of aberrations.

Equation 1-11 provides the basis for understanding its operation. Consider a

one-dimensional coronagraph with monochromatic light as in 1.2.3. We again model the

telescope entrance aperture as a top-hat in the pupil. The question is: "What function,

or set of functions, when convolved with the telescope entrance aperture, create an ideal

diffraction pattern at the Lyot pupil?" (Fig. 2-1).

An example of an ideal mask function is one that places all of the starlight exterior to

a certain region or distance from the optical axis. A simple stop, one that is opaque on the

outside and transparent in the center, can then block it all while still passing light from

the companion. Such a function would satisfy the following criterion,


e/2

and

M(u) = 0, for Ju > e / 2 (2-2)

where M(u) is the image mask spatial frequency function and 0 < c < 1 is a dimensionless

parameter that controls the bandwidth. The function is said to be band-limited because

only a range of low spatial-frequencies are present. Equ. 2-1 ensures that no starlight

"1. .:- through the coronagraph when the A(u) and M(u) functions overlap during

convolution, while Equ. 2-2 ensures the same when the functions do not overlap.











I 0- X I





Figure 2-1. Convolving A(u) with a band-limited mask function M(u) produces an
optimal diffraction pattern at the Lyot pupil plane (Kuchner & Traub 2002).
The resultant electric field is multiplied by another top-hat, the Lyot stop (not
shown), in order to remove all on-axis starlight.


The mask function shown in Fig. 2-1 is


M(u)=N 6(u) 11 ) (2-3)


where N is a normalization constant. The Fourier transform of Equ. 2-3 gives the

amplitude transmission,

M(x) = N[1 sinc(7cx)]. (2-4)

Band-limited masks are graded masks. Their intensity transmission, 0 < |M(x)|2 < 1 (i.e.

the part we actually build), varies smoothly in opacity. In broadband light, we design the

mask to operate at Amax, since shorter wavelengths are diffracted outside the Lyot stop.

Examples of other band-limited functions are: M(x) = sin2(7cx/2), 1 -i, (wex/n),

where n is an integer, and 1-Jo(wex). They generally trade IWA with off-axis attenuation.

In other words, masks with intrinsically close IWA's, such as the sin2(..) design, have more
'ringing' (opaque regions) in the search area. If c is increased to improve the IWA, then

the Lyot stop throughput decreases.

For instance, consider the linear 1 since2 (rcx/2) mask. A two-dimensional

coronagraph with an IWA of 4A/D, where IWA is taken as the location where the

intensity transmission reaches 0.5, would have a Lyot stop throughput of 6 !' Other

band-limited masks, such as the radial design, M -+ ]M((r), and separable design,

M -+ M(x) M(y), are also available. They likewise trade search space for throughput.









2.2 Eighth-Order Masks

A linear combination of band-limited functions creates another band-limited function.

The masks described in 2 are "fourth-order" masks: their intensity transmission near

the optical axis increases as the fourth-power with distance. It is possible to generate

higher-order mask functions, such as an eighth-order (Kuchner, Crepp, & Ge 2005) or

twelfth-order mask, by combining fourth-order mask functions .

The motivation for this concept is that intrinsically wider masks help filter low-order

aberration content. They are also more robust to pointing errors and the finite size of

stars. For example, an eighth-order mask would allow the TPF-C to operate with a

pointing accuracy no better than that of the Hubble Space Telescope, ~ 3 mas, whereas

a fourth-order mask would require ~ 0.7 mas. The price for relaxing such tolerances is a

modest cost in off-axis throughput.

To construct an eighth-order mask, we need the amplitude transmission term

responsible for quadratic leakage to equal zero,

d M(x) 0. (2-5)


This can be accomplished by adding an appropriately weighted C sin2 (kix) w (C/2)(kix)2

function to any 1 sinc"(k2x/n) w (k2 x)/(6n) function. Notice that the individual terms

also automatically satisfy Equ. 2-1 and 2-2. Setting k, = k2 we find C = -1/(3n). To

ensure M(x) < 1, we renormalize the mask by multiplying M(x) by a constant, N.

Putting everything together and using physical units yields a series of eighth-order

band-limited masks,

F 3n 1 tTXCE 1 TXCE
MBL(x) =N -3 -"+ cos-f- ,- (2-6)
m 3n ncsaxf 3n \max f

where f is the focal ratio at the mask and Amax is the longest wavelength at which the

mask is to operate. Figure 2-2 shows M(x) for the first few linear masks in the series.













0.6 -







0 1 2 3 4 5
distance from center of mask (1 / e D)
Figure 2-2. Eighth-order band-limited mask functions described by Equation 2-6 for
n=1-5.
In-
0.-










We can create another series of eighth-order masks with less off-axis attenuation by
combining two 1 sine" masks using the same procedure:

MBL(x) =N smc +- (2-7)
L I IAmax f I mAma j
This series is parameterized by two integer exponents, I and m; we assume 1 > m.
Figure 2-3 shows M(x) for m = 1 and I =2-5. The m = 1 and 1 -2-3 masks have
throughput similar to the n = 3 sin2 mask from above. Using large values of m and I
reduces the 'ringing' further, but also decreases the Lyot stop throughput.
Figure 2-4 compares the intensity transmission, |f(x) 2, for the 1 since2 fourth-order
mask and the m = 1, I = 3 eighth-order mask. While the 1 -ii, 2 mask has an IWA
of (1.448/e)(A/D), the m = 1, I 3 eighth-order mask has an IWA of (1.788/e)(A/D).
The m = 1, 1 3 mask offers a good compromise between ringing and throughput, and
also reaches 1(' '. transmission at its first maximum, a critical region for planet searching.
This mask design is recommended for the TPF-C.






















0.4k 1= 2


0 1 2 3 4 5
distance from center of mask ( / e D)

Figure 2-3. Eighth-order band-limited mask functions described by Equation 2-7 for
m 1, I 2 -5.


distance from optical axis (X / D)
4 6


2 3
distance from center of mask (1/ e D)


Figure 2-4.


Intensity transmission for the 1 since2 fourth-order mask, the n = 3
eighth-order mask, and the m 1, I = 3 eighth-order mask. Coronagraph
throughput and distance from optical axis were calculated with e = 0.6. The
m 1, I 3 eighth-order mask, recommended for TPF-C, has 10"'.
transmission at its first maximum.









Masks of higher-order can also be derived. They suppress low spatial-frequency

aberrations even further, but have significantly less Lyot stop throughput. The twelfth-order

mask is a viable tool when the IWA is large for example if one wanted to search the

extended habitable zone of a giant star (3).

2.3 Higher Spatial-Frequencies

There is an additional degree of freedom that we can exploit to construct band-limited

masks that are potentially easier to fabricate. Close inspection of Fig. 2-1 and Equ. 2-2

reveals that power at mask spatial frequencies Jul > 1 e/2 results in starlight being

diffracted well outside the Lyot stop opening. Masks that utilize this design freedom are

called notch-filter masks (Kuchner & Spergel 2003). They need not have smooth intensity

transmission profiles. Instead, notch filter masks can be sampled or binary, or both. In

the following, we use a technique similar to the one employ, -1 in 2.2 to find eighth-order

notch filter masks (Kuchner, Crepp, & Ge 2005). To be consistent with 2.2, we refer to

the various designs by the exponents of their constituent functions (n, 1, m).

We start with a linear combination of fourth-order notch filter masks,

S, .(x) = N [ (x) + CM^ch4B(x) (2-8)

where N ensures that f (x) < 1. The constant C is found by substituting Equ. 2-8

into Equ. 2-5, where

d2 M(x) (-27 iu)2M(u)du = 0, (2-9)
dX X= J-/2

and the derivatives are taken only over the low spatial frequencies (see Kuchner, Crepp, &

Ge 2005 for details). The answer is:
S,/2 2
C =u--2 -(fd (2-10)
f/2 u2Mnotch4 (u) du
wheree 4B0.

where -t< C<0.








To finish the derivation, we need to calculate Motch () ( Motch4 (x). Fourth-order
sampled masks are defined by the following prescription (Kuchner & Spergel 2003):

Mnotch4X) Maimp (x) (2- 11)

where

Msamp4x W Px) (MBL4 Ax 6(x (k + Ax)) (2-12)
k )

Msamp4 () P() (MBL4 (U) 6( k/Ax)-27rizx) (2-13)
\ /k
and

] Msamp1(u) du MBL4(U)P(u) du = MI(x) P(x) (2-14)
-eD/(2A) --o X=0
Here, MBL4 represents any fourth-order band-limited mask function and k ranges over all
integers. The sampling points are offset from the mask center by a fraction ( of Ax. The
kernel, P(x), can represent the "b, o,,1 of a nanofabrication tool. It should be normalized
so that fl P(x) dx = 1, and P(x) must be everywhere < 1/(Ax), so Msamp4 (x) remains
< 1. The constant ft, ensures that the mask satisfies Equation 2-1. Though the sampled
mask is derived from MBL4 (x), the function being sampled is MBL4 (Wa)- i
Substituting Equ. 2-11 into Equation 2-8 we have

S,f (x) N [( ,, (x) + C( (x) ) (2-15)

and using Equ. 2-13 and 2-14 the constant C becomes

f6/2 U2P(U)MBL ) du
C -_C21 (2- 16)
f2 U2P(u)MBL4 (u) du
We can now construct a v i. I v of eighth-order notch filter masks analogous to the variety
of eighth-order band-limited masks.









In the following, we provide example calculations for making sampled binary and

sampled graded eighth-order notch filter masks using the m = 1, I = 3 design. We assume

a linear mask geometry and consider broadband light.

2.3.1 Binary Masks

Binary masks are everywhere either completely opaque or completely transparent. To

build one that satisfies the various diffraction criterion we assemble a collection of identical

parallel stripes, where a notch filter mask function provides the width of each stripe,

1 where y < 1, (x) Amif (2

0 elsewhere.

The mask function is
OO
(, (x,y) ..ipe(x, y- jAmnf), (2 18)


where Amin is the shortest wavelength in the band of interest. Band-limited masks leak

light at wavelengths longer than Amax, whereas notch filter masks can also leak light

at wavelengths shorter than Amin. In other words, the notch filter mask operates like a

band-limited mask so long as the optical system does not resolve its intricate features.

If we like, we can use the band-limited mask functions described by Equations 2-6

or 2-7 in place of If (x), resulting in a mask formed of continuous curves. However,

sampled binary masks may prove to be easier to manufacture since their features are not

as small near the optical axis. The binary mask shown in Fig. 2-6 is sampled. It can be

made entirely from rectangles of opaque material using e-beam lithography (5).

The function we actually sample is N[(fMBLA (x) A) + C(MBL4B(X) .)]

Figure 2-5 shows a plot of this function to illustrate how ( may be chosen. To guarantee

that f (x) > 0, the parameter ( must be in the range I(| < (o, where (o is defined by

the condition MBL4A((oA minf) + CMBL4B(L oi(( f) M ijA + Ci'L,. For our binary mask,

we choose ( = (o, to make the central rectangles contiguous.


















2j
m
<73

+ 0


I -1



-2



-1.0


0.4 0.6 0.8


Figure 2-5. An example of the function N[(MBL4A(x) 'A) + C(MBL4B(X) -~'U,,)] for
an rm 1, I = 3 sampled mask. Choosing ( = (o allows us to create a binary
mask of contiguous stripes. C'! ....- i ( 0 allows us to create a graded mask
with the most favorable optical density requirement.






F,,_m

Fi


Figure 2-6.


Simulated low and high magnification pictures of an m 1, I = 3 linear
eighth-order sampled binary mask. Dark areas are completely opaque and
white areas perfectly transmissive. The high-magnification picture (right)
illustrates the sampling. See 5 for microscope photographs of linear
eighth-order binary masks.


x 10-4


-0.8 -0.6 -0.4 -0.2 0.0 0.2
X (f min)









For the m = 1, I = 3 mask with IWA = 3 Amax/D, spacing Ax A= minf, and bandpass

0.5-0.8 pm, we find that ,'A -= 0.00630889, i-,,,. 0.01882618, C = -0.33935486,

and (o = 0.25941279. Table 2.3.2 lists normalization constants and sampled mask

parameters for eighth-order notch filter masks of various IWA's using a top-hat kernel,

P(x) = (D/Amin)I(xD/Amin), and 0.5-0.8 pm bandpass.

If the resolution of our nanotool is ~ 20 nm, we require a telescope with an f/115

or slower beam (see Kuchner & Spergel 2003). The physical size of an entire mask is

generally a few hundred diffraction widths. A 1" x 1" mask would consist of > 440

vertically repeating segments, where each segment is < A\minf 57.5 pm wide. This

coronagraph design would have a Lyot stop throughput of ,!iI'. Figure 2-6 shows an

example of what an m = 1, I = 3 linear eighth-order binary mask would look like.

2.3.2 Sampled Graded Masks

Sampled graded masks may be easier to construct than smooth graded masks.

Moreover, they can be designed so that they do not require their darkest regions to be

perfectly opaque. This flexibility limits the demands on the lithography tool used to make

the masks. The 1 since2 mask with IWA = 2.9 Amax/D, e = 0.4, can be built with a

maximum optical density of 4. The sin2 mask with e = 0.4 can be built with a maximum

optical density of 3.

When we design eighth-order graded notch filter masks, we can reduce the required

maximum optical density by beginning the sampling at ( = 0, so long as our sampling

size is large enough to straddle the valleys shown in Figure 2-5. C'! ..-ig Ax = minf

satisfies this condition for all of the masks listed in Table 2.3.2. Figure 2-7 shows a graded

version of the m = 1, I = 3 eighth-order mask described in 4.1. The mask is defined by

M(x, y) if (x); its optical density is logo '.1 (x)|2. To make the darkest stripe

of the mask as transparent as possible, we chose ( = 0. With this choice, the darkest

stripe of the mask has optical density -2logo10 '.-A' (0)| 1 7.882. Table 2.3.2 lists the

maximum optical densities (O.D.max) of sampled graded masks with ( = 0.



















I^M -0^0 0= 0 -,z c 03I- =O C101 = 3)0


Lr- C,o m oc Ce


oc Lro'0 CIAOI-
0o 0-0z00l0 000t0 o 0 (Mb 00 0C
o oc zt- o^ oc C- o 1 t- t- =) Cio CY- I^- CIA I- o o o t



cc L 0 0 Co >y- cc o c c o tL- C1 oc


O C HCO0003CMt0^ 0 0 OD O t O Ost' Ot' O t


I CI I I t- I I CI Io Io tI IrCM =I I









DG O NV H M meL-L OO O



Lm m O Lmw -w LOL4 L-mLO O
OC O M C o o o cE 03t oI O CI
















5 L L O L O t L cl L OrL CY I
I- I-o ^ 3o -z CIA cc- tC- oc to ( s CM t C- 03







00 C 0 0A 0000 0 z lOM) lO ccO C =) lo




000000000000 000000000
O C":)m 0 -o=o I-oIA0z -zt -zt o i o



C0 : C cc cc1 OCUO I-

















Ac oc CVL CCAI
CCI
oc ll clO CIA CC C CI cy OO O ^ O OO OC O -)







S- O C A I CC I- CIOA cc OO I-
LrO tO t0 Lr3 03t CIA L L' CIA cc I- =- r1 1 3030 l (
000000000000 000000000

000000000t0 00 t O O ^t' 030 0 00 0000^O^O^t
C c( r' CIA =) cc ccs 0 -z Lrl CIA -r' C11 ztM o
0^03 y- ( O CIA Lr CI -z CIA oc ^ -t (- C0I '0



CI -I0 (- 0 -t t0 I- CIA I- 0I- I- ccC

000000000000 000000000
l t- oc llO C -cl O t- clO -Iz r c- CO O zt~t LrC-- o0
( I O lt -, CO -zt -Y- 0 (z1t C'tM O ~ ^- 0






















00000000000 00000000;=
00000000000 00000000
C.) cc C C- CO C, C (- CO oo t'- =) (- CA LC5 cy-) Lr- Co CA












ccmm e e m ccn cc-t-t z o
CI cyl Cqc-
c o m m m m ^^ "
ad dd d






















Figure 2-7. Simulated low and high magnification pictures of an m 1, I = 3 linear
eighth-order sampled graded mask with ( = 0. The low magnification picture
(left) shows ~ 400 diffraction widths. Each stripe has uniform shading and is
fAin, wide.


In summary, we conclude that eighth-order masks can control diffracted starlight

while simultaneously offering resistance to tip/tilt and low spatial-frequency optical

aberrations compared to fourth-order masks. This is confirmed with explicit lab tests in

5. Eighth-order masks also help to prevent leakage due to the finite size of stars, as is

shown with numerical simulations in the next chapter. Graded designs can be fabricated

with HEBS (High-Energy-Beam-Sensitive) glass, and notch-filter masks can be fabricated

with HEBS glass or regular glass and a deposition of opaque material that is subsequently

etched by an electron-beam lithography machine. We provided examples of sampled

binary, smooth binary, and sampled graded eighth-order masks. The m 1, I = 2 design is

recommended for the TPF-C.









CHAPTER 3
PROSPECTS FOR SPACE OBSERVATIONS

This C'! pter describes the technologies associated with a space-based internally

occulting coronagraph that using band-limited image masks. Quasi-static wavefront

errors and scattered light removal are first briefly described. Then, the performance of a

TPF-C-like instrument is examined as a function of stellar angular diameter.

It is shown that incoherent light leakage resulting from the finite size of stars can be

suppressed by using the eighth-order image masks from Ch'! pter 2. This benefit enables

sensitive imaging measurements of the circumstellar regions surrounding nearby evolved

stars. We discuss the science that such observations can deliver regarding both terrestrial

and Jovian exoplanets.

3.1 Introduction: Quasi-Static Wavefront Errors and "The Dark Hole"

The TPF-C will generate unprecedented contrast within several AU of nearby stars

(see Traub et al. (2006) for a review). Currently, there are two different architectures

undergoing feasibility studies: (i) an internal occulter that utilizes one (or more) of the

promising designs mentioned in 1.3, and (ii) an external occulter design that utilizes a

distant, specially shaped, star-shade that casts a dark shadow over the entire telescope

(Cash (2006); Lyon et al. (2007)). Each have their advantages.

The internal occulter allows for integration of all optical components locally into a

single instrument, whereas the external occulter must be separated from its detector by

, 50, 000 km, hence requiring a sophisticated orbital dynamics scheme. To maximize

observing efficiency, the external occulter will also likely require at least two star-shades.

While one is aligned, the others) will travel to the next target. The concept expends

copious amounts of energy but is still less expensive than any internal occulting design by

nearly a factor of 2, since it does not require as large a primary mirror. These practical

and budgetary considerations along with the intended scope of the general astrophysics

program will decide the TPF-C's architecture. Hybrid designs are also being considered.









For instance, a discovery-class instrument could eventually operate as the detector for a

star-shade launched several years later (Shaklan & Levine 2007), or a closer-in star-shade

could work in tandem with an internal occulter to save fuel.

Any internal occulter design will have to deal with wavefront phase and amplitude

errors introduced by the telescope primary mirror and subsequent optics, such as

beam-splitters, dichroics, condensers, filters, lenses, ... etc. The effects of these systematic

disturbances manifest as slowly undulating, quasi-static speckles in the image plane

(see 1.2.3) that change on a timescale commensurate with thermal fluctuations. Such

aberrations are inherent to all of the coronagraphs mentioned in 1.3 and unavoidable at

the contrast levels required for circumstellar science.

Speckle-nulling is the act of removing quasi-static residual starlight from a pre-selected

region of the image plane. By including one or more deformable mirrors (DM's) in the

optical train to reshape the phase of starlight (or, more generally, to alter the complex

field), a sharply defined region of deeper contrast can be generated over a fraction of the

search area. The size of this so-called "dark hole" is governed by the number of DMs and

their actuator densities. This technique greatly improves the chances for direct detection

by properly isolating the companion's signal.

As with most correction schemes, scattered light removal generally relies upon

three steps: (i) wavefront sensing, (ii) wavefront reconstruction, and (iii) wavefront

manipulation or control. The steps are often executed in succession and each may require

the development of specialized algorithms to optimize the procedure for a given active

optics system. For instance, from space it is possible to perform wavefront sensing at

the science camera since the speckle lifetime is long compared to a typical integration.

This approach requires phase diversity to reconstruct the shape of the wavefront but

it minimizes non-common-path errors (6.3) and the number of optics. Ground-based

instruments, on the other hand, must sense the wavefront directly in order to keep pace

with the rapidly changing field. In fact, high-contrast imaging instruments such as GPI









(\! 1,!losh et al. 2006a) and the PALM-3k/P1640 (Dekany et al. 2007) will need to sense

the wavefront twice, before and after the coronagraph, in order to generate a dark hole

while simultaneously correcting for the atmosphere.

Figure 3-1 shows simulated images from a coronagraph operating in tandem with a

single deformable mirror in broadband light after correction has been applied. The dark

hole (hereafter, DH) is the central square region surrounding the star in the image. Its

maximal extent, smax, is related to the number of actuators across the DM by smax =

(Nact/2) Amin/Dtel, where N/et is the total number of actuators. The right-hand-side of
the DH is deeper than the left because this simulation includes amplitude errors, which

break the symmetry between the location of speckles on either side of the optical axis (see

Bord6 & Traub (2006)). Amplitude errors might be caused by reflectivity variations across

a mirror for example. The complex field was reconstructed on the right-hand-side of the

DH, so that is the side with optimal sensitivity.

The DM surface shape is calculated using an energy minimization technique invented

by Give'On et al. (2007). We briefly describe the method as it would be used in practice.

First, the electric field (phase and amplitude) at the detector is reconstructed by changing

the shape of the DM several times with relatively arbitrary phase ripples sines or cosines

for instance. Then, the DM shape is commanded to be flat and each actuator is poked

individually. The resultant wave is propagated through the coronagraph numerically (i.e.

with a computer model) and the electric field at the detector is recorded each time. This

data cube of electric fields is finally compared to the original electric field to provide a first

estimate for the actuator heights. Several iterations converge upon the optimal shape.

Figure 3-2 shows an image of a 12x12 Boston Micromachines DM. The maximum

surface stroke is 1.5 pm (3 pm max phase correction) and the electronics provide 14-bit

resolution, corresponding to 1.5 pm / 214 1A precision. This device will be used in

laboratory experiments to test the theoretical predictions shown in the next section.












DM Surface Heinht in Nannomtera


Figure 3-1.


Simulated images of a 64x64 DM and resulting dark hole. The DM
compensates for scattered starlight up to a spatial frequency equal to the
Nyquist limit, in this case smax 32 Amin/Dtei away from the optical axis.
Contrast levels of order 10-10 are generated in the region on the right. Details
of the model are discussed in 3.2.3.


Figure 3-2. Boston Micromachines 12x12 deformable mirror. This device has recently been
integrated into the University of Florida coronagraphic testbed.


Dark Hole









3.2 Targeting Evolved Stars

The current preliminary TPF-C observing strategy is optimized to search for

Earth-like planets orbiting a highly selective list of nearby F, G, and K main-sequence

stars. In this section, we provide motivation for potentially expanding this set of targets to

include evolved stars that subtend an appreciable angular size on the sky. To substantiate

this concept, we calculate the light leakage resulting from the finite size of such stars in

terms of contrast for one of the front-running TPF-C design candidates.

3.2.1 Motivation

To gain a fundamental understanding of planet formation and evolution, and to place

the existence of Earth in the broadest possible context, a large and relatively unbiased

sample of stars must be searched. This precept can be understood by considering the

potential for diversity amongst extrasolar planetary systems. One notable effect is that the

physical processes governing planet formation and evolution are nonlinear. Small changes

in initial conditions can lead to large-scale differences in overall system architecture. As a

result, stars of comparable mass and composition can yield a substantially dissimilar set

of companions. Significant diversity is implicated on these grounds alone. This inherent

complexity, however, is further amplified by the v ,ii. I in stellar hosts that supply the

material out of which planets originate. Their bulk characteristics are markedly disparate:

* the range of masses over the full span of the main sequence covers more than 3
orders of magnitude

the range of metallicities in the solar neighborhood covers ~ 1.5 orders of magnitude
(Luck & Heiter 2006, 2007)

most stars are members of multiple systems (Tokovinin 2004)

and individual stellar luminosities can vary by as rni, as ~ 7 orders of magnitude
over a lifetime, when the red giant to early compact object stages of stellar evolution
are included (Iben 1967; Iben & Laughlin 1989)

Given this information, there is no reason to expect that extrasolar planets will be any less

unique or complex than the satellites of our solar system.









Direct imaging offers an efficient approach towards exploring this large parameter

space for it is a technique whereby the members of entire planetary systems can, in

principle, be detected and characterized simultaneously, depending on the separation and

brightness of the inner-most companion. It is reasonable that sensitive space instruments,

such as the TPF-C, TPF-I, and Darwin, consider a moderately comprehensive set of

targets, otherwise a limited scope or severe predisposition to certain kinds of stars neglects

large classes of interesting systems, including those that may tell us where to look next.

In addition to single main-sequence stars of intermediate spectral-type, which

comprise the canonical list of high-contrast imaging targets, evolved stars, binaries, and

M-dwarfs offer av ii. I v of environments for testing theories of planetary science and other

promising avenues in the search for life (Lopez et al. 2005; Haghighipour & Raymond

2007; Tarter et al. 2007). The motivation for observing them stems from their statistical

significance: all stars will eventually evolve off of the main-sequence to become giants;

binaries constitute approximately 50' of all stellar systems (Duquennoy & AT, i, or 1991);

and M-dwarfs represent approximately 7 .'. of all stars in the Galaxy (Henry 2004).

Moreover, recent radial velocity, transit photometry, and astrometric observations have

already provided strong evidence for the existence of planets in each category (Johnson

2007; Bonfils et al. 2007; Mugrauer et al. 2007, and references therein).

In this section, it is -i-.--- -1. 1 that high-contrast imaging observations of different

types of stars is more than just a compelling notion. The discussion focuses primarily on

evolved stars (luminosity classes IV-I), their habitable zones, and the interface between

"point" sources and resolved sources. As such, calculations of achievable sensitivity

as a function of stellar angular diameter are provided for one of the leading TPF-C

design candidates. It is shown that a Lyot coronagraph (Lyot 1939) with wavefront

control (Trauger & Traub 2007) and access to an assortment of band-limited image

masks (Kuchner & Traub 2002; Kuchner, Crepp, & Ge 2005) can handle a diverse set









of observations. This work is also relevant to close-separation visual binaries.1 We do

not deal with M-dwarfs since interferometers are likely required to access their narrow

temperate surroundings.

3.2.2 Extended Sources

High-contrast imaging is contingent upon the destructive interference of starlight

(1.3). Losses in spatial coherence due to the finite size of a star, whose surface is

comprised of many independently radiating elements, can therefore result in light leakage.

This places a fundamental limitation on a coronagraph's sensitivity.

MT ii nearby stars subtend an appreciable angle on the sky compared to the spatial

resolution of a large optical telescope. Evolved stars, in particular, have intrinsically large

radii and may be several A /Dt D in width, even though they tend to be somewhat more

distant than the closest main-sequence stars. For instance, Betelgeuse, the largest star in

the Northern sky, D, = 55 mas, illuminates an 'area of coherence' (Born & Wolf 1999)

that is smaller than the primary mirror with which TPF-C may operate only 2.3m in

diameter when observed in quasi-monochromatic light centered on A = 0.55 pm. For

comparison, a star of radius Re = 6.96 x 1010 cm located at 10 pcs would coherently

illuminate an area of diameter ~ 138 m. An interesting regime lies between these two

values where: (i) the stars are marginally resolved and (ii) their habitable zones are

extended but expanding at a rate slow enough to provide sufficient time for life to develop

and proliferate.

3.2.2.1 Imaging terrestrial planets

As stars evolve off of the main-sequence, their luminosity increases and the habitable

zone widens as it moves outward. Planets that were previously too cold to support life



1 It is possible to suppress the light from two stars simultaneously by employing
a coronagraph with a linear attenuation profile. This principle has recently been
demonstrated from the ground using adaptive optics (7).









will warm. A recent study of the continuously habitable zone by Lopez et al. (2005) has

shown that there are two eras of post-main-sequence evolution where hospitable conditions

may persist. They occur during the sub-giant and horizontal branches. Terrestrial planets

orbiting a solar mass star in the 2-9 AU range, before the Helium flash, and 7-22 AU

range, after the Helium flash, may have moderate climates for 108 109 years.

Life emerged on the Earth within the first t 109 years after formation (Lazcano &

Miller 1996). However, progress was hindered by frequent asteroidal impacts. Life may

have been extinguished several times, even as late as 800 million years after formation

(I! ,.Vr & Stevenson 1988). This raises the question of whether life can arise significantly

faster under quiescent conditions, such as those provided by an older planet that is

member of a more dynamically inactive system. Spectroscopic measurements of terrestrial

planets orbiting evolved stars at several AU can help to constrain this timescale.

More distant planets will, depending on their albedo and radius (see Seager et al.

(2007) for a discussion of super-Earths), generally be fainter than the Earth-Sun

system (contrast a 2 x 10-10; 1.2.1.1) in reflected light. A coronagraph can, however,

accommodate for this effect by sacrificing spatial resolution. Observations at longer

wavelengths decreases the intensity of quasi-static speckles by a factor of ~ (A/Ao)2 in the

search area. Another option is to increase the inner-working-angle. With a band-limited

mask design, this results in higher Lyot stop throughput, which increases the amount of

companion light, decreases integration time, and makes the point-spread-function (PSF)

more spatially succinct.2 Notice that both approaches, and combinations thereof, improve

the coronagraph's resistance to stellar size.

Figure 3-3 shows how the habitable zone scales linearly with stellar angular size, a

relationship that can be derived from the Stefan-Boltzman law. Members of the TPF-C



2 Highly concentrated PSF's facilitate discrimination of companion light amongst diffuse
zodiacal and exozodiacal dust emission.











"Top 100 List" (http://sco.stsci.edu/starvault/), red-giant stars within 30 pcs from

Lopez et al. (2005), and sources from Ochsenbein & Halbwachs (1982) with large angular

diameters, which were directly measured using interferometry, are included in the plot.

The habitable zones of several dozen evolved stars are accessible in the near-IR. This

is a lower-limit to the number of potential targets since the list is only representative

and not complete. The habitable zone of super-giant stars, such as Betelgeuse and R

Doradus, may be as large as an arcsecond, but they are likely too young for life to develop.

Discovery-class missions that employ a small aperture cannot afford further sacrifices in

spatial resolution but will be capable of detecting Jovian planets orbiting giant stars at

visible wavelengths.


* *
* @ F
*.


IWA at 2.3 i




IWA at 0.6 vm


o 2 **u a -

o -.. ,
ore *
o % 0

*%, ~ o


* TPI
Lop
* Oct


WA at2_3jpm_


IWAat 0.6pin

F-C Top 100
ez et al. 2005
hsenbein & Halbwachs 1982


103


Cd


C

102
1u


Stellar Angular Diameter / mas


Figure 3-3.


Inner and outer-edge of the habitable zone for nearby stars. Targets with a
large angular diameter leak light through a coronagraph (3.2.4) but also have
more distant habitable zones. Observations in the near-IR, or with a
coronagraph having a larger inner-working-angle (IWA), improve sensitivity at
the expense of spatial resolution and permit the direct detection of terrestrial
planets orbiting at several AU. The IWA's shown are for an 8m telescope
operating at 4 A/Dte. To first order, the ratio of the habitable zone outer-edge
distance to the inner-edge depends only on the temperature of water,
HZouter/ HZinner (373 K/ 273 K)2 1.87.









3.2.2.2 Imaging Jovian planets

Precision RV measurements have now established baselines exceeding 10 years making

possible the detection of Jovian planets orbiting several AU from their host stars. Not

only are giant planets being discovered orbiting main-sequence stars, but they are also

being discovered orbiting giant stars (Johnson et al. 2008), which rotate slowly and have

sharp spectral features. Preliminary results have already revealed correlations between

stellar mass and planet properties. For instance, more massive stars tend to produce more

massive Jovian planets in wider orbits (Johnson 2007).

An example of such a system with a known exoplanet is the bright (V 1.15) K-giant

3 Gem (POLLUX). RV observations spanning nearly 25 years are consistent with the

presence of an Msini = 2.6Mjup planet with a semi- i, ri" axis of 1.6 AU (Hatzes et al.

2006). 3 Gem is a KO III star at a distance of 10.3 pcs with an angular diameter of

7.96 0.09 mas (Nordgren et al. 2001) and mass of 1.7 0.4 Me (Allende Prieto &

Lambert 1999).

A space-based direct imaging instrument will be capable of fully characterizing such

planets. Moreover, their orbit will already be determined and the spectra will have a high

signal-to-noise ratio compared to terrestrial planets. As the sample of target stars on the

high-mass-end of the stellar spectrum grows, we will acquire a better understanding of

the planet formation process. In the following, we explore the challenges of generating

sufficient sensitivity to detect planets orbiting partially resolved stars.

3.2.3 Numerical Simulations

We model a TPF-C-like instrument with code written in Matlab assuming an

internally occulting Lyot-- I .- design. The simulations are broadband and incorporate:

primary mirror phase and amplitude errors, image mask phase errors, a single 64x64

actuator DM, and the finite size of the star. We assume that all optics are located in pupil

or image planes and use Fourier transforms to propagate the electric field. The telescope is

circular and unobscured.









Stars are modeled by a uniform disk of mutually incoherent point sources. Light

from each source is sent through the optical train with a tip/tilt error that corresponds

to its location on the stellar surface. The number of sources across the disk well exceeds

the Nyquist frequency in Amin/Dtel units. The intensity from each add together at the

detector to form the final image. Ten wavelength channels sample the various 100 nm wide

bandpasses.

Primary mirror phase errors follow a broken power-law power-spectral-density (PSD)

given by:

PSD(k) Ao (3-1)
1 + (k/ko)-
where Ao is a constant with units m4, k is the spatial frequency, ko 0 4 cycles / m, and

n = 3. This is the PSD typical of an 8m primary mirror (Shaklan & Green 2006; Bord6

& Traub 2006). The mirror surface figure is scaled to have an rms value of 1 nm (2 nm in

wave-front phase). Amplitude errors are modeled as white noise with an rms of 0.005 and

maximum value of unity. We do not include scattering from other optics in the path other

than the glass on the image mask.

Mask defects are included because different sections of the stellar surface fall onto

different locations in the image plane. These non-common-path errors limit the achievable

sensitivity since they cannot each be compensated for simultaneously; correcting for one

may amplify another. The imperfections are modeled as uncorrelated phase errors, e.g. the

worst case scenario.

We use both 4th-order and 8th-order linear band-limited masks to make a comparison

study since they have different resistances to stellar size. Their amplitude transmissions

follow sinc(..)2 and m = 1, I = 2 profiles respectively (see 2 for details). The default

inner-working-angle is 4 Amax/Dte.

The DM is placed at a pupil and its surface is shaped by a square grid of actuators

that map perfectly onto the primary mirror. The influence of each actuator is modeled

with a Gaussian function that drops to ,'. of its peak value at the location of .i1] ,'ent









actuators. The 64x64 system can correct for wavefront errors with spatial frequencies

as high as 32 cycles per aperture, creating the dark-hole region shown in Fig. 3-1 that

defines the search area. We sacrifice correction of the highest spatial frequencies, 30-32

cycles per aperture, to improve correction of the lower-order modes, further reducing the

intensity of speckles close to the optical axis. A smaller search area can yield even deeper

contrast, such as is done at the HCIT (Give'on et al. 2007), but here we are also interested

in distant planets. The sensitivity is limited by DM fitting errors.

We calculate the optimal DM shape using the linear energy minimization algorithm

developed by Give'On et al. (2007). The technique is quite general and relies upon

accurate modeling of the coronagraph, electric-field reconstruction at the science camera,

and a form of phase diversity to solve for the actuator heights. The procedure is efficient

once a rather computationally expensive metric, the "G-i iii r: is established for the

optical system. It needs calculating only once, unless changes to the coronagraph are

made. In this chapter, we use several different coronagraphs, of different order, bandpass,

inner-working-angle, and size of mask phase errors, so had to utilize multiple processors

in parallel (but with no message passing interface). The optimal DM shape is found using

only the central (on-axis) portion of the star. The surface is then fixed a DM cannot

compensate for stellar size and contrast is measured as a function of angular diameter.

Sensitivity calculations use information from a single image. The instantaneous

contrast, C, is found using the formula in Green & Shaklan (2003), Shaklan & Green

(2005), and Crepp et al. (2007), which we show here:
C(ry I(x, y)
1(0,0) M(x, ) (3 2)

where I(x, y) is the intensity at the coordinates, (x, y), in the final image, 1(0, 0) is the

peak stellar intensity as would be measured without the image mask in the optical train,

and \M(x, y) 2 is the mask intensity transmission. Both I(x, y) and 1(0, 0) are measured

with the Lyot stop in place. A linear mask has no dependence on y. We do not model the









integral field unit that will take low-resolution spectra and use this color information to

discriminate between speckles and companions.

3.2.4 Contrast vs. Angular Size

We compare 4th and 8th-order masks in systems optimized for two different

bandpasses at visible wavelengths, A = 0.5 0.6 pm and A = 0.7 0.8 pm, and a bandpass

in the near-IR, A = 2.2 2.3 pm. We also include a mask with a larger inner-working-angle

and place limits on the size of mask phase errors as a function of stellar diameter. Results

from our simulations are shown in Fig. 3-4. The smallest and largest targets from the

TPF-C Top 100 list and the largest star in the sky, R Doradus, are shown for comparison.

The upper horizontal axis of each plot also indicates the characteristic angular diameter of

a variety of stars placed at 15 pcs.

The top panel of Fig. 3-4 shows how the 8th-order mask has a higher tolerance than

the 4th-order mask to stellar angular size. This result makes intuitive sense since the

8th-order mask is less susceptible to tip/tilt errors (2, 4, 5). Both masks, however, leak

diffracted starlight before the stellar surfaces are fully resolved: 0.55 pm / 8m = 14.2 mas;

0.75 pm / 8m 19.3 mas; 2.25 pm / 8m 58.0 mas.

It is evident that the sensitivity improves at longer wavelengths according to the

scaling relation C oc (Ao/A)2. For small stars, the instantaneous contrast in the near-IR

is an order of magnitude deeper than in the visible, at the expense of a factor of 3-4 in

spatial resolution. This trade-off is well justified for evolved stars with extended habitable

zones. The relative improvement grows to several orders of magnitude with further

increases in angular diameter.

We also notice that the largest TPF-C Top 100 List candidate target requires an

8th-order mask in the visible. One might guess that a star with an angular diameter of

8.6 mas is near the lower-end of the priority list; however, this star is ranked #1. It is a

Centauri A.









Table 3-1.


Physical parameters for the ~ 5 Gyr old a Centauri triple system. The third
component, Proxima Centauri, is a distant M dwarf that appears to be weakly
bound (Wertheimer & Laughlin 2006). The TPF-C rank is currently defined by
the first-visit completeness per integration time
(http://sco.stsci.edu/starvault/).
a Cen A B C
Spec. Type G2 V K1 V M5.5 V
v mag -0.01 1.35 11.1
mass (M.D) 1.11 0.93 0.12
radius (R.) 1.24 0.87 0.15
luminosity (L.) 1.60 0.45 0.0002
[Fe/H] 0.22 0.26 -1.00
a (AU) 23.4 23.4 t 12,000


e
i
diameter (mas)
TPF-C Rank


0.52
79.20
8.6
#1


0.52
79.20
6.0
#2


?

1.0


In addition to the usual reasons for targeting the Sun's closest neighbor, d = 1.35 pcs,

the a Centauri AB system offers a unique testing ground for planet formation theories.

Depending on the orbital phase, the stars may be separated by 11.2-35.6 AU. Currently, it

is not clear whether the presence of an intermediately spaced stellar companion promotes

or inhibits formation, and the answer likely differs for terrestrial planets compared to

Jovian planets. The leading theories of "core-accretion" (Lissauer & Stevenson 2007;

Pollack et al. 1996) and ,'i ,,l ,I ,i!, ,I instability" (Durisen et al. 2007) must account

for this extra source of radiation and gravitational perturbations. Thus, high-contrast

imaging observations of a Centauri AB may help to discriminate between the two. Indeed,

numerical simulations indicate that planets in the habitable zone, should they form in

the first place, can remain stable provided the inclination angle between the stellar and

planetary orbital planes is not large (Quintana et al. 2007). Table 3-1 lists the a Centauri

system parameters.

The bottom panel of Fig. 3-4 compares 8th-order masks with different surface errors,

arms = 0.5, 2.3, and 5.0 nm. An 8th-order mask with an IWA of 7.27 Amax/Dt = 150









mas is also shown. Each were optimized for the 0.7 0.8 pm bandpass. The arms = 0.5

nm, IWA 4 Amax/Dtei curve is the same from the upper panel.

Increases to the size of mask errors scatters more light into the dark hole. The

relationship obeys a similar quadratic dependence, C oc (arms/arms0o)2, as with the size

of primary mirror phase errors and wavelength. Notice that the 0.5 nm -+ 2.3 nm case

does not scale according to this relation, because the primary mirror phase errors, surface

rms 1.0 nm, dominate.

Diffracted light from the mutually incoherent sources on the stars' surface quickly

degrade contrast when the angular diameter exceeds 10 mas. The system with IWA=

7.27 Amax/Dtel passes more planet light and is also less susceptible to stellar size. Changes

to the telescope diameter slide the curves in both graphs horizontally if we neglect

differences in the manufacturing processes that change the PSD and thus the speckle

pattern.

Table 3-2 di-pl-,1 a series of high-contrast images for three nearby stars of increasing

angular diameter. The current inner and outer-edge of the habitable zone for each is

overlaid for reference. Only half of the dark-hole is accessible since we include primary

mirror amplitude errors and only one deformable mirror (Bord6 & Traub 2006). The

gi ,i--~ ,!.. is on a logarithmic stretch and indicates the value of I(x, y)/I(0, 0).

The images qualitatively verify the results from Fig. 3-4. Starlight leakage is a serious

problem for the 4th-order mask in both visible bandpasses, whereas the 8th-order mask

is able to suppress the light from extended sources to more acceptable levels. Sacrificing

spatial resolution by conducting observations in the near-IR provides a substantial

improvement in dark-hole depth and resistance to stellar size. Equipping the TPF-C with

a near-IR camera can increase the signal-to-noise ratio of spectra, enable the detection of

more distant planets, and complement visible light observations.

These considerations also -ir.-.- -I that near-IR observations may be more appropriate

for accessing the habitable zone of the TPF-C's highest priority target, a Centauri A.










TPF-C Sensitivity


Stellar Angular Diameter / mas


TPF-C Sensitivity


Stellar Angular Diameter / mas


Figure 3-4.


TPF-C stellar angular diameter sensitivity for an 8m telescope. The
characteristic size of various stars placed at 15 pcs are shown across the top
axis for reference. R Doradus is the largest star in the sky. The largest TPF-C
Top 100 star, a Centauri, also has the highest priority. Triangles represent
A = 0.7 0.8 pm data. To avoid confusion between curves, the near-IR
4th-order mask result is not shown.










High-contrast images of stars with large angular diameters. The g' i,-, .. is on
a log-stretch and shows the value of I(x, y)/I(O, 0).
D, = 8.6 mas D = 11.6 mas D, = 26.0 mas


.6.5





-10
-10.5










a Cen A, TPF-C #1
G2 V
d = 1.4 pcs
HZinner 0.8 AU
HZinner 1.6 AU


.5










K9.5
10























dinner 8.2 AU
HZouter 155 AU 10
,11



HD 124897
K1.5 III
d 11.3pcs
HZinner 8.2 AU
HZouter = 15.5 AU


-ii


HD 146051
M0.5 III
d 52.2 pcs
HZinner = 19.1 AU
HZouter 36.1 AU


Table 3-2.










Otherwise, a DM with more than 64x64 actuators may be required. Near-IR observations

of evolved stars are preferable when searching for the reflected light of distant terrestrial

planets. It is possible to detect planets orbiting HD 146051 in the visible, as well as

targets with similarly large angular diameters, but an 8th-order mask is necessary.

3.2.5 PSF Role-Subtraction

Depending on the bandpass, the signal of many terrestrial planets may lie just

beneath the instantaneous noise floor, even inside the darkest regions of the dark-hole.

Point-spread function (PSF) subtraction can enhance the effective contrast by more than

an order of magnitude and help to discriminate between planets and speckles. Figure 3-5

illustrates the technique.

PSF Subtraction
211: riarlon




I










Figure 3-5. PSF subtraction enables unambiguous detection of planets that are fainter
than the instantaneous noise floor.


Our PSF subtraction model combines images that differ by a small role-angle

through which the telescope rotates. Since the wavefront errors are produced solely by

the telescope and instrument optics, the speckle pattern rotates by the same amount.

Companions, however, do not move. When the images are difference, the speckles cancel

and companions generate two characteristic spots, one dark and one bright, that are

separated by the role-angle. The technique relies on the stability of the environment.









In space, the speckle lifetime is sufficiently long to preserve the structure of sequential

images.

We added two sources of realistic noise that limit the subtraction of scattered light

from within the dark-hole. The first and most consequential affect is thermal changes to

the system that occur during and in between exposures. They were modeled by adding

low-order aberrations to the previously optimized wavefront. Equal contributions from the

first 10 Zernike modes were combined to form a wavefront that differed by 10 picometers

rms in phase. We also added 5 e- / pixel of rms read noise to each image.

Fig. 3-5 demonstrates the detection of a terrestrial planet that is 3 x 10-11 times as

bright as its host star in the A = 0.7 0.8 pm band. The separation is 6 Amax,/Dtae and

an 8th-order mask was used. The star has an angular diameter of 0.709 mas the median

value of TPF-C Top 100 List targets. The planet is not detectable in a single image using

these parameters.

We also performed PSF subtraction with larger stars. The purpose of the experiment

was to determine whether the speckle noise floor, which is presumably smoother

for resolved sources, can be subtracted out with higher precision. We find that the

improvement is negligibly small, of order a few percent for an Dtde < 8m primary mirror in

the visible.

3.3 Conclusions

We have quantified the sensitivity of a space-based coronagraph as a function of

stellar angular diameter. Observations of resolved sources would complement the TPF-C

baseline strategy by sampling planet formation as a function of stellar mass. Detections of

terrestrial planets in the extended habitable zones of sub-giant and horizontal giant-branch

stars can place constraints on the timescale for the development of life. It is also possible

to study previously clement planets that are now located interior to the habitable zone.

These hot companions would provide a lab for investigating the run-away green house

effect and making comparisons to Venus. Forecasts regarding Earth's eventual fate are









also implicit. The radial velocity technique has detected many Jovian planets with orbital

separations exceeding 1 AU. Their physical characteristics, surface gravity, chemical

composition, and effective temperature could be measured.

Our results show that a fourth-order mask leaks starlight for the TPF-C's highest

priority star, a Centauri A. Observations with an 8th-order mask generate sufficient

levels of contrast for this star and even larger targets. However, the outer-edge of the

dark-hole generated by a 64x64 DM truncates critical regions of the search area. Near-IR

observations can help remedy the situation; they would also provide complementary

spectra, increase the signal-to-noise ratio for characterization, and quite naturally enable

studies of distant terrestrial planets orbiting giant stars.









CHAPTER 4
PROSPECTS FOR GROUND-BASED OBSERVATIONS

As adaptive optics technology continues to improve, the stellar coronagraph will

p1 iv an ever increasing role in ground-based high-contrast imaging observations.

Though several different image masks exist for the most common type of coronagraph,

the Lyot Coronagraph, it is not yet clear what level of wavefront correction must

be reached in order to gain, either in starlight suppression or observing efficiency,

by implementing a more sophisticated design. In this chapter, we model image plane

Lyot-- I le coronagraphs and test their response to a range of wavefront correction levels,

in order to identify regimes of atmospheric compensation where the use of hard-edge,

Gaussian, and band-limited image masks becomes observationally advantageous. To

delineate performances, we calculate the speckle noise floor mean intensity. We find that

apodized masks provide little improvement over hard-edge masks until on-sky Strehl

ratios, S, exceed ~ 0.88 Sqs, where Sqs is the intrinsic Strehl ratio provided by the optical

system. Above this value, 4th-order band-limited masks out-perform Gaussian masks by

generating comparable contrast with higher Lyot stop throughput. Below this level of

correction, hard-edge masks may be preferentially chosen, since they are less susceptible

to low-order aberration content. The use of higher-order band-limited masks is relegated

to situations where quasi-static residual starlight cannot be sufficiently removed from the

search area with speckle-nulling hardware.

4.1 Introduction

In recent years, great strides in the development of adaptive optics (AO) technology

have ushered in a new era of high resolution diffraction-limited imaging. Despite these

advances, the ability of the stellar coronagraph to generate deep contrast remains limited

by insufficient levels of wavefront control: uncorrected phase and amplitude errors induced

by the atmosphere and instrument optics manifest as bright, dynamic 'speckles' of

scattered light in the search area. Even the most basic coronagraph, a Lyot coronagraph









equipped with a focal plane hard-edge occulter (Lyot 1939), is incapable of reaching its

peak performance when coupled to state-of-the-art AO (Oppenheimer et al. 2004).

Numerous high-contrast observations have been conducted using AO on the world's

largest telescopes (\! ,-rois et al. 2006; AT ,- ,i1 ,, et al. 2006; Itoh et al. 2006; Carson et al.

2005; Close et al. 2005; Metchev & Hillenbrand 2004; Debes et al. 2002; Liu et al. 2002,

and references therein); some rely solely on AO ii, -ii while others combine AO with

corni ,.-i ,!.ild and/or speckle reduction techniques. These efforts have provided the first

image of a candidate extrasolar planet (C'!i ,vin et al. 2005a), as well as direct detections

of sub-stellar companions near the planet-brown dwarf boundary (Biller et al. 2006;

Neuhauser et al. 2005; C'!i vin et al. 2005b), as shown in 1. However, to image older,

less-massive, and closer-in companions from the ground, wavefront sensing and correction

techniques must improve substantially.

"Extreme" advances in high-contrast imaging technology are anticipated in the

coming years. Deformable mirrors employing several thousand actuators and wavefront

sensing of laser guide stars can, in principle, drive Strehl ratios above 9n' on 8-O1m class

telescopes. With the proper coronagraph, these systems will be capable of detecting the

near-IR emission of Jovian planets over a broader range of ages, masses, and separations

(\! ,, ill osh et al. 2003). Extremely large telescopes such as the proposed Thirty Meter

Telescope (TAIT) (\! ,. ,,lIosh et al. 2006b; Troy et al. 2006; Ellerbroek et al. 2005) and

100m OverWhelmingly Large telescope (OWL) (Brunetto et al. 2004) will improve spatial

resolution, and hence the inner-working-angle (hereafter IWA) on the sky.

An interesting and more immediate alternative, which uses current AO technology,

can also provide highly corrected wavefronts by instead sacrificing spatial resolution in



1 Interferometers are likewise capable of suppressing starlight, and generally have a
better inner-working-angle but a more restricted search area (Absil et al. 2006; Serabyn
et al. 2005).









return for improved pupil sampling. Serabyn et al. (2007) have demonstrated K-band

Strehl ratios approaching I!' by reimaging a 1.5m diameter circular unobstructed

subaperture of the Hale 200-inch telescope onto the existing deformable mirror via relay

optics. Combining this technique with a coronagraph that has an intrinsically small IWA

(< 3 A/D) shows promise for generating deep contrast for separations as close as ~ 0.5"

(6).

These considerations motivate the need for a quantitative understanding of how the

stellar coronagraph's utility will depend on future gains in AO proficiency. To address

this topic, we have modeled systems that are equipped with a variety of amplitude

image masks, and examined their performance in a broad, nearly continuous range of

corrected wavefront levels. In essence, we seek to provide a concise guide to the use of

Lyot-- I le image plane coronagraphs. Most notably, we answer the question: "What is the

appropriate choice of image mask for an extreme AO system operating at a given Strehl

ratio?".

Mask performances are compared by calculating the direct output of the coronagraph,

i.e. the mean intensity, with the understanding that differential and post-processing

techniques can alv-, be used on top of direct imaging to improve the prospects for

discovery.

4.2 Model of Atmosphere & Wavefront Correction

The theoretical model used for our simulations consists of an extreme AO system

linked in series to a Lyot coronagraph that is observing a stellar point source. Wavefront

correction levels spanning from not quite diffraction limited (~ 77' Strehl) to highly

corrected (~ '-,. Strehl) are generated with an IDL routine based on simulations

described in Carson et al. (2005). The code is optimized to simulate the operation of

PHARO (Hayward et al. 2001) with the PALAO system (Troy et al. 2000) on the Hale

200-inch telescope at Palomar.









To clearly elucidate the sometimes subtle differences in performance between

coronagraphic image masks, we restrict our analysis to monochromatic light (A = 2.2 p/m),

and ignore the effects of central obstructions, their support structures, and inter-segment

mirror gaps. To first order, the addition of each of these complexities can be understood

by convolving the telescope entrance aperture with the spatial frequency spectrum of

the mask, and observing the resultant light distribution in the Lyot plane (1.3). The

net effect is often simply a loss in off-axis throughput, as the Lyot stop size is necessarily

reduced to reject the additional diffracted starlight. Abe et al. (2006), Sivaramakrishnan

& Yaitskova (2005), Sivaramakrishnan & Lloyd (2005), Soummer (2005), and Murakami

& Baba (2005) discuss the prospects for Lyot (.in, .i ,!1.'v with non-trivial entrance

aperture geometries. We use a circular unobstructed entrance aperture, radial image mask,

and (hence) a circular Lyot stop.

Kolmogorov phase screens mimic the effects of atmospheric turbulence, where a

fixed Fried parameter of 20 cm at 2.0 microns, which has previously been found to best

match actual PHARO data (Carson et al. 2005), is used throughout. To emulate AO

correction, the phase screens are Fourier transformed, multiplied by a parabolic high-pass

filter (Sivaramakrishnan et al. 2001; Makidon et al. 2005), and then inverse-transformed.

Improving the degree of wavefront correction is accomplished by increasing the actuator

density, which, in turn, raises the critical frequency of the high-pass spatial filter. The

linear number of actuators across the pupil ranges from 35 to 94 (962 to 6939 total

actuators). In terms of root-mean-square (rms) residual error, this provides a range in

correction from A/13 to A/30.

The resulting AO-corrected wavefronts are then sent to a separate MATLAB

coronagraph code for analysis, where the starlight passes through a series of consecutive

pupil and image planes. We assume idealized interactions with the optical elements and

the image mask (i.e. no scattered light, dust, fabrication errors, ... etc.), and use scalar

diffraction theory to calculate the propagation of the electric field. The telescope pupil









is constructed as a perfect disk of unit transmission and diameter 512 pixels placed at

the center of a 3072 x 3072 padding matrix in order to provide sufficient image plane

resolution (6 pixels per A/D). This choice of matrice sizes results in numerical noise levels

below 10-12 in contrast, which is negligible compared to the physical speckle noise floor set

by the AO system.

We do not explicitly simulate speckle-nulling on top of atmospheric correction.

Instead, in 4.3.1 and 4.3.2, we assert that the quasi-static aberrations are compensated

for to the level of the noise floor mean intensity set by diffraction and the atmosphere, for

a given AO actuator density. Speckle-nulling is discussed more in depth in 4.3.3. This

assumption is justified given the HCIT laboratory experiments at JPL that demonstrate

removal of residual starlight to contrast levels below 10-9 within the fractional search area;

although, in practice more timely methods for finding the optimal shapes of the extra

DMs (preferably < 1 minute) will need to be employ, -1

4.3 Comparative Lyot Coronagraphy

Our study focuses on the subclass of Lyot coronagraphs that control diffracted

starlight with amplitude image masks that is, focal-plane masks that do not modulate

the phase of transmitted light in theory.2 Such masks reside in the focal-plane wheel of

many coronagraphs in operation at in i"r observatories. Among the choices of amplitude

image masks, band-limited masks (Kuchner & Traub 2002) can perform the best in

principle. In the ideal case, they diffract all transmitted on-axis starlight into a narrow

region surrounding the edges of the Lyot pupil, and leave an area of infinite dynamic range

in the center (2). Moreover, band-limited masks with arbitrarily broad central nulls can



2 Masks that manipulate the phase of starlight in the image plane generally have better
inner-working-angles but poorer broadband performance (Roddier & Roddier 1997; Rouan
et al. 2000); although, fully achromatic designs are being developed (\! Iwet et al. 2005,
e.g.). See Guyon et al. (2006) for a review of the myriad of other different coronagraphic
designs and how they compare in a space-based application, such as the TPF-C.









also be constructed (Kuchner, Crepp, & Ge 2005), and have been shown to help combat

low-spatial-frequency optical aberrations in numerical simulations (Shaklan & Green 2005)

and in laboratory experiments (5; Crepp et al. (2006)).

We include a hard-edge mask, a Gaussian mask, and band-limited masks (hereafter,

BL mask or BLM) with 4th-order (sinc2), 8th-order since -ii, "), and 12th-order since ,

since since ) intensity transmission profiles near the optical axis (Figure 1). Each mask

is azimuthally symmetric and designed with an IWA- 4 A/D, so as to make fair

comparisons. The IWA is defined as the half-width-at-half-maximum of the intensity

transmission profile; for these masks, this value differs by less than 1 from the equivalent

width, which can also be used as an alternative definition (Aime 2005). The masks are not

truncated in the image plane; in practice, it is easy to include enough resolution elements

such that this effect does not contribute significantly to the noise floor. Equations

describing the masks are shown below. The radial coordinate, r, measures the distance

from the optical axis, where r = r D/A. Constants, which can be derived from (Kuchner,

Crepp, & Ge 2005), are given to four decimals of precision. The amplitude transmissions,

MA(r), are:

MH(r) circ (i/4) (4-1)

MG(r) 1 e-(f/3.6097)2 (42)

MBLM4th (r) 1 sinC2(0.4500 ), (4-3)

MBLM8th (r) = 0.9485 + 0.4743 sinc(1.4043 r) (4-4)
1.4228 sinc3(0.4681 F),

MBLM12th (r) = 0.7526 0.9408 sinc(1.9006 f) (4-5)
+ 5.2684 sinc2(0.9503 r)

5.0802 sinc3(0.6335 r),

where circ (v/a) is a step-function equal to zero for r < a and unity elsewhere.









To provide intuition for each mask's potential performance, we first present

coronagraph simulations using perfect incident wavefronts (Fig. 4-2). A qualitative

understanding of the coronagraph's functionality can be gleaned by examining the light

distribution pattern in the Lyot pupil plane, since the total amount of rejected starlight

depends strongly on the Lyot stop size and shape. For hard-edge and Gaussian masks, the

contrast is limited by residual diffracted starlight, whereas the combination of a BLM with

a matching Lyot stop can completely remove all on-axis starlight, in this ideal case. This

capability is seen in the 4th-, 8th-, and 12th-order BLM mask final image plane patterns;

they are composed entirely of numerical noise.

"Deg( i ,, i in contrast can occur however when large phase errors are present.

In other words, different masks may generate indistinguishable similar levels of contrast

when uncorrected atmospheric scattered starlight, rather than diffracted starlight, is the

dominant source of noise. Under these circumstances, throughput, quasi-static aberration

sensitivities, and fabrication considerations should more heavily influence the decision for

which mask to implement in practice.

In the following sections, image mask performances are quantified in terms of these

parameters and as a function of AO system correction. References to both the rms

wavefront error (WFE), rAO, in the pupil plane and resulting Strehl ratio, SAO, in the

image plane are made. The relationship SAO t 1 (27wAO)2 is valid in the high Strehl

regime, and is adopted for our calculations. We begin by comparing hard-edge masks to

the class of graded or apodized masks as a whole.

At this point it is convenient to define contrast, C(r), as it will be used throughout

the remainder of the text:

C (r) ( (4-6)
1(0) |M(r)|2
where 1(r) is the intensity at the radial coordinate in the final image, I(0) is the peak

stellar intensity as would be measured without the image mask in the optical train, and

IM(r)|2 is the mask intensity transmission. Note that 1(r) and 1(0) are both measured









with the Lyot stop in place. This is the non-differential (i.e non-SDI, single roll-angle, .

etc.) contrast.

4.3.1 Hard-Edge vs. Apodized Image Masks

A stellar coronagraph will begin to noticeably improve contrast relative to standard

AO imaging only when a sufficient amount of starlight is concentrated in the Airy pattern

central core. This occurs at Strehl ratios as low as 50' however, substantial gains over

a significant fraction of the search area are not attained until the Strehl ratio exceeds

~ 11' (Sivaramakrishnan et al. 2001). We seek to identify the required level of wavefront

correction above this value where apodized masks begin to out-perform hard-edge masks.3

For this comparison, we hold the Lyot stop size fixed at ,i .'. throughput; images

from the Lyot Plane column in Fig. 4-2 and results from 4.3.2 help to clarify why this is

a useful simulation control. Contrast curves for the hard-edge, Gaussian, and 4th-order

BLMs are shown in Figure 4-3 using several different levels of wavefront correction. For

clarity, higher-order BLMs are not included here, but are discussed in the next sections.

They provide intermediate levels of contrast, between that of the hard-edge and the

4th-order BLM.

At ~ 77'~ Strehl (rms WFE = A/13), the advantage in using the image plane

coronagraph is evident only for separations smaller than ~ 8 A/D; this is a result of

the limited wavefront correction and reduced aperture stop in the Lyot plane. Moreover,

the Gaussian and 4th-order BLMs provide only a factor of ~ 1.6 improvement over the

hard-edge occulter at the IWA, and contrast degeneracy sets in at a distance of ~ 1.5 A/D

from there. As AO correction improves, starlight is redistributed from the scattered light

halo into the Airy diffraction pattern, the PSF 'shoulder' drops and extends, and the



3 Notice that the IWA is rather loosely defined, and apodized masks can, in principle,
work interior to the hard-edge mask. This benefit is likely difficult to exploit in practice,
but constitutes an important caveat to the analysis.









diffracted light limitations of the hard-edge mask are revealed. The sharp edges of the

mask prevent further improvements in contrast below ~ 10-4 at the IWA, even as Strehl

ratios exceed ~ .

The Gaussian and 4th-order BLMs, which more effectively diffract starlight onto the

opaque portions of the Lyot stop, are capable of generating contrast levels of ~ 6 x 10-6

at IWA = 4 A/D with ~ '-I'. Strehl. They provide an improvement in contrast at the

IWA over the hard-edge mask by factors of approximately 2.7 at ~ $'2. Strehl (rms

WFE A/15), 5.1 at ~ -'. Strehl (rms WFE A/18), and 21.7 at ~ !'. Strehl (rms

WFE = A/26). These results are consistent with the hard-edge versus Gaussian mask lab

experiments of Park et al. 2006, taking into consideration the differences in PSF structure

and IWAs.

Curves showing contrast at the IWA and the relative improvement are shown in

Figure 4-4 as a more continuous function of wavefront correction. Though Gaussian and

4th-order BLMs out-perform the hard-edge occulter at currently achievable Strehl ratios,

they remain degenerate with one another into the realm of extreme AO. We next identify

the conditions and parameters for which this performance degeneracy is broken.

4.3.2 Gaussian vs. Band-Limited Masks

In order to compare apodized masks to one another, consideration of the light

distribution pattern in the Lyot pupil plane must be made. It is clear from the previous

section that Gaussian masks are competitive with BLMs in terms of contrast even at very

high Strehl ratios. Thus, we can use the Lyot plane patterns shown in the third column of

Fig. 4-2 for qualitative guidance.

Consider the effect of changing the Lyot stop diameter, DL, for each of the apodized

masks. With small non-zero stop sizes, the contrast at a given location on the detector

is governed by the competing effects of speckle noise intensity and the achievable peak

intensity of an off-axis source. The speckle noise intensity scales as D whereas the

companion peak intensity, I(0) |M(r) 2, scales as D The result is a net improvement in









contrast and the apodized masks perform comparably, until DL grows large enough to leak

significant levels of diffracted starlight.

As the Lyot stop size increases further, the contrast generated by BLMs does not

degrade in as smooth a fashion as the Gaussian mask, since the diffracted light is tightly

concentrated into a small region that follows the contour of the telescope entrance aperture.

Instead, the transition away from optimal performance is more abrupt. The width of the

transition region in the Lyot plane narrows as the wave front correction improves, and the

transition occurs at progressively smaller Lyot stop sizes for masks of higher-order (8th-,

12th-, ... etc.).

These effects are seen in Figure 4-5, where we plot contrast at the IWA against Lyot

stop throughput for two levels of wavefront correction. At ~ 91 i'. Strehl (rms WFE

= A/20), the apodized masks are clustered to within an order of unity in contrast from

one another, but clearly out-perform the hard-edge occulter. At ~ .' Strehl (rms

WFE = A/30), the apodized mask performance degeneracy is broken, and optimum Lyot

stop sizes become more evident. In particular, the 4th-order band-limited mask affords

an ~ 10'. gain in Lyot stop throughput over the Gaussian mask (1.1i1' vs. 50'.). The

8th-order and 12th-order masks generate slightly worse contrast and with < !ii', and

S15'. throughput respectively. These exact values depend upon the entrance aperture

geometry, operating bandwidth, IWA, mask-function, and mask-type (linear, radial, or

separable), but the trend is nevertheless the same at this level of wave front correction.

Generating Strehl ratios beyond '".'. on large ground-based telescopes in the near

future is rather unlikely.4 Additional complications such as differential chromatic

wavefront sensing and correction limitations and photon noise are significant at this

level (N 1\:. I. i i,, 2006; Guyon 2005). The potential benefits in using higher-order BLMs



4 The JWST however will provide a unique and stable platform for coronagraphy in the
3 5 pm band from space (Green et al. 2005).









from the ground are thus restricted to guarding against low-order aberrations introduced

downstream from the AO system, but at the expense of contrast, throughput, and angular

resolution.

4.3.3 Tip/Tilt and Low-order Aberrations

Thus far we have neglected quasi-static phase errors, or, at least, have assumed that

the resulting scattered light has been judiciously removed with speckle-nulling hardware.5

In this section we take a closer look at the issue. To get a feel for the problem, we

calculate the contrast degradation due to just one error, systematic misalignment, at

several characteristic levels of AO correction. Then we combine the results with theoretical

low-order phase aberration information gathered from other studies and discuss the

implications. This analysis along with that laid out in the previous two sections provides

important first-order guidelines for selecting coronagraphic image masks for extreme AO

systems.

Image mask response to quasi-static aberrations impacts the dynamic range

and duty-cycle efficiency of high-contrast observations. For instance, in the case of

tip/tilt errors, on-sky tracking latency or telescope-to-instrument flexure may lead to

misalignments that leak significant amounts of light. Clearly, the masks presented here

have different levels of resistance to such errors.

To assess pointing sensitivities, systematic tilt phase aberrations were added to the

wavefront at the AO-coronagraph (IDL-MATLAB) interface. Optimum Lyot stop sizes

were used for each mask, and median, instead of mean, intensities were evaluated to

prevent bias towards poor contrast. The 1 A/D annulus directly outside the coronagraph



5 Actually the light must go somewhere in order to conserve energy. It is sometimes
preferable to simply place it on the other side of the image plane during a given
integration.









IWA remained centered on the star as it was methodically shifted relative to the mask.

Results are shown in Fig. 4-6 for linear alignment errors up to 5 A/D.

At relatively low Strehl ratios (< -'- .), hard-edge masks perform comparably with

apodized masks provided that the pointing error does not exceed ~ 2 A/D. At higher

levels of correction (> -'- .), mask alignment becomes more critical. In this regime,

apodized masks are capable of generating significantly deeper contrast than the hard-edge

mask. In particular, the Gaussian and 4th-order BLMs provide optimum contrast when

aligned to better than ~ 1 A/D at ~ ,-'- Strehl and ~ 0.5 A/D at ~ !'. Strehl. If such

accuracy is difficult to manage, higher-order BLMs may be chosen over the Gaussian and

4th-order BLM, with the usual tradeoffs (4.3.2).

This analysis is also applicable to low-order aberrations in a more general sense.

Shaklan & Green (2005) have shown that the 'order' of the mask (4th, 8th, 12th, ...

etc.) uniquely determines a coronagraph's sensitivity to aberrations (tip/tilt, focus,

astigmatism, coma, trefoil, spherical, ... etc.). The result is that higher-order masks, which

are intrinsically broader, are naturally better filters of any given low-spatial-frequency

phase error. For example, expansion of Equ. 4-2 shows that the Gaussian mask intensity

transmission profile near the optical axis depends on r raised to the fourth power; thus,

it is a 4th-order mask (Fig. 5-1). Figure 4-6 confirms that the Gaussian mask follows the

4th-order BLM tilt sensitivity curve, and that higher-order BLMs follow suit.

The hard-edge mask may be considered in the limit as the exponent of the intensity

transmission approaches infinity. It is effectively a mask of infinite order, and thus

the most resistant to low-spatial-frequency aberration content. The sharp boundaries

of the hard-edge mask however also make the coronagraph leak the most starlight.

Combining this information, we recognize that Fig. 4-6 is qualitatively illustrative of

a trend applicable to all individual phase aberrations, and sums of orthogonall) phase

aberrations, introduced downstream from the AO DM and wavefront sensor. As the phase









errors increase, the contrast generated by apodized masks will rise (degrade) from the AO

noise floor and eventually intersect the hard-edge mask curve.

In general, quasi-static phase errors further reduce the Strehl ratio. Therefore the

situation is slightly more complicated than with tip/tilt alone, which, strictly -I" ii.- is

a change to the pointing vector and not an aberration. Nevertheless, we can extend the

principle to quantitatively include them all.

Consider the final measured Strehl ratio, S, written as a decomposition of uncorrelated

errors (Sandler et al. 1994):

S S1S2S3 ... S., (4-7)

where each Si with 1 < I < n represents an independent Strehl degradation. An equivalent

statement is that uncorrelated wavefront errors add in quadrature. Since the Strehl

ratio produced by the AO system is unrelated to the subsequent optical path, we let

S = SAO Sqs describe the final stellar image, where SAO is the AO-corrected Strehl ratio

(as has been used throughout the text and figures) and Sqs is the Strehl ratio due to all

quasi-static phase aberrations introduced downstream from the AO DM and wavefront

sensor.

Results from 4.3.1 and Fig. 4-6 show that use of an apodized mask, preferably the

4th-order BLM (4.3.2), is justified only when SAo S Thus, we require that the

measured Strehl ratio satisfy the condition:


S > 0.88 S (4-8)


where 0 < Sqs < 1 is the intrinsic Strehl of the optical system. With an internal

fiber-coupled source, such as a calibration lamp, Sqs can be measured when the AO DM is

inactive and flat, so far as one might trust zeroing the actuator voltages. We note that this

relationship is valid only in the high-Strehl regime (oa < A/27).

The effects of speckle-nulling can be incorporated by noticing that contrast curves

such as those shown in Fig. 4-6, and similar graphs for the other phase errors present in a









real system, will be "flattened" by the additional DMs (see 3). In other words, the extra

degrees of freedom afforded with this hardware compensate for quasi-static aberrations

whose spatial-frequencies match the intended search area. Long-lived speckles may be

nulled to an intensity level where the contrast curves in Fig. 4-6 intersect the vertical axes;

this is true for any such aberration. A candidate companion would then be noticed by the

inability of the instrument to remove its mutually incoherent signal. Subsequent changes

to the shape of the DMs and hence location of the dark hole might indicate the presence

of other faint sources.

As an example, consider a measured Strehl ratio S = 85'. with a system that has an

intrinsic Strehl ratio Sqs = 1!' According to Equ. 4-8, we are indeed justified in using

the 4th-order BLM for this application. However, if the additional DMs cannot remove

quasi-static speckles from the region of interest down to the intensity of the AO-limited

noise floor, we may consider switching to a higher-order mask, such as the 8th-order or

12th-order BLM, to help filter stellar residuals before they illuminate the detector.

These results allow us to make rather strong conclusions regarding the implementation

guidelines for image masks included in this study. We state them concisely in the next

section. For further discussion of low-order phase aberrations within the context of Lyot

corn.i ,.- I ,1y,, see 5 and Crepp et al. (2006), Sivaramakrishnan et al. (2005), Lloyd &

Sivaramakrishnan (2005), Shaklan & Green (2005).

4.4 Conclusions

One should select an image mask whose rejection of starlight is commensurate with

the noise floor set by the AO system. Our numerical simulations imply the following:

(1) Apodized masks should replace the hard-edge mask only when on-sky Strehl

ratios, S, exceed ~ 0.88 Sqs, where Sqs is the Strehl ratio due to all quasi-static phase

aberrations introduced by the instrument downstream from the AO system e.g.,

non-common-path errors. Below this level of correction, the hard-edge mask outperforms

apodized masks, not by reaching deeper levels of contrast, but by generating similar









contrast (4.3.1) and throughput (4.3.2) with more resistance to quasi-static errors. This

result is independent of entrance aperture geometry and bandpass.

(2) Since 4th-order BLMs yield more Lyot stop throughput than the Gaussian mask,

and apodized masks with smooth intensity transmission gradients are equally difficult to

manufacture, Gaussian masks should not be implemented under any foreseeable conditions

on telescopes with uniform transmission entrance apertures.

(3) The selection of higher-order BLMs over the 4th-order BLM is relegated to

situations where both the ability to correct for the atmosphere to a very high degree and

the inability to adequately null quasi-static speckles is simultaneously present.

For the operating range often considered with a traditional Lyot coronagraph, IWA

3- 5 \max/D, the exact contrast and throughput values will deviate from those reported

in 4.3, but in a rather predictable manner. The italicized conclusions however do not

change with these considerations. It is also important to mention that Strehl ratios can be

somewhat pesky to calculate in practice. Experimentally determined values are accurate

only to several percent if the image is not spatially sampled at a rate higher than twice the

Nyquist frequency (Roberts et al. 2004).

The hard-edge occulting mask is a remarkably relevant coronagraphic tool in an age

of sophisticated wavefront correction techniques and clever applications of Fourier optics.

Apodized masks, or binary versions of apodized masks (Kuchner & Spergel 2003), require

nano-fabrication capabilities at visible and near-IR wavelengths (Balasubramanian et al.

2006; Crepp et al. 2006; Carson et al. 2005; Debes et al. 2004; Trauger et al. 2004); this

can be a strong deterrent and should be avoided unless Equ. 4-8 is satisfied (although,

in a fast optical system, the focal ratio may impose stringent tolerances when building a

hard-edge mask as well). In the realm of extreme AO, the 4th-order BL mask should be

implemented, so long as quasi-static phase aberrations are manageable with speckle-nulling

hardware.










Finally, our calculations sir-'-- -I that the wavefront correction levels required for

ground-based observations preclude reliable spectroscopic measurements of close-separation

companions that are more than approximately one million times dimmer than their host

star without use of an integral-field spectrograph. Presumably, space-based instruments

will be able to do much better. Nevertheless, this result is still more than an order of

magnitude deeper than current AO-coronagraphs provide.


~lI
I,


4-


, 11 118th-
12th


-edge
isian
order BL
order BL
-order BL


0 5 10 15
Distance from Optical Axis (X/D)

Figure 4-1. Intensity transmission profiles for each radial image mask. The IWA- 4 A/D.
Band-limited masks (BLMs) have extended off-axis attenuation, which allows
them to be composed of a finite range of low spatial-frequencies. This feature
offers unlimited dynamic range as the Strehl ratio approaches 1(A', A
Lyot-- I le coronagraph equipped with a BLM is one of the leading candidate
designs for the Terrestrial Planet Finder Coronagraph (TPF-C) space mission
(Ford et al. 2006).















Mask


Hard-Edge



Gaussian



4th-order



8th-order



12th-order


Star x Mask


Lyot Plane
' i/ l


Final Image
-5

-15


Figure 4-2.


Coronagraph simulations with perfect incident wavefronts. Intensities in the
first two columns are shown on the same logarithmic scale using the mask
profiles, 0 < IM(r)|2 < 1, in Fig. 1 and a normalized Airy pattern. The spatial
extent of the image planes are identical and can be estimated from knowing
that the hard-edge mask has a diameter of 8 A/D. A dashed line in the 'Lyot
Plane' column indicates the outline of the circular unobstructed entrance
aperture. An 1.11',- throughput Lyot stop was used for the hard-edge,
Gaussian, and 4th-order BLMs. The 8th-order and 12th-order BLMs offer
better rejection of low-order aberrations at a cost of throughput and angular
resolution. The 'Final Image' column shows the contrast generated by each
mask using the logarithmic scale in the hard-edge mask row; BLMs remove
on-axis starlight down to the numerical noise level of the simulations
(< 10-12).


S
L A-''



A


A A


.9-
0
As-^


0^-
L'






























rms WFE=X113
(SAo-0.77)












no mask
hard-edge
Gaussian
4th-order BL

5 10 15 20 25 3(
Distance from Optical Axis (ViD)


10 15 20
Distance from Optical Axis (VD)


rms WFE=XJ15
(SAo~0.82)


10




103 I


Distance from Optical Axis (VID)


10


102


10'


10 4


rms WFE=X/26
(SAo~0.94)


10 15 20
Distance from Optical Axis (VD)


Figure 4-3.


Azimuthally averaged contrast curves for the hard-edge, Gaussian, and

4th-order BLM's using a fixed circular Lyot stop size with 1l', throughput.

The Lyot stop for the Airy pattern has 1(111' throughput.


101


102


103


104


105















AO Strehl Ratio
90%


...... hard-edge
- 4th-order BL


1/15


1/20
rms WFE (waves)


Figure 4-4.


Average contrast within the 1 A/D wide annulus directly outside of the
coronagraph IWA as a continuous function of atmospheric wavefront correction

and the relative gain (shown by arrows) achieved by switching to the 4th-order
BLM. The hard-edge mask's performance is limited by starlight diffracted into
the interior of the ~ i 1 r throughput Lyot stop. This prevents significant
improvements beyond -~ Strehl.


rmsWFE = X/30
(SAO ~ 0.96)





... .. ... ..S '


Figure 4-5.


80% 100%


20% 40% 60%
Lyot Stop Throughput


80% 100%


Average contrast within the 1 A/D wide annulus directly outside the
coronagraph IWA as a function of Lyot stop throughput for ~ 91' Strehl

(left) and ~ ',. Strehl (right).


80% 85%


V.


95%


10-4




0
U


x 18


10-6
1/10


1/25


-- 4th-order BL
- Gaussian
...... 8th-order BL
--- 12th-order BL
hard-edae


20% 40% 60%
Lyot Stop Throughput




























10



104



10 5 hard-edge
-- 4th-order BL
Gaussian
... 8th-order BL
12th-order BL
106


rms WFE=X/13
(SAo~0.77)


2 3
Mask Alignment Error (X/D)


rms WFE=X/18
(SAo~0.88)


2 3
Mask Alignment Error (X/D)


4 5


Mask Alignment Error (X/D)


rms WFE=X/26
(SAo~0.94)


2 3
Mask Alignment Error (X/D)


Figure 4-6.


Median contrast within the 1 A/D annulus outside the coronagraph IWA as a
function of systematic tilt error for several characteristic levels of wavefront
correction using optimal Lyot stop sizes. Note that the Gaussian mask is a

4th-order mask. The non-monotonic changes in contrast are a result of
calculating the median intensity with alignment errors in a circular geometry
and phasing between the Airy pattern and the mask intensity transmission

(see Lloyd & Sivaramakrishnan 2005).









CHAPTER 5
LABORATORY TESTS

We have built a series of notch filter image masks that make the Lyot coronagraph

less susceptible to low-spatial-frequency optical aberrations. In this chapter, we present

experimental results of their performance in the lab using monochromatic light. Our

tests show that these eighth-order masks (2) are resistant to tilt and focus alignment

errors, and can generate contrast levels of 2 x 10-6 at 3 A/D and 6 x 10-7 at 10 A/D

without wavefront correction. This work supports recent theoretical studies I.-. -. -I i.-;

that eighth-order masks can provide the TPF-C with a large search area, high off-axis

throughput, practical requisite pointing accuracy, and resistance to stellar size.

5.1 Mask Design and Fabrication

We have manufactured four binary notch filter image masks using e-beam lithography:

one fourth-order mask and three eighth-order masks. These masks represent a second

generation of technology development, where we have improved upon the prototype mask

presented in Debes et al. (2004). In the following, we briefly describe our design strategy

and nanofabrication techniques.

The base structure used to mechanically support the opaque portions of the masks

is a 0.7 mm thick piece of Boroaluminosilicate glass with a scratch/dig of 20/10. A 270

nm thick 1 r,.r of Chromium serves as the on-axis occulting material, and was deposited

onto one side of the glass using a Semicore e-gun evaporator. Small structures were then

dry-etched from the C!,i ii .. -i.-vr with an applied materials cluster tool using a high

density decoupled plasma composed of Argon, Chlorine, and Oxygen. No anti-reflection

coating was applied. Figure 5-1 shows a photo of the substrate containing all of the

designs.

Each mask is designed for an f/163 or slower beam with a 40 nm bandwidth centered

on the A = 632.8 nm HeNe laser source. The focal ratio of the system is large to facilitate

the fabrication of small features in the masks. The physical size or extent of the masks are










.... Chromium


Figure 5-1. The four linear binary notch filer image masks (left), and optical microscope
false color images of the m = 1, I = 2 eighth-order mask at 5x magnification
(middle) and 20x magnification (right). The dark areas in the microscope
images are transparent; this is where the C'li. ii,, has been etched away. The
spacing between stripes and the spacing between samples is
Amin //# 100 pm.


2 cm to a side. Although truncation sets an outer-working-angle and degrades contrast,

notch filter masks can easily be manufactured large enough to ensure that these effects

do not place significant constraints on the search area and are not the dominant source of

error. Notch filter masks can be designed to have an azimuthally symmetric search area;

however, we have chosen to make linear masks so that the effective opacity changes in only

one direction. This property simplified the testing of their response to pointing errors.

The FWHM of the image masks (i.e. 2x IWA) were designed to be roughly equivalent

such that fair comparisons of their performance could be made (Table 5-1). Aime

(2005) -,i--.- -1 that the mask equivalent-width serves as a better proxy for making such

comparisons; the authors note that the FWHM value differs from the equivalent-width

value by < 1 for each of the individual masks presented here.

Linear binary masks consist of vertically repeating parallel stripes, where band-limited

or notch filter functions describe the curves in each stripe (Kuchner & Spergel 2003).

We have made binary masks using the notch filter functions, because sampling makes

the intricate features near the optical axis a part of the design, and not the result of the

finite resolution of the lithography machine. In general, the sampling is not symmetric


r
m-1, 1-3 ir--3









(Fig. 5-1). The low-frequency amplitude transmission of the eighth-order masks follow

Equations 2-6 and 2-7.

The smallest features in a mask are often found near the optical axis. Their size

depends upon both the IWA and bandwidth, among other parameters. Generally, as the

IWA improves (i.e. gets smaller), the size of the smallest features in the mask increases,

and as the bandwidth widens, the size of the smallest features decreases. If the IWA is too

large or the bandwidth too wide, the smallest features may be too small to build.

An additional constraint is that the minimum feature sizes should not be smaller

than the thickness of the opaque material. This helps to minimize the waveguide effects

associated with binary masks, and other vector electromagnetic effects that can degrade

contrast, especially with broadband light. Lay et al. (2005) describe some of these

potential limiting factors for the TPF-C mission, and -ir.-.-, -i several alternatives for

compensation; one of which includes dramatically increasing the focal ratio at the mask (>

f/60), as was done in this experiment. This design strategy was also implemented in the

Debes et al. (2004) experiment for similar reasons.

Minimum feature size requirements both practical and theoretical limited

our ability to make eighth-order masks with high Lyot stop throughput. In theory,

eighth-order masks can achieve -~ 1.1'. Lyot stop throughput with IWAs of ~ 4 max/D.

Our masks were designed however to achieve only ~ 21i' throughput at most, because

we were restricted to making features larger than the thickness of the C'!i. 1ii. the

smallest feature size in each of the eighth-order masks is ~ 270 nm, whereas the smallest

feature size in the fourth-order mask is 7119 nm. To increase the throughput, we would

have to increase the f/#, decrease the bandwidth, or decrease the thickness of the

C'!i. ii,,, Clearly the focal ratio is already large and the bandwidth is already narrow.

Also, we show in 5.3 that increasing the thickness of the C'!i i. is the most notable

improvement we have made upon the mask presented in Debes et al. 2004. Thus, future

mask development will necessarily involve using a material that is intrinsically more









opaque at visible wavelengths, such as Aluminum (Semaltianos 2001; Lay et al. 2005).

This will enable the fabrication of masks that have more opacity and smaller minimum

features sizes.

The equations describing the exact structure of linear, binary, sampled eighth-order

notch filter image masks are derived in KCG05 Table 5-1 di-tp'1vh the relevant quantities

for our designs, using the same notation (except in KCG05 f/# f). For each mask,

sampling began at a horizontal distance of x = (o Amin f/# from the optical axis.

Table 5-1. Mask design parameters for a bandpass of 632.8 20 nm. For an elliptical or
circular primary mirror, the Lyot stop throughput of a linear mask is given by:
T 1 1[e\/ 02 + arcsin(e)], where 0 < e < 1 is a dimensionless parameter
that controls the width of the zones of diffracted starlight at the edges of the
Lyot stop. We were able to achieve ~ 7".'. of the maximum theoretical Lyot
stop throughput for each mask in the experiment.
Mask since2 n = 3 m r 1, I 2 m r 1, I 3
order 4th 8th 8th 8th
IWA/(Amax/D) 2.350 2.372 2.332 2.356
e 0.488 0.674 0.716 0.759
N 1.01444077 0.99098830 1.9 :10370 1.47114548
I ,'A 0.01423518 0.07s :', 1 0.05989364 0.06702707
1,, 0.0181 o 1sl 0.03028228 0.02278117
C -0.25123206 -0.51959437 -0. ;.i 11301
(0 0.28800972 0.25875213 0.25877876 0.25874218
Smallest Feature 7119 nm 271 nm 270 nm 270 nm
Theoretical Throughput 40. !'_, 21.-, 17. .!' 13.7'-
Experimental Throughput 30.7'-. 15.7'-. 13.0'_. 10. !'.


5.2 Experimental Setup

The design of the University of Florida coronagraphic testbed is that of a standard

transmissive Lyot coronagraph without wavefront correction, as depicted in Figure 1-8,

and similar to the setup described in Debes et al. (2004). "St oij!iII generated by

a A 632.8 nm HeNe laser for monochromatic J. -I ii:. passes first through a set of

neutral density (ND) filters and is then focused by a microscope objective lens into a 4 pm

single-mode fiber for spatial filtering. The fiber exit-tip serves as a bright point source.

This expanding beam, N.A. 0.12, is collimated and then truncated by a circular ~ 3 mm









diameter iris, simulating the primary mirror of an off-axis telescope. Optics downstream

from the iris are high quality achromat doublets capable of handling future broadband

tests. The first achromat, f = 500 mm, focuses the light onto the substrate containing all

of the notch filter image masks. The substrate is mounted onto a precision x-y-z stage for

fine adjustments. The light is then re-collimated by an identical achromat. In the Lyot

plane, an optimized Lyot stop blocks the light diffracted by the mask at the location of

the reimaged entrance pupil. The Lyot stop size is adjustable and takes the shape of the

intersection of two overlapping circles, since the masks are linear. The remaining light

is then focused onto an SBIG ST-2000XM CCD detector where images are taken for

analysis. The images are sampled approximately 10x more frequently than the Nyquist

frequency with 7.4 pm pixels. The anolog-to-digital converter has a bit depth of 16, and

the CCD has a factory quoted RMS read noise of 7.9 e-. These sources of noise are

alv-o- at least two orders of magnitude smaller than the measured contrast values when

used in concert with our experimental techniques, which are described in the following.

In order to measure contrast, we perform a comparison of images taken with and

without the coronagraph in place. Due to the extreme contrast levels involved, we use a

combination of the ND filters and the linearity of the CCD to calculate relative intensities

and to generate high signal-to-noise ratio images in a reasonable amount of time. We

first attenuate the laser light with the ND filters, which are placed upstream from the

single-mode-fiber to ensure that their aberration effects are negated, and take an image

of the star without the mask and without the Lyot stop in the optical train. Then, the

mask and Lyot stop are inserted into place, and the ND filters are removed. In this final

image, the intensity values at each pixel are divided by the average flux within the FWHM

of the image of the star taken without the coronagraph, and normalized to the integration

times and ND filters used. We define the resulting value, at each pixel, as the relative

intensity. The contrast then is simply the relative intensity divided by the Lyot stop

throughput and band-limited (i.e. low-frequency) part of the mask intensity transmission










at that position. Figure 5-2 shows images of the star at various steps in the procedure. We

could have chosen a less conservative definition of contrast by instead normalizing to the

interpolated peak intensity of the imaged source, rather than the average flux within the

FWHM (Shaklan & Green 2005); however, these two values differ by less than a factor of

two. It is not necessary to add and remove the Lyot stop in order to measure contrast, but

we find that doing so facilitates calculation of the off-axis throughput.


205---1% 7 --MM______


-35 -7 5
25
--4



Figure 5-2. Laboratory images of the simulated star without the coronagraph (left), the
m = 1, I = 2 mask aligned over the star (middle), and the star with both the
mask and Lyot stop in place (right). Intensities are plotted on a logarithmic
scale. The image of the star shows the angular size scale of the telescope.
Speckles created by imperfections in the optics limit the dynamic range of the
coronagraph creating a noise floor at the ~ 10-7 level near the IWA. The
contrast is calculated by dividing the relative intensity, shown in the image on
the right and later in Fig. 5-3, by the Lyot stop throughput and mask intensity
transmission; this accounts for the off-axis attenuation of the coronagraph.


Linear binary masks approximate band-limited masks only when the vertical angular

size of the stripes in the mask are smaller than Amin/D, the resolution of the telescope.

To ensure that the masks diffract light appropriately, we increased the focal ratio of the

system in the first image plane from the initial design of f/# = 163 to f/# m 187,

by shrinking the size of the entrance aperture. This also resulted in an improvement of

the masks' effective IWA by the same factor. The Lyot stop size was set conservatively

to obtain ~ 7.'. of the maximum theoretical throughput, so that small mis-alignments

did not result in diffracted light leakage through the center of the stop onto the detector.









Table 5-1 shows the designed IWAs before increasing the focal ratio, and the experimental

Lyot stop throughput achieved.

5.3 Results

5.3.1 Chrome Transmission and Relative Intensities

The performance of the prototype mask presented in Debes et al. (2004) was limited

by the transmission of light directly through the ('!iiiiiilini occulting -V, -'. In this

study, we have increased the thickness of this 1-rv from 105 nm to 270 nm. Using

the transmission curve in Debes et al. 2004, we calculate that the peak transmission

should improve from 7.5 x 10-4 to 9.2 x 10-'. We measure a peak transmission of

2.3 x 10-8. This is slightly worse than predicted, but opaque enough for this application

nevertheless (Fig. 5-3). The discrepency in these values can be understood by considering

inhomogenieties in the thickness of the ('!i ,i,,l ini, l S -. A < 5 nm deviation in each

makes up the difference. The contribution of transmission directly through the C'!i,,i.l.in,,

to the limiting contrast in this experiment is approximately one order of magnitude

smaller than the scattered light floor near the IWA, and less so in the regions where the

masks have little off-axis attenuation. A more demanding application, such as the TPF-C,

would, of course, require a material with a higher opacity.

Figure 5-3 also shows a difference in the amount of light transmitted near the optical

axis, r < A/D, between the fourth-order mask and the eighth-order masks. This is

evidence that the eighth-order masks are blocking more scattered light, simply because

they are wider, and reducing the effects of low-order aberrations (we test this latter claim

more carefully in 5.3.3). These properties are not seen as clearly in contrast curves,

where, interior to the IWA, the intensity transmission of the mask controls the detection

threshold.

5.3.2 Contrast Measurements

We find that the coronagraph's performance is limited by quasi-static scattered light.

The image plane speckles seen in Figure 5-2 are the result of wavefront distortions, created












Sm=1, 1=2 8th-Order
10-
10-2 .



10






Chrome Transmisgion '
10
0 5 10 15
10 K since2 4th-Order
10

10
10-1'






1'
10 TrM
10'


Figure 5-3.


10
nm=1, 1=3 8th-Order
10













0 5 10 15
100 1
n=3 8th-Order
10 5 10 15
10

10 r
1 0 2


distance from optical axis, r (X / D) distance from optical axis, r (X / D)

Telescope PSF, coronagraph PSF, and Chrome transmission for each mask
using a circular entrance aperture. The Chrome transmission was measured at
the center of the substrate. Inside the IWA, the eighth-order masks block more
scattered light and reduce the effects of low-order aberrations. The thickness
of the Ch!i i.... in does not limit the performance of the coronagraph, but does
transmit a non-negligible amount of light which contributes to the noise floor.
Contrast is calculated by dividing the coronagraph PSF by the intensity
transmission of the mask and the Lyot stop throughput.


by imperfections in the optics. In practice, speckles can mimic and often overwhelm the

light of dim companions (1.2.3,3, 4).

We calculated contrast for pixels within a 10 A/D x 30 A/D section across the center of

the PSF by dividing the relative intensities by the Lyot stop throughput and band-limited

part of the mask intensity transmission, I|(x)|2, at each position, x, the horizontal

distance of pixels from the optical axis. That way, the direction in which the halo of

speckles decreased in flux coincided with the direction of opacity change in the masks. We

were able to achieve 2 x 10-6 contrast at 3 A/D and 6 x 10-7 contrast at 10 A/D, as quoted










in the abstract. In Figure 5-4, we plot the corresponding 3 a detection limits, where a is

defined as the standard deviation of the scattered light noise floor at a given location in

the final image plane. The eighth-order masks reduce the amount of scattered light close

to the optical axis, and slightly out-perform the fourth-order mask near the IWA as a

result of their more steeply increasing intensity transmission in that region. The contrasts

in the rest of the search area are essentially identical.

To calculate the Strehl ratio of our system, we compared a model of the Airy pattern

incident onto the mask with experimental data. We find that the Strehl ratio exceeds '-'.

Combining this with the fact that the coronagraph is speckle dominated and the optical

quality of our achromats are high (see 5.3.3), we conclude that the detection limits shown

in Figure 5-4 represent the approximate deepest contrast that is achievable from the

ground with current AO systems, using this type of coronagraph.


100 -- since2 4th-order
m=1, 1=2
..... m=1, 1=3
10-1- -- n=3

10-2 :







10- w, 37 detection levels




10'
0 5 10 15
distance from mask center, x ( / D)

Figure 5-4. Experimental 3 a detection limits for each mask. The effective IWAs were
calculated taking into consideration the change in focal ratio from the initial
mask designs.









5.3.3 Tip/Tilt and Focus Sensitivity

We tested the tilt and focus aberration sensitivities of each mask by introducing small

alignment errors to the substrate in the image plane. The results are shown in Figure 5-5,

where we plot the contrast at 3 A/D as a function of the distance that the masks were

displaced. The scattered light floor limits the dynamic range of the coronagraph at small

aberration levels; in this regime, the masks generate contrasts to within a factor of two of

one another, as shown in the previous section (Fig. 5-4). At large aberration levels, where

diffracted light dictates the contrast, there is a clear dichotomy in the masks' behavior.

To measure the tilt aberration sensitivity of each mask, we moved the substrate

laterally across the center of the image of the star in 5 pm increments. We find that

the eighth-order masks are easier to point than the fourth-order mask. To quantify this

statement, we calculated the width of the pointing -v.- I--pI' for each mask, where the

contrast at 3 A/D is flat to within 2 a and limited by scattered light. The mean width

of this zone for the eighth-order masks is 1.06 0.03 A/D; the width of this zone for the

fourth-order mask is 0.20 0.05 A/D, a factor of ~ 5 smaller. With an 8 m telescope

operating at A = 0.5 pm, these tolerances correspond to pointing accuracies of 6.8 mas

and 1.3 mas respectively. (Lloyd & Sivaramakrishnan (2005) discuss tip/tilt errors in

Lyot coronagraphs in detail. For a practical application, see the description of the AEOS

coronagraph by Lloyd et al. (2001).)

To measure the focus aberration sensitivity of each mask, we moved the substrate

along the optical axis in logarithmic increments of 0.18 dex. With a similar analysis, we

find that the eighth-order masks are also less susceptible than the fourth-order mask to

focal misalignments. The eighth-order masks provide the same contrast as the fourth-order

mask in a system with ~ 4 times as large an RMS wavefront error.

These results (Fig. 5-5) depend upon the amount of scattered light present in the

system. If the scattered light levels were reduced, it would be possible to measure the

response of the masks to smaller aberrations; the width of the tilt and focus sweet-spots










would decrease as the contrast improves, and the relaxation ratios would change.

KCG05 estimate that eighth-order masks should relax pointing requirements relative

to fourth-order masks by a factor of ~ 6 in a system with no scattered light designed

to achieve 10-10 contrast at 3 A/D. SG05 have performed more careful calculations and

predict an even larger relaxation ratio of 16 in the allowable tilt RMS wavefront deviation,

when comparing eighth-order masks to fourth-order masks in an ideal system designed to

achieve 10-12 contrast at 4 A/D.

Tilt Aberration Sensitivity Defocus Aberration Sensitivity
103[ Eighth-Order
Masks SV i /


Figure 5-5.


C


2

0
0 10-


10 10' 10 10 10
Aberration Level (waves RMS) Aberration Level (waves RMS)

Coronagraph sensitivities to tilt (left) and focus (right) aberrations for each
mask. The theoretical predictions of Shaklan & Green (2005) are over-plotted
for comparison (see text). Scattered light prevented measurement of the
diffracted light response of the masks at small aberration levels. Uncertainties
in the measurements for the fourth-order mask are shown in the tilt graph; the
errorbars are on the order of the size of the datapoints and representative for
all of the experimental curves shown in both graphs. The focal ratio of our
system was large enough to warrant tilt realignment for each focus datapoint,
but not focus realignment for each tilt datapoint; this motivated the linear
versus logarithmic measurement increments used for acquiring data.


For comparison, the SG05 theoretical tilt and focus curves are over-plotted in Fig. 5-5

(the triangular data points); these represent the steepest possible slopes that can be

achieved in practice, since the model accounts only for diffraction. The general location

of our experimental data are in good agreement with theory, and, to first order, simply

adding a constant level of scattered light to the Shaklan & Green (2005) diffracted light









curves recovers the eighth-order masks' experimental contrast to within the uncertainty of

the measurements. The fourth-order mask however makes exception, by providing better

contrast in practice than expected from theory. This apparent discrepancy is resolved by

considering a subtle difference between the two studies: the Lyot stop size;1 the SG05

simulations maximize off-axis throughput by choosing the largest possible Lyot stop shape,

whereas we have undersized the Lyot stop in this experiment by ~ 25'. for each mask. In

the presence of aberrations, the contrast of a band-limited mask depends upon the size of

the Lyot stop. If the light diffracted in the Lyot plane due to aberrations is non-uniform

and less intense near the optical axis, decreasing the size of the Lyot stop can improve

contrast, at a cost of throughput and resolution (Sivaramakrishnan et al. 2005, see). We

find that the introduction of tilt and focus aberrations produces patterns in the Lyot plane

that fit this description (Fig. 5-6), and that the undersizing of the Lyot stop is responsible

for an enhanced resistance to aberrations. Furthermore, this effect is more pronounced

with the fourth-order mask than the eighth-order mask, since low-order aberrations can be

partially or completely filtered in the image plane before reaching the Lyot pupil.

It is a good assumption that the fourth- and eighth-order mask phase aberration

contrast curves (Fig. 5-5) do not intersect at more than one point for a given aberration:

the slope of a mask's dependence on ni; low-order Zernike mode is .,Jv li,- at least as

steep for eighth-order masks as it is for fourth-order masks (Shaklan & Green 2005). Since

we see the intersection in both graphs in Fig. 5-5, we conclude that the eighth-order masks

can achieve better contrast than the fourth-order mask when small levels of tilt and focus

aberrations are present, even though this regime was not available for direct measurement

in our experiment. At intermediate aberration levels, we do indeed see an improvement



1 Other differences between this study and Shaklan & Green (2005) are: (1) we used a
circular entrance aperture, instead of an elliptical entrance aperture, and (2) the contrast
was measured at 3 A/D, instead of 4 A/D.









-6


-2


-3.5



Figure 5-6. CI'! i ,:'teristic Lyot plane images with optimum mask alignment (left), and
2 x 10-1 waves RMS tilt aberration (middle), and 9 x 10-2 waves RMS focus
aberration (right) using the m = 1, I = 2 mask. Intensities are normalized to
the peak intensity of the focus image and are on a logarithmic scale. Shrinking
the Lyot stop can improve contrast when certain aberrations are present, as is
the case here. These images can be compared to the analytic predictions in
Fig. 3 of Sivaramakrishnan et al. (2005). Evidently, small amplitude tilt and
focus phase aberrations produce a uniform leakage of light into the Lyot pupil
interior. Although the aberrations presented here are rather large, aspects of
both images appear to reflect this phenomena. More complicated processes
such as cross-talk between induced and inherent aberrations as well as
frcqu'- i -folding from mask construction errors also contribute to the Lyot
pupil field, and can create an intensity gradient.


in contrast with the eighth-order masks. This is more evident with tilt, because the

intersection between experimental curves occurs well above the scattered light floor.

Reducing the amount of scattered light in the coronagraph by approximately

two orders of magnitude will enable a more reliable extrapolation of data to smaller

aberrations with future work; however, polishing the optics with such precision is not

feasible. The achromat doublets in this experiment are the same that were used in Debes

et al. (2004), with rms surface roughnesses of < 1 nm on spatial frequency scales that

correspond to the search area. A better technique to compensate for the scattered light

present in the system at this level would be to implement a deformable mirror (Trauger

et al. 2004, e.g.).









5.4 Summary & Concluding Remarks

We have built and tested three eighth-order notch filter masks and one fourth-order

notch filter mask each with the same IWA to make a comparitive study of low-spatial-frequency

optical aberration sensitivities within the context of Lyot coronagraphy, using monochromatic

light. We find that the eighth-order masks are less susceptible to the low-order aberrations

of tilt and focus than the fourth-order mask: they provide the same contrast as the

fourth-order mask in a system with either ~ 5 times as large a pointing error or ~ 4

times as large an RMS focus wavefront error. Additionally, the eighth-order masks show

a stronger dependence to both tilt and focus at large aberration levels (i.e. a steeper

slope), as predicted by theory. There was excellent agreement with our results and the

SG05 numerical model, once the differences in each study were accounted for. We were

unable to extrapolate our data to calculate the exact aberration levels necessary to achieve

< 10-10 contrast at the IWA because of the amount of scattered light in the system;

doing so would require implementing a deformable mirror to reduce the scattered light

levels by approximately two orders of magnitude. Transmission of light directly through

the C'!,iiiilinii occulting 1'v r accounted for ~ 1(,'. of the noise floor at the IWA, but

significantly less in the extended search area.

With "perfect" alignment, we find that all of the masks generate contrast levels of

~ 2 x 10-6 at 3 A/D and ~ 6 x 10-7 at 10 A/D. In essence, the on-axis ('stellar') flux was

reduced by 7 orders of magnitude at the expense of attenuating off-axis light by a factor

of 4 10. Since our system is "diffraction limited" (i.e. > 1 I'- Strehl ratio), we conclude

that the 3a detection thresholds shown in Fig. 5-4 represent the approximate deepest

instantaneous contrast that is achievable from the ground with current AO, using this type

of coronagraph.

The Lyot stop throughput penalty in switching from a fourth-order mask to an

eighth-order mask was greatly c:I:: -rated in this study, because of nanofabrication

limitations. We were able to achieve ~ 31 Lyot stop throughput with the fourth-order









mask and ~ 1C'- 1D.'. with the eighth-order masks. With a material that is more

opaque than Chrome at visible wavelengths, such as Aluminum, eighth-order masks will be

able to reach their full potential in future experiments.

These results support the recent theoretical studies of Kuchner, Crepp, & Ge (2005)

and Shaklan & Green (2005) sI--.; ii.; that eighth-order image masks can meet the

demands of a space mission designed to image extrasolar terrestrial planets by providing

the Lyot coronagraph with a large dynamic range, high off-axis throughput, a large search

area, and resistance to low-spatial-frequency optical aberrations.









CHAPTER 6
A BAND-LIMITED MASK FOR P.H.A.R.O.

It was shown in Ch'! pters 1 and 4 that large stroke, high bandwidth, high actuator-density

DMs are required to detect self-luminous Jovian planets from the ground in the near-IR.

These "extreme" AO systems are currently being built and will eventually form the

core of next generation high-contrast imaging instruments, such as GPI at Gemini

South (\! I. "iilosh et al. 2006a), SPHERE at the VLT (Beuzit et al. 2006), and the

PALM-3k/P1640 at Palomar (Dekany et al. 2007). However, due to their complexity, they

will not be available for another 3-5 years. To test a BLM on a real .,-I i, 1.11-ii i1 source,

we must somehow boost image qualities without replacing the existing DM.

6.1 Relay Optics

Fitting errors between the wavefront phase and DM surface limit the ability of an AO

system to correct for the atmosphere (Fig. 1-6). For instance, in the case of Kolmogorov

turbulence, the residual wavefront variance, a t, can be related to the effective wavefront

sensor subaperture size, d = DtI/Nact, and Fried parameter, ro, by




where the constant of proportionality depends (weakly) on the type of actuator influence

function (a Gaussian shape here), Nact is the linear number of actuators across the DM,

and a least-squares phase-conjugation approach is assumed (Hudgin, JOSA 1977). If

the number of actuators in a square grid array used for correction is approximately

Qr(Dtei/d)2/4, then Equ. 6-1 can be rewritten as


fit 0.25 [ Nc "t rad2. (6-2)

In other words, doubling Nact (i.e. quadrupling the total number of actuators) reduces

the rms wavefront error by a factor of ~ 1.8, which in turn improves the instantaneous

contrast by a factor of ~ (1.8)2 (1.2.3). However, increasing the DM sampling by









even a factor of a few, while maintaining minimal electro-mechanical cross-talk between

actuators, presents a substantial challenge. A relatively simple method for temporarily

side-stepping this obstacle is described below.

DM's are used most often to correct the entire "beam" of starlight, from one edge of

the aperture to the other. However, instead of applying corrections over the full diameter

of a large telescope, it is possible to improve sampling by correcting only a portion of

the pupil. For instance, optics placed between the secondary mirror and AO system

can be used to map, or relay, a particular region of the pupil onto the existing DM by

shifting and magnifying the beam. The result is an improved spacing between actuators as

projected onto the sky.

This concept has recently been demonstrated in practice by Serabyn et al. 2007 at

Palomar. They have installed relay optics that turn the Hale 200-inch telescope into a

powerful off-axis imager. Fig. 6-1 di-pl'1, a simplified version of the optical path. A fold

mirror inserted before the Cassegrain focus picks off the telescope beam and sends it to a

custom circular stop that selects one quadrant of the aperture, conveniently avoiding the

central obstruction and secondary support spiders. The relay optics manipulate the beam

such that the new pupil fits tightly onto the existing Xinetics 241-actuator Palomar AO

system (PALAO) DM (Troy et al. 2000). The net effect is finer sampling at the expense of

angular resolution (Dtel = 5.1m --D Dt= 1.5m) and the brightness of stars for which the

AO system can maintain a stable lock (V< 12 -- V< 9). These tradeoffs are justified since

coronagraphs with intrinsically small IWA's can still probe sub-arcsecond separations in

the near-IR, where numerous dim companions lay hidden (Veras, Crepp & Ford 2008).


Benefits of the technique can be summarized as follows:

* It is possible to generate extreme-AO-quality wavefronts immediately with only
moderate changes to hardware. As a result, one can gain experience with coronagraphy
in the high-Strehl regime before the next generation of DM's become available.









* The location and orientation of the subaperture can be chosen so as to avoid
vignetting elements, such as the secondary substructure, thus producing an optimal
diffraction pattern for the coronagraph.

* PSF stability provides the unique opportunity to develop methods for explicit removal
of quasi-static instrument scattered light based on phase diversity (3).

* Relay optics can be combined with laser-guide-star and upgrades to the DM.

Under good seeing conditions, the relay optics and PALAO have already demonstrated

on-sky Strehl ratios of S 'i!' in the K-band (Serabyn et al. 2007). We know from

C'!hi pter 4 that use of an apodized mask is appropriate only when the Strehl ratio exceeds:

S > 0.88 Sqs, where Sqs is the intrinsic Strehl ratio delivered by the instrument ('qs' stands

for quasi-static). The near-IR camera PHARO at Palomar consistently provides image

qualities exceeding Sqs > 0.95 for sources near the optical axis. Thus, Equ. 4-8 is indeed

satisfied. These considerations serve as the technical justification for building the first

band-limited coronagraphic image mask for on-sky tests. The remainder of the chapter

outlines the design of such a device (6.2), its performance with the PALAO stimulus

(6.3), and preliminary on-sky tests (6.4).


relay optics


1Pi1 '-O-.p
1_1


Cassegrain
focus

AO
focus


Figure 6-1. Layout of the Hale 200-inch relay optics, courtesy of Eugene Serabyn.




























Figure 6-2. Image of the relay optics subaperture pupil at the Hale 200-inch telescope.
Light from only one quadrant of the full aperture is used.


0 10 20 30 40
ro (cm) @ 2.2 microns


50 60 70


Figure 6-3. Predicted Strehl ratio as a function of the Fried parameter, ro, in the K-band
at the Hale 200-inch telescope with relay optics (top curve) and without
(bottom curve), courtesy of Gene Serabyn.










6.2 Design & Fabrication

The Palomar High Angular Resolution Observer (PHARO) is a near-IR imager /

spectrograph with a coronagraphic operating mode (Hayward et al. 2001). It utilizes a

1024 x 1024 HgCdTe HAWAII detector that is sensitive from 1.0 < A < 2.5/pm, with read

noise typically < 10 e / pixel. Spectrographic and coronagraphic image masks are housed

in a slit wheel in the first image plane, where there are 10 available slots. Filter, grism,

and Lyot stop wheels are located further downstream near the pupil. Figure 6-4 shows a

schematic of the instrument.

A 25 mas / pixel plate scale mode enables critical sampling of diffraction-limited

images from the full Hale 200-inch aperture in the J-band. With relay optics in place, the

plate scale changes by the ratio of the telescope diameter, 25 x 5.093 / 1.5 = 84.88 mas /

pixel. We have designed a mask for the K-band, where the sampling corresponds to ~ 3.6

pixels per diffraction width. The K-band offers better image qualities than the J-band, but

the sky background is brighter.

Algrwnm Ft- .^ L m ..........A W Wi m r OAP

I /
l ....................... .......... .... ... F lan'




.0 i mv upper Mowor



HAWAII 2414 -------
HgCdTlIe De.t r 1
and Mounbng 2_-5---- ----_ __ fmasoiwdi
S'AP Minor



FuR" Flat 1S _______
Shutler Mohu W noh4e


Figure 6-4. Component layout of the PHARO near-IR camera, courtesy of Tom Hayward.









6.2.1 Binary Image Mask

The focal ratio at the slit wheel and bandpass constrain the range of possible

coronagraphic mask designs. Fast optical systems can force the size of features in the

image plane to be too small whereas broad wavelength coverage affects the IWA and

Lyot stop throughput. These tradeoffs are important with binary masks (5) since they

can potentially leak light at both ends of the bandpass, but graded masks, which can

leak light only at long wavelengths, are made from HEBS glass and therefore more

expensive. Other interesting performance differences exist between the list of potential

designs smooth binary, sampled binary, smooth graded, and sampled graded such as

polarization dependence and chromaticity (Lay et al. 2005), but they are unimportant at

the sensitivities achievable from the ground. Since we have the tools and experience to

build binary masks, we built a binary mask for PHARO.

PHARO receives an f/15.64 beam from the PALAO system. The desired operation

range for our observations includes the Kshort: 1.99 2.30 pm, Bry: 2.16 2.18 pm,

and CO: 2.29 2.31 pm filters. The Kshort filter serves as the primary science

channel whereas independent experiments in all three filters can be used to measure

any chromatic dependent performances, should they exist, since only monochromatic

tests were previously conducted in the lab (Crepp et al. 2006). To prevent diffracted light

leakage from the edges of the filter transmission profiles, the minimum and maximum

wavelengths, Amin = 1.79 pm and Amax 2.39 pm, were chosen conservatively.

Two different masks were designed and built: a linear fourth-order smooth binary

notch filter mask and a linear hard-edge binary mask (Crepp et al. 2007). The latter of

which was used as a baseline to make comparative studies. An eighth-order mask design,

which has less Lyot stop throughput than a fourth-order mask, could not be justified,

given the already large sacrifice in photons from the relay optics. Each mask was designed

with the same .- .-ressive IWA = 2.678 Amax/Dtei = 880 mas. They were placed .,I.i I,:ent

to one another on the same 0.7 mm thick Boro-Aluminosilicate glass substrate, Corning









model 1737 10/5 scratch/dig1 with sufficient separation to ensure that diffracted light

cross-talk was negligible. The K-band glass transmission is quoted at 92'.

The masks were fabricated using e-beam lithography at the University of Florida

nanofabrication facility in June 2006. Aluminum was used as the opaque material deposit,

since it is less transmissive than C':i ii. (5) in the near-IR. Lab measurements placed an

upper limit on the intensity transmission directly through the 200 nm 1-v, r of Aluminum

at 1 x 10-7. The minimum feature size was set equal to the 1'Iv-r thickness.

The height, Mnotch (x), of a single stripe of the smooth binary linear band-limited

mask (see Equ. 2-17; binary masks are technically notch filter masks) is:


Mnotch(X) f/# Amin 1 since 2 Tf/ &)_ pm (6-3)

= 28 1 since2 (0.0179857x pm, (6-4)
pm ,j

where e = 0.428 and x has units of pm. This profile was repeated vertically 256 times.

The key to the binary mask's operation is that each stripe is smaller than the resolution

of the optical system, hence allowing it to diffract light like a graded mask. The hard-edge

mask design is much simpler; it is literally a bar of width 2 f/# 2.678 Amax = 200/m.

Figure 6-6 shows images of the mask before it was shipped to JPL, where it was cut

out of the substrate with a dicing saw to physical dimensions of 0.60 x 0.30 inches and

then cleaned in an ultrasonic bath of acetone to remove the protective lIv-r of photoresist.

Simulations were run to ensure that truncation at the edge of the mask would not diffract

starlight into the search area at contrast levels above 10-6. The mask was installed in

PHARO in September 2006.



1 A scratch is a defect on a polished optical surface whose length is many times its
width. A dig is a defect on a polished optical surface that is equal in terms of its length
and width. A scratch/dig of 10/5 indicates that the average length of a scratch is 0.10 mm
and the average diameter of a dig is 0.05 mm (http://www.esourceoptics.com/).























Figure 6-5. (left) The binary mask after e-beam lithography. A thick 1iv,-r of photoresist
was applied to protect the surface for shipping to JPL. (right) Microscope
image of the band-limited mask. Each stripe is 28 pm wide. 'Ringing' features
in the sinc2(...) function (6-4), which are responsible for controlling diffracted
light, can be seen above (x > 0) and below (x < 0) the main occulting region.


6.2.2 Aluminum Fastener & Lyot Stop

An Aluminum holder was built to fasten the coronagraphic mask to the PHARO slit

wheel (Figs. 6-6, 6-7). The design incorporated a single solid piece, instead of two separate

fasteners, to facilitate installation. It was necessary to allow extra space for thermal

contraction since PHARO operates at 77 K. The thermal contraction of the glass substrate

and differential contraction between the glass and thin 1Iv -r of Aluminum deposit on the

mask were negligible. The masks are oriented perpendicular to the direction of rotation

of the PHARO slit wheel. This is an important detail and has implications for the science

conducted in C '! ter 7.

The physical size of the pupil at the Lyot plane in PHARO is 16.88 mm (Hayward et

al. 2001). A band-limited mask will diffract light into a region that is smaller than this

value by a factor of 1 c. A custom circular Lyot stop of clear diameter (1 0.428) *

16.88 mm = 9.65 mm was built at the University of Florida using a laser cutter (Fig. 6-8).

The total throughput of an off-axis source at 880 mas, including attenuation from the

band-limited image mask and Lyot stop, is t 16.;:'. The throughput increases to a 3 ; '

for sources further from the optical axis.












Slit Hole Detail


Drill 1/32' blind
hole 1/16' dp.


Figure 6-6. Available slot in PHARO image plane wheel. The units are inches.


Figure 6-7.


Aluminum fastener made with 0.003 inch precision at the University of
Florida machine shop.


- 0 52


0 95
0620 RO 031 T'
4 PLCS

+
0 220 0 2E
0 32D


5D

I
Plj


























Figure 6-8. Lyot stop installed in PHARO. The University of Florida laser cutter provides
cuts that are rough on the order of tens of microns. This roughness does not
limit sensitivity.


6.3 White Light Tests

A typical observing run begins with installation of the relay optics. Alignment

takes anywhere from 4-8 hours depending on the circumstances. With the remaining

d light hours it is possible to conduct lab experiments using the PALAO stimulus.

This white light source well-simulates a G-dwarf star and passes through most of the

optics before reaching PHARO. Experimental tests were conducted with the new binary

coronagraphic mask in December 2006, April 2007, and May 2008 during the d-4vtime and

when conditions were poor after nightfall.

The goals of the tests were to:

confirm that the coronagraphic masks suppress diffraction

calculate contrast presumably, on-sky observations can never do better

identify effects that limit sensitivity

study differences in performance between the BLM and hard-edge mask

study the masks' chromatic behavior

Results are shown in Figs. 6-9 and 6-10 where each of the bullet points are addressed.









Coronagraph PSF


Figure 6-9. PHARO images with BLM aligned to the white light source. (left) Optimal
mask position is found using the PHARO stepper motor with the Lyot stop
out of the beam. (middle) Resulting coronagraphic PSF with Lyot stop in
place. The Airy rings have been removed. The waffle-mode peaks ( I ,: 11.[. i
et al. 2005) are ,1,000 times fainter than the stellar peak intensity and clearly
visible. In fact, they saturate PHARO if the integration time is not limited.
(right) Pupil image showing diffracted starlight pattern and residuals from
non-common-path errors. Compare this image with Fig. 5-6.


We find that both coronagraphic masks are capable of suppressing diffraction and

that the sensitivity is limited by non-common-path errors between the AO system and the

detector. The DM corrects for wavefront errors introduced upstream from its position in

the optical path but is blind to errors introduced downstream, such as those created by

fold optics and the coronagraph itself. Fig. 6-9 shows how the peaks of residual starlight

near the interior of the Lyot pupil correspond to the position of actuators on the DM.

Since phase errors in the DM pupil generate intensity errors at the Lyot pupil, we know

that the DM shape is not fully optimized. This is not surprising given that the wavefront

is sensed before the science camera.2 The amount of light remaining in the central portion

of the Lyot plane -.:, that sensitivities can improve by an order of magnitude with

future experiments using the BLM.



2 Recall that the complex field was measured at the final image plane in 3.2.3.


MaskAlignment









Fig. 6-10 di-pl~ 1 sensitivity curves for a variety of experiments and a theoretical

on-sky prediction for comparison (see 4.3). Contrast is currently limited to a 3 x 10-4 at

the IWA, or one order of magnitude below the Airy pattern. The green and brown curves

indicate that the BLM and hard-edge mask have a similar performance but that the

hard-edge mask is better at filtering low-order content a result that is consistent with

a system with large static aberrations (4.3.3, 5.3.3). These (non-common-path) errors

create an intensity 'plateau' near the edge of the DM control region which can also be seen

in Fig. 6-9. The blue BLM curve shows the relative improvement in sensitivity near the

optical axis when the DM shape is iteratively tuned using the first several Zernike modes

by measuring the intensity at the detector. We were unable to fully optimize the DM


Engineering Runs, December 2006 May 2008


1 2 3 4 5 6 7
separation / arcseconds


Figure 6-10. Experimental contrast results using the PALAO internal white light source.
No post-processing tricks, such as PSF subtraction, have been applied. The
BLM can make detections inside of the 0.88" IWA but no closer than the
Lyot stop spatial resolution limit.









shape with the canonical observing staff and hours of operation. More formal engineering

time will be scheduled in the near-future.

All measurements taken prior to Fall 2007 were acquired at a time when two

of the DM actuators were pinned. Their lack of response to instructions scattered a

significant amount of starlight. Maintenance to fix these actuators resulted in a noticeable

improvement (black circles) allowing sensitivities to approach the theoretical expectation.

There appears to be no significant chromatic issues. Data taken with the Br, filter in

December 2006 (pink curve) closely follows the other sensitivity curves with the exception

that the integration time was not sufficiently long: the Br, bandpass is 15 times narrower

than Kshort. We also confirmed that the BLM does leak diffracted starlight in the J-band

where the mask stripes are no longer smaller than Amin/Dtel (see 2.3.1).

We were unable to test the effects of mask defects on the speckle noise floor, since the

white light source did not have a translation stage to shift its position within the FOV.3

Significant changes to the speckle pattern as the white light source is moved down the long

axis of the mask would indicate that it makes non-negligible contributes to the static error

budget. We have no reason to expect the mask itself would scatter a large amount of light

but its features are three times smaller than the masks built in 5. Nevertheless, a DM

can compensate for such static errors (3.2.3).

6.4 On-Sky Demonstration

In this section, we report results from the first on-sky demonstration of a band-limited

coronagraphic mask. This study also represents the first tests of a TPF-C front-running

candidate design operating in tandem with an extreme AO system. We are sensitive to

brown dwarf companions over a wide range of ages and very young massive exoplanets.

Contrast is limited by a combination of AO lag time and the non-common-path errors

described above. Target selection is discussed in 7.



3 However, one was recently installed (A. Bouchez, private communication).









6.4.1 Data Acquisition & Reduction

There are three critical sets of images required to calculate the companion mass-sensitivity

for observations of a given star. In addition to the usual darks and flats, one must obtain:

(i) non-coronagraph images, where the star is not occulted by the mask, in order to

determine the throughput of an off-axis source, 1(0, 0) (see 3.2.3); (ii) coronagraphic

images, where the star is occulted by the mask, for the obvious reasons; and (iii) off-source

images, for calibration of the bright sky background. It is also useful to obtain on-source

images with the DM off to measure the seeing.

The total time spent on a bright source is often 30-45 minutes with a duty cycle

efficiency of roughly i ,' when including the time necessary to slew to the target, place

it within the unvignetted region (see Fig. 6-11), close the AO loop, and align the mask.

Nearly ",i '. of the time is spent on the sky background. More overhead is required when

the "flex-< o,i is running. The flex-cam picks off unused blue light from the wavefront

sensor beam and sends extra tip/tilt instructions to the DM to maintain precise mask

alignment by correcting for differential drifts flexuress) that occur between the telescope

and PHARO over the length of an exposure.

Once the images (.fits files) are in hand, they are backed up and processed with

an in-house Matlab program designed specifically for PHARO high-contrast data. A

simplified description of the reduction procedure is as follows:

* upload and tile the four separate read-out quadrants of the PHARO array

* cull pertinent information from .fits header

* apply flat field to correct pixel-to-pixel sensitivity variations (Fig. 6-11)

* determine peak intensity of the star, 1(0, 0), with AO locked

* median combine coronagraph PSF images with sub-pixel precision using high-pass
Fourier filter, 2D cross-correlation, Gaussian fit, and flux redistribution routines
similar to the "Drizzle" method employ, ,1 by Fruchter & Hook (2002)

subtract sky background










* fix bad pixels

* scale the final coronagraph PSF image by the appropriate factors, including
integration time and neutral density filters used, to obtain the relative intensity

obtain contrast by dividing the relative intensity by the mask intensity attenuation
profile incorporating the mask angle and errors in alignment

calculate standard deviation in contrast over the search areas of interest, typically a
Amax/Dtel wide strip above and below the mask

convert contrast to 5o sensitivity levels in terms of Jupiter masses using the Baraffe
et al. (2003) substellar atmospheric models

6.4.2 HIP 72567

We observed the star HIP 72567 on 2007-04-29 (UT) using the BLM. Its X-ray

activity, lithium abundance, rotation, and space motion -,i--.- -1 that is has an age


Flat-Field


1000

900

800

700

600

500

400

300

200

100


ZUU 4UU bUU 8UU


1UUU


-1.2


Figure 6-11. Flat-field image showing relay optics vignetting elements. Stars must be
placed within the central region that resembles Africa.









of 300 800 Myrs (Potter et al. 2002; Gaidos et al. 2000), making it an excellent

high-contrast imaging target. Table 6-1 lists the star's physical parameters and other

important observational information, including the Smithsonian A-I .1 1r,~ i1 J Observatory

number (SAO), J2000 right-ascension (RA) and declination (DEC), distance in parsecs,

spectral type, apparent visual magnitude (V), approximate age, total exposure time on

source (Atsource) and on sky (Atsky), median airmass, seeing, and Strehl ratio.

Table 6-1. Physical parameters and observational information for HIP 72567.
SAO 83553 distance 17.9 pcs age 300-800 Myrs airmass 1.07
RA 14 50 15.8 sp. type G2V Atsource = 595 s seeing 1.3"
DEC = +23 54 42.6 Vmag = 5.9 Atky 595 s Strehl = 77.8 0.9


Figs. 6-12 and 6-13 show the star with and without the coronagraph. A high-pass

Fourier filter has been applied to amplify the signal of sources with intrinsic widths of

order Amax/Dtel or smaller compared to low-frequency (i.e. blurry) structure. Several Airy


Before Fourier Filter After Fourier Filter


















Figure 6-12. Calibration image of HIP 72567 used to calculate the Strehl ratio and off-axis
throughput. Image intensities are on a logarithmic stretch and the FOV is
the same in each. Fourier filtering can artificially enhance the photometric
signature of a companion. This companion is not real but the result of an
internal reflection from a neutral-density-filter.









Before Fourier Filter


Figure 6-13. Fully processed coronagraphic images of HIP 72567 before and after Fourier
filtering. Fourier filtered data are also used internally by the reduction code
to facilitate precision stacking of individual images prior to median
combination. The orientation of the BLM is indicated by a dotted line. The
ghost from Fig. 6-12 is no longer present because the neutral-density-filter
was removed to maximize flux.


rings can be seen before the BLM and Lyot stop combination suppress the star to reveal

features in its immediate vicinity. The four waffle-mode peaks (C w 1 x 10-3) can barely

be detected in the calibration image, but are clearly visible with the coronagraph in place.

Exact contrast levels are shown in Fig. 6-14 and 6-15.

Anti-symmetric speckles due to quasi-static wavefront phase errors can be seen

above and below the mask. It is possible to exploit this symmetry4 by fli1pp1-i, folding,

and subtracting the image, but we find that the effective contrast does not improve

significantly. This line of reasoning is precisely what has lead to the development of

simultaneous differential chromatic (Close et al. 2005), polarimetric (Perrin et al. 2008),

and spatial imaging ('\! ,rois et al. 2006). That is, the structure of quasi-static speckles



4 Amplitude errors are a <10-8 effect (3) and thus ahv-- negligible from the ground.


After Fourier Filter













HIP 72567
12



10-



8-



6-








--Above Mask
-Below Mask


0 1 2 3 4 5 6 7 8 9 10

separation / arcseconds



Figure 6-14. HIP 72567 coronagraph sensitivity above and below mask in magnitudes.






HIP 72567
90

Brown Dwarf/Star Boundary
80------- ---------------------------------


70


60


S 50-
6 500 Myrs

40-


projected separation / AU



Figure 6-15. HIP 72567 coronagraph sensitivity in Jupiter masses as a function of age.









changes on a timescale shorter than typical integration, which last several minutes. Close

inspection of Fig. 6-13, for example, shows that the bright speckles do not have the same

shape nor intensity. This logic likewise applies to PSF subtraction using a nearby star.

In the near-future (2009), we will be the only high-contrast imaging group capable of

, ,l.. ./,; removing this dominant source of noise. PSF stability provided by the relay

optics affords us the opportunity. The Strehl for this particular target was low, but not

characteristic of the performance.

Upon converting the contrast levels from Fig. 6-14 to companion mass at 5o

(Fig. 6-15), where a is the local standard deviation in the signal, we find that we are

sensitive to M-dwarfs, brown dwarfs, and very young, very massive, and very distant

planets, such as those shown in 1.2.1.3. HIP 72567 is the first star ever to be observed

with a BLM or any legitimate TPF-C design candidate.

We note that this star is actually a triple system with a faint brown-dwarf-brown-dwarf

pair orbiting at 2.6" from the primary (Potter et al. 2002). We are capable of detecting

this set of companions, but they are located at an inopportune position angle and were

completely occulted by the BLM. This circumstance is the result of not knowing a

priori the ring angle of the imaging system with the relay optics in place. This was the

first observing run, and the angle changes slightly with each installation by an amount

comparable to the slit-wheel stepper motor range of motion within the FOV, which

also changes location. (This is the strongest selection constraint when we target visual

binary stars in 7.) It is possible to rotate the Cass-cage by 90 increments, which would

permit detection of HIP 72567BC, but we did not get a chance to go on-sky with the

(non-default) orthogonal orientation in April 2007 or T ,- 2008.

6.4.3 HIP 83389

We observed the star HIP S :' on 2007-04-29 (UT) using the BLM. Its physical

parameters along with relevant observational information are shown in Table 6-2. This

star is intriguing because it hosts a Jupiter-like exoplanet (\! sin i = 0.95Mjpiter, a 4.2









Table 6-2. Physical parameters and observational information for HIP S : :',.
SAO 46452 distance 18.1 pcs age 0.5-9 Gyrs airmass 1.03
RA 17 02 36.4 sp. type G8V Atsource = 595 s seeing 1.0"
DEC = +47 04 54.8 Vmag = 6.7 Atky 297 s Strehl = 84.6 0.4


AU, e-0.04; (Wright & Vogt 2008, in press)). The multiplicity of exoplanet host stars is

at least 21'". (M\!Isii ,., r et al. 2007) and a brown dwarf has recently been directly imaged

orbiting the star HD 3651, which hosts an eccentric sub-Saturn-mass planet at 0.3 AU

(Fischer et al. 2003). HIP S : :,'I is also on M. Turnbull's list of i l.-i for SETI and

the TPF missions (Turnbull 2008).

Although this star does not exhibit signs of youth, we are sensitive to massive brown

dwarfs exterior to 60 AU (Figs. 6-16, 6-17, and 6-18.). The contrast is limited by AO

latency (fDM = 200 Hz) and systematic tip/tilt alignment errors (4.3.3, 5.3.3) as a result

of flexure between the Cass-cage and telescope (flex cam was not operational). Depending

on the position of targets in the sky, the flexure may be more problematic. At times,

the drifts conveniently follow the opaque portions of the linear mask, but, in this case,

movements were in the orthogonal direction.


Before Fourier Filter After Fourier Filter


Figure 6-16. Fully processed coronagraphic images of HIP S :'













HIP 83389
1 1 i ------------ r ------------ i ------ i ------------------------- i -----


Above Mask
2 --Below Mask

I I I --L A M
0 1 2 3 4 5 6 7 8 9 10
separation / arcseconds



Figure 6-17. HIP i ') coronagraph sensitivity above and below mask in magnitudes.






HIP 83389
95


90 -


85-

Brown Dwarf/ Star Boundary
80 ------------- -----------------------------------------------
t 5000 Myrs
S75


70-


65-


60- 1000 Myrs


55-


40 60 80 100 120 140 160 180
projected separation / AU



Figure 6-18. HIP S ;') coronagraph sensitivity in Jupiter masses as a function of age.









6.4.4 HD 102195, a.k.a. ET-1

We observed the star HD 102195 on 2007-04-30 (UT) using the BLM. HD 102195

is also known as "ET-1" and is the first planet-bearing star that the local University of

Florida radial velocity team discovered (Ge et al. 2006). Throughout graduate school,

I spent 40 nights at Kitt Peak National Observatory using the single object Exoplanet

Tracker (ET) RV instrument and 31 nights at Apache Point Observatory using the

multi-object Keck-ET RV instrument. I thought it would be interesting to target this

star and place limits on the presence of substellar companions. HD 102195 also appears

to be relatively young, although uncertainties still remain regarding its age. Its physical

parameters and relevant observational data are shown in Table 6-3.

Sensitivity was limited by AO latency errors as is indicated by the blurring pattern

seen surrounding the mask in Fig. 6-19. The DM refresh rate was again set to only 200

Hz, in order to collect sufficient flux in each wavefront sensor subaperture. The faintest

target for which the relay optics will provide a substantial boost in Strehl is Vmag 9.

We were able to rule out substellar companions orbiting exterior to 50 AU down to

the levels shown in Fig. 6-21. There are no brown dwarfs more massive than: 25 Mjupiter

and younger than 100 Myrs outside of t 125 AU; 50 Mjupiter and younger than 500 Myrs

outside of t 150 AU; and 70 Mjupiter and younger than 1 Gyrs outside of a 150 AU

(Baraffe et al. 2003) at 5a above the noise floor.

Table 6-3. Physical parameters and observational information for ET-1.
SAO 119033 distance 29.0 pcs age 0.6-4.2 Gyrs airmass 1.19
RA 11 45 42.3 sp. type KO V Atsource = 595 s seeing 1.2"
DEC +02 49 17.34 Vmag 8.1 Atsky 297 s Strehl 75.4 0.7











RpforA Fnurior FiltAr


After Fourier Filter
, --jW. ..


Figure 6-19. Fully processed coronagraphic images of ET-1.






HD 102195, aka ET-1


- below mask
--- above mask


- / I


0 1


4 5 6 7 8 9 10


separation / arcseconds


Figure 6-20. ET-1 coronagraph sensitivity above and below mask in magnitudes.


























HD 102195


50 100 150 200 250 300 350 400
projected separation / AU


Figure 6-21. ET-1 coronagraph sensitivity in Jupiter masses as a function of age.









CHAPTER 7
MINI-PILOT-SURVEY FOR LOW-MASS CIRCUMBINARY COMPANIONS

7.1 Motivation

Binaries are a natural result of the star formation process and constitute a substantial

fraction, approximately 50'. of all nearby stellar systems (Tokovinin 2004; Duquennoy

& Mayor 1991). To date, however, they have been quite purposefully avoided by

high-contrast imaging instruments due to an inability to suppress the light from both stars

simultaneously. Depending on the separation, nearby stellar companions will either: (i)

add unnecessary pointing errors, or (ii) completely overwhelm a portion of the final image.

The cartoon in Fig. 7-1 depicts the situation for a ground-based telescope with perfect AO

and a coronagraph. Resolving the stellar pair results in significant contrast degradation

and dramatically reduces the prospects for discovering faint tertiary companions.

Such configurations occur frequently at near-IR wavelengths with large aperture

telescopes. For example, there exists a distinct peak in the orbital period distribution of

binary stars with G-type primaries at 104.8 d,,- (Duquennoy & Mayor 1991). This

number corresponds to an angular spacing of 0.5" on the sky if we take 75 pcs as a

characteristic distance to targets in the solar neighborhood. The spatial resolution of a

diffraction-limited 5m telescope at 2.0 microns is a 0.1". Thus, the ,n,,1 j..,: of nearby

intermediate-spectral-type binary stars are separated by several diffraction widths.

To circumvent this problem, a linear occulting mask, which has an intensity

transmission that depends on only one Cartesian coordinate, may be used. Since there

are no pointing penalties down the long axis of the mask, simultaneous alignment to each

stellar component can provide high-contrast images of the circumbinary environment,

and faint off-axis sources may be detected at the IWA. For example, the 'x' in Fig. 7-1

indicates the potential location of a companion executing a p-type orbit around a binary

star system that has a large inclination relative to the plane of the sky.













ZtQ1'" z 'Z.













Figure 7-1. Qualitative simulation images comparing circular to linear masks. (a) Binary
stars separated by several A/D. The pointing errors are significant. (b) A
linear mask aligned to both stars simultaneously. (c) Binary stars separated by
many A/D. The search-space is severely limited. (d) A linear mask can
accommodate any such geometry. These images were generated using perfect
wavefronts, equally luminous stars, hard-edge masks with high transmission
(0.05), and no Lyot stop. Intensity is shown on a logarithmic scale.


Numerical simulations have shown that companions are stable in such configurations

over a wide range of separations, mass ratios, and orbital eccentricities (Holman &

Wiegert 1999). Moreover, recent Spitzer observations have detected several circumbinary

debris disks (Trilling et al. 2007), lending credence to potential low-mass companion

formation in these dynamically more complex environments, and '21' of short period

planets orbit a single member of a binary system (\Ii i, nii r et al. 2007). Given this

information, it is hardly justifiable to make conclusions regarding the frequency of

substellar companions without considering binary stars.

In addition to searching a new parameter space, other poignant reasons for targeting

binaries are:

* RV measurements have revealed a paucity of brown-dwarfs orbiting within several
AU of single stars ('\ ircy & Butler 2000). Subsequent imaging surveys show that
this so-called lii'.- it-dwarf desert" extends as far as ~1000 AU (\ I Carthy &
Zuckerman 2004; Carson et al. 2006). The existence of a similar desert with binary









stars remains open question. The current paradigm of 'environment-dependent'
star formation (Duchene et al. 2007) predicts that large-separation brown-dwarfs
should be slightly more common around binaries than single stars, based solely on
arguments of binding-energy. Such observations can test this prediction.

Direct detections made in a variety of settings can help to break the brown-dwarf
massage degeneracy for a given spectral type.

The existence of a tertiary companion constrains a system's orbital history.

Based on these scientific justifications, we were awarded on-sky time at Palomar to

conduct the first high-contrast imaging observations of visual binary stars using the

coronagraphic masks from 6. The remainder of this chapter describes target selection

criterion and results from our "mini-pilot-- i v

7.2 Target Selection

The following constraints were used for selecting viable binary targets:

primary with V< 9 for AO locking

secondary with V< 12 for mask alignment

DEC > -50

d < 70 pcs

angular separation, 50 < 0 mas < 1800

accessible position angles

A distance cut is included to maintain a close physical IWA and remove intrinsically

bright stars that meet the apparent magnitude criterion. The angular separation between

stars, 0, should be large enough that an 8-O1m telescope resolves the binary, but small

enough that circumbinary orbits in the search area are reasonably stable. [Notice that

we could use the small aperture to our advantage again by targeting stars that we do not

resolve (50 < 0 mas < 300) but those that a large telescope would specifically, situation

(a) in Fig. 7-1. In this case, a circular mask is ideal.]

The most restrictive criterion is the position angle. The slit-wheel range of motion

within the PHARO FOV, with the relay optics in place, is only 7.50. If we include









the degeneracies in binary star position angles (180 = 360, ... etc.) and allow for 90

rotations of the Cass-cage, we can access 60/360 1/6 of all random orbital position

angles. This implies that not all targets can be selected by youth, especially since we

require the orbit in order to forecast the position angle and angular separation for

the observing run dates. Selection is further complicated by the fact that we have to

recalibrate the Cass-cage ring angle each time the relay optics are installed, as was

mentioned in 6.4.2. In other words, we do not know with certainty whether a particular

binary is observable until we go on-sky(!)

In total, 690 targets (0 < RA < 24 hrs) were selected from the Sixth Catalog

of Orbits of Visual Binary Stars (\! ,son et al. 2002), Scardia et al. (2008), Makarov

(2003), Zuckerman & Song (2004), L6pez-Santiago et al. (2006), and several young

unpublished targets provided by Mari-Cruz Galvez-Ortiz. Of these stars, 115 were

purportedly younger than 500 Myrs and satisfied the first 5 criterion listed above, but only

7/115 had well-determined orbits. Given the 1/12 probability of accessing their position

angles in a given Cass-cage orientation (and poor weather), we managed to observe only

1 young binary star system. Nevertheless, we were able to generate sensitivities to brown

dwarfs for 4/5 of the other systems we did observe even though they were older.

7.3 Tertiary Companion Sensitivity

It is reasonable to expect the sensitivity on two stars to be somewhat worse than

twice that of a single star due to non-common-path errors and isoplanatism. These effects

are, however, small for binaries with t 1" separations. Another interesting feature is that

companions can be detected in between the stars so long as they are located outside of the

mask IWA (Fig. 7-1b). The amount of scattered light in this region may be less than that

very close to one of the sources.

Contrast levels will be different for each star, since, in general, they differ in

brightness, but the mass-sensitivity must be the same: "If there were a brown-dwarf

tertiary located right here, would I see it?". In the following, we report contrast in a









Amax /Dte-wide strip above and below the mask relative to the brighter of the two stars

and starting from their photo-center. The mass-sensitivity curves show an average of the

contrast curves above and below the mask, as was done in 6.

T ,i'v of the individual K-band apparent magnitudes are not available since 2MASS is

seeing limited. It is, however, possible to use the combined flux recorded by 2MASS with

our diffraction-limited calibration images to obtain the apparent K-band magnitudes:

K, =K [\S + 5/2 log(1 +F2/i) (7 1)

K2 K [SS + 5/2 log(1+Fi/F2) (7 2)


where K2-A- \S is the combined (unresolved) apparent K-band magnitude measured

by 2MASS (Skrutskie et al. 2006) and F1 and F2 are the fluxes measured from our

calibration images in arbitrary units. Apparent magnitudes are then converted to absolute

magnitudes in order to calculate contrast in Jupiter-masses using the Girardi et al. (2002)

and Baraffe et al. (2003) atmospheric models, which are consistent with one another near

the brown-dwarf stellar boundary for ages greater than 50 Myrs.

7.3.1 HIP 88637

We observed the binary star system HIP 88637 on 2008-5-26 (UT) using the BLM.

HIP 88637 is a kinematic member of the Pleiades moving group and has an age < 150

Myrs (1 I.; ,rov 2003). Table 7-1 lists its physical parameters and relevant observational

information. Seeing measurements usually recorded by the Palomar MASS-DIMM system

(Thomsen et al. 2007) are not available for this run due to inconsistent weather conditions.

We did not measure the seeing directly on account of these time constraints.

Table 7-1. Physical parameters and observational information for HIP 88637.
SAO = ,.7- ; distance = 37.7 pcs age < 150 Myrs airmass = 1.05
RA 18 05 49.7 sep / PA" 0.49" / 91.4 Atsource 991 s seeing unav.
DEC = +21 26 45.2 Vmag = 7.6 / 8.4 Atky 991 s Strehl = 89.8 0.9
"Position angles are measured in degrees East from North.






































Figure 7-2. Calibration and high-pass Fourier-filtered coronagraph images of HIP 88637.



Results are shown in Figs. 7-2, 7-3, and 7-4. Reflections from a neutral-density filter

are visible for each star in the calibration image, but not seen in the coronagraph image


since the filter is removed once the mask is aligned. There are now eight waffle-mode

peaks. The contrast is comparable to levels achieved around single stars in 6.4 (see




11

10-



8

7-



S 5- 7

4-

3- -above mask
below mask
2

0 2 4 6 8 10 12
separation / arcseconds


Figure 7-3. HIP 88637 coronagraph sensitivity in magnitudes. The ...i iiin. i ry in flux
above and below the mask is a result of mechanical flexure.












HIP 88637
110-

100-

90-
Brown Dwarf Star Boundary
80

t 70-
Itf)
c 60-

50-

40-
100 Myrs
30

20-
Planet Brown Dwarf Boundary
10-

0 50 100 150 200 250 300 350 400 450
projected separation / AU


Figure 7-4. HIP 88637 coronagraph sensitivity in Jupiter masses for an age of 100 Myrs.



below). We were able to generate sensitivities to brown-dwarfs and massive extrasolar

planets orbiting exterior to 50 AU and 275 AU respectively at the 5oJ level. No tertiary

companions were detected.

7.3.2 HIP 82510

The direct imaging measurements made on the previous target, HIP 88637, were very

sensitive due to its young age but also an improvement to the hardware. This next data

set, HIP 82510, shows how the sensitivity was enhanced by switching to a Lyot stop, the

medium cross (Hayward et al. 2001), that suppresses the non-common-path errors shown

in Fig. 6-9. It also has higher throughput and spatial resolution, although the design in

6.2.2, which was used for all observations in April 2007, should work best in the ideal

case.

Table 7-2. Physical parameters and observational information for HIP 82510 in April 2007.

SAO = 84655 distance = 56.9 pcs age = unknown airmass = 1.02
RA 16 51 50.1 sep / PA 1.36" / 102.5 Atsource = 297 s seeing 0.9"
DEC +28 39 59.0 Vmag 7.0 / 8.5 Atsky 149 s Strehl 85.9 0.;:',










200720


Figure 7-5. Calibration images of HIP 82510 in April 2007 and May 2008. Spatial
resolution and throughput are improved on account of a wider Lyot stop.


2007 2008






















Figure 7-6. Coronagraph images of HIP 82510 in April 2007 and T' ,- 2008.



We observed the binary star system HIP 82510 on 2007-4-29 and 2008-5-26 (UT)

using the hard-edge mask and BLM respectively.. Table 7-2 di-pl '1v its physical


1.36"







Fflter Ghosts

Hard-Edge Mask













HIP 82510




--- --
0072007


2008 ''






i


0 1 2 3 4 5 6
separation I arcseconds


7 8 9 10


Figure 7-7. HIP 82510 coronagraph sensitivity in magnitudes in 2007 and 2008.






HIP 82510


220 -


200 -


180-


140-


120-


100 -


2008


5000 Myrs


Brown Dwarf -- Star Boundary


0 100 200 300 400
projected separation / AU


500 600 700


Figure 7-8.


HIP 82510 coronagraph sensitivity in Jupiter masses in 2007 and 2008.
Although different masks were used, the enhanced performance is the result of

switching to a Lyot stop better suited to handle non-common-path errors.









parameters and relevant observational information for the first run. On the second

run, the airmass and Strehl ratio were 1.01 and 84.0 1.;;'. respectively.

The position angle relative to PHARO changed by 11.40 in between runs, but only

0.5 is due to orbital motion (PA=103 in May 2008), implying that the Cass-ring angle

changed by 10.9. This is a significant amount and affects target selection since the

slit-wheel range of motion is only 15 (7.2). The effect will be accounted for in the

future by compiling lists of targets that span the range of position angles surrounding the

Cass-ring I -.. --p'- (i.e. where an unobscured quadrant of the telescope aperture can

be selected) or by building masks that are not parallel to one another (8).

The difference in relative position angle made it mandatory to use different masks

for the two runs. Although the BLM has the potential to outperform the hard-edge

mask (4), the improved sensitivity shown in Figs. 7-7 and 7-8 is a result of blocking

non-common-path errors and passing more off-axis light with the medium cross Lyot stop.

The scattered light floor drops just enough to detect massive brown-dwarfs. We note that

the K-band flux ratio, F2/F1, was measured to be 0.319 in 2007 and 0.318 in 2008.

7.3.3 HIP 88964

We observed the star HIP So_-, [ on 2008-5-26 (UT) using the BLM. Table 7-3

di-pv its physical parameters and relevant observational information. Results are shown

in Figs. 7-9, 7-10, and 7-11. The DM operated at 500 HZ, which is faster than most of

the observations presented here using the relay optics. Frequencies approaching 2 kHz are

ideal for minimizing AO lag-time errors.

Table 7-3. Physical parameters and observational information for HIP 88964.
SAO = 123187 distance = 50.1 pcs age = unknown airmass 1.18
RA 18 09 33.9 sep / PA 0.62" / 288.2 Atsource = 977 s seeing unav.
DEC = +03 59 35.8 Vmag = 6.1 / 7.4 Atky 489 s Strehl = 88.8 1.5'.


Mass-sensitivity depends strongly on age only below the brown dwarf star boundary

(< 80Mjupiter). This is the result of cooling since substellar bodies are unable to sustain





























Figure 7-9. Calibration and coronagraph images of HIP S~'-.


HIP 88964


separation / arcseconds


Figure 7-10. HIP 88964 coronagraph sensitivity in magnitudes.











HIP 88964

240-

220-
2 --5000 Myrs
200- -- -1000 Myrs
-500 Myrs
180-

160-

140

120-

100-
80 "- -Brown Dwarf Star Boundary
80------------ ---- ---- ------------------------------------------

60- '-- -- .

40-

20
0 100 200 300 400 500 600
projected separation / AU


Figure 7-11. HIP 88964 coronagraph sensitivity in Jupiter masses for various ages.


hydrogen fusion reactions. The contrast reaches a 40Mjupiter at an age of 500 Myrs. No

companions were detected.

7.3.4 HIP 66458

We observed the binary star HIP 66458 (Table 7-4) on 2008-5-26 (UT) using the

BLM. Impending clouds prevented acquisition of a calibration image. Nevertheless, we

were able to calculate the K-band magnitudes via Equ. 7-2 from the waffle-mode peaks(!)

Several point-sources are visible above and below the mask (Fig. 7-12). Symmetries

in the image -,-- -1 the presence of long-lived speckles (so-called "super--1., '1.1' ),

which are the result of quasi-static errors, but not all of the sources have a symmetric or

anti-symmetric partner, which might be the result of slightly different mask alignments for

each star. Follow-up observations are required to discriminate speckles from companions.

The evidence in this case is, however, likely too weak to warrant a proposal.










Table 7-4.
SAO
RA-
DEC


Physical parameters and observational information for HIP 66458.
= :1 !, distance = 58.8 pcs age = unknown airmass
13 37 27.6 sep / PA 1.74" / 96.9 Atsource 942 s seeing -
- +36 17 41.6 Vmag 5.0 / 7.1 Atky 248 s Strehl -


Figure 7-12. Coronagraph image of HIP 66458.





HIP 66458


0 1 2 3 4 5 6
separation / arcseconds


Figure 7-13. HIP 66458 coronagraph sensitivity in magnitudes.


- 1.05
unav.
unav.


--- above mask
- below mask


7 8 9 10











HIP 66458
250-

5000 Myrs
---1000 Myrs
200 -500 Myrs


150


100 -,
Brown Dwarf Star Boundary

50 ~---------~-~
50-



0 100 200 300 400 500 600 700
projected separation / AU


Figure 7-14. HIP 66458 coronagraph sensitivity in Jupiter masses for various ages.


7.3.5 HIP 76952

We observed HIP 76952 (Table 7-5) on 2008-5-26 (UT) using the hard-edge mask.

The DM was operating at 500 Hz. Results are shown in Figs. 7-15, 7-16, and 7-17.

Sensitivities sufficient to detect massive brown dwarfs were generated at projected

separations greater than 250 AU. No nearby point sources were detected.

Table 7-5. Physical parameters and observational information for HIP 76952.
SAO = 83958 distance = 44.5 pcs age = unknown airmass 1.01
RA 15 42 44.6 sep / PA 0.72" / 112.4 Atsource = 439 s seeing unav.
DEC = +26 17 44.3 Vmag = 4.1 / 5.6 Atky 439 s Strehl = 92.3 1.7'



7.3.6 HIP 82898

We observed HIP 82898 (Table 7-6) on 2007-4-29 (UT) using the BLM. The DM was

operating at 500 Hz. Results are shown in Figs. 7-18, 7-19, and 7-20. We were unable to

generate sensitivities to brown dwarfs independent of age. No tertiaries were detected.

Table 7-6. Physical parameters and observational information for HIP 82898.
SAO = 17'- distance = 67.1 pcs age = unknown airmass = 1.18
RA 16 56 25.3 sep / PA 1.29" / 67.70 Atsource = 142 s seeing 0.9"
DEC +65 02 20.8 Vmag 7.1 / 7.4 At=ky 71 s Strehl 89.5 0.;:',





























Figure 7-15. Calibration and coronagraph images of HIP 76952.


HIP 76952


separation / arcseconds


Figure 7-16. HIP 76952 coronagraph sensitivity in magnitudes.












HIP 76952


220

200


- 5000 Myrs
--- -1000 Myrs
-500 Myrs


Brown Dwarf Star Boundary


201 5- I I I I I I I I -
0 50 100 150 200 250 300 350 400 450 500
projected separation / AU


Figure 7-17. HIP 76952 coronagraph sensitivity in Jupiter masses for various ages.






























Figure 7-18. Calibration and unfiltered coronagraphic images of HIP 82898.


---------------------
------ ----------- ------


------------------------












HIP 82898


S" sky residuals

6-



4-


2-1- -above mask
b- elow mask


0 1 2 3 4 5 6 7 9 10
separation / arcseconds



Figure 7-19. HIP 82898 coronagraph sensitivity above and below mask in magnitudes.






HIP 82898


Brown Dwarf/ Star Boundary


projected separation / AU



Figure 7-20. HIP 82898 coronagraph sensitivity in Jupiter masses for an age of 5 Gyrs.









7.4 Discussion

The observational results reported in the last two chapters (3 single stars and 6

double stars) were obtained with only 7 hrs of on-sky time. We were awarded 6.5 nights

but most was lost to southern California fires, which burned down power-lines leading to

the observatory in October 2007, and high humidity, including snow-fall, in May 2008. It

should be possible to target a 40 more binary systems and several bright young single

stars with the 3 more nights we were awarded in November 2008 to recoup lost time.

In any case, we have learned a lot. The BLM clearly works and we have identified

the effects that can limit sensitivity. The flex-camera will soon operate smoothly and

correct for the drifts seen with HIP S >::-'I and HIP 88637. We now have a handle on the

preferred Cass-cage ring angles and how they translate to on-sky measurements relative to

our mask within PHARO. Combining this information with more on-sky time will permit

observations that better favor young systems. Moreover, we expect significant gains in

sensitivity (see 8) by removing the non-common-path errors shown in Fig. 6-9. Once

enough sources are observed and the above hardware adjustments are made, it will be

possible to make apple-to-apple comparisons of the hard-edge mask versus the BLM and

to the full aperture using data obtained previously by Joe Carson.

We anticipate an experiment in the near-term where a very bright source, like Vega,

is imaged onto a quadrant of the array. This will reduce the read-time and allow for

better speckle tracking. We also plan to fully characterize both the hard-edge mask and

BLM by moving the white light source down their long axis (6.3). If non-common-path

errors associated with visual binary stars, which land on different locations of the mask

(see 3.2.3), can be neglected, or at least minimized using an optimal DM setting, it may

be possible to perform high-fidelity PSF subtraction (3.2.5), by modeling the speckle

pattern.

A sensitive and statistically significant survey of visual binary stars will place new

constraints on the population of substellar tertiary companions, which is important for the









reasons discussed in 7.1. It is interesting to consider how the search area of a linear mask

affects the results of a Monte Carlo simulation where artificial brown dwarfs are inserted.

Of course, a few detections would be most exciting.

I am also naturally curious about circumbinary planets. If they are more massive

(on average) compared to planets orbiting single stars, due to a surplus of material from

which they can form, or if their orbits are more eccentric (on average), due to stochastic

processes, they will be easier to image!









CHAPTER 8
AFTERWORD: PROJECT CONCLUSIONS & LONG-TERM PROSPECTS

This section reiterates the main conclusions from C!i ,pters 2-7 and briefly describes

the project's likely path over the next few years.

In summary, we find that:

* Eighth-order BLMs are useful from the ground and space. They control diffraction
while helping to attenuate residual low spatial-frequency errors and also guard
against light leakage due to the finite size of stars.

Eighth-order BLMs can be built using nanofabrication techniques and their
performance aligns well with theoretical predictions.

There are certain guidelines, or "rules of thumb", that govern the selection of
image-plane occulters from the ground.

Preliminary tests of the first BLM operating in concert with the first extreme
AO system generate instantaneous contrast levels sufficient to detect substellar
companions orbiting single and double stars over a relatively wide range of ages.
Sensitivity is limited by wavefront control.

The basic premise of this work is straightforward: contrast is most important in the game

of high-contrast ii: ,-ii- especially with the field in its current state: one or maybe two

images of extrasolar planets thus far that did not even require a coronagraph to detect(!)

Simultaneous differential imaging techniques have generated the deepest sensitivities

to date, but they can alvb--- be applied after the instrument scattered light has been

explicitly removed using hardware. Since star-planet separations span several orders of

magnitude (0.018 AU -275 AU, HD 41004 Bb and AB Pic respectively), there should

be an abundant number of companions with > 0.5" separations. For example, Epsilon

Eridani b will reach its greatest elongation of 1.6" in the year 2010 (Benedict et al. 2006).

It is thus quite reasonable to sacrifice spatial resolution to help overcome fundamentally

challenging problems, such as the exquisite positioning of numerous, closely-spaced

actuators to correct for the atmosphere while removing instrument scattered light. R. 1i

optics can address these issues several years before the next generation of AO systems









come on-line. I plan to use them well into my first post-doe appointment which permits

the continuation of work along these lines.

This project has a lot of potential and there are several obvious next steps to take:

Remove the waffle-mode peaks. They occupy valuable search area. This can be
accomplished with software by modifying the wavefront reconstructor.

Compensate for non-common-path errors using the techniques in 3 and/or by
poking individual actuators and looking at the result in the Lyot pupil plane.

Build a BLM for the J-band where young planets are brighter, the IWA improves by
,!2'. and the sky background is significantly fainter.

Couple the relay optics with the PALM-3k AO system. The PALM-3k by itself will
"only" generate Strehl ratios of s 1', over the full aperture of the Hale 200-inch
(Dekany et al. 2007).

Figure 8-1 shows predictions for bright single stars using relay optics with and without

compensation for non-common-path errors and then with the upgrade to PALM-3k.

Instantaneous contrast levels of order 10-6 are possible. An integral-field-unit should be

capable of discriminating between speckles and companions using color information to

improve the effective sensitivity by another order of magnitude.

There may be insufficient flux for all 64x64 wavefront sensor subapertures using

the relay optics, but, as we have shown in 3.2.3, it is not necessary to correct near

the outer-most edges of the dark-hole. This sacrifice in search area permits use of less

subapertures while improving the dark-hole depth. Laser-guide star AO may be another

alternative in this situation since the 'cone-effect' associated with illuminating a nearby

l-1-r of the atmosphere (i.e., the fact that the laser does not create a perfect point source)

is relatively small for a 1.5m telescope.
















Instantaneous Sensitivity


1 2 3 4 5 6
separation I arcseconds


Figure 8-1.


Contrast as a function of angular separation for the Hale telescope using relay
optics. It is possible to remove (quasi-static) scattered light (created by
non-common-path errors) down to the noise floor set by the atmosphere at
, 7 x 10-6 in the K-band (red curve). These methods may then be applied to
teh PALM-3k system in the J-band and with a new BLM (blue curve). The
IWA will improve from 880 mas to 510 mas and the contrast will drop to
2 x 10-6 and extend to 5400 mas. Sacrifices of the outer search area may drop
the instantaneous noise floor even further. The full aperture can probe smaller
separations but cannot match the sensitivity. With post-processing techniques,
the effective contrast may reach 10-". Young massive exoplanets are detectable
with this technology.


10-1


10-2


10-3


10-4


10-5

10-


10-7
-
0









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BIOGRAPHICAL SKETCH

Justin Robert Crepp was born in Ellwood City, Pennsylvania, USA in 1979 to parents

Robert and Jennie Crepp. He has a younger brother, Adam, and a large family with many

aunts, uncles, and cousins. Justin graduated from Penn State Erie The Behrend College,

with a bachelors degree in physics and minor in mathematics in December 2002. On

October 16th, 2006, he married Amy Lynn Slozat on Holmes Beach near the Tampa Bay.

Their first child, Aaron Justin, was born just d,,- before the final version of this work was

submitted to the University of Florida Department of A-i n '1 in iv.





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Iamgratefulforthesupportandkindnessofmanypeopleoverthepastseveralyearswhohavehelpedmethroughoutgraduateschoolandwithlifeingeneral.IthankMom,Dad,Adam,&Kristinaforyourcontinuedloveandsupport{ithasbeendiculttobesofarawayforsolong;Larry&GaySlozat,forthegreatChristmasparties,yourhelpwithourrsthome,and,mostimportantly,allowingmetowhiskyourdaughterawaytoFlorida;Lori,Tim,&Jaxon,forgivingmeaplacetosleepbeforeandafterobservingruns;BrianSands,forthelate-nightphysicsconversations,get-rich-quickschemes,andteachingmetheartofyourgreatpatience(ofwhichIamstilllearning);AndrewVandenHeuvel,foryourcontagiousenthusiasm,beingmypartnerincrimeourrsttwoyearsinFlorida,andconqueringRomewithmeinasingleday;MatthewTurk,forsharingwithmeyourmad-scientist-likecomputerskills,diningwithJudyandIatIPandHerwig'sbeforebecomingavegetarian,andgivingmeaplacetostayduringpost-docinterviews;Anthony,Craig,Curtis,Dave,Ji,Jorge,Mark,andPC,forkeepingmeinvolvedinathletics{becauseofyou,mysanityis,Ithink,stillintact;KnicoleandPaolaforkeepingmecompanyintheocewhileworkingintotheweehoursofthemorning;Dimitriforyourfamous\LateNightCookieTime"andtrivia;SunMi,foryourkaraokeskills,loveofIndianfood,andmultiplebirthdayparties(peryear);Leah,forgivingmealifttoandfromtheGainesvilleairportatamoment'snotice;KellyBradley,forhiringmeattheAthleticTutoringCenter;CharlotteDare,forhiringmeasthebilliardsleisurecourseinstructor;PamFitzgerald,forkeepingmeinvolvedinpublicoutreachwiththelocalgradeschools;Steamers,forservingsuchdelectabledishes,and,toalesserextent,theKrishnafolks.IthankDarrenWilliams,myundergraduateadvisor,BlairTuttle,andtheotherprofessorsatPennStateBehrendforpreparingmeforgraduateschoolandshowingmetheimportanceofbalanceinlife;JianGe,mygraduatethesisadvisor,forsettingagoodexampleofwork-ethic,improvingmyproposalwritingskills,payingmyfeesevery 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 9 LISTOFFIGURES .................................... 10 LISTOFSYMBOLS .................................... 13 ABSTRACT ........................................ 14 CHAPTER 1INTRODUCTIONTOHIGH-CONTRASTIMAGING .............. 16 1.1BackgroundInformation ............................ 16 1.2EssentialConcepts ............................... 20 1.2.1FaintCompanions ............................ 21 1.2.1.1Visiblewavelengths ...................... 21 1.2.1.2Mid-infraredwavelengths ................... 23 1.2.1.3Near-infraredwavelengths .................. 24 1.2.2DiractionManagement ........................ 26 1.2.3SpeckleFormation ............................ 28 1.3TheLyotCoronagraph ............................. 32 2THEBAND-LIMITEDMASK ........................... 35 2.1BasicPrinciple ................................. 35 2.2Eighth-OrderMasks .............................. 37 2.3HigherSpatial-Frequencies ........................... 40 2.3.1BinaryMasks .............................. 42 2.3.2SampledGradedMasks ......................... 44 3PROSPECTSFORSPACEOBSERVATIONS ................... 47 3.1Introduction:Quasi-StaticWavefrontErrorsand\TheDarkHole" ..... 47 3.2TargetingEvolvedStars ............................ 51 3.2.1Motivation ................................ 51 3.2.2ExtendedSources ............................ 53 3.2.2.1Imagingterrestrialplanets .................. 53 3.2.2.2ImagingJovianplanets .................... 56 3.2.3NumericalSimulations ......................... 56 3.2.4Contrastvs.AngularSize ....................... 59 3.2.5PSFRole-Subtraction .......................... 64 3.3Conclusions ................................... 65 6

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............ 67 4.1Introduction ................................... 67 4.2ModelofAtmosphere&WavefrontCorrection ................ 69 4.3ComparativeLyotCoronagraphy ....................... 71 4.3.1Hard-Edgevs.ApodizedImageMasks ................ 74 4.3.2Gaussianvs.Band-LimitedMasks ................... 75 4.3.3Tip/TiltandLow-orderAberrations .................. 77 4.4Conclusions ................................... 80 5LABORATORYTESTS ............................... 87 5.1MaskDesignandFabrication ......................... 87 5.2ExperimentalSetup ............................... 90 5.3Results ...................................... 93 5.3.1ChromeTransmissionandRelativeIntensities ............ 93 5.3.2ContrastMeasurements ......................... 93 5.3.3Tip/TiltandFocusSensitivity ..................... 96 5.4Summary&ConcludingRemarks ....................... 100 6ABAND-LIMITEDMASKFORP.H.A.R.O. ................... 102 6.1RelayOptics ................................... 102 6.2Design&Fabrication .............................. 106 6.2.1BinaryImageMask ........................... 107 6.2.2AluminumFastener&LyotStop .................... 109 6.3WhiteLightTests ................................ 111 6.4On-SkyDemonstration ............................. 114 6.4.1DataAcquisition&Reduction ..................... 115 6.4.2HIP72567 ................................ 116 6.4.3HIP83389 ................................ 120 6.4.4HD102195,a.k.a.ET-1 ......................... 123 7MINI-PILOT-SURVEYFORLOW-MASSCIRCUMBINARYCOMPANIONS 126 7.1Motivation .................................... 126 7.2TargetSelection ................................. 128 7.3TertiaryCompanionSensitivity ........................ 129 7.3.1HIP88637 ................................ 130 7.3.2HIP82510 ................................ 132 7.3.3HIP88964 ................................ 135 7.3.4HIP66458 ................................ 137 7.3.5HIP76952 ................................ 139 7.3.6HIP82898 ................................ 139 7.4Discussion .................................... 143 8AFTERWORD:PROJECTCONCLUSIONS&LONG-TERMPROSPECTS 145 7

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....................................... 148 BIOGRAPHICALSKETCH ................................ 159 8

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Table page 1-1Comparisonchartofplanetdetectiontechniques{February2008 ........ 17 1-2Directimagingtradeoswithbandpass ....................... 27 2-1Sampledeighth-ordermaskparameters ....................... 45 3-1PhysicalparametersforCentauri ......................... 60 3-2High-contrastimagesofstarswithlargeangulardiameters. ............ 63 5-1Maskdesignparametersforlabexperiments .................... 90 6-1PhysicalparametersforHIP72567. ......................... 117 6-2PhysicalparametersforHIP83389. ......................... 121 6-3PhysicalparametersforET-1. ............................ 123 7-1PhysicalparametersforHIP88637. ......................... 130 7-2PhysicalparametersforHIP82510 ......................... 132 7-3PhysicalparametersforHIP88964. ......................... 135 7-4PhysicalparametersforHIP66458. ......................... 138 7-5PhysicalparametersforHIP76952. ......................... 139 7-6PhysicalparametersforHIP82898. ......................... 139 9

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Figure page 1-1Numberofplanetsorbitingotherstars ....................... 18 1-2SAOmodelofthesolarsystemasseenfrom10pcs ................ 22 1-3Contrastvs.wavelengthforvariousagesandmasses ............... 25 1-4Firstimagesofcandidateextrasolarplanets .................... 26 1-5TheAirypattern(mustberemoved) ........................ 28 1-6PhaseconjugationwithaDM ............................ 30 1-7Monochromaticspecklesfromalaboratoryexperiment .............. 31 1-8OpticallayoutofatransmissiveLyotcoronagraph ................. 34 2-1Convolutionofthetelescopeentranceaperturewithacoronagraphicmask ... 36 2-2Eighth-orderBLMfunctionsdescribedbyEquation 2{6 forn=15. ...... 38 2-3Eighth-orderBLMfunctionsdescribedbyEquation 2{7 form=1,l=25. .. 39 2-4IntensitytransmissionsforvariousBLM's. ..................... 39 2-5Anexampleofthesamplingfunctionforanm=1,l=3mask .......... 43 2-6Simulatedpicturesofanm=1,l=3eighth-ordersampledbinarymask .... 43 2-7Simulatedpicturesofanm=1,l=3eighth-ordersampledgradedmask .... 46 3-1Simulateddeformablemirrorsurfaceandresultingdarkhole. ........... 50 3-2BostonMicromachines12x12deformablemirror. .................. 50 3-3Innerandouter-edgeofthehabitablezonefornearbystars. ........... 55 3-4TPF-Cstellarangulardiametersensitivityforan8mtelescope. ......... 62 3-5PSFrole-subtraction. ................................. 64 4-1Intensitytransmissionprolesforeachradialimagemask. ............ 82 4-2Coronagraphsimulationswithperfectincidentwavefronts ............. 83 4-3Contrastcurvesforthehard-edge,Gaussian,and4th-orderBLM's ........ 84 4-4Contrastversuswavefrontcorrection ........................ 85 4-5ContrastversusLyotstopthroughput ........................ 85 10

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............................ 86 5-1Linearbinarynotchlterimagemasks ....................... 88 5-2Laboratoryimagesofthesimulatedstar. ...................... 92 5-3TelescopePSF,coronagraphPSF,andChrometransmission. ........... 94 5-4Experimental3detectionlimits. .......................... 95 5-5Coronagraphsensitivitiestotiltandfocus. ..................... 97 5-6Lyotpupilplaneexperimentalimages ........................ 99 6-1Layoutofrelayoptics. ................................ 104 6-2Imageofsubaperturepupil. ............................. 105 6-3AnticipatedStrehlasfunctionofFriedparameter. ................. 105 6-4ThePHAROnear-IRcamera. ............................ 106 6-5CoronagraphicmaskforPHARO. .......................... 109 6-6AvailableslotinPHAROslitwheel. ........................ 110 6-7Aluminumfastener. .................................. 110 6-8LyotstopinstalledinPHARO. ........................... 111 6-9Whitelighttests:maskalignment,PSF,andLyotpupilimage. ......... 112 6-10ExperimentalcontrastusingthePALAOinternalwhitelightsource. ....... 113 6-11Flat-eldimageshowingrelayopticsvignettingelements. ............. 116 6-12CalibrationimageofHIP72567. ........................... 117 6-13FullyprocessedcoronagraphicimagesofHIP72567. ................ 118 6-14HIP72567coronagraphsensitivityaboveandbelowmaskinmagnitudes. .... 119 6-15HIP72567coronagraphsensitivityinJupitermassesasafunctionofage. .... 119 6-16FullyprocessedcoronagraphicimagesofHIP83389. ................ 121 6-17HIP83389coronagraphsensitivityaboveandbelowmaskinmagnitudes. .... 122 6-18HIP83389coronagraphsensitivityinJupitermassesasafunctionofage. .... 122 6-19FullyprocessedcoronagraphicimagesofET-1. ................... 124 6-20ET-1coronagraphsensitivityaboveandbelowmaskinmagnitudes. ....... 124 11

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....... 125 7-1Qualitativeimagescomparingcirculartolinearmaskswithbinarystars. .... 127 7-2CalibrationandcoronagraphimagesofHIP88637. ................ 131 7-3HIP88637coronagraphsensitivityinmagnitudes. ................. 131 7-4HIP88637coronagraphsensitivityinJupitermassesforanageof100Myrs. .. 132 7-5CalibrationimagesofHIP82510inApril2007andMay2008. .......... 133 7-6CoronagraphimagesofHIP82510inApril2007andMay2008. ......... 133 7-7HIP82510coronagraphsensitivityinmagnitudesin2007and2008. ....... 134 7-8HIP82510coronagraphsensitivityinJupitermassesin2007and2008. ..... 134 7-9CalibrationandcoronagraphimagesofHIP88964. ................ 136 7-10HIP88964coronagraphsensitivityinmagnitudes. ................. 136 7-11HIP88964coronagraphsensitivityinJupitermassesforvariousages. ...... 137 7-12CoronagraphimagesofHIP66458showingo-axissources. ............ 138 7-13HIP66458coronagraphsensitivityinmagnitudes. ................. 138 7-14HIP66458coronagraphsensitivityinJupitermassesforvariousages. ...... 139 7-15CalibrationandcoronagraphimagesofHIP76952. ................ 140 7-16HIP76952coronagraphsensitivityinmagnitudes. ................. 140 7-17HIP76952coronagraphsensitivityinJupitermassesforvariousages. ...... 141 7-18CalibrationandcoronagraphicimagesofHIP82898. ............... 141 7-19HIP82898coronagraphsensitivityaboveandbelowmaskinmagnitudes. .... 142 7-20HIP82898coronagraphsensitivityinJupitermassesforanageof5Gyrs. ... 142 8-1ContrastpredictionsusingthePALM-3kAOsystemintheJ-band. ....... 147 12

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BLMband-limitedmaskDHdarkholeDMdeformablemirrorFOVeldofviewGPIGeminiPlanetImagerIWAinner-working-angleJPLJetPropulsionLaboratoryPALAOPALomarAdaptiveOpticssystemPHAROPalomarHighAngularResolutionObserverPSFpoint-spreadfunctionRVradialvelocitySETISearchforExtraTerrestrialIntelligenceSIMSpaceInterferometryMissionSPHERESpectro-PolarimetricHigh-contrastExoplanetREsearchinstrumentTPF-CTheTerrestrialPlanetFinder{CoronagraphTPF-ITheTerrestrialPlanetFinder{InterferometerWFEwavefronterror 13

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Wepresentacomprehensivestudyoftheband-limitedcoronagraphicmask.Emphasisisplacedonitsabilitytodetectfaintsubstellarcompanionswhenoperatinginconcertwithahigh-actuator-densitydeformablemirror.Bothspaceandground-basedapplicationsareconsidered. Itisshownthatanewkindofband-limitedmask,the\eighth-order"mask,canremovediractedstarlightwhileprovidingmoreresistancetotip/tilterrorsandlow-orderaberrationsascomparedtootherdesigns.Thisfeaturealsonaturallytranslatestoanimprovedresistancetothenitesizeofstars.OurnumericalsimulationsindicatethataTPF-C-likeinstrumentequippedwithaneighth-ordermaskcan,inadditiontoachievingitsbaselinegoalofcharacterizing\Earth-like"planetsorbitingmain-sequencestars,alsoaddressfundamentalquestionsregardingplanetformationandevolutionbytargetingnearbyevolvedstars.Weshowthatsuchobservationscanprobetheexoplanetpopulationnearthehigh-mass-endofthespectral-sequenceandalsopossiblyconstrainthetimescaleforthedevelopmentoflife. Wenextmakeacomparativestudyoftheperformanceofvariouscoronagraphicmaskswheninthepresenceofatmosphericturbulence.Itisshownthatthereareseveralguidelinesfordecidingthedesignofaground-basedimage-planeocculter:(i)tojustifytheuseofaband-limitedmask,theon-skyStrehlratiodeliveredbytheadaptiveopticssystemmustexceed0:88Sqs,whereSqsistheintrinsic(quasi-static)Strehlratioprovidedby 14

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Wethenbuilttherstseriesofeighth-orderband-limitedmasksusingelectron-beamlithographyandtesttheirperformanceinthelab.Ourexperimentsshowthateighth-ordermasksfollowthetheoreticalpredictionsforresistancetotip/tiltandfocusalignmenterrorsandcangeneratecontrastlevelsof2106at3=Dinasystemwith1nmofrmswavefronterroroverthesurfaceofcriticaloptics. Thisworkculminateswiththedesignandfabricationoftherstband-limitedmaskforon-skyobservations{ademonstrationthatalsoconstitutesthersttestsofaleadingTPF-Cdesigncandidateusing\extreme"AO.Contrastlevelssucienttodetectbrowndwarfsoverawiderangeofagesaregeneratedatprojectedseparations&100AUforthestars:HIP72567,HIP83389,andHD102195,a.k.a.ET-1.Thesensitivityislimitedbynon-common-patherrorsandAOlag-timeforthefaintertargets. Takingadvantageofthemask'slineargeometry,wealsoconductedthersthigh-contrastimagingobservationsofvisualbinarystarsbysuppressingbothsourcessimultaneouslytosearchforfainttertiarycompanions. 15

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Therstdemonstrationofhigh-contrastimagingtechnologytookplaceinthelate1930swhenBernardLyotbuiltaninstrumenttoblocklightfromthediskoftheSuninordertostudyitsperipheries.Hewasparticularlyinterestedinthesolarcoronaandplannedtoconductextensiveobservationswheneverdesired,insteadofwaitingfortheinfrequentoccurrenceofaneclipse.Hisinvention,whichnowbaresthename:theLyotcoronagraph(x ),hasbecomeanindispensabletoolintheeld.Itcanbefoundatmostground-basedobservatories.Moreover,theHubbleSpaceTelescope(HST)hasacoronagraphicoperatingmode( Krist 2007 ),theJamesWebbSpaceTelescope(JWST)willbeequippedwithcoronagraphicstarlightsuppressionhardware( Clampin 2007 ),andoneoftheTerrestrialPlanetFinder(TPF)missions(x )willlikelyutilizesomevariationofLyot'soriginalconcepttogenerateunprecedentedsensitivity( Shaklan&Levine 2007 ). Modernhigh-contrastimagingismotivatedprimarilybyextrasolarplanetresearch.Todate,nearly300planetshavebeendetectedorbitingotherstars(http://exoplanet.eu/;http://exoplanets.org/);however,thevastmajoritywerediscoveredusingindirecttechniques.Radialvelocity(RV)( Marcy&Butler 2000 ),transitphotometry( Charbonneauetal. 2000 ),gravitationalmicrolensing( Gaudietal. 2008 ),astrometry( Benedictetal. 2006 ),andpulsartiming( Wolszczan&Frail 1992 )eachrelyuponmeasurementsofthestarbutnottheplanetitself.Theevidenceisoftenaperiodicsignalsuperposedontothestar'ssignature(e.g.,itsrelativepositioninthesky,brightness,locationofspectral 16

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1-1 ).Directimagingisanintuitivealternativethatyieldsexplicitphotometricandspectroscopicinformation.Inthisregard,itrepresentsthefutureofexoplanetaryscience. Table1-1. Comparisonchartofplanetdetectiontechniques{February2008 RVTransitsAstrometryLensingPulsarTimingImaging MassXXXRadiusxXxxxXTeffxxxxXCompositionxxxxXOrbitaproj.Xproj.proj.proj.proj.Obser.Biasbage,PPPPneutronstarsPEciency1P2P1Phours1PhourscDetections22136d1e651 Benedictetal. 2006 ),andshownanothercandidate,HD33636b,tobealow-massstar( Beanetal. 2007 ). Linetal. 1996 ).However,toaddressotherquestionsregardingtheoriginandstructureofplanetarysystems,itisnecessarytodetectlower-massbodies,of Mullallyetal. 2008 ). 17

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11 )andtheleadingformationtheoryof\core-accretion"( Pollacketal. 1996 )suggestthatlow-massplanetsmayindeedbecommon( Ida&Lin 2004 ). Figure1-1. Numberofplanetsdetectedorbitingotherstarsasafunctionofmass(datafromtheExoplanetEncyclopedia,Schneider,J.{March7,2008).Evidenceforapaucityofbrown-dwarfsisclear,giventhecurrentsensitivity,1m/s,ofRVinstruments( Marcy&Butler 2000 ).Theprospectsforanabundanceoflow-massplanetsarepromising. Oneofastronomy'sprinciplegoalsinthenextcenturyistodetectaterrestrialplanetorbitinginthehabitablezone( Kastingetal. 1993 )ofanearbystar.ThespacemissionsCOROT(transitphotometry{launchedDecember2006),Kepler(transitphotometry{scheduledlaunch2009),andSIM(astrometry{launchdateuncertain)willeachbesensitivetorockyworldslocatedatorbitaldistanceswherewatercanpersistintheliquidphase.Theirobservationswillplacetherstconstraintsonthepopulationstatisticsofplanetswithpotentiallyhospitableenvironments.However,onlyadirectimaging 18

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Kalteneggeretal. 2007 ). NASAhasthereforeproposedtwoadditionalmissions,aseriesofTerrestrialPlanetFinders,thatwillobtainspectraof\Earth-like"exoplanets(shouldtheyexist).Therstinstrument,TPF{C,willutilizeacoronagraphandsingle-dishtelescopeoperatingatvisiblewavelengthstocollectreectedlight(x ),whilethesecond,TPF{I,willcomplementtheseobservationsatmid-IRwavelengths,withalong-baselineinterferometer.TheTPF{CwillbelaunchedbeforeTPF{I,eventhoughthedierenceinbrightnessbetweenastarandplanetismorefavorableintheinfrared(x ).Thisdecisionisbasedonthefactthatcoronagraphictechnologies,suchasthosedescribedinthisthesis,arematuringrapidly(seealsohttp://www.lyot2007.org/),whileinterferometric-nullingtechnologies( Wallaceetal. 2000 ),suchasprecisionformationying Fridlund 2004 ).) ThereareseveralprospectivedesignsfortheTPF{C.Oneofthemostpromisingcandidatesutilizesaband-limitedmask:anocculterthatresidesinthefocalplaneoftheLyotcoronagraphandcontrolsdiractionbymanipulatingtheamplitudeofstarlight.Theband-limitedmaskprovidesnumerousbenetsforhigh-contrastimaging,suchasdeepsuppressionofstarlightoverabroadbandpass,higho-axistransmission,closeinner-working-angle,resistancetolow-orderaberrations,resistancetonitestellarsize,andexibilityindesignandmanufacturing.Italsorequiresaminimalnumberofoptics 19

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Thefollowingworkdescribestheband-limitedmask(x )anditsperformanceinnumericalsimulations(withrespecttobothspace(x )andground-based(x )observations)andlabexperiments(x ),aswellason-skytestsusingan\extreme"adaptiveopticssystem(x )andcoronagraphicobservationsofvisualbinarystars(x ).Theremainderofthischapteroutlinesthevariousgoalsandchallengesofhigh-contrastimagingingeneralandintroducestheLyotcoronagraph.Thediscussionassumessinglemain-sequencestarsastheastrophysicaltargetsofinterest,unlessotherwisestated. whereminandmaxindicatethebandpass.Itsvaluedependsstronglyonthemassratioandsystemage,andcanchangebyseveralordersofmagnitudewhenobservationsareconductedinvisibleversusmid-infraredwavelengths.DirectdetectionrequiresthatinstrumentsgeneratesensitivitiescomparabletoCatagivenangularseparation,otherwisecompanionswillremainhiddenbeneathstellarresiduals. \High"-contrastimaging,asisoftenwrittenintheliterature(eventhoughEqu. 1{1 istheconventionaldenition),isdicultbecauseopticalphenomenathatarecommonplaceandunavoidable,suchasdiractionorreectionfromamirror,scatteralargeamountofstarlightintothesearcharea.Moreover,thepattern,orfrequencyspectrum,ofnoiseisstructuredsuchthatcontaminationincreasesforregionsclosertothestar,makingdetectionaconsiderablechallenge.Thedegreeofdicultydependsonthetypeofcompanionsincetheformationmechanisms,whichgovernthemassandcharacteristicorbitalseparation,ofterrestrialplanets,giantplanets,andbrowndwarfs,fundamentallydier. 20

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1.2.1.1Visiblewavelengths whereisanorderunityfactorthattakesintoaccountreectioneciencyeects,suchasalbedoandorbitalphase. ThecanonicalexampleisthatofanEarth-likeplanet,Rp=6400km,locatedinthehabitablezone,dp=1AU.Using=0:4,Equ. 1{2 yieldsC41010.Morecarefulcalculations,thatincludespectralfeaturesandareasonablebandpass,ndC21010( DesMaraisetal. 2002 ),asisnominallyquoted. Measurementofanyquantitytoanaccuracyof1partin1010requirescompensationforavarietyofsubtleeects.Acomparisontoexperimentalresultsforthevaluesoffundamentalphysicalconstantsplacesthenumberintocontext:themassoftheelectron,Boltzmann'sconstant,Newton'sgravitationalconstant,Planck'sconstant,andtheelementarychargehaverelativeuncertaintiesof4:9108,1:7106,1:0104,5:0108,2:5108respectively(NationalInstituteofStandards{http://www.nist.gov/).Oneofthemostimportantandreliablymeasuredquantities,thenestructureconstant,,hasarelativeuncertaintyof6:81010.Itsvaluewasmostrecentlydeterminedbycomparingtheresultsfromaone-electronquantumcyclotrontoaQEDcalculationinvolving891eighth-orderFeynmandiagrams( Gabrielseetal. 2006 ).Theanalogyisnotwithoutaw,butrightfullyconveysthemessagethatimaginganEarth-likeexoplanetisnon-trivial.Jupiterwouldbetheeasiestplanettodetectifthesolarsystemweretargetedbyadistantobserver,butitisstillafactorof109timesfainterthantheSuninthevisible(Fig. 1-2 ). 21

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SmithsonianAstrophysicalObservatorycodemodelofthesolarsystemasseenfrom10pcs(from DesMaraisetal. ( 2002 )).Contrastisfoundbycomparingthestellaruxtoplanetuxinaparticularwavelengthrange,where`J'isJupiter,`V'isVenus,`E'isEarth,`M'isMars,and`Z'isthezodiacaldustcloud.Importanttrade-osexistbetweenrequiredsensitivity,spatialresolution,atmosphericcorrection,andbackgroundnoisewhenconsideringthebandpassofobservations. Instrumentsmustgeneratethesecontrastlevelsatangularseparationssmallerthan1"(4.8microradians)sincethecloseststarsareseveralparsecsaway.Theseconsiderationsessentiallyprecludeground-basedimagingdetectionsofplanetsatshortwavelengthsduetotheblurringeectsoftheatmosphere(seex ),evenintheforeseeablefuture.OnlytheTPF-C(x )orsimilarspace-missioncanbegintoaccessthisobservationalparameterspace. 22

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1-2 ).Recentlabdemonstrationshaveachievedcomparablesensitivities,C=6105,atcloseseparationsusingaTPF-Icandidatedesign( Labadieetal. 2007 ). Anumberofground-basedinstrumentsoperateinthisspectralrange.Theyarediractionlimitedandsomeareevenequippedwithacoronagraph( Telescoetal. 1998 ; Telesco 2007 ; Kasperetal. 2007 ).Nevertheless,exoplanetshaveyettobediscoveredinthemid-IRbecausebrightthermalemissionfromtheskycanonlybesubtractedouttoonepartin105atthephotonnoiselimit,e.g.,whenshortexposuresaretakeninanattemptto\freeze"thethermalpatternbeforesubstantialuctuationsoccur.Theskyisroughlyasbrightasa6thmagnitudestarintheL-band( Phillipsetal. 1999 )andbrighterinMandN. Companionssuchas2MASS1207,GQLupi,andABPic,whosenear-IRimagesareshowninthenextsection,maybejustbrightenoughtooutshinethisseaofthermalnoise(Telescoetal.2008,inprep.).MandN-bandphotometrycanplacetightconstraintsontheireectivetemperatureandmass.However,onlytheyoungestandmostmassiveJovianplanetswithlargeorbitalseparationswillsatisfythedetectioncriteriontocircumventthesefundamentallimitations.Ground-basedimagingatinfraredwavelengthslongwardsof5mcanthusplayonlyaminorroleinextrasolarplanetdirectimagingdetectioninthenear-term.Thestudyofbrowndwarfs,however,isnotpreclusive. Currentspacemissions,suchasSpitzer( Fazioetal. 2004 ),donothavetherequisitespatialresolution,whichisanissueevenfor8-10mtelescopes.Instead,TPF-IandDarwinwillexploittheadvantagesofthemid-IRusinginterferometry.AswithSIMandTPF-C,theirfundsarelimitedandschedulescurrentlyuncertain. 23

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1-3 ). Contrastlevelsoforder108arerequiredtodetect100MyroldJovianplanets( Burrowsetal. 2004 ; Marleyetal. 2007 ),butmanystellarclusters,associations,andmovinggroupsareyoungerandhostbrighter,moreeasilydetectablecompanions(see Lopez-Santiagoetal. ( 2006 )foranexcellentreference).Forinstance,theexpectedJ-bandcontrastofa1MJupplanetorbitingaK0Vstarat5Myrsand50Myrsisabout1:2105and3:3107respectively( Baraeetal. 2003 ; Girardietal. 2002 ).Theonlyremainingcomplicationisthatyoungstarstendtoberelativelydistant,andlargeaperturetelescopescannotachievethenecessaryatmosphericcorrection(x )without\extreme"adaptiveoptics(AO)systems(x ),whichdonotyetexist. Thenextgenerationofhigh-contrastinstruments,namelyGPI( Macintoshetal. 2006a )andSPHERE( Dohlenetal. 2006 ),whichwillbeginoperationswithinthenextthree-fouryears,willfeaturehigh-actuator-densitydeformablemirrors(x ,x )andcoronagraphscoupledtointegraleldunits( McElwainetal. 2007 ).Near-IRsensitivitiesof107at0.2"areanticipated.Thisissucienttodirectlydetectself-luminousJovianplanets. CurrentAO-coronagraphinstrumentshavegeneratedcontrastlevelsoforder104at0.5"-1.0"separations,withnaleectivesensitivitiesof105followingpost-processing 24

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Atmosphericmodelpredictionsofcontrastvs.wavelengthforvariousages(top)andmasses(bottom)ofJovianexoplanets(from Burrowsetal. ( 2004 )). 25

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Lafreniereetal. ( 2007 ); Nielsenetal. ( 2008 )).Theyhaveplacedtightconstraintsonthepopulationstatisticsofbrowndwarfs(13MJupM80MJup)orbitingsinglestarsatintermediatetolarge(&10AU)separations( Carsonetal. 2006 ; Metchev&Hillenbrand 2004 )andhaveproducedtherstimagesofcandidateplanetarymasscompanions. Figure1-4. Therstimagesofcandidateextrasolarplanets:(upper-left)2MASS1207from Chauvinetal. ( 2005a ),(upper-middle)GQLupifrom Neuhauseretal. ( 2005 ),(upper-right)ABPicfrom Chauvinetal. ( 2005b ),(lower-left)SCR1845from Billeretal. ( 2006 ),and(lower-right)UScoCTIOfrom Bejaretal. ( 2008 ). )istoointenseandcannotbeproperlymanagedwithoutsimultaneouslyattenuatingthecompanion. 26

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Directimagingtradeoswithbandpass VisibleNear-IRMid-IR bandpass(m)0:50:81:02:5520IWAa(mas)62193387,773,1547contrastneeded<109<107<105AOcorrectionnotfeasible\extreme"AOlow-orderAOactiveopticsbprecision<1Aprecision<1nmlow-ordercorrectionskybackgroundnegligiblemanageablelimiting(exo)zodiacallightfaintmoderatebrightterrestrialspacespacespaceJovianspaceground/spacespacec aInner-working-angle(IWA)isdenedhereas3max=D,whereD=8m.Themid-IR IWA'sareformax=5,10,and20mrespectively. ).Valuesarequotedforspaceapplications. 1-5 .Itisclearlynotanoptimaldirectimagingpoint-spreadfunction(hereafter,PSF):thecontrastat3=Dis1:4103.AcoronagraphcansuppresstheAirypatternwhileecientlypassingo-axislight.Entranceapertureswithcentralobstructionsandsupportstructurescomplicatetheissuebyrequiringmorerestrictivestopstoblockdiraction,resultinginthroughputlosses.Forthisreason,thebaselinedesignforTPF-Cincorporatesano-axisprimarymirror( Fordetal. 2006 ).Chapter 6 describesaground-basedapproachinvolvingaclearaperture. InterferometerscancreateaPSFconsistingofverydeepnullsbychangingthephaseoflightinoneormorearms.Thiscircumventstheproblemofbuildingoccultingspotsthathaveaphysicalsizeofseveraldiractionwidths Kasdinetal. 2003 )isaformerTPF-Cdesigncandidate{atleastinthisauthor'sopinion.Itrequiresthattoomuchthroughputbesacricedtobeviable. 27

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Diraction-limitedpoint-spread-functionfromanunobstructedcircularaperture.Thecontrastisinsucienttodetectextrasolarplanets. tradeoisaresultofinterference,whichformsthebasisfordiraction.Themathematicsforunderstandingcoronagraphy(x )aresimilartohigh-contrastinterferometry;incoronagraphy,however,themultiple(virtual)dishescanoverlap. Phaseerrorsresultfromtemperatureuctuationsintheatmosphere(whichleadtochangesintheindexofrefraction)andthesurfaceroughnessofopticalcomponents.Atmosphericphaseerrorschangeonamillisecondtimescaleandhavealargeramplitudethanthesystematicsproducedbytelescopeandinstrumentoptics.Leftuncorrected,bothsourcescanlimitsensitivitiesatthe103level. 28

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). Wavefronterrorsmanifestasspecklesintheimageplane.Onecangainanintuitionfortheirformationfromthefollowingexample.Consideracomplexeldpassingthroughaone-dimensionaltelescopeentranceaperturegivenbyA(u)whereuisthephysicalcoordinateandhasunitsofD=.Assumethatthephaseaberration,(u),consistsofasinglesine-waverippleoffrequencyfcyclesperapertureandamplitudeainradians.Theelectriceldinthepupilplaneis: whereA(u)isatop-hatfunction, Forsmallaberrations(a<<1)wecanexpandtheexponentialandkeeptherstterm,ei(u)1+iasin(2fu).IntheFraunhoferorfar-elddiractionregime( Hecht&Zajac 1974 ),theelectriceldintheimageplaneisfoundbytakingaFouriertransform,FTf:::g: ^E(x)=FTfE(u)g=FTfA(u)g((x)a=2[(x+f)(xf)])(1{5) wherethehat,^,denotesanimageplanequantity,istheconvolutionoperator,andxcorrespondstoananglewithunits=D. WenowletFTfA(u)g=^A(x),whichissimplythediraction-limitedPSF,andrecognizethatitiscopiedatthelocationofthethreedeltafunctions,x=0,x=f,and 29

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^E(x)=^A(x)a=2^A(x+f)+a=2^A(xf):(1{6) Anidealcoronagraphwillremovethezero-frequencycomponent,^A(x),butcannoteliminatetheothertwoterms,otherwisethecompanionwouldbeattenuated.Thus,asine-wavephaseripplecreatestwopeaksoflight,orspeckles,atlocationsintheimageplanethatcorrespondtothespatialfrequencyf.Thisformsthebasisforunderstandinghigh-contrastimagingwavefrontaberrationtheory,sinceanygeneralwavefrontshapecanbeconstructedfromofaseriesofsinesandcosines.Adeformablemirror(DM)cansuppressspecklesbyreshapingthephaseofstarlight(Fig. 1-6 ). Figure1-6. Cartoonofasinglefrequency1nmpeak-to-troughphaseerroracrossthetelescopeentranceapertureanda19actuatorDMforconjugation.Thef=3sine-waveaberrationwouldnormallycreate2specklesat3=Dintheimageplane.Instead,thephaseerrorsaresuppressedtoalevelgivenbyhowwelltheDMcanmatchthein-comingwavefrontshape(tting-errors).TheDMsurfaceneedonlybehalfthewavefrontphaseheightduetothereection.Thelightisthensenttothecoronagraph. 30

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MonochromaticspecklesatthedetectorofalabexperimentusingaLyotcoronagraph.Thecontrastisoforder106(x )asisindicatedbytheintensitygray-scaleshowntotheright. Noticealsothatthespeckleintensity,j^Ej2(x ),scalesasa2.Thisrelationhasbeenveriedwithnumericalsimulationsinx .Phaseerrorsoforder1nmlimitcontrastatthe107levelatthecoronagraphIWAinthevisible.Therefore,todetectanEarth-likeplanet,thephaseoflightmustbecontrolledtobetterthan1=p Thephaseamplitudes,a(f),formafrequencyspectrum(x )thatdictatesthespatialdistributionofpowerorenergyintheimage.Thepower-spectraofatmosphericaberrationsdierfromthatoflensesandmirrors,butbothcanbereasonablywell-modeledwithamonotonicallydecreasingpower-laworbrokenpower-lawinf.Inotherwords,morestellarresidualsarelocatedclosetotheopticalaxisthanfurtheraway. Figure 1-7 showsquasi-staticspecklesfromalabexperimentusingacoronagraph( Creppetal. 2006 ).Thecontrastislimitedatthe106levelattheIWA,implyingthatwavefrontphaseerrorsareseveralnanometersinsize.Thiswasveriedexplicitlywithprolometermeasurementsofthesurfaceofthemostcriticaloptic. ImagequalityisoftencharacterizedbytheStrehlratio,S,whichisdenedas, theoreticalmaxpeakintensityofsource<1:(1{7) 31

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TheStrehlratiocanberelatedtothermswavefronterrorbytheMarichalformula, wherermsistheroot-mean-squarewavefronterrorinradians.Ifwesubstituteforrmsthepreviousresultthatthewavefrontmustbecontrolledtobetterthan1=p Guyon ( 2005 )forotherreasons). Atnear-IRwavelengths,theStrehlratioof8-10mtelescopesisoftenlessthan10%withoutwavefrontcorrection.Withcurrentadaptiveoptics(AO)technology,Strehlratiosof40%arepossible.Thisvalueisstillinsucientandservesasthemotivationforthedevelopmentof\extreme"AOandtheworkdoneinChapter 6 Guyonetal. ( 2006 )havecompiledalistofcoronagraphicconceptsthatcan,inprinciple,achieve1010contrastat5=D{theso-called\CoronagraphTreeofLife".Theirabbreviatednamesare:theAIC,CPAIC,VNC,PSC,CPA,PPA,PIAAC,PIZZA,APLC,APLCN,BLM4,BLM8,PM,4QPM,APKC,OVCm,AGPMC,andODC. Guyonetal. ( 2006 )havealsocomparedtheirperformanceonanequalfootingusinga`usefulthroughput'metric.Intheidealcase,theOVC{OpticalVortex( Mawetetal. 2007 ),PIAAC{PhaseInducedAmplitudeApodization( Guyon 2003 ),BLM4{4th-orderBand-limitedMask( Kuchner&Traub 2002 ),andBLM8{8th-orderBand-limitedMask 32

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Kuchner,Crepp,&Ge 2005 )coronagraphsyieldthebestresults.Thedierencesbetweentheirindividualbenetsare:theOVCandPIAAChavesharperPSF's,betterIWA's,andhigherthroughputthantheBLM4andBLM8,andcanthereforedetectmoretargetspertime,butaresignicantlymoresusceptibletolow-orderopticalaberrations(x ,x ,x )andnitestellarsize(x ).Thesepracticaltradeos(whicharestudiedinthiswork),alongwithchromaticityconsiderations,willdeterminethedesignoftheTPF-C(seealso Cash ( 2006 )andx ).TheBLM4andBLM8areuniqueamongstthiselitelistinthattheyarealsousefulfromtheground(x ,x ,x ).They,alongwiththeopticalvortex(phase)mask,arelocatedintheimageplaneoftheLyotcoronagraph,whichisdescribedbelow.TheBLM4andBLM8aredescribedindetailinx TheLyotcoronagraph( Lyot 1939 )controlsdiractionwithacombinationofanimagemaskandaperturestop.Themaskandstopworktogethertosuppresslightfromasourcethatisalignedtotheopticalaxis.Lightemanatingfromano-axissource,suchasadebrisdiskorsubstellarcompanion,entersthecoronagraphatasmallangleandsuersminimalattenuation.Theresultisagainintherelativenumberofphotonsreceivedfromfaintobjectslocatedincloseangularproximitytothestar.Awell-calibratedcoronagraphoperateslikeahigh-passlterandcanimprovesensitivitiesbymanyordersofmagnitude.Figure 1-8 depictsatransmissivedesignwithoutwavefrontcontrol. Therst-orderdiractiontheoryforlightpropagationthroughtheLyotcoronagraphisasfollows:Theelectric-eldattheentranceapertureisgivenby, whereE0isthecomplexeldandu,varepupilplanequantities.Forsimplicity,weassumeherethatnoaberrationsarepresentandsetE0=1.WealsoneglecttelescopeobstructionssothatA(u;v)isjustacircleortwo-dimensionaltop-hatfunction. 33

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OpticallayoutofatransmissiveLyotcoronagraph.Thedesignissimilartoaspectrograph,exceptthereisamaskandstopinsteadofaslitandgrating. Lightenteringthecoronagraphisfocusedontoanoccultingmaskintherstimageplane.Theelectric-eldisthen, ^E(x;y)=^A(x;y)^M(x;y);(1{10) whereM(x;y)isthemaskamplitudetransmissionprole.Themaskintensitytransmissionisj^M(x;y)j2and,typically,M(x=0;y=0)=0. TheelectriceldatthesubsequentpupilplaneisfoundbytakinganotherFouriertransform, ThisequationisthekeytounderstandingLyotcoronagraphy.TheeldattheLyotstopistheconvolutionoftheentranceaperturewiththemaskspatialfrequencyfunction.Inordertogeneratedynamicrange,thelightpatternmustbefaintnearthecenterofthepupilandbrightneartheedges.ThiswaytheLyotstopcaneectivelyremovestarlightwhileallowingmostoftheo-axislighttoreachthedetector. Theeldatthedetectoris, ^Efinal=^L(x;y)^A(x;y)^M(x;y);(1{12) whereL(u;v)^L(x;y)istheLyotstop.Theintensityisj^Efinalj2.Imagesoftheeldatvariouslocationsalongthepathareshowninx 34

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Kuchner&Traub 2002 ).Itdiractsstarlightintospatiallysuccinctregionsthatfollowthecontourofthetelescopeentranceaperture.Thecombinationofaband-limitedmaskandappropriatelyshapedLyotstopcancompletelyremovetheon-axislightfromanopticalsystemwhenitisfreeofaberrations. Equation 1{11 providesthebasisforunderstandingitsoperation.Consideraone-dimensionalcoronagraphwithmonochromaticlightasinx .Weagainmodelthetelescopeentranceapertureasatop-hatinthepupil.Thequestionis:\Whatfunction,orsetoffunctions,whenconvolvedwiththetelescopeentranceaperture,createanidealdiractionpatternattheLyotpupil?"(Fig. 2-1 ). Anexampleofanidealmaskfunctionisonethatplacesallofthestarlightexteriortoacertainregionordistancefromtheopticalaxis.Asimplestop,onethatisopaqueontheoutsideandtransparentinthecenter,canthenblockitallwhilestillpassinglightfromthecompanion.Suchafunctionwouldsatisfythefollowingcriterion, and whereM(u)istheimagemaskspatialfrequencyfunctionand01isadimensionlessparameterthatcontrolsthebandwidth.Thefunctionissaidtobeband-limitedbecauseonlyarangeoflowspatial-frequenciesarepresent.Equ. 2{1 ensuresthatnostarlight\leaks"throughthecoronagraphwhentheA(u)andM(u)functionsoverlapduringconvolution,whileEqu. 2{2 ensuresthesamewhenthefunctionsdonotoverlap. 35

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ConvolvingA(u)withaband-limitedmaskfunctionM(u)producesanoptimaldiractionpatternattheLyotpupilplane( Kuchner&Traub 2002 ).Theresultantelectriceldismultipliedbyanothertop-hat,theLyotstop(notshown),inordertoremoveallon-axisstarlight. ThemaskfunctionshowninFig. 2-1 is (2{3) whereNisanormalizationconstant.TheFouriertransformofEqu. 2{3 givestheamplitudetransmission, ^M(x)=N[1sinc(x)]:(2{4) Band-limitedmasksaregradedmasks.Theirintensitytransmission,0j^M(x)j21(i.e.thepartweactuallybuild),variessmoothlyinopacity.Inbroadbandlight,wedesignthemasktooperateatmax,sinceshorterwavelengthsarediractedoutsidetheLyotstop. Examplesofotherband-limitedfunctionsare:^M(x)=sin2(x=2),1sincn(x=n),wherenisaninteger,and1J0(x).TheygenerallytradeIWAwitho-axisattenuation.Inotherwords,maskswithintrinsicallycloseIWA's,suchasthesin2(::)design,havemore`ringing'(opaqueregions)inthesearcharea.IfisincreasedtoimprovetheIWA,thentheLyotstopthroughputdecreases. Forinstance,considerthelinear1sinc2(x=2)mask.Atwo-dimensionalcoronagraphwithanIWAof4=D,whereIWAistakenasthelocationwheretheintensitytransmissionreaches0:5,wouldhaveaLyotstopthroughputof64%.Otherband-limitedmasks,suchastheradialdesign,^M!^M(r),andseparabledesign,^M!^M(x)^M(y),arealsoavailable.Theylikewisetradesearchspaceforthroughput. 36

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are\fourth-order"masks:theirintensitytransmissionneartheopticalaxisincreasesasthefourth-powerwithdistance.Itispossibletogeneratehigher-ordermaskfunctions,suchasaneighth-order( Kuchner,Crepp,&Ge 2005 )ortwelfth-ordermask,bycombiningfourth-ordermaskfunctions. Themotivationforthisconceptisthatintrinsicallywidermaskshelplterlow-orderaberrationcontent.Theyarealsomorerobusttopointingerrorsandthenitesizeofstars.Forexample,aneighth-ordermaskwouldallowtheTPF-CtooperatewithapointingaccuracynobetterthanthatoftheHubbleSpaceTelescope,3mas,whereasafourth-ordermaskwouldrequire0:7mas.Thepriceforrelaxingsuchtolerancesisamodestcostino-axisthroughput. Toconstructaneighth-ordermask,weneedtheamplitudetransmissiontermresponsibleforquadraticleakagetoequalzero, ThiscanbeaccomplishedbyaddinganappropriatelyweightedCsin2(k1x)(C=2)(k1x)2functiontoany1sincn(k2x=n)(k2x)2=(6n)function.NoticethattheindividualtermsalsoautomaticallysatisfyEqu. 2{1 and 2{2 .Settingk1=k2wendC=1=(3n).Toensure^M(x)1,werenormalizethemaskbymultiplying^M(x)byaconstant,N. Puttingeverythingtogetherandusingphysicalunitsyieldsaseriesofeighth-orderband-limitedmasks, ^MBL(x)=N3n1 3nsincnx nmaxf+1 3ncosx maxf;(2{6) wherefisthefocalratioatthemaskandmaxisthelongestwavelengthatwhichthemaskistooperate.Figure 2-2 shows^M(x)fortherstfewlinearmasksintheseries. 37

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Eighth-orderband-limitedmaskfunctionsdescribedbyEquation 2{6 forn=15. Wecancreateanotherseriesofeighth-ordermaskswithlesso-axisattenuationbycombiningtwo1sincnmasksusingthesameprocedure: ^MBL(x)=Nlm lsinclx lmaxf+m lsincmx mmaxf:(2{7) Thisseriesisparameterizedbytwointegerexponents,landm;weassumel>m.Figure 2-3 shows^M(x)form=1andl=2{5.Them=1andl=2{3maskshavethroughputsimilartothen=3sin2maskfromabove.Usinglargevaluesofmandlreducesthe`ringing'further,butalsodecreasestheLyotstopthroughput. Figure 2-4 comparestheintensitytransmission,j^M(x)j2,forthe1sinc2fourth-ordermaskandthem=1,l=3eighth-ordermask.Whilethe1sinc2maskhasanIWAof(1:448=)(=D),them=1,l=3eighth-ordermaskhasanIWAof(1:788=)(=D).Them=1,l=3maskoersagoodcompromisebetweenringingandthroughput,andalsoreaches100%transmissionatitsrstmaximum,acriticalregionforplanetsearching.ThismaskdesignisrecommendedfortheTPF-C. 38

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Eighth-orderband-limitedmaskfunctionsdescribedbyEquation 2{7 form=1,l=25. Figure2-4. Intensitytransmissionforthe1sinc2fourth-ordermask,then=3eighth-ordermask,andthem=1,l=3eighth-ordermask.Coronagraphthroughputanddistancefromopticalaxiswerecalculatedwith=0:6.Them=1,l=3eighth-ordermask,recommendedforTPF-C,has100%transmissionatitsrstmaximum. 39

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). 2-1 andEqu. 2{2 revealsthatpoweratmaskspatialfrequenciesjuj>1=2resultsinstarlightbeingdiractedwelloutsidetheLyotstopopening.Masksthatutilizethisdesignfreedomarecallednotch-ltermasks( Kuchner&Spergel 2003 ).Theyneednothavesmoothintensitytransmissionproles.Instead,notchltermaskscanbesampledorbinary,orboth.Inthefollowing,weuseatechniquesimilartotheoneemployedinx tondeighth-ordernotchltermasks( Kuchner,Crepp,&Ge 2005 ).Tobeconsistentwithx ,werefertothevariousdesignsbytheexponentsoftheirconstituentfunctions(n,l,m). Westartwithalinearcombinationoffourth-ordernotchltermasks, ^Mnotch8(x)=Nh^Mnotch4A(x)+C^Mnotch4B(x)i;(2{8) whereNensuresthat^Mnotch8(x)1.TheconstantCisfoundbysubstitutingEqu. 2{8 intoEqu. 2{5 ,where andthederivativesaretakenonlyoverthelowspatialfrequencies(seeKuchner,Crepp,&Ge2005fordetails).Theansweris: where1C0. 40

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Kuchner&Spergel 2003 ): ^Mnotch4(x)=^Msamp4(x)^M0;(2{11) where ^Msamp4(x)=^P(x)^MBL4(x)xXk(x(k+)x)!; and ^M0=ZD=(2)D=(2)Msamp4(u)du=Z1MBL4(u)P(u)du=^MBL4(x)^P(x)x=0:(2{14) Here,MBL4representsanyfourth-orderband-limitedmaskfunctionandkrangesoverallintegers.Thesamplingpointsareosetfromthemaskcenterbyafractionofx.Thekernel,^P(x),canrepresentthe\beam"ofananofabricationtool.ItshouldbenormalizedsothatR1^P(x)dx=1,and^P(x)mustbeeverywhere1=(x),so^Msamp4(x)remains1.Theconstant^M0ensuresthatthemasksatisesEquation 2{1 .Thoughthesampledmaskisderivedfrom^MBL4(x),thefunctionbeingsampledis^MBL4(x)^M0. SubstitutingEqu. 2{11 intoEquation 2{8 wehave ^Mnotch8(x)=Nh(^Msamp4A(x)^M0A)+C(^Msamp4B(x)^M0B)i;(2{15) andusingEqu. 2{13 and 2{14 theconstantCbecomes Wecannowconstructavarietyofeighth-ordernotchltermasksanalogoustothevarietyofeighth-orderband-limitedmasks. 41

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^Mstripe(x;y)=8><>:1wherey<^Mnotch(x)minf0elsewhere:(2{17) Themaskfunctionis ^Mbinary(x;y)=1Xj=^Mstripe(x;yjminf);(2{18) whereministheshortestwavelengthinthebandofinterest.Band-limitedmasksleaklightatwavelengthslongerthanmax,whereasnotchltermaskscanalsoleaklightatwavelengthsshorterthanmin.Inotherwords,thenotchltermaskoperateslikeaband-limitedmasksolongastheopticalsystemdoesnotresolveitsintricatefeatures. Ifwelike,wecanusetheband-limitedmaskfunctionsdescribedbyEquations 2{6 or 2{7 inplaceof^Mnotch(x),resultinginamaskformedofcontinuouscurves.However,sampledbinarymasksmayprovetobeeasiertomanufacturesincetheirfeaturesarenotassmallneartheopticalaxis.ThebinarymaskshowninFig. 2-6 issampled.Itcanbemadeentirelyfromrectanglesofopaquematerialusinge-beamlithography(x ). ThefunctionweactuallysampleisN[(^MBL4A(x)^M0A)+C(^MBL4B(x)^M0B)].Figure 2-5 showsaplotofthisfunctiontoillustratehowmaybechosen.Toguaranteethat^Mnotch(x)0,theparametermustbeintherangejj0,where0isdenedbythecondition^MBL4A(0minf)+C^MBL4B(0minf)=^M0A+C^M0B.Forourbinarymask,wechoose=0,tomakethecentralrectanglescontiguous. 42

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AnexampleofthefunctionN[(^MBL4A(x)^M0A)+C(^MBL4B(x)^M0B)]foranm=1,l=3sampledmask.Choosing=0allowsustocreateabinarymaskofcontiguousstripes.Choosing=0allowsustocreateagradedmaskwiththemostfavorableopticaldensityrequirement. Figure2-6. Simulatedlowandhighmagnicationpicturesofanm=1,l=3lineareighth-ordersampledbinarymask.Darkareasarecompletelyopaqueandwhiteareasperfectlytransmissive.Thehigh-magnicationpicture(right)illustratesthesampling.Seex formicroscopephotographsoflineareighth-orderbinarymasks. 43

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2.3.2 listsnormalizationconstantsandsampledmaskparametersforeighth-ordernotchltermasksofvariousIWA'susingatop-hatkernel,^P(x)=(D=min)(xD=min),and0.5{0.8mbandpass. Iftheresolutionofournanotoolis20nm,werequireatelescopewithanf/115orslowerbeam(see Kuchner&Spergel 2003 ).Thephysicalsizeofanentiremaskisgenerallyafewhundreddiractionwidths.A1"1"maskwouldconsistof&440verticallyrepeatingsegments,whereeachsegmentisminf=57:5mwide.ThiscoronagraphdesignwouldhaveaLyotstopthroughputof40%.Figure 2-6 showsanexampleofwhatanm=1,l=3lineareighth-orderbinarymaskwouldlooklike. Whenwedesigneighth-ordergradednotchltermasks,wecanreducetherequiredmaximumopticaldensitybybeginningthesamplingat=0,solongasoursamplingsizeislargeenoughtostraddlethevalleysshowninFigure 2-5 .Choosingx=minfsatisesthisconditionforallofthemaskslistedinTable 2.3.2 .Figure 2-7 showsagradedversionofthem=1,l=3eighth-ordermaskdescribedinx4.1.Themaskisdenedby^M(x;y)=^Mnotch(x);itsopticaldensityislog10j^Mnotch(x)j2.Tomakethedarkeststripeofthemaskastransparentaspossible,wechose=0.Withthischoice,thedarkeststripeofthemaskhasopticaldensity2log10j^Mnotch(0)j7:882.Table 2.3.2 liststhemaximumopticaldensities(O.D.max)ofsampledgradedmaskswith=0. 44

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Sampledeighth-ordermaskparameters nNaIWA(max=D)^M0A^M0BC0O.D.maxb 20.99992704666730.4870.006320780.01883265-0.341133440.259442287.9690.99996763707840.3660.003577160.01068997-0.337693990.259539138.9690.99999148784350.2920.002279030.00682024-0.336095630.259584829.757 30.99435571692830.5330.005050610.02250740-0.229646710.259412767.8600.99296789800140.4000.002849440.01275232-0.226350500.259522948.8680.99224976435750.3200.001825100.00818418-0.224848790.259574049.649 40.99992050204630.5780.004456060.02640459-0.173845710.259378697.7440.99995902962040.4340.002516290.01499184-0.170652280.259503688.7511.00000664913550.3470.001609750.00961517-0.169196460.259561869.534 21.86578517244530.5570.008256810.01646433-0.505054000.259426807.9231.86209698948440.4120.004529720.00904463-0.502747610.259534568.9771.85623085316150.3340.002980280.00595415-0.501801010.259579209.710 31.4342168716053c0.5960.006308890.01882618-0.339354860.259412797.8821.42955247325040.4470.003556420.01063737-0.336694580.259523078.8901.42734970151450.3570.002270760.00679929-0.335469730.259574409.674 41.31250667296630.6370.005408010.02147409-0.256239970.256239977.8131.30894749703940.4780.003051040.01215389-0.253481520.259510798.8191.30622059872050.3820.001950330.00778076-0.252214080.259566479.603

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Simulatedlowandhighmagnicationpicturesofanm=1,l=3lineareighth-ordersampledgradedmaskwith=0.Thelowmagnicationpicture(left)shows400diractionwidths.Eachstripehasuniformshadingandisfminwide. Insummary,weconcludethateighth-ordermaskscancontroldiractedstarlightwhilesimultaneouslyoeringresistancetotip/tiltandlowspatial-frequencyopticalaberrationscomparedtofourth-ordermasks.Thisisconrmedwithexplicitlabtestsinx .Eighth-ordermasksalsohelptopreventleakageduetothenitesizeofstars,asisshownwithnumericalsimulationsinthenextchapter.GradeddesignscanbefabricatedwithHEBS(High-Energy-Beam-Sensitive)glass,andnotch-ltermaskscanbefabricatedwithHEBSglassorregularglassandadepositionofopaquematerialthatissubsequentlyetchedbyanelectron-beamlithographymachine.Weprovidedexamplesofsampledbinary,smoothbinary,andsampledgradedeighth-ordermasks.Them=1,l=2designisrecommendedfortheTPF-C. 46

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ThisChapterdescribesthetechnologiesassociatedwithaspace-basedinternallyoccultingcoronagraphthatusingband-limitedimagemasks.Quasi-staticwavefronterrorsandscatteredlightremovalarerstbrieydescribed.Then,theperformanceofaTPF-C-likeinstrumentisexaminedasafunctionofstellarangulardiameter. Itisshownthatincoherentlightleakageresultingfromthenitesizeofstarscanbesuppressedbyusingtheeighth-orderimagemasksfromChapter 2 .Thisbenetenablessensitiveimagingmeasurementsofthecircumstellarregionssurroundingnearbyevolvedstars.WediscussthesciencethatsuchobservationscandeliverregardingbothterrestrialandJovianexoplanets. Traubetal. ( 2006 )forareview).Currently,therearetwodierentarchitecturesundergoingfeasibilitystudies:(i)aninternalocculterthatutilizesone(ormore)ofthepromisingdesignsmentionedinx ,and(ii)anexternalocculterdesignthatutilizesadistant,speciallyshaped,star-shadethatcastsadarkshadowovertheentiretelescope( Cash ( 2006 ); Lyonetal. ( 2007 )).Eachhavetheiradvantages. Theinternalocculterallowsforintegrationofallopticalcomponentslocallyintoasingleinstrument,whereastheexternaloccultermustbeseparatedfromitsdetectorby50;000km,hencerequiringasophisticatedorbitaldynamicsscheme.Tomaximizeobservingeciency,theexternalocculterwillalsolikelyrequireatleasttwostar-shades.Whileoneisaligned,theother(s)willtraveltothenexttarget.Theconceptexpendscopiousamountsofenergybutisstilllessexpensivethananyinternaloccultingdesignbynearlyafactorof2,sinceitdoesnotrequireaslargeaprimarymirror.ThesepracticalandbudgetaryconsiderationsalongwiththeintendedscopeofthegeneralastrophysicsprogramwilldecidetheTPF-C'sarchitecture.Hybriddesignsarealsobeingconsidered. 47

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Shaklan&Levine 2007 ),oracloser-instar-shadecouldworkintandemwithaninternaloccultertosavefuel. Anyinternalocculterdesignwillhavetodealwithwavefrontphaseandamplitudeerrorsintroducedbythetelescopeprimarymirrorandsubsequentoptics,suchasbeam-splitters,dichroics,condensers,lters,lenses,...etc.Theeectsofthesesystematicdisturbancesmanifestasslowlyundulating,quasi-staticspecklesintheimageplane(seex )thatchangeonatimescalecommensuratewiththermaluctuations.Suchaberrationsareinherenttoallofthecoronagraphsmentionedinx andunavoidableatthecontrastlevelsrequiredforcircumstellarscience. Speckle-nullingistheactofremovingquasi-staticresidualstarlightfromapre-selectedregionoftheimageplane.Byincludingoneormoredeformablemirrors(DM's)intheopticaltraintoreshapethephaseofstarlight(or,moregenerally,toalterthecomplexeld),asharplydenedregionofdeepercontrastcanbegeneratedoverafractionofthesearcharea.Thesizeofthisso-called\darkhole"isgovernedbythenumberofDMsandtheiractuatordensities.Thistechniquegreatlyimprovesthechancesfordirectdetectionbyproperlyisolatingthecompanion'ssignal. Aswithmostcorrectionschemes,scatteredlightremovalgenerallyreliesuponthreesteps:(i)wavefrontsensing,(ii)wavefrontreconstruction,and(iii)wavefrontmanipulationorcontrol.Thestepsareoftenexecutedinsuccessionandeachmayrequirethedevelopmentofspecializedalgorithmstooptimizetheprocedureforagivenactiveopticssystem.Forinstance,fromspaceitispossibletoperformwavefrontsensingatthesciencecamerasincethespecklelifetimeislongcomparedtoatypicalintegration.Thisapproachrequiresphasediversitytoreconstructtheshapeofthewavefrontbutitminimizesnon-common-patherrors(x )andthenumberofoptics.Ground-basedinstruments,ontheotherhand,mustsensethewavefrontdirectlyinordertokeeppacewiththerapidlychangingeld.Infact,high-contrastimaginginstrumentssuchasGPI 48

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Macintoshetal. 2006a )andthePALM-3k/P1640( Dekanyetal. 2007 )willneedtosensethewavefronttwice,beforeandafterthecoronagraph,inordertogenerateadarkholewhilesimultaneouslycorrectingfortheatmosphere. Figure 3-1 showssimulatedimagesfromacoronagraphoperatingintandemwithasingledeformablemirrorinbroadbandlightaftercorrectionhasbeenapplied.Thedarkhole(hereafter,DH)isthecentralsquareregionsurroundingthestarintheimage.Itsmaximalextent,smax,isrelatedtothenumberofactuatorsacrosstheDMbysmax=(Nact=2)min=Dtel,whereN2actisthetotalnumberofactuators.Theright-hand-sideoftheDHisdeeperthantheleftbecausethissimulationincludesamplitudeerrors,whichbreakthesymmetrybetweenthelocationofspecklesoneithersideoftheopticalaxis(see Borde&Traub ( 2006 )).Amplitudeerrorsmightbecausedbyreectivityvariationsacrossamirrorforexample.Thecomplexeldwasreconstructedontheright-hand-sideoftheDH,sothatisthesidewithoptimalsensitivity. TheDMsurfaceshapeiscalculatedusinganenergyminimizationtechniqueinventedby Give'Onetal. ( 2007 ).Webrieydescribethemethodasitwouldbeusedinpractice.First,theelectriceld(phaseandamplitude)atthedetectorisreconstructedbychangingtheshapeoftheDMseveraltimeswithrelativelyarbitraryphaseripples{sinesorcosinesforinstance.Then,theDMshapeiscommandedtobeatandeachactuatorispokedindividually.Theresultantwaveispropagatedthroughthecoronagraphnumerically(i.e.withacomputermodel)andtheelectriceldatthedetectorisrecordedeachtime.Thisdatacubeofelectriceldsisnallycomparedtotheoriginalelectriceldtoprovidearstestimatefortheactuatorheights.Severaliterationsconvergeupontheoptimalshape. Figure 3-2 showsanimageofa12x12BostonMicromachinesDM.Themaximumsurfacestrokeis1.5m(3mmaxphasecorrection)andtheelectronicsprovide14-bitresolution,correspondingto1.5m/2141Aprecision.Thisdevicewillbeusedinlaboratoryexperimentstotestthetheoreticalpredictionsshowninthenextsection. 49

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Simulatedimagesofa64x64DMandresultingdarkhole.TheDMcompensatesforscatteredstarlightuptoaspatialfrequencyequaltotheNyquistlimit,inthiscasesmax=32min=Dtelawayfromtheopticalaxis.Contrastlevelsoforder1010aregeneratedintheregionontheright.Detailsofthemodelarediscussedinx Figure3-2. BostonMicromachines12x12deformablemirror.ThisdevicehasrecentlybeenintegratedintotheUniversityofFloridacoronagraphictestbed. 50

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Luck&Heiter 2006 2007 ) Tokovinin 2004 ) Iben 1967 ; Iben&Laughlin 1989 ) Giventhisinformation,thereisnoreasontoexpectthatextrasolarplanetswillbeanylessuniqueorcomplexthanthesatellitesofoursolarsystem. 51

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Inadditiontosinglemain-sequencestarsofintermediatespectral-type,whichcomprisethecanonicallistofhigh-contrastimagingtargets,evolvedstars,binaries,andM-dwarfsoeravarietyofenvironmentsfortestingtheoriesofplanetaryscienceandotherpromisingavenuesinthesearchforlife( Lopezetal. 2005 ; Haghighipour&Raymond 2007 ; Tarteretal. 2007 ).Themotivationforobservingthemstemsfromtheirstatisticalsignicance:allstarswilleventuallyevolveoofthemain-sequencetobecomegiants;binariesconstituteapproximately50%ofallstellarsystems( Duquennoy&Mayor 1991 );andM-dwarfsrepresentapproximately75%ofallstarsintheGalaxy( Henry 2004 ).Moreover,recentradialvelocity,transitphotometry,andastrometricobservationshavealreadyprovidedstrongevidencefortheexistenceofplanetsineachcategory( Johnson 2007 ; Bonlsetal. 2007 ; Mugraueretal. 2007 ,andreferencestherein). Inthissection,itissuggestedthathigh-contrastimagingobservationsofdierenttypesofstarsismorethanjustacompellingnotion.Thediscussionfocusesprimarilyonevolvedstars(luminosityclassesIV-I),theirhabitablezones,andtheinterfacebetween\point"sourcesandresolvedsources.Assuch,calculationsofachievablesensitivityasafunctionofstellarangulardiameterareprovidedforoneoftheleadingTPF-Cdesigncandidates.ItisshownthataLyotcoronagraph( Lyot 1939 )withwavefrontcontrol( Trauger&Traub 2007 )andaccesstoanassortmentofband-limitedimagemasks( Kuchner&Traub 2002 ; Kuchner,Crepp,&Ge 2005 )canhandleadiverseset 52

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).Lossesinspatialcoherenceduetothenitesizeofastar,whosesurfaceiscomprisedofmanyindependentlyradiatingelements,canthereforeresultinlightleakage.Thisplacesafundamentallimitationonacoronagraph'ssensitivity. Manynearbystarssubtendanappreciableangleontheskycomparedtothespatialresolutionofalargeopticaltelescope.Evolvedstars,inparticular,haveintrinsicallylargeradiiandmaybeseveral=Dtelinwidth,eventhoughtheytendtobesomewhatmoredistantthantheclosestmain-sequencestars.Forinstance,Betelgeuse,thelargeststarintheNorthernsky,D=55mas,illuminatesan`areaofcoherence'( Born&Wolf 1999 )thatissmallerthantheprimarymirrorwithwhichTPF-Cmayoperate{only2.3mindiameterwhenobservedinquasi-monochromaticlightcenteredon=0:55m.Forcomparison,astarofradiusR=6:961010cmlocatedat10pcswouldcoherentlyilluminateanareaofdiameter138m.Aninterestingregimeliesbetweenthesetwovalueswhere:(i)thestarsaremarginallyresolvedand(ii)theirhabitablezonesareextendedbutexpandingatarateslowenoughtoprovidesucienttimeforlifetodevelopandproliferate. ). 53

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Lopezetal. ( 2005 )hasshownthattherearetwoerasofpost-main-sequenceevolutionwherehospitableconditionsmaypersist.Theyoccurduringthesub-giantandhorizontalbranches.Terrestrialplanetsorbitingasolarmassstarinthe2-9AUrange,beforetheHeliumash,and7-22AUrange,aftertheHeliumash,mayhavemoderateclimatesfor108109years. LifeemergedontheEarthwithintherst109yearsafterformation( Lazcano&Miller 1996 ).However,progresswashinderedbyfrequentasteroidalimpacts.Lifemayhavebeenextinguishedseveraltimes,evenaslateas800millionyearsafterformation( Mayer&Stevenson 1988 ).Thisraisesthequestionofwhetherlifecanarisesignicantlyfasterunderquiescentconditions,suchasthoseprovidedbyanolderplanetthatismemberofamoredynamicallyinactivesystem.SpectroscopicmeasurementsofterrestrialplanetsorbitingevolvedstarsatseveralAUcanhelptoconstrainthistimescale. Moredistantplanetswill,dependingontheiralbedoandradius(see Seageretal. ( 2007 )foradiscussionofsuper-Earths),generallybefainterthantheEarth-Sunsystem(contrast21010;x )inreectedlight.Acoronagraphcan,however,accommodateforthiseectbysacricingspatialresolution.Observationsatlongerwavelengthsdecreasestheintensityofquasi-staticspecklesbyafactorof(=0)2inthesearcharea.Anotheroptionistoincreasetheinner-working-angle.Withaband-limitedmaskdesign,thisresultsinhigherLyotstopthroughput,whichincreasestheamountofcompanionlight,decreasesintegrationtime,andmakesthepoint-spread-function(PSF)morespatiallysuccinct. Figure 3-3 showshowthehabitablezonescaleslinearlywithstellarangularsize,arelationshipthatcanbederivedfromtheStefan-Boltzmanlaw.MembersoftheTPF-C 54

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Lopezetal. ( 2005 ),andsourcesfrom Ochsenbein&Halbwachs ( 1982 )withlargeangulardiameters,whichweredirectlymeasuredusinginterferometry,areincludedintheplot.Thehabitablezonesofseveraldozenevolvedstarsareaccessibleinthenear-IR.Thisisalower-limittothenumberofpotentialtargetssincethelistisonlyrepresentativeandnotcomplete.Thehabitablezoneofsuper-giantstars,suchasBetelgeuseandRDoradus,maybeaslargeasanarcsecond,buttheyarelikelytooyoungforlifetodevelop.Discovery-classmissionsthatemployasmallaperturecannotaordfurthersacricesinspatialresolutionbutwillbecapableofdetectingJovianplanetsorbitinggiantstarsatvisiblewavelengths. Figure3-3. Innerandouter-edgeofthehabitablezonefornearbystars.Targetswithalargeangulardiameterleaklightthroughacoronagraph(x )butalsohavemoredistanthabitablezones.Observationsinthenear-IR,orwithacoronagraphhavingalargerinner-working-angle(IWA),improvesensitivityattheexpenseofspatialresolutionandpermitthedirectdetectionofterrestrialplanetsorbitingatseveralAU.TheIWA'sshownareforan8mtelescopeoperatingat4=Dtel.Torstorder,theratioofthehabitablezoneouter-edgedistancetotheinner-edgedependsonlyonthetemperatureofwater,HZouter=HZinner(373K=273K)2=1:87. 55

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Johnsonetal. 2008 ),whichrotateslowlyandhavesharpspectralfeatures.Preliminaryresultshavealreadyrevealedcorrelationsbetweenstellarmassandplanetproperties.Forinstance,moremassivestarstendtoproducemoremassiveJovianplanetsinwiderorbits( Johnson 2007 ). Anexampleofsuchasystemwithaknownexoplanetisthebright(V=1.15)K-giantGem(POLLUX).RVobservationsspanningnearly25yearsareconsistentwiththepresenceofanMsini=2:6MJupplanetwithasemi-majoraxisof1.6AU( Hatzesetal. 2006 ).GemisaK0IIIstaratadistanceof10.3pcswithanangulardiameterof7:960:09mas( Nordgrenetal. 2001 )andmassof1:70:4M( AllendePrieto&Lambert 1999 ). Aspace-baseddirectimaginginstrumentwillbecapableoffullycharacterizingsuchplanets.Moreover,theirorbitwillalreadybedeterminedandthespectrawillhaveahighsignal-to-noiseratiocomparedtoterrestrialplanets.Asthesampleoftargetstarsonthehigh-mass-endofthestellarspectrumgrows,wewillacquireabetterunderstandingoftheplanetformationprocess.Inthefollowing,weexplorethechallengesofgeneratingsucientsensitivitytodetectplanetsorbitingpartiallyresolvedstars. 56

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Primarymirrorphaseerrorsfollowabrokenpower-lawpower-spectral-density(PSD)givenby: PSD(k)=A0 whereA0isaconstantwithunitsm4,kisthespatialfrequency,k0=4cycles/m,andn=3.ThisisthePSDtypicalofan8mprimarymirror( Shaklan&Green 2006 ; Borde&Traub 2006 ).Themirrorsurfacegureisscaledtohaveanrmsvalueof1nm(2nminwave-frontphase).Amplitudeerrorsaremodeledaswhitenoisewithanrmsof0:005andmaximumvalueofunity.Wedonotincludescatteringfromotheropticsinthepathotherthantheglassontheimagemask. Maskdefectsareincludedbecausedierentsectionsofthestellarsurfacefallontodierentlocationsintheimageplane.Thesenon-common-patherrorslimittheachievablesensitivitysincetheycannoteachbecompensatedforsimultaneously;correctingforonemayamplifyanother.Theimperfectionsaremodeledasuncorrelatedphaseerrors,e.g.theworstcasescenario. Weuseboth4th-orderand8th-orderlinearband-limitedmaskstomakeacomparisonstudysincetheyhavedierentresistancestostellarsize.Theiramplitudetransmissionsfollowsinc(::)2andm=1,l=2prolesrespectively(seex fordetails).Thedefaultinner-working-angleis4max=Dtel. TheDMisplacedatapupilanditssurfaceisshapedbyasquaregridofactuatorsthatmapperfectlyontotheprimarymirror.TheinuenceofeachactuatorismodeledwithaGaussianfunctionthatdropsto6%ofitspeakvalueatthelocationofadjacent 57

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3-1 thatdenesthesearcharea.Wesacricecorrectionofthehighestspatialfrequencies,30-32cyclesperaperture,toimprovecorrectionofthelower-ordermodes,furtherreducingtheintensityofspecklesclosetotheopticalaxis.Asmallersearchareacanyieldevendeepercontrast,suchasisdoneattheHCIT( Give'onetal. 2007 ),butherewearealsointerestedindistantplanets.ThesensitivityislimitedbyDMttingerrors. WecalculatetheoptimalDMshapeusingthelinearenergyminimizationalgorithmdevelopedby Give'Onetal. ( 2007 ).Thetechniqueisquitegeneralandreliesuponaccuratemodelingofthecoronagraph,electric-eldreconstructionatthesciencecamera,andaformofphasediversitytosolvefortheactuatorheights.Theprocedureisecientoncearathercomputationallyexpensivemetric,the\G-matrix",isestablishedfortheopticalsystem.Itneedscalculatingonlyonce,unlesschangestothecoronagrapharemade.Inthischapter,weuseseveraldierentcoronagraphs,ofdierentorder,bandpass,inner-working-angle,andsizeofmaskphaseerrors,sohadtoutilizemultipleprocessorsinparallel(butwithnomessagepassinginterface).TheoptimalDMshapeisfoundusingonlythecentral(on-axis)portionofthestar.Thesurfaceisthenxed{aDMcannotcompensateforstellarsize{andcontrastismeasuredasafunctionofangulardiameter. Sensitivitycalculationsuseinformationfromasingleimage.Theinstantaneouscontrast,C,isfoundusingtheformulain Green&Shaklan ( 2003 ), Shaklan&Green ( 2005 ),and Creppetal. ( 2007 ),whichweshowhere: whereI(x;y)istheintensityatthecoordinates,(x,y),inthenalimage,I(0;0)isthepeakstellarintensityaswouldbemeasuredwithouttheimagemaskintheopticaltrain,andjM(x;y)j2isthemaskintensitytransmission.BothI(x;y)andI(0;0)aremeasuredwiththeLyotstopinplace.Alinearmaskhasnodependenceony.Wedonotmodelthe 58

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3-4 .ThesmallestandlargesttargetsfromtheTPF-CTop100listandthelargeststarinthesky,RDoradus,areshownforcomparison.Theupperhorizontalaxisofeachplotalsoindicatesthecharacteristicangulardiameterofavarietyofstarsplacedat15pcs. ThetoppanelofFig. 3-4 showshowthe8th-ordermaskhasahighertolerancethanthe4th-ordermasktostellarangularsize.Thisresultmakesintuitivesensesincethe8th-ordermaskislesssusceptibletotip/tilterrors(x 4 5 ).Bothmasks,however,leakdiractedstarlightbeforethestellarsurfacesarefullyresolved:0:55m/8m=14.2mas;0:75m/8m=19.3mas;2:25m/8m=58.0mas. ItisevidentthatthesensitivityimprovesatlongerwavelengthsaccordingtothescalingrelationC/(0=)2.Forsmallstars,theinstantaneouscontrastinthenear-IRisanorderofmagnitudedeeperthaninthevisible,attheexpenseofafactorof3-4inspatialresolution.Thistrade-oiswelljustiedforevolvedstarswithextendedhabitablezones.Therelativeimprovementgrowstoseveralordersofmagnitudewithfurtherincreasesinangulardiameter. WealsonoticethatthelargestTPF-CTop100Listcandidatetargetrequiresan8th-ordermaskinthevisible.Onemightguessthatastarwithanangulardiameterof8.6masisnearthelower-endoftheprioritylist;however,thisstarisranked#1.ItisCentauriA. 59

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Physicalparametersforthe5GyroldCentauritriplesystem.Thethirdcomponent,ProximaCentauri,isadistantMdwarfthatappearstobeweaklybound(Wertheimer&Laughlin2006).TheTPF-Crankiscurrentlydenedbytherst-visitcompletenessperintegrationtime(http://sco.stsci.edu/starvault/).CenABC Spec.TypeG2VK1VM5.5Vvmag-0.011.3511.1mass(M)1.110.930.12radius(R)1.240.870.15luminosity(L)1.600.450.0002[Fe/H]0.220.26-1.00a(AU)23.423.412,000e0.520.52?i79.2o79.2o?diameter(mas)8.66.01.0TPF-CRank#1#2{ InadditiontotheusualreasonsfortargetingtheSun'sclosestneighbor,d=1:35pcs,theCentauriABsystemoersauniquetestinggroundforplanetformationtheories.Dependingontheorbitalphase,thestarsmaybeseparatedby11.2-35.6AU.Currently,itisnotclearwhetherthepresenceofanintermediatelyspacedstellarcompanionpromotesorinhibitsformation,andtheanswerlikelydiersforterrestrialplanetscomparedtoJovianplanets.Theleadingtheoriesof\core-accretion"( Lissauer&Stevenson 2007 ; Pollacketal. 1996 )and\gravitationalinstability"( Durisenetal. 2007 )mustaccountforthisextrasourceofradiationandgravitationalperturbations.Thus,high-contrastimagingobservationsofCentauriABmayhelptodiscriminatebetweenthetwo.Indeed,numericalsimulationsindicatethatplanetsinthehabitablezone,shouldtheyformintherstplace,canremainstableprovidedtheinclinationanglebetweenthestellarandplanetaryorbitalplanesisnotlarge( Quintanaetal. 2007 ).Table 3-1 liststheCentaurisystemparameters. ThebottompanelofFig. 3-4 compares8th-ordermaskswithdierentsurfaceerrors,rms=0:5,2:3,and5:0nm.An8th-ordermaskwithanIWAof7.27max=Dtel=150 60

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Increasestothesizeofmaskerrorsscattersmorelightintothedarkhole.Therelationshipobeysasimilarquadraticdependence,C/(rms=rms0)2,aswiththesizeofprimarymirrorphaseerrorsandwavelength.Noticethatthe0.5nm!2.3nmcasedoesnotscaleaccordingtothisrelation,becausetheprimarymirrorphaseerrors,surfacerms=1.0nm,dominate. Diractedlightfromthemutuallyincoherentsourcesonthestars'surfacequicklydegradecontrastwhentheangulardiameterexceeds10mas.ThesystemwithIWA=7:27max=Dtelpassesmoreplanetlightandisalsolesssusceptibletostellarsize.ChangestothetelescopediameterslidethecurvesinbothgraphshorizontallyifweneglectdierencesinthemanufacturingprocessesthatchangethePSDandthusthespecklepattern. Table 3-2 displaysaseriesofhigh-contrastimagesforthreenearbystarsofincreasingangulardiameter.Thecurrentinnerandouter-edgeofthehabitablezoneforeachisoverlaidforreference.Onlyhalfofthedark-holeisaccessiblesinceweincludeprimarymirroramplitudeerrorsandonlyonedeformablemirror( Borde&Traub 2006 ).Thegray-scaleisonalogarithmicstretchandindicatesthevalueofI(x;y)=I(0;0). TheimagesqualitativelyverifytheresultsfromFig. 3-4 .Starlightleakageisaseriousproblemforthe4th-ordermaskinbothvisiblebandpasses,whereasthe8th-ordermaskisabletosuppressthelightfromextendedsourcestomoreacceptablelevels.Sacricingspatialresolutionbyconductingobservationsinthenear-IRprovidesasubstantialimprovementindark-holedepthandresistancetostellarsize.EquippingtheTPF-Cwithanear-IRcameracanincreasethesignal-to-noiseratioofspectra,enablethedetectionofmoredistantplanets,andcomplementvisiblelightobservations. Theseconsiderationsalsosuggestthatnear-IRobservationsmaybemoreappropriateforaccessingthehabitablezoneoftheTPF-C'shighestprioritytarget,CentauriA. 61

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TPF-Cstellarangulardiametersensitivityforan8mtelescope.Thecharacteristicsizeofvariousstarsplacedat15pcsareshownacrossthetopaxisforreference.RDoradusisthelargeststarinthesky.ThelargestTPF-CTop100star,Centauri,alsohasthehighestpriority.Trianglesrepresent=0:70:8mdata.Toavoidconfusionbetweencurves,thenear-IR4th-ordermaskresultisnotshown. 62

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High-contrastimagesofstarswithlargeangulardiameters.Thegray-scaleisonalog-stretchandshowsthevalueofI(x;y)=I(0;0).D=8:6masD=11:6masD=26:0mas 4th-order 63

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3-5 illustratesthetechnique. Figure3-5. PSFsubtractionenablesunambiguousdetectionofplanetsthatarefainterthantheinstantaneousnoiseoor. OurPSFsubtractionmodelcombinesimagesthatdierbyasmallrole-anglethroughwhichthetelescoperotates.Sincethewavefronterrorsareproducedsolelybythetelescopeandinstrumentoptics,thespecklepatternrotatesbythesameamount.Companions,however,donotmove.Whentheimagesaredierenced,thespecklescancelandcompanionsgeneratetwocharacteristicspots,onedarkandonebright,thatareseparatedbytherole-angle.Thetechniquereliesonthestabilityoftheenvironment. 64

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Weaddedtwosourcesofrealisticnoisethatlimitthesubtractionofscatteredlightfromwithinthedark-hole.Therstandmostconsequentialaectisthermalchangestothesystemthatoccurduringandinbetweenexposures.Theyweremodeledbyaddinglow-orderaberrationstothepreviouslyoptimizedwavefront.Equalcontributionsfromtherst10Zernikemodeswerecombinedtoformawavefrontthatdieredby10picometersrmsinphase.Wealsoadded5e-/pixelofrmsreadnoisetoeachimage. Fig. 3-5 demonstratesthedetectionofaterrestrialplanetthatis31011timesasbrightasitshoststarinthe=0:70:8mband.Theseparationis6max=Dtelandan8th-ordermaskwasused.Thestarhasanangulardiameterof0.709mas{themedianvalueofTPF-CTop100Listtargets.Theplanetisnotdetectableinasingleimageusingtheseparameters. WealsoperformedPSFsubtractionwithlargerstars.Thepurposeoftheexperimentwastodeterminewhetherthespecklenoiseoor,whichispresumablysmootherforresolvedsources,canbesubtractedoutwithhigherprecision.Wendthattheimprovementisnegligiblysmall,oforderafewpercentforanDtel8mprimarymirrorinthevisible. 65

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Ourresultsshowthatafourth-ordermaskleaksstarlightfortheTPF-C'shighestprioritystar,CentauriA.Observationswithan8th-ordermaskgeneratesucientlevelsofcontrastforthisstarandevenlargertargets.However,theouter-edgeofthedark-holegeneratedbya64x64DMtruncatescriticalregionsofthesearcharea.Near-IRobservationscanhelpremedythesituation;theywouldalsoprovidecomplementaryspectra,increasethesignal-to-noiseratioforcharacterization,andquitenaturallyenablestudiesofdistantterrestrialplanetsorbitinggiantstars. 66

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Asadaptiveopticstechnologycontinuestoimprove,thestellarcoronagraphwillplayaneverincreasingroleinground-basedhigh-contrastimagingobservations.Thoughseveraldierentimagemasksexistforthemostcommontypeofcoronagraph,theLyotCoronagraph,itisnotyetclearwhatlevelofwavefrontcorrectionmustbereachedinordertogain,eitherinstarlightsuppressionorobservingeciency,byimplementingamoresophisticateddesign.Inthischapter,wemodelimageplaneLyot-stylecoronagraphsandtesttheirresponsetoarangeofwavefrontcorrectionlevels,inordertoidentifyregimesofatmosphericcompensationwheretheuseofhard-edge,Gaussian,andband-limitedimagemasksbecomesobservationallyadvantageous.Todelineateperformances,wecalculatethespecklenoiseoormeanintensity.Wendthatapodizedmasksprovidelittleimprovementoverhard-edgemasksuntilon-skyStrehlratios,S,exceed0:88Sqs,whereSqsistheintrinsicStrehlratioprovidedbytheopticalsystem.Abovethisvalue,4th-orderband-limitedmasksout-performGaussianmasksbygeneratingcomparablecontrastwithhigherLyotstopthroughput.Belowthislevelofcorrection,hard-edgemasksmaybepreferentiallychosen,sincetheyarelesssusceptibletolow-orderaberrationcontent.Theuseofhigher-orderband-limitedmasksisrelegatedtosituationswherequasi-staticresidualstarlightcannotbesucientlyremovedfromthesearchareawithspeckle-nullinghardware. 67

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Lyot 1939 ),isincapableofreachingitspeakperformancewhencoupledtostate-of-the-artAO( Oppenheimeretal. 2004 ). Numeroushigh-contrastobservationshavebeenconductedusingAOontheworld'slargesttelescopes( Maroisetal. 2006 ; Mayamaetal. 2006 ; Itohetal. 2006 ; Carsonetal. 2005 ; Closeetal. 2005 ; Metchev&Hillenbrand 2004 ; Debesetal. 2002 ; Liuetal. 2002 ,andreferencestherein);somerelysolelyonAOimaging,whileotherscombineAOwithcoronagraphy Chauvinetal. 2005a ),aswellasdirectdetectionsofsub-stellarcompanionsneartheplanet-browndwarfboundary( Billeretal. 2006 ; Neuhauseretal. 2005 ; Chauvinetal. 2005b ),asshowninx .However,toimageolder,less-massive,andcloser-incompanionsfromtheground,wavefrontsensingandcorrectiontechniquesmustimprovesubstantially. \Extreme"advancesinhigh-contrastimagingtechnologyareanticipatedinthecomingyears.Deformablemirrorsemployingseveralthousandactuatorsandwavefrontsensingoflaserguidestarscan,inprinciple,driveStrehlratiosabove90%on8-10mclasstelescopes.Withthepropercoronagraph,thesesystemswillbecapableofdetectingthenear-IRemissionofJovianplanetsoverabroaderrangeofages,masses,andseparations( Macintoshetal. 2003 ).ExtremelylargetelescopessuchastheproposedThirtyMeterTelescope(TMT)( Macintoshetal. 2006b ; Troyetal. 2006 ; Ellerbroeketal. 2005 )and100mOverWhelminglyLargetelescope(OWL)( Brunettoetal. 2004 )willimprovespatialresolution,andhencetheinner-working-angle(hereafterIWA)onthesky. Aninterestingandmoreimmediatealternative,whichusescurrentAOtechnology,canalsoprovidehighlycorrectedwavefrontsbyinsteadsacricingspatialresolutionin Absiletal. 2006 ; Serabynetal. 2005 ). 68

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Serabynetal. ( 2007 )havedemonstratedK-bandStrehlratiosapproaching94%byreimaginga1.5mdiametercircularunobstructedsubapertureoftheHale200-inchtelescopeontotheexistingdeformablemirrorviarelayoptics.CombiningthistechniquewithacoronagraphthathasanintrinsicallysmallIWA(<3=D)showspromiseforgeneratingdeepcontrastforseparationsascloseas0:5"(x ). Theseconsiderationsmotivatetheneedforaquantitativeunderstandingofhowthestellarcoronagraph'sutilitywilldependonfuturegainsinAOprociency.Toaddressthistopic,wehavemodeledsystemsthatareequippedwithavarietyofamplitudeimagemasks,andexaminedtheirperformanceinabroad,nearlycontinuousrangeofcorrectedwavefrontlevels.Inessence,weseektoprovideaconciseguidetotheuseofLyot-styleimageplanecoronagraphs.Mostnotably,weanswerthequestion:\WhatistheappropriatechoiceofimagemaskforanextremeAOsystemoperatingatagivenStrehlratio?". Maskperformancesarecomparedbycalculatingthedirectoutputofthecoronagraph,i.e.themeanintensity,withtheunderstandingthatdierentialandpost-processingtechniquescanalwaysbeusedontopofdirectimagingtoimprovetheprospectsfordiscovery. Carsonetal. ( 2005 ).ThecodeisoptimizedtosimulatetheoperationofPHARO( Haywardetal. 2001 )withthePALAOsystem( Troyetal. 2000 )ontheHale200-inchtelescopeatPalomar. 69

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).Theneteectisoftensimplyalossino-axisthroughput,astheLyotstopsizeisnecessarilyreducedtorejecttheadditionaldiractedstarlight. Abeetal. ( 2006 ), Sivaramakrishnan&Yaitskova ( 2005 ), Sivaramakrishnan&Lloyd ( 2005 ), Soummer ( 2005 ),and Murakami&Baba ( 2005 )discusstheprospectsforLyotcoronagraphywithnon-trivialentranceaperturegeometries.Weuseacircularunobstructedentranceaperture,radialimagemask,and(hence)acircularLyotstop. Kolmogorovphasescreensmimictheeectsofatmosphericturbulence,whereaxedFriedparameterof20cmat2.0microns,whichhaspreviouslybeenfoundtobestmatchactualPHAROdata( Carsonetal. 2005 ),isusedthroughout.ToemulateAOcorrection,thephasescreensareFouriertransformed,multipliedbyaparabolichigh-passlter( Sivaramakrishnanetal. 2001 ; Makidonetal. 2005 ),andtheninverse-transformed.Improvingthedegreeofwavefrontcorrectionisaccomplishedbyincreasingtheactuatordensity,which,inturn,raisesthecriticalfrequencyofthehigh-passspatiallter.Thelinearnumberofactuatorsacrossthepupilrangesfrom35to94(962to6939totalactuators).Intermsofroot-mean-square(rms)residualerror,thisprovidesarangeincorrectionfrom=13to=30. TheresultingAO-correctedwavefrontsarethensenttoaseparateMATLABcoronagraphcodeforanalysis,wherethestarlightpassesthroughaseriesofconsecutivepupilandimageplanes.Weassumeidealizedinteractionswiththeopticalelementsandtheimagemask(i.e.noscatteredlight,dust,fabricationerrors,...etc.),andusescalardiractiontheorytocalculatethepropagationoftheelectriceld.Thetelescopepupil 70

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Wedonotexplicitlysimulatespeckle-nullingontopofatmosphericcorrection.Instead,inx andx ,weassertthatthequasi-staticaberrationsarecompensatedfortothelevelofthenoiseoormeanintensitysetbydiractionandtheatmosphere,foragivenAOactuatordensity.Speckle-nullingisdiscussedmoreindepthinx .ThisassumptionisjustiedgiventheHCITlaboratoryexperimentsatJPLthatdemonstrateremovalofresidualstarlighttocontrastlevelsbelow109withinthefractionalsearcharea;although,inpracticemoretimelymethodsforndingtheoptimalshapesoftheextraDMs(preferably<1minute)willneedtobeemployed. Kuchner&Traub 2002 )canperformthebestinprinciple.Intheidealcase,theydiractalltransmittedon-axisstarlightintoanarrowregionsurroundingtheedgesoftheLyotpupil,andleaveanareaofinnitedynamicrangeinthecenter(x ).Moreover,band-limitedmaskswitharbitrarilybroadcentralnullscan Roddier&Roddier 1997 ; Rouanetal. 2000 );although,fullyachromaticdesignsarebeingdeveloped( Mawetetal. 2005 ,e.g.).See Guyonetal. ( 2006 )forareviewofthemyriadofotherdierentcoronagraphicdesignsandhowtheycompareinaspace-basedapplication,suchastheTPF-C. 71

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Kuchner,Crepp,&Ge 2005 ),andhavebeenshowntohelpcombatlow-spatial-frequencyopticalaberrationsinnumericalsimulations( Shaklan&Green 2005 )andinlaboratoryexperiments(x ; Creppetal. ( 2006 )). Weincludeahard-edgemask,aGaussianmask,andband-limitedmasks(hereafter,BLmaskorBLM)with4th-order(sinc2),8th-order(sinc,sinc3),and12th-order(sinc,sinc2,sinc3)intensitytransmissionprolesneartheopticalaxis(Figure1).EachmaskisazimuthallysymmetricanddesignedwithanIWA=4=D,soastomakefaircomparisons.TheIWAisdenedasthehalf-width-at-half-maximumoftheintensitytransmissionprole;forthesemasks,thisvaluediersbylessthan1%fromtheequivalentwidth,whichcanalsobeusedasanalternativedenition( Aime 2005 ).Themasksarenottruncatedintheimageplane;inpractice,itiseasytoincludeenoughresolutionelementssuchthatthiseectdoesnotcontributesignicantlytothenoiseoor.Equationsdescribingthemasksareshownbelow.Theradialcoordinate,r,measuresthedistancefromtheopticalaxis,where~r=rD=.Constants,whichcanbederivedfrom( Kuchner,Crepp,&Ge 2005 ),aregiventofourdecimalsofprecision.Theamplitudetransmissions,M(r),are: (4{1) (4{4) (4{5) +5:2684sinc2(0:9503~r)5:0802sinc3(0:6335~r); 72

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4-2 ).Aqualitativeunderstandingofthecoronagraph'sfunctionalitycanbegleanedbyexaminingthelightdistributionpatternintheLyotpupilplane,sincethetotalamountofrejectedstarlightdependsstronglyontheLyotstopsizeandshape.Forhard-edgeandGaussianmasks,thecontrastislimitedbyresidualdiractedstarlight,whereasthecombinationofaBLMwithamatchingLyotstopcancompletelyremoveallon-axisstarlight,inthisidealcase.Thiscapabilityisseeninthe4th-,8th-,and12th-orderBLMmasknalimageplanepatterns;theyarecomposedentirelyofnumericalnoise. \Degeneracies"incontrastcanoccurhoweverwhenlargephaseerrorsarepresent.Inotherwords,dierentmasksmaygenerateindistinguishablysimilarlevelsofcontrastwhenuncorrectedatmosphericscatteredstarlight,ratherthandiractedstarlight,isthedominantsourceofnoise.Underthesecircumstances,throughput,quasi-staticaberrationsensitivities,andfabricationconsiderationsshouldmoreheavilyinuencethedecisionforwhichmasktoimplementinpractice. Inthefollowingsections,imagemaskperformancesarequantiedintermsoftheseparametersandasafunctionofAOsystemcorrection.Referencestoboththermswavefronterror(WFE),AO,inthepupilplaneandresultingStrehlratio,SAO,intheimageplanearemade.TherelationshipSAO1(2AO)2isvalidinthehighStrehlregime,andisadoptedforourcalculations.Webeginbycomparinghard-edgemaskstotheclassofgradedorapodizedmasksasawhole. Atthispointitisconvenienttodenecontrast,C(r),asitwillbeusedthroughouttheremainderofthetext: ^I(0)jM(r)j2;(4{6) whereI(r)istheintensityattheradialcoordinateinthenalimage,^I(0)isthepeakstellarintensityaswouldbemeasuredwithouttheimagemaskintheopticaltrain,andjM(r)j2isthemaskintensitytransmission.NotethatI(r)and^I(0)arebothmeasured 73

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Sivaramakrishnanetal. 2001 ).Weseektoidentifytherequiredlevelofwavefrontcorrectionabovethisvaluewhereapodizedmasksbegintoout-performhard-edgemasks. 4-2 andresultsfromx helptoclarifywhythisisausefulsimulationcontrol.Contrastcurvesforthehard-edge,Gaussian,and4th-orderBLMsareshowninFigure 4-3 usingseveraldierentlevelsofwavefrontcorrection.Forclarity,higher-orderBLMsarenotincludedhere,butarediscussedinthenextsections.Theyprovideintermediatelevelsofcontrast,betweenthatofthehard-edgeandthe4th-orderBLM. At77%Strehl(rmsWFE==13),theadvantageinusingtheimageplanecoronagraphisevidentonlyforseparationssmallerthan8=D;thisisaresultofthelimitedwavefrontcorrectionandreducedaperturestopintheLyotplane.Moreover,theGaussianand4th-orderBLMsprovideonlyafactorof1:6improvementoverthehard-edgeocculterattheIWA,andcontrastdegeneracysetsinatadistanceof1:5=Dfromthere.AsAOcorrectionimproves,starlightisredistributedfromthescatteredlighthalointotheAirydiractionpattern,thePSF`shoulder'dropsandextends,andthe 74

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TheGaussianand4th-orderBLMs,whichmoreeectivelydiractstarlightontotheopaqueportionsoftheLyotstop,arecapableofgeneratingcontrastlevelsof6106atIWA=4=Dwith94%Strehl.TheyprovideanimprovementincontrastattheIWAoverthehard-edgemaskbyfactorsofapproximately2.7at82%Strehl(rmsWFE==15),5.1at88%Strehl(rmsWFE==18),and21.7at94%Strehl(rmsWFE==26).Theseresultsareconsistentwiththehard-edgeversusGaussianmasklabexperimentsofParketal.2006,takingintoconsiderationthedierencesinPSFstructureandIWAs. CurvesshowingcontrastattheIWAandtherelativeimprovementareshowninFigure 4-4 asamorecontinuousfunctionofwavefrontcorrection.ThoughGaussianand4th-orderBLMsout-performthehard-edgeocculteratcurrentlyachievableStrehlratios,theyremaindegeneratewithoneanotherintotherealmofextremeAO.Wenextidentifytheconditionsandparametersforwhichthisperformancedegeneracyisbroken. 4-2 forqualitativeguidance. ConsidertheeectofchangingtheLyotstopdiameter,DL,foreachoftheapodizedmasks.Withsmallnon-zerostopsizes,thecontrastatagivenlocationonthedetectorisgovernedbythecompetingeectsofspecklenoiseintensityandtheachievablepeakintensityofano-axissource.ThespecklenoiseintensityscalesasD2L,whereasthecompanionpeakintensity,^I(0)jM(r)j2,scalesasD4L.Theresultisanetimprovementin 75

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AstheLyotstopsizeincreasesfurther,thecontrastgeneratedbyBLMsdoesnotdegradeinassmoothafashionastheGaussianmask,sincethediractedlightistightlyconcentratedintoasmallregionthatfollowsthecontourofthetelscopeentranceaperture.Instead,thetransitionawayfromoptimalperformanceismoreabrupt.ThewidthofthetransitionregionintheLyotplanenarrowsasthewavefrontcorrectionimproves,andthetransitionoccursatprogressivelysmallerLyotstopsizesformasksofhigher-order(8th-,12th-,...etc.). TheseeectsareseeninFigure 4-5 ,whereweplotcontrastattheIWAagainstLyotstopthroughputfortwolevelsofwavefrontcorrection.At90%Strehl(rmsWFE==20),theapodizedmasksareclusteredtowithinanorderofunityincontrastfromoneanother,butclearlyout-performthehard-edgeocculter.At96%Strehl(rmsWFE==30),theapodizedmaskperformancedegeneracyisbroken,andoptimumLyotstopsizesbecomemoreevident.Inparticular,the4th-orderband-limitedmaskaordsan10%gaininLyotstopthroughputovertheGaussianmask(60%vs.50%).The8th-orderand12th-ordermasksgenerateslightlyworsecontrastandwith.40%and.15%throughputrespectively.Theseexactvaluesdependupontheentranceaperturegeometry,operatingbandwidth,IWA,mask-function,andmask-type(linear,radial,orseparable),butthetrendisneverthelessthesameatthislevelofwavefrontcorrection. GeneratingStrehlratiosbeyond96%onlargeground-basedtelescopesinthenearfutureisratherunlikely. Nakajima 2006 ; Guyon 2005 ).Thepotentialbenetsinusinghigher-orderBLMs Greenetal. 2005 ). 76

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Imagemaskresponsetoquasi-staticaberrationsimpactsthedynamicrangeandduty-cycleeciencyofhigh-contrastobservations.Forinstance,inthecaseoftip/tilterrors,on-skytrackinglatencyortelescope-to-instrumentexuremayleadtomisalignmentsthatleaksignicantamountsoflight.Clearly,themaskspresentedherehavedierentlevelsofresistancetosucherrors. Toassesspointingsensitivities,systematictiltphaseaberrationswereaddedtothewavefrontattheAO-coronagraph(IDL-MATLAB)interface.OptimumLyotstopsizeswereusedforeachmask,andmedian,insteadofmean,intensitieswereevaluatedtopreventbiastowardspoorcontrast.The1=Dannulusdirectlyoutsidethecoronagraph 77

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4-6 forlinearalignmenterrorsupto5=D. AtrelativelylowStrehlratios(.88%),hard-edgemasksperformcomparablywithapodizedmasksprovidedthatthepointingerrordoesnotexceed2=D.Athigherlevelsofcorrection(&88%),maskalignmentbecomesmorecritical.Inthisregime,apodizedmasksarecapableofgeneratingsignicantlydeepercontrastthanthehard-edgemask.Inparticular,theGaussianand4th-orderBLMsprovideoptimumcontrastwhenalignedtobetterthan1=Dat88%Strehland0:5=Dat94%Strehl.Ifsuchaccuracyisdiculttomanage,higher-orderBLMsmaybechosenovertheGaussianand4th-orderBLM,withtheusualtradeos(x ). Thisanalysisisalsoapplicabletolow-orderaberrationsinamoregeneralsense. Shaklan&Green ( 2005 )haveshownthatthe`order'ofthemask(4th,8th,12th,...etc.)uniquelydeterminesacoronagraph'ssensitivitytoaberrations(tip/tilt,focus,astigmatism,coma,trefoil,spherical,...etc.).Theresultisthathigher-ordermasks,whichareintrinsicallybroader,arenaturallybetterltersofanygivenlow-spatial-frequencyphaseerror.Forexample,expansionofEqu. 4{2 showsthattheGaussianmaskintensitytransmissionproleneartheopticalaxisdependsonrraisedtothefourthpower;thus,itisa4th-ordermask(Fig. 5-1 ).Figure 4-6 conrmsthattheGaussianmaskfollowsthe4th-orderBLMtiltsensitivitycurve,andthathigher-orderBLMsfollowsuit. Thehard-edgemaskmaybeconsideredinthelimitastheexponentoftheintensitytransmissionapproachesinnity.Itiseectivelyamaskofinniteorder,andthusthemostresistanttolow-spatial-frequencyaberrationcontent.Thesharpboundariesofthehard-edgemaskhoweveralsomakethecoronagraphleakthemoststarlight.Combiningthisinformation,werecognizethatFig. 4-6 isqualitativelyillustrativeofatrendapplicabletoallindividualphaseaberrations,andsumsof(orthogonal)phaseaberrations,introduceddownstreamfromtheAODMandwavefrontsensor.Asthephase 78

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Ingeneral,quasi-staticphaseerrorsfurtherreducetheStrehlratio.Thereforethesituationisslightlymorecomplicatedthanwithtip/tiltalone,which,strictlyspeaking,isachangetothepointingvectorandnotanaberration.Nevertheless,wecanextendtheprincipletoquantitativelyincludethemall. ConsiderthenalmeasuredStrehlratio,S,writtenasadecompositionofuncorrelatederrors( Sandleretal. 1994 ): whereeachSiwith1inrepresentsanindependentStrehldegradation.Anequivalentstatementisthatuncorrelatedwavefronterrorsaddinquadrature.SincetheStrehlratioproducedbytheAOsystemisunrelatedtothesubsequentopticalpath,weletS=SAOSqsdescribethenalstellarimage,whereSAOistheAO-correctedStrehlratio(ashasbeenusedthroughoutthetextandgures)andSqsistheStrehlratioduetoallquasi-staticphaseaberrationsintroduceddownstreamfromtheAODMandwavefrontsensor. Resultsfromx andFig. 4-6 showthatuseofanapodizedmask,preferablythe4th-orderBLM(x ),isjustiedonlywhenSAO&88%.Thus,werequirethatthemeasuredStrehlratiosatisfythecondition: where0Sqs1istheintrinsicStrehloftheopticalsystem.Withaninternalber-coupledsource,suchasacalibrationlamp,SqscanbemeasuredwhentheAODMisinactiveandat,sofarasonemighttrustzeroingtheactuatorvoltages.Wenotethatthisrelationshipisvalidonlyinthehigh-Strehlregime(.=2). Theeectsofspeckle-nullingcanbeincorporatedbynoticingthatcontrastcurvessuchasthoseshowninFig. 4-6 ,andsimilargraphsfortheotherphaseerrorspresentina 79

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).Inotherwords,theextradegreesoffreedomaordedwiththishardwarecompensateforquasi-staticaberrationswhosespatial-frequenciesmatchtheintendedsearcharea.Long-livedspecklesmaybenulledtoanintensitylevelwherethecontrastcurvesinFig. 4-6 intersecttheverticalaxes;thisistrueforanysuchaberration.Acandidatecompanionwouldthenbenoticedbytheinabilityoftheinstrumenttoremoveitsmutuallyincoherentsignal.SubsequentchangestotheshapeoftheDMsandhencelocationofthedarkholemightindicatethepresenceofotherfaintsources. Asanexample,considerameasuredStrehlratioS=85%withasystemthathasanintrinsicStrehlratioSqs=94%.AccordingtoEqu. 4{8 ,weareindeedjustiedinusingthe4th-orderBLMforthisapplication.However,iftheadditionalDMscannotremovequasi-staticspecklesfromtheregionofinterestdowntotheintensityoftheAO-limitednoiseoor,wemayconsiderswitchingtoahigher-ordermask,suchasthe8th-orderor12th-orderBLM,tohelplterstellarresidualsbeforetheyilluminatethedetector. Theseresultsallowustomakeratherstrongconclusionsregardingtheimplementationguidelinesforimagemasksincludedinthisstudy.Westatethemconciselyinthenextsection.Forfurtherdiscussionoflow-orderphaseaberrationswithinthecontextofLyotcoronagraphy,seex and Creppetal. ( 2006 ), Sivaramakrishnanetal. ( 2005 ), Lloyd&Sivaramakrishnan ( 2005 ), Shaklan&Green ( 2005 ). (1)Apodizedmasksshouldreplacethehard-edgemaskonlywhenon-skyStrehlratios,S,exceed0:88Sqs,whereSqsistheStrehlratioduetoallquasi-staticphaseaberrationsintroducedbytheinstrumentdownstreamfromtheAOsystem{e.g.,non-common-patherrors.Belowthislevelofcorrection,thehard-edgemaskoutperformsapodizedmasks,notbyreachingdeeperlevelsofcontrast,butbygeneratingsimilar 80

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)andthroughput(x )withmoreresistancetoquasi-staticerrors.Thisresultisindependentofentranceaperturegeometryandbandpass. (2)Since4th-orderBLMsyieldmoreLyotstopthroughputthantheGaussianmask,andapodizedmaskswithsmoothintensitytransmissiongradientsareequallydiculttomanufacture,Gaussianmasksshouldnotbeimplementedunderanyforeseeableconditionsontelescopeswithuniformtransmissionentranceapertures. (3)Theselectionofhigher-orderBLMsoverthe4th-orderBLMisrelegatedtosituationswhereboththeabilitytocorrectfortheatmospheretoaveryhighdegreeandtheinabilitytoadequatelynullquasi-staticspecklesissimultaneouslypresent. FortheoperatingrangeoftenconsideredwithatraditionalLyotcoronagraph,IWA=35max=D,theexactcontrastandthroughputvalueswilldeviatefromthosereportedinx ,butinaratherpredictablemanner.Theitalicizedconclusionshoweverdonotchangewiththeseconsiderations.ItisalsoimportanttomentionthatStrehlratioscanbesomewhatpeskytocalculateinpractice.ExperimentallydeterminedvaluesareaccurateonlytoseveralpercentiftheimageisnotspatiallysampledataratehigherthantwicetheNyquistfrequency( Robertsetal. 2004 ). Thehard-edgeoccultingmaskisaremarkablyrelevantcoronagraphictoolinanageofsophisticatedwavefrontcorrectiontechniquesandcleverapplicationsofFourieroptics.Apodizedmasks,orbinaryversionsofapodizedmasks( Kuchner&Spergel 2003 ),requirenano-fabricationcapabilitiesatvisibleandnear-IRwavelengths( Balasubramanianetal. 2006 ; Creppetal. 2006 ; Carsonetal. 2005 ; Debesetal. 2004 ; Traugeretal. 2004 );thiscanbeastrongdeterrentandshouldbeavoidedunlessEqu. 4{8 issatised(although,inafastopticalsystem,thefocalratiomayimposestringenttoleranceswhenbuildingahard-edgemaskaswell).IntherealmofextremeAO,the4th-orderBLmaskshouldbeimplemented,solongasquasi-staticphaseaberrationsaremanageablewithspeckle-nullinghardware. 81

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Figure4-1. Intensitytransmissionprolesforeachradialimagemask.TheIWA=4=D.Band-limitedmasks(BLMs)haveextendedo-axisattenuation,whichallowsthemtobecomposedofaniterangeoflowspatial-frequencies.ThisfeatureoersunlimiteddynamicrangeastheStrehlratioapproaches100%.ALyot-stylecoronagraphequippedwithaBLMisoneoftheleadingcandidatedesignsfortheTerrestrialPlanetFinderCoronagraph(TPF-C)spacemission( Fordetal. 2006 ). 82

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Coronagraphsimulationswithperfectincidentwavefronts.Intensitiesinthersttwocolumnsareshownonthesamelogarithmicscaleusingthemaskproles,0jM(r)j21,inFig.1andanormalizedAirypattern.Thespatialextentoftheimageplanesareidenticalandcanbeestimatedfromknowingthatthehard-edgemaskhasadiameterof8=D.Adashedlineinthe`LyotPlane'columnindicatestheoutlineofthecircularunobstructedentranceaperture.An60%throughputLyotstopwasusedforthehard-edge,Gaussian,and4th-orderBLMs.The8th-orderand12th-orderBLMsoerbetterrejectionoflow-orderaberrationsatacostofthroughputandangularresolution.The`FinalImage'columnshowsthecontrastgeneratedbyeachmaskusingthelogarithmicscaleinthehard-edgemaskrow;BLMsremoveon-axisstarlightdowntothenumericalnoiselevelofthesimulations(<1012). 83

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Azimuthallyaveragedcontrastcurvesforthehard-edge,Gaussian,and4th-orderBLM'susingaxedcircularLyotstopsizewith60%throughput.TheLyotstopfortheAirypatternhas100%throughput. 84

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Averagecontrastwithinthe1=DwideannulusdirectlyoutsideofthecoronagraphIWAasacontinuousfunctionofatmosphericwavefrontcorrectionandtherelativegain(shownbyarrows)achievedbyswitchingtothe4th-orderBLM.Thehard-edgemask'sperformanceislimitedbystarlightdiractedintotheinteriorofthe60%throughputLyotstop.Thispreventssignicantimprovementsbeyond88%Strehl. Figure4-5. Averagecontrastwithinthe1=DwideannulusdirectlyoutsidethecoronagraphIWAasafunctionofLyotstopthroughputfor90%Strehl(left)and96%Strehl(right). 85

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Mediancontrastwithinthe1=DannulusoutsidethecoronagraphIWAasafunctionofsystematictilterrorforseveralcharacteristiclevelsofwavefrontcorrectionusingoptimalLyotstopsizes.NotethattheGaussianmaskisa4th-ordermask.Thenon-monotonicchangesincontrastarearesultofcalculatingthemedianintensitywithalignmenterrorsinacirculargeometryandphasingbetweentheAirypatternandthemaskintensitytransmission(seeLloyd&Sivaramakrishnan2005). 86

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WehavebuiltaseriesofnotchlterimagemasksthatmaketheLyotcoronagraphlesssusceptibletolow-spatial-frequencyopticalaberrations.Inthischapter,wepresentexperimentalresultsoftheirperformanceinthelabusingmonochromaticlight.Ourtestsshowthattheseeighth-ordermasks(x )areresistanttotiltandfocusalignmenterrors,andcangeneratecontrastlevelsof2106at3=Dand6107at10=Dwithoutwavefrontcorrection.Thisworksupportsrecenttheoreticalstudiessuggestingthateighth-ordermaskscanprovidetheTPF-Cwithalargesearcharea,higho-axisthroughput,practicalrequisitepointingaccuracy,andresistancetostellarsize. Debesetal. ( 2004 ).Inthefollowing,webrieydescribeourdesignstrategyandnanofabricationtechniques. Thebasestructureusedtomechanicallysupporttheopaqueportionsofthemasksisa0.7mmthickpieceofBoroaluminosilicateglasswithascratch/digof20/10.A270nmthicklayerofChromiumservesastheon-axisoccultingmaterial,andwasdepositedontoonesideoftheglassusingaSemicoree-gunevaporator.Smallstructureswerethendry-etchedfromtheChromelayerwithanappliedmaterialsclustertoolusingahighdensitydecoupledplasmacomposedofArgon,Chlorine,andOxygen.Noanti-reectioncoatingwasapplied.Figure 5-1 showsaphotoofthesubstratecontainingallofthedesigns. Eachmaskisdesignedforanf/163orslowerbeamwitha40nmbandwidthcenteredonthe=632:8nmHeNelasersource.Thefocalratioofthesystemislargetofacilitatethefabricationofsmallfeaturesinthemasks.Thephysicalsizeorextentofthemasksare 87

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Thefourlinearbinarynotchlerimagemasks(left),andopticalmicroscopefalsecolorimagesofthem=1,l=2eighth-ordermaskat5xmagnication(middle)and20xmagnication(right).Thedarkareasinthemicroscopeimagesaretransparent;thisiswheretheChromehasbeenetchedaway.Thespacingbetweenstripesandthespacingbetweensamplesisminf=#=100m. 2cmtoaside.Althoughtruncationsetsanouter-working-angleanddegradescontrast,notchltermaskscaneasilybemanufacturedlargeenoughtoensurethattheseeectsdonotplacesignicantconstraintsonthesearchareaandarenotthedominantsourceoferror.Notchltermaskscanbedesignedtohaveanazimuthallysymmetricsearcharea;however,wehavechosentomakelinearmaskssothattheeectiveopacitychangesinonlyonedirection.Thispropertysimpliedthetestingoftheirresponsetopointingerrors.TheFWHMoftheimagemasks(i.e.2IWA)weredesignedtoberoughlyequivalentsuchthatfaircomparisonsoftheirperformancecouldbemade(Table 5-1 ). Aime ( 2005 )suggeststhatthemaskequivalent-widthservesasabetterproxyformakingsuchcomparisons;theauthorsnotethattheFWHMvaluediersfromtheequivalent-widthvalueby.1%foreachoftheindividualmaskspresentedhere. Linearbinarymasksconsistofverticallyrepeatingparallelstripes,whereband-limitedornotchlterfunctionsdescribethecurvesineachstripe( Kuchner&Spergel 2003 ).Wehavemadebinarymasksusingthenotchlterfunctions,becausesamplingmakestheintricatefeaturesneartheopticalaxisapartofthedesign,andnottheresultoftheniteresolutionofthelithographymachine.Ingeneral,thesamplingisnotsymmetric 88

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5-1 ).Thelow-frequencyamplitudetransmissionoftheeighth-ordermasksfollowEquations 2{6 and 2{7 Thesmallestfeaturesinamaskareoftenfoundneartheopticalaxis.TheirsizedependsuponboththeIWAandbandwidth,amongotherparameters.Generally,astheIWAimproves(i.e.getssmaller),thesizeofthesmallestfeaturesinthemaskincreases,andasthebandwidthwidens,thesizeofthesmallestfeaturesdecreases.IftheIWAistoolargeorthebandwidthtoowide,thesmallestfeaturesmaybetoosmalltobuild. Anadditionalconstraintisthattheminimumfeaturesizesshouldnotbesmallerthanthethicknessoftheopaquematerial.Thishelpstominimizethewaveguideeectsassociatedwithbinarymasks,andothervectorelectromagneticeectsthatcandegradecontrast,especiallywithbroadbandlight. Layetal. ( 2005 )describesomeofthesepotentiallimitingfactorsfortheTPF-Cmission,andsuggestseveralalternativesforcompensation;oneofwhichincludesdramaticallyincreasingthefocalratioatthemask(>f/60),aswasdoneinthisexperiment.Thisdesignstrategywasalsoimplementedinthe Debesetal. ( 2004 )experimentforsimilarreasons. Minimumfeaturesizerequirements-bothpracticalandtheoretical-limitedourabilitytomakeeighth-ordermaskswithhighLyotstopthroughput.Intheory,eighth-ordermaskscanachieve60%LyotstopthroughputwithIWAsof4max=D.Ourmasksweredesignedhowevertoachieveonly20%throughputatmost,becausewewererestrictedtomakingfeatureslargerthanthethicknessoftheChrome;thesmallestfeaturesizeineachoftheeighth-ordermasksis270nm,whereasthesmallestfeaturesizeinthefourth-ordermaskis7119nm.Toincreasethethroughput,wewouldhavetoincreasethef=#,decreasethebandwidth,ordecreasethethicknessoftheChrome.Clearlythefocalratioisalreadylargeandthebandwidthisalreadynarrow.Also,weshowinx thatincreasingthethicknessoftheChromeisthemostnotableimprovementwehavemadeuponthemaskpresentedinDebesetal.2004.Thus,futuremaskdevelopmentwillnecessarilyinvolveusingamaterialthatisintrinsicallymore 89

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Semaltianos 2001 ; Layetal. 2005 ).Thiswillenablethefabricationofmasksthathavemoreopacityandsmallerminimumfeaturessizes. Theequationsdescribingtheexactstructureoflinear,binary,sampledeighth-ordernotchlterimagemasksarederivedinKCG05.Table 5-1 displaystherelevantquantitiesforourdesigns,usingthesamenotation(exceptinKCG05f=#=f).Foreachmask,samplingbeganatahorizontaldistanceofx=0minf=#fromtheopticalaxis. Table5-1. Maskdesignparametersforabandpassof632:820nm.Foranellipticalorcircularprimarymirror,theLyotstopthroughputofalinearmaskisgivenby:T=12 Masksinc2n=3m=1,l=2m=1,l=3 order4th8th8th8thIWA=(max=D)2.3502.3722.3322.3560.4880.6740.7160.759N1.014440770.990988301.936403701.47114548^M0A0.014235180.078339840.059893640.06702707^M0B|0.018032810.030282280.02278117C|-0.25123206-0.51959437-0.3564430100.288009720.258752130.258778760.25874218SmallestFeature7119nm271nm270nm270nmTheoreticalThroughput40.4%21.2%17.4%13.7%ExperimentalThroughput30.7%15.7%13.0%10.4% 1-8 ,andsimilartothesetupdescribedin Debesetal. ( 2004 ).\Starlight",generatedbya=632:8nmHeNelaserformonochromatictesting,passesrstthroughasetofneutraldensity(ND)ltersandisthenfocusedbyamicroscopeobjectivelensintoa4msingle-modeberforspatialltering.Theberexit-tipservesasabrightpointsource.Thisexpandingbeam,N.A.=0:12,iscollimatedandthentruncatedbyacircular3mm 90

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Inordertomeasurecontrast,weperformacomparisonofimagestakenwithandwithoutthecoronagraphinplace.Duetotheextremecontrastlevelsinvolved,weuseacombinationoftheNDltersandthelinearityoftheCCDtocalculaterelativeintensitiesandtogeneratehighsignal-to-noiseratioimagesinareasonableamountoftime.WerstattenuatethelaserlightwiththeNDlters,whichareplacedupstreamfromthesingle-mode-bertoensurethattheiraberrationeectsarenegated,andtakeanimageofthestarwithoutthemaskandwithouttheLyotstopintheopticaltrain.Then,themaskandLyotstopareinsertedintoplace,andtheNDltersareremoved.Inthisnalimage,theintensityvaluesateachpixelaredividedbytheaverageuxwithintheFWHMoftheimageofthestartakenwithoutthecoronagraph,andnormalizedtotheintegrationtimesandNDltersused.Wedenetheresultingvalue,ateachpixel,astherelativeintensity.ThecontrastthenissimplytherelativeintensitydividedbytheLyotstopthroughputandband-limited(i.e.low-frequency)partofthemaskintensitytransmission 91

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5-2 showsimagesofthestaratvariousstepsintheprocedure.Wecouldhavechosenalessconservativedenitionofcontrastbyinsteadnormalizingtotheinterpolatedpeakintensityoftheimagedsource,ratherthantheaverageuxwithintheFWHM( Shaklan&Green 2005 );however,thesetwovaluesdierbylessthanafactoroftwo.ItisnotnecessarytoaddandremovetheLyotstopinordertomeasurecontrast,butwendthatdoingsofacilitatescalculationoftheo-axisthroughput. Figure5-2. Laboratoryimagesofthesimulatedstarwithoutthecoronagraph(left),them=1,l=2maskalignedoverthestar(middle),andthestarwithboththemaskandLyotstopinplace(right).Intensitiesareplottedonalogarithmicscale.Theimageofthestarshowstheangularsizescaleofthetelescope.Specklescreatedbyimperfectionsintheopticslimitthedynamicrangeofthecoronagraphcreatinganoiseooratthe107levelneartheIWA.Thecontrastiscalculatedbydividingtherelativeintensity,shownintheimageontherightandlaterinFig. 5-3 ,bytheLyotstopthroughputandmaskintensitytransmission;thisaccountsfortheo-axisattenuationofthecoronagraph. Linearbinarymasksapproximateband-limitedmasksonlywhentheverticalangularsizeofthestripesinthemaskaresmallerthanmin=D,theresolutionofthetelescope.Toensurethatthemasksdiractlightappropriately,weincreasedthefocalratioofthesystemintherstimageplanefromtheinitialdesignoff=#=163tof=#187,byshrinkingthesizeoftheentranceaperture.Thisalsoresultedinanimprovementofthemasks'eectiveIWAbythesamefactor.TheLyotstopsizewassetconservativelytoobtain75%ofthemaximumtheoreticalthroughput,sothatsmallmis-alignmentsdidnotresultindiractedlightleakagethroughthecenterofthestopontothedetector. 92

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5-1 showsthedesignedIWAsbeforeincreasingthefocalratio,andtheexperimentalLyotstopthroughputachieved. 5.3.1ChromeTransmissionandRelativeIntensities Debesetal. ( 2004 )waslimitedbythetransmissionoflightdirectlythroughtheChromiumoccultinglayer.Inthisstudy,wehaveincreasedthethicknessofthislayerfrom105nmto270nm.UsingthetransmissioncurveinDebesetal.2004,wecalculatethatthepeaktransmissionshouldimprovefrom7:5104to9:2109.Wemeasureapeaktransmissionof2:3108.Thisisslightlyworsethanpredicted,butopaqueenoughforthisapplicationnevertheless(Fig. 5-3 ).ThediscrepencyinthesevaluescanbeunderstoodbyconsideringinhomogenietiesinthethicknessoftheChromiumlayers.A<5nmdeviationineachmakesupthedierence.ThecontributionoftransmissiondirectlythroughtheChromiumtothelimitingcontrastinthisexperimentisapproximatelyoneorderofmagnitudesmallerthanthescatteredlightoorneartheIWA,andlesssointheregionswherethemaskshavelittleo-axisattenuation.Amoredemandingapplication,suchastheTPF-C,would,ofcourse,requireamaterialwithahigheropacity. Figure 5-3 alsoshowsadierenceintheamountoflighttransmittedneartheopticalaxis,r.=D,betweenthefourth-ordermaskandtheeighth-ordermasks.Thisisevidencethattheeighth-ordermasksareblockingmorescatteredlight,simplybecausetheyarewider,andreducingtheeectsoflow-orderaberrations(wetestthislatterclaimmorecarefullyinx ).Thesepropertiesarenotseenasclearlyincontrastcurves,where,interiortotheIWA,theintensitytransmissionofthemaskcontrolsthedetectionthreshold. 5-2 aretheresultofwavefrontdistortions,created 93

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TelescopePSF,coronagraphPSF,andChrometransmissionforeachmaskusingacircularentranceaperture.TheChrometransmissionwasmeasuredatthecenterofthesubstrate.InsidetheIWA,theeighth-ordermasksblockmorescatteredlightandreducetheeectsoflow-orderaberrations.ThethicknessoftheChromiumdoesnotlimittheperformanceofthecoronagraph,butdoestransmitanon-negligibleamountoflightwhichcontributestothenoiseoor.ContrastiscalculatedbydividingthecoronagraphPSFbytheintensitytransmissionofthemaskandtheLyotstopthroughput. byimperfectionsintheoptics.Inpractice,specklescanmimicandoftenoverwhelmthelightofdimcompanions(x 3 4 ). Wecalculatedcontrastforpixelswithina10=D30=DsectionacrossthecenterofthePSFbydividingtherelativeintensitiesbytheLyotstopthroughputandband-limitedpartofthemaskintensitytransmission,j^M(x)j2,ateachposition,x,thehorizontaldistanceofpixelsfromtheopticalaxis.Thatway,thedirectioninwhichthehaloofspecklesdecreasedinuxcoincidedwiththedirectionofopacitychangeinthemasks.Wewereabletoachieve2106contrastat3=Dand6107contrastat10=D,asquoted 94

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5-4 ,weplotthecorresponding3detectionlimits,whereisdenedasthestandarddeviationofthescatteredlightnoiseooratagivenlocationinthenalimageplane.Theeighth-ordermasksreducetheamountofscatteredlightclosetotheopticalaxis,andslightlyout-performthefourth-ordermaskneartheIWAasaresultoftheirmoresteeplyincreasingintensitytransmissioninthatregion.Thecontrastsintherestofthesearchareaareessentiallyidentical. TocalculatetheStrehlratioofoursystem,wecomparedamodeloftheAirypatternincidentontothemaskwithexperimentaldata.WendthattheStrehlratioexceeds98%.Combiningthiswiththefactthatthecoronagraphisspeckledominatedandtheopticalqualityofourachromatsarehigh(seex ),weconcludethatthedetectionlimitsshowninFigure 5-4 representtheapproximatedeepestcontrastthatisachievablefromthegroundwithcurrentAOsystems,usingthistypeofcoronagraph. Figure5-4. Experimental3detectionlimitsforeachmask.TheeectiveIWAswerecalculatedtakingintoconsiderationthechangeinfocalratiofromtheinitialmaskdesigns. 95

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5-5 ,whereweplotthecontrastat3=Dasafunctionofthedistancethatthemasksweredisplaced.Thescatteredlightoorlimitsthedynamicrangeofthecoronagraphatsmallaberrationlevels;inthisregime,themasksgeneratecontraststowithinafactoroftwoofoneanother,asshownintheprevioussection(Fig. 5-4 ).Atlargeaberrationlevels,wherediractedlightdictatesthecontrast,thereisacleardichotomyinthemasks'behavior. Tomeasurethetiltaberrationsensitivityofeachmask,wemovedthesubstratelaterallyacrossthecenteroftheimageofthestarin5mincrements.Wendthattheeighth-ordermasksareeasiertopointthanthefourth-ordermask.Toquantifythisstatement,wecalculatedthewidthofthepointing\sweet-spot"foreachmask,wherethecontrastat3=Disattowithin2andlimitedbyscatteredlight.Themeanwidthofthiszonefortheeighth-ordermasksis1:060:03=D;thewidthofthiszoneforthefourth-ordermaskis0:200:05=D,afactorof5smaller.Withan8mtelescopeoperatingat=0:5m,thesetolerancescorrespondtopointingaccuraciesof6:8masand1:3masrespectively.( Lloyd&Sivaramakrishnan ( 2005 )discusstip/tilterrorsinLyotcoronagraphsindetail.Forapracticalapplication,seethedescriptionoftheAEOScoronagraphby Lloydetal. ( 2001 ).) Tomeasurethefocusaberrationsensitivityofeachmask,wemovedthesubstratealongtheopticalaxisinlogarithmicincrementsof0.18dex.Withasimilaranalysis,wendthattheeighth-ordermasksarealsolesssusceptiblethanthefourth-ordermasktofocalmisalignments.Theeighth-ordermasksprovidethesamecontrastasthefourth-ordermaskinasystemwith4timesaslargeanRMSwavefronterror. Theseresults(Fig. 5-5 )dependupontheamountofscatteredlightpresentinthesystem.Ifthescatteredlightlevelswerereduced,itwouldbepossibletomeasuretheresponseofthemaskstosmalleraberrations;thewidthofthetiltandfocussweet-spots 96

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Figure5-5. Coronagraphsensitivitiestotilt(left)andfocus(right)aberrationsforeachmask.Thetheoreticalpredictionsof Shaklan&Green ( 2005 )areover-plottedforcomparison(seetext).Scatteredlightpreventedmeasurementofthediractedlightresponseofthemasksatsmallaberrationlevels.Uncertaintiesinthemeasurementsforthefourth-ordermaskareshowninthetiltgraph;theerrorbarsareontheorderofthesizeofthedatapointsandrepresentativeforalloftheexperimentalcurvesshowninbothgraphs.Thefocalratioofoursystemwaslargeenoughtowarranttiltrealignmentforeachfocusdatapoint,butnotfocusrealignmentforeachtiltdatapoint;thismotivatedthelinearversuslogarithmicmeasurementincrementsusedforacquiringdata. Forcomparison,theSG05theoreticaltiltandfocuscurvesareover-plottedinFig. 5-5 (thetriangulardatapoints);theserepresentthesteepestpossibleslopesthatcanbeachievedinpractice,sincethemodelaccountsonlyfordiraction.Thegenerallocationofourexperimentaldataareingoodagreementwiththeory,and,torstorder,simplyaddingaconstantlevelofscatteredlighttothe Shaklan&Green ( 2005 )diractedlight 97

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Sivaramakrishnanetal. 2005 ,see).WendthattheintroductionoftiltandfocusaberrationsproducespatternsintheLyotplanethattthisdescription(Fig. 5-6 ),andthattheundersizingoftheLyotstopisresponsibleforanenhancedresistancetoaberrations.Furthermore,thiseectismorepronouncedwiththefourth-ordermaskthantheeighth-ordermask,sincelow-orderaberrationscanbepartiallyorcompletelylteredintheimageplanebeforereachingtheLyotpupil. Itisagoodassumptionthatthefourth-andeighth-ordermaskphaseaberrationcontrastcurves(Fig. 5-5 )donotintersectatmorethanonepointforagivenaberration:theslopeofamask'sdependenceonanylow-orderZernikemodeisalwaysatleastassteepforeighth-ordermasksasitisforfourth-ordermasks( Shaklan&Green 2005 ).SinceweseetheintersectioninbothgraphsinFig. 5-5 ,weconcludethattheeighth-ordermaskscanachievebettercontrastthanthefourth-ordermaskwhensmalllevelsoftiltandfocusaberrationsarepresent,eventhoughthisregimewasnotavailablefordirectmeasurementinourexperiment.Atintermediateaberrationlevels,wedoindeedseeanimprovement Shaklan&Green ( 2005 )are:(1)weusedacircularentranceaperture,insteadofanellipticalentranceaperture,and(2)thecontrastwasmeasuredat3=D,insteadof4=D. 98

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CharacteristicLyotplaneimageswithoptimummaskalignment(left),and2101wavesRMStiltaberration(middle),and9102wavesRMSfocusaberration(right)usingthem=1,l=2mask.Intensitiesarenormalizedtothepeakintensityofthefocusimageandareonalogarithmicscale.ShrinkingtheLyotstopcanimprovecontrastwhencertainaberrationsarepresent,asisthecasehere.TheseimagescanbecomparedtotheanalyticpredictionsinFig.3of Sivaramakrishnanetal. ( 2005 ).Evidently,smallamplitudetiltandfocusphaseaberrationsproduceauniformleakageoflightintotheLyotpupilinterior.Althoughtheaberrationspresentedhereareratherlarge,aspectsofbothimagesappeartoreectthisphenomena.Morecomplicatedprocessessuchascross-talkbetweeninducedandinherentaberrationsaswellasfrequency-foldingfrommaskconstructionerrorsalsocontributetotheLyotpupileld,andcancreateanintensitygradient. incontrastwiththeeighth-ordermasks.Thisismoreevidentwithtilt,becausetheintersectionbetweenexperimentalcurvesoccurswellabovethescatteredlightoor. Reducingtheamountofscatteredlightinthecoronagraphbyapproximatelytwoordersofmagnitudewillenableamorereliableextrapolationofdatatosmalleraberrationswithfuturework;however,polishingtheopticswithsuchprecisionisnotfeasible.Theachromatdoubletsinthisexperimentarethesamethatwereusedin Debesetal. ( 2004 ),withrmssurfaceroughnessesof.1nmonspatialfrequencyscalesthatcorrespondtothesearcharea.Abettertechniquetocompensateforthescatteredlightpresentinthesystematthislevelwouldbetoimplementadeformablemirror( Traugeretal. 2004 ,e.g.). 99

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With\perfect"alignment,wendthatallofthemasksgeneratecontrastlevelsof2106at3=Dand6107at10=D.Inessence,theon-axis(`stellar')uxwasreducedby7ordersofmagnitudeattheexpenseofattenuatingo-axislightbyafactorof410.Sinceoursystemis\diractionlimited"(i.e.&80%Strehlratio),weconcludethatthe3detectionthresholdsshowninFig. 5-4 representtheapproximatedeepestinstantaneouscontrastthatisachievablefromthegroundwithcurrentAO,usingthistypeofcoronagraph. TheLyotstopthroughputpenaltyinswitchingfromafourth-ordermasktoaneighth-ordermaskwasgreatlyexaggeratedinthisstudy,becauseofnanofabricationlimitations.Wewereabletoachieve31%Lyotstopthroughputwiththefourth-order 100

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Theseresultssupporttherecenttheoreticalstudiesof Kuchner,Crepp,&Ge ( 2005 )and Shaklan&Green ( 2005 )suggestingthateighth-orderimagemaskscanmeetthedemandsofaspacemissiondesignedtoimageextrasolarterrestrialplanetsbyprovidingtheLyotcoronagraphwithalargedynamicrange,higho-axisthroughput,alargesearcharea,andresistancetolow-spatial-frequencyopticalaberrations. 101

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ItwasshowninChapters 1 and 4 thatlargestroke,highbandwidth,highactuator-densityDMsarerequiredtodetectself-luminousJovianplanetsfromthegroundinthenear-IR.These\extreme"AOsystemsarecurrentlybeingbuiltandwilleventuallyformthecoreofnextgenerationhigh-contrastimaginginstruments,suchasGPIatGeminiSouth( Macintoshetal. 2006a ),SPHEREattheVLT( Beuzitetal. 2006 ),andthePALM-3k/P1640atPalomar( Dekanyetal. 2007 ).However,duetotheircomplexity,theywillnotbeavailableforanother3-5years.TotestaBLMonarealastrophysicalsource,wemustsomehowboostimagequalitieswithoutreplacingtheexistingDM. 1-6 ).Forinstance,inthecaseofKolmogorovturbulence,theresidualwavefrontvariance,2t,canberelatedtotheeectivewavefrontsensorsubaperturesize,d=Dtel=Nact,andFriedparameter,r0,by r05=3rad2;(6{1) wheretheconstantofproportionalitydepends(weakly)onthetypeofactuatorinuencefunction(aGaussianshapehere),NactisthelinearnumberofactuatorsacrosstheDM,andaleast-squaresphase-conjugationapproachisassumed(Hudgin,JOSA1977).Ifthenumberofactuatorsinasquaregridarrayusedforcorrectionisapproximately(Dtel=d)2=4,thenEqu. 6{1 canberewrittenas Inotherwords,doublingNact(i.e.quadruplingthetotalnumberofactuators)reducesthermswavefronterrorbyafactorof1:8,whichinturnimprovestheinstantaneouscontrastbyafactorof(1:8)2(x ).However,increasingtheDMsamplingby 102

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DM'sareusedmostoftentocorrecttheentire\beam"ofstarlight,fromoneedgeoftheaperturetotheother.However,insteadofapplyingcorrectionsoverthefulldiameterofalargetelescope,itispossibletoimprovesamplingbycorrectingonlyaportionofthepupil.Forinstance,opticsplacedbetweenthesecondarymirrorandAOsystemcanbeusedtomap,orrelay,aparticularregionofthepupilontotheexistingDMbyshiftingandmagnifyingthebeam.Theresultisanimprovedspacingbetweenactuatorsasprojectedontothesky. ThisconcepthasrecentlybeendemonstratedinpracticebySerabynetal.2007atPalomar.TheyhaveinstalledrelayopticsthatturntheHale200-inchtelescopeintoapowerfulo-axisimager.Fig. 6-1 displaysasimpliedversionoftheopticalpath.AfoldmirrorinsertedbeforetheCassegrainfocuspicksothetelescopebeamandsendsittoacustomcircularstopthatselectsonequadrantoftheaperture,convenientlyavoidingthecentralobstructionandsecondarysupportspiders.TherelayopticsmanipulatethebeamsuchthatthenewpupiltstightlyontotheexistingXinetics241-actuatorPalomarAOsystem(PALAO)DM( Troyetal. 2000 ).Theneteectisnersamplingattheexpenseofangularresolution(Dtel=5.1m!Dtel=1:5m)andthebrightnessofstarsforwhichtheAOsystemcanmaintainastablelock(V<12!V<9).ThesetradeosarejustiedsincecoronagraphswithintrinsicallysmallIWA'scanstillprobesub-arcsecondseparationsinthenear-IR,wherenumerousdimcompanionslayhidden( Veras,Crepp&Ford 2008 ). Benetsofthetechniquecanbesummarizedasfollows: 103

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). Undergoodseeingconditions,therelayopticsandPALAOhavealreadydemonstratedon-skyStrehlratiosofS94%intheK-band(Serabynetal.2007).WeknowfromChapter 4 thatuseofanapodizedmaskisappropriateonlywhentheStrehlratioexceeds:S&0:88Sqs,whereSqsistheintrinsicStrehlratiodeliveredbytheinstrument(`qs'standsforquasi-static).Thenear-IRcameraPHAROatPalomarconsistentlyprovidesimagequalitiesexceedingSqs&0:95forsourcesneartheopticalaxis.Thus,Equ. 4{8 isindeedsatised.Theseconsiderationsserveasthetechnicaljusticationforbuildingtherstband-limitedcoronagraphicimagemaskforon-skytests.Theremainderofthechapteroutlinesthedesignofsuchadevice(x ),itsperformancewiththePALAOstimulus(x ),andpreliminaryon-skytests(x ). Figure6-1. LayoutoftheHale200-inchrelayoptics,courtesyofEugeneSerabyn. 104

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ImageoftherelayopticssubaperturepupilattheHale200-inchtelescope.Lightfromonlyonequadrantofthefullapertureisused. Figure6-3. PredictedStrehlratioasafunctionoftheFriedparameter,r0,intheK-bandattheHale200-inchtelescopewithrelayoptics(topcurve)andwithout(bottomcurve),courtesyofGeneSerabyn. 105

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6-4 showsaschematicoftheinstrument. A25mas/pixelplatescalemodeenablescriticalsamplingofdiraction-limitedimagesfromthefullHale200-inchapertureintheJ-band.Withrelayopticsinplace,theplatescalechangesbytheratioofthetelescopediameter,25x5:093=1:5=84:88mas/pixel.WehavedesignedamaskfortheK-band,wherethesamplingcorrespondsto3:6pixelsperdiractionwidth.TheK-bandoersbetterimagequalitiesthantheJ-band,buttheskybackgroundisbrighter. Figure6-4. ComponentlayoutofthePHAROnear-IRcamera,courtesyofTomHayward. 106

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)sincetheycanpotentiallyleaklightatbothendsofthebandpass,butgradedmasks,whichcanleaklightonlyatlongwavelengths,aremadefromHEBSglassandthereforemoreexpensive.Otherinterestingperformancedierencesexistbetweenthelistofpotentialdesigns{smoothbinary,sampledbinary,smoothgraded,andsampledgraded{suchaspolarizationdependenceandchromaticity( Layetal. 2005 ),buttheyareunimportantatthesensitivitiesachievablefromtheground.Sincewehavethetoolsandexperiencetobuildbinarymasks,webuiltabinarymaskforPHARO. PHAROreceivesanf/15.64beamfromthePALAOsystem.ThedesiredoperationrangeforourobservationsincludestheKshort:1:992:30m,Br:2:162:18m,andCO:2:292:31mlters.TheKshortlterservesastheprimarysciencechannelwhereasindependentexperimentsinallthreelterscanbeusedtomeasureanychromaticdependentperformances,shouldtheyexist,sinceonlymonochromatictestswerepreviouslyconductedinthelab( Creppetal. 2006 ).Topreventdiractedlightleakagefromtheedgesoftheltertransmissionproles,theminimumandmaximumwavelengths,min=1:79mandmax=2:39m,werechosenconservatively. Twodierentmasksweredesignedandbuilt:alinearfourth-ordersmoothbinarynotchltermaskandalinearhard-edgebinarymask( Creppetal. 2007 ).Thelatterofwhichwasusedasabaselinetomakecomparativestudies.Aneighth-ordermaskdesign,whichhaslessLyotstopthroughputthanafourth-ordermask,couldnotbejustied,giventhealreadylargesacriceinphotonsfromtherelayoptics.EachmaskwasdesignedwiththesameaggressiveIWA=2:678max=Dtel=880mas.Theywereplacedadjacenttooneanotheronthesame0.7mmthickBoro-Aluminosilicateglasssubstrate,Corning 107

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Themaskswerefabricatedusinge-beamlithographyattheUniversityofFloridananofabricationfacilityinJune2006.Aluminumwasusedastheopaquematerialdeposit,sinceitislesstransmissivethanChrome(x )inthenear-IR.Labmeasurementsplacedanupperlimitontheintensitytransmissiondirectlythroughthe200nmlayerofAluminumat1107.Theminimumfeaturesizewassetequaltothelayerthickness. Theheight,^Mnotch(x),ofasinglestripeofthesmoothbinarylinearband-limitedmask(seeEqu. 2{17 ;binarymasksaretechnicallynotchltermasks)is: ^Mnotch(x)=f=#min1sinc2x (6{3) =281sinc20:0179857x mm; where=0:428andxhasunitsofm.Thisprolewasrepeatedvertically256times.Thekeytothebinarymask'soperationisthateachstripeissmallerthantheresolutionoftheopticalsystem,henceallowingittodiractlightlikeagradedmask.Thehard-edgemaskdesignismuchsimpler;itisliterallyabarofwidth2f=#2:678max=200m. Figure 6-6 showsimagesofthemaskbeforeitwasshippedtoJPL,whereitwascutoutofthesubstratewithadicingsawtophysicaldimensionsof0.60x0.30inchesandthencleanedinanultrasonicbathofacetonetoremovetheprotectivelayerofphotoresist.Simulationswereruntoensurethattruncationattheedgeofthemaskwouldnotdiractstarlightintothesearchareaatcontrastlevelsabove106.ThemaskwasinstalledinPHAROinSeptember2006. 108

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(left)Thebinarymaskaftere-beamlithography.AthicklayerofphotoresistwasappliedtoprotectthesurfaceforshippingtoJPL.(right)Microscopeimageoftheband-limitedmask.Eachstripeis28mwide.`Ringing'featuresinthesinc2(:::)function( 6{4 ),whichareresponsibleforcontrollingdiractedlight,canbeseenabove(x>0)andbelow(x<0)themainoccultingregion. 6-6 6-7 ).Thedesignincorporatedasinglesolidpiece,insteadoftwoseparatefasteners,tofacilitateinstallation.ItwasnecessarytoallowextraspaceforthermalcontractionsincePHAROoperatesat77K.ThethermalcontractionoftheglasssubstrateanddierentialcontractionbetweentheglassandthinlayerofAluminumdepositonthemaskwerenegligible.ThemasksareorientedperpendiculartothedirectionofrotationofthePHAROslitwheel.ThisisanimportantdetailandhasimplicationsforthescienceconductedinChapter 7 ThephysicalsizeofthepupilattheLyotplaneinPHAROis16.88mm(Haywardetal.2001).Aband-limitedmaskwilldiractlightintoaregionthatissmallerthanthisvaluebyafactorof1.AcustomcircularLyotstopofcleardiameter(10:428)16:88mm=9:65mmwasbuiltattheUniversityofFloridausingalasercutter(Fig. 6-8 ).Thetotalthroughputofano-axissourceat880mas,includingattenuationfromtheband-limitedimagemaskandLyotstop,is16:3%.Thethroughputincreasesto33%forsourcesfurtherfromtheopticalaxis. 109

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AvailableslotinPHAROimageplanewheel.Theunitsareinches. Figure6-7. Aluminumfastenermadewith0:003inchprecisionattheUniversityofFloridamachineshop. 110

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LyotstopinstalledinPHARO.TheUniversityofFloridalasercutterprovidescutsthatareroughontheorderoftensofmicrons.Thisroughnessdoesnotlimitsensitivity. Thegoalsofthetestswereto: ResultsareshowninFigs. 6-9 and 6-10 whereeachofthebulletpointsareaddressed. 111

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PHAROimageswithBLMalignedtothewhitelightsource.(left)OptimalmaskpositionisfoundusingthePHAROsteppermotorwiththeLyotstopoutofthebeam.(middle)ResultingcoronagraphicPSFwithLyotstopinplace.TheAiryringshavebeenremoved.Thewae-modepeaks( Makidonetal. 2005 )are1,000timesfainterthanthestellarpeakintensityandclearlyvisible.Infact,theysaturatePHAROiftheintegrationtimeisnotlimited.(right)Pupilimageshowingdiractedstarlightpatternandresidualsfromnon-common-patherrors.ComparethisimagewithFig. 5-6 Wendthatbothcoronagraphicmasksarecapableofsuppressingdiractionandthatthesensitivityislimitedbynon-common-patherrorsbetweentheAOsystemandthedetector.TheDMcorrectsforwavefronterrorsintroducedupstreamfromitspositionintheopticalpathbutisblindtoerrorsintroduceddownstream,suchasthosecreatedbyfoldopticsandthecoronagraphitself.Fig. 6-9 showshowthepeaksofresidualstarlightneartheinterioroftheLyotpupilcorrespondtothepositionofactuatorsontheDM.SincephaseerrorsintheDMpupilgenerateintensityerrorsattheLyotpupil,weknowthattheDMshapeisnotfullyoptimized.Thisisnotsurprisinggiventhatthewavefrontissensedbeforethesciencecamera. 112

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6-10 displayssensitivitycurvesforavarietyofexperimentsandatheoreticalon-skypredictionforcomparison(seex ).Contrastiscurrentlylimitedto3104attheIWA,oroneorderofmagnitudebelowtheAirypattern.ThegreenandbrowncurvesindicatethattheBLMandhard-edgemaskhaveasimilarperformancebutthatthehard-edgemaskisbetteratlteringlow-ordercontent{aresultthatisconsistentwithasystemwithlargestaticaberrations(x ,x ).These(non-common-path)errorscreateanintensity`plateau'neartheedgeoftheDMcontrolregionwhichcanalsobeseeninFig. 6-9 .TheblueBLMcurveshowstherelativeimprovementinsensitivityneartheopticalaxiswhentheDMshapeisiterativelytunedusingtherstseveralZernikemodesbymeasuringtheintensityatthedetector.WewereunabletofullyoptimizetheDM Figure6-10. ExperimentalcontrastresultsusingthePALAOinternalwhitelightsource.Nopost-processingtricks,suchasPSFsubtraction,havebeenapplied.TheBLMcanmakedetectionsinsideofthe0.88"IWAbutnocloserthantheLyotstopspatialresolutionlimit. 113

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AllmeasurementstakenpriortoFall2007wereacquiredatatimewhentwooftheDMactuatorswerepinned.Theirlackofresponsetoinstructionsscatteredasignicantamountofstarlight.Maintenancetoxtheseactuatorsresultedinanoticeableimprovement(blackcircles)allowingsensitivitiestoapproachthetheoreticalexpectation. Thereappearstobenosignicantchromaticissues.DatatakenwiththeBrlterinDecember2006(pinkcurve)closelyfollowstheothersensitivitycurveswiththeexceptionthattheintegrationtimewasnotsucientlylong:theBrbandpassis15timesnarrowerthanKshort.WealsoconrmedthattheBLMdoesleakdiractedstarlightintheJ-bandwherethemaskstripesarenolongersmallerthanmin=Dtel(seex ). Wewereunabletotesttheeectsofmaskdefectsonthespecklenoiseoor,sincethewhitelightsourcedidnothaveatranslationstagetoshiftitspositionwithintheFOV. .Nevertheless,aDMcancompensateforsuchstaticerrors(x ). 114

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);(ii)coronagraphicimages,wherethestarisoccultedbythemask,fortheobviousreasons;and(iii)o-sourceimages,forcalibrationofthebrightskybackground.Itisalsousefultoobtainon-sourceimageswiththeDMotomeasuretheseeing. Thetotaltimespentonabrightsourceisoften30-45minuteswithadutycycleeciencyofroughly30%,whenincludingthetimenecessarytoslewtothetarget,placeitwithintheunvignettedregion(seeFig. 6-11 ),closetheAOloop,andalignthemask.Nearly30%ofthetimeisspentontheskybackground.Moreoverheadisrequiredwhenthe\ex-cam"isrunning.Theex-campicksounusedbluelightfromthewavefrontsensorbeamandsendsextratip/tiltinstructionstotheDMtomaintainprecisemaskalignmentbycorrectingfordierentialdrifts(exures)thatoccurbetweenthetelescopeandPHAROoverthelengthofanexposure. Oncetheimages(.tsles)areinhand,theyarebackedupandprocessedwithanin-houseMatlabprogramdesignedspecicallyforPHAROhigh-contrastdata.Asimplieddescriptionofthereductionprocedureisasfollows: 6-11 ) Fruchter&Hook ( 2002 ) 115

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Baraeetal. ( 2003 )substellaratmosphericmodels Figure6-11. Flat-eldimageshowingrelayopticsvignettingelements.StarsmustbeplacedwithinthecentralregionthatresemblesAfrica. 116

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Potteretal. 2002 ; Gaidosetal. 2000 ),makingitanexcellenthigh-contrastimagingtarget.Table 6-1 liststhestar'sphysicalparametersandotherimportantobservationalinformation,includingtheSmithsonianAstrophysicalObservatorynumber(SAO),J2000right-ascension(RA)anddeclination(DEC),distanceinparsecs,spectraltype,apparentvisualmagnitude(V),approximateage,totalexposuretimeonsource(tsource)andonsky(tsky),medianairmass,seeing,andStrehlratio. Table6-1. PhysicalparametersandobservationalinformationforHIP72567. SAO=83553distance=17.9pcsage=300-800Myrsairmass=1.07RA=145015.8sp.type=G2Vtsource=595sseeing=1.3"DEC=+235442.6Vmag=5.9tsky=595sStrehl=77:80:9 Figs. 6-12 and 6-13 showthestarwithandwithoutthecoronagraph.Ahigh-passFourierlterhasbeenappliedtoamplifythesignalofsourceswithintrinsicwidthsofordermax=Dtelorsmallercomparedtolow-frequency(i.e.blurry)structure.SeveralAiry Figure6-12. CalibrationimageofHIP72567usedtocalculatetheStrehlratioando-axisthroughput.ImageintensitiesareonalogarithmicstretchandtheFOVisthesameineach.Fourierlteringcanarticiallyenhancethephotometricsignatureofacompanion.Thiscompanionisnotrealbuttheresultofaninternalreectionfromaneutral-density-lter. 117

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FullyprocessedcoronagraphicimagesofHIP72567beforeandafterFourierltering.Fourierltereddataarealsousedinternallybythereductioncodetofacilitateprecisionstackingofindividualimagespriortomediancombination.TheorientationoftheBLMisindicatedbyadottedline.TheghostfromFig. 6-12 isnolongerpresentbecausetheneutral-density-lterwasremovedtomaximizeux. ringscanbeseenbeforetheBLMandLyotstopcombinationsuppressthestartorevealfeaturesinitsimmediatevicinity.Thefourwae-modepeaks(C1103)canbarelybedetectedinthecalibrationimage,butareclearlyvisiblewiththecoronagraphinplace.ExactcontrastlevelsareshowninFig. 6-14 and 6-15 Anti-symmetricspecklesduetoquasi-staticwavefrontphaseerrorscanbeseenaboveandbelowthemask.Itispossibletoexploitthissymmetry Closeetal. 2005 ),polarimetric( Perrinetal. 2008 ),andspatialimaging( Maroisetal. 2006 ).Thatis,thestructureofquasi-staticspeckles )andthusalwaysnegligiblefromtheground. 118

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HIP72567coronagraphsensitivityaboveandbelowmaskinmagnitudes. Figure6-15. HIP72567coronagraphsensitivityinJupitermassesasafunctionofage. 119

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6-13 ,forexample,showsthatthebrightspecklesdonothavethesameshapenorintensity.ThislogiclikewiseappliestoPSFsubtractionusinganearbystar.Inthenear-future(2009),wewillbetheonlyhigh-contrastimaginggroupcapableofexplicitlyremovingthisdominantsourceofnoise.PSFstabilityprovidedbytherelayopticsaordsustheopportunity.TheStrehlforthisparticulartargetwaslow,butnotcharacteristicoftheperformance. UponconvertingthecontrastlevelsfromFig. 6-14 tocompanionmassat5(Fig. 6-15 ),whereisthelocalstandarddeviationinthesignal,wendthatwearesensitivetoM-dwarfs,browndwarfs,andveryyoung,verymassive,andverydistantplanets,suchasthoseshowninx .HIP72567istherststarevertobeobservedwithaBLMoranylegitimateTPF-Cdesigncandidate. Wenotethatthisstarisactuallyatriplesystemwithafaintbrown-dwarf-brown-dwarfpairorbitingat2.6"fromtheprimary( Potteretal. 2002 ).Wearecapableofdetectingthissetofcompanions,buttheyarelocatedataninopportunepositionangleandwerecompletelyoccultedbytheBLM.Thiscircumstanceistheresultofnotknowingaprioritheringangleoftheimagingsystemwiththerelayopticsinplace.Thiswastherstobservingrun,andtheanglechangesslightlywitheachinstallationbyanamountcomparabletotheslit-wheelsteppermotorrangeofmotionwithintheFOV,whichalsochangeslocation.(Thisisthestrongestselectionconstraintwhenwetargetvisualbinarystarsinx .)ItispossibletorotatetheCass-cageby90oincrements,whichwouldpermitdetectionofHIP72567BC,butwedidnotgetachancetogoon-skywiththe(non-default)orthogonalorientationinApril2007orMay2008. 6-2 .ThisstarisintriguingbecauseithostsaJupiter-likeexoplanet(Msini=0:95MJupiter,a=4.2 120

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PhysicalparametersandobservationalinformationforHIP83389. SAO=46452distance=18.1pcsage=0.5-9Gyrsairmass=1.03RA=170236.4sp.type=G8Vtsource=595sseeing=1.0"DEC=+470454.8Vmag=6.7tsky=297sStrehl=84:60:4 AU,e=0.04;( Wright&Vogt 2008 ,inpress)).Themultiplicityofexoplanethoststarsisatleast20%( Mugraueretal. 2007 )andabrowndwarfhasrecentlybeendirectlyimagedorbitingthestarHD3651,whichhostsaneccentricsub-Saturn-massplanetat0.3AU( Fischeretal. 2003 ).HIP83389isalsoonM.Turnbull'slistof\habstars"forSETIandtheTPFmissions( Turnbull 2008 ). Althoughthisstardoesnotexhibitsignsofyouth,wearesensitivetomassivebrowndwarfsexteriorto60AU(Figs. 6-16 6-17 ,and 6-18 .).ThecontrastislimitedbyAOlatency(fDM=200Hz)andsystematictip/tiltalignmenterrors(x ,x )asaresultofexurebetweentheCass-cageandtelescope(excamwasnotoperational).Dependingonthepositionoftargetsinthesky,theexuremaybemoreproblematic.Attimes,thedriftsconvenientlyfollowtheopaqueportionsofthelinearmask,but,inthiscase,movementswereintheorthogonaldirection. Figure6-16. FullyprocessedcoronagraphicimagesofHIP83389. 121

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HIP83389coronagraphsensitivityaboveandbelowmaskinmagnitudes. Figure6-18. HIP83389coronagraphsensitivityinJupitermassesasafunctionofage. 122

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Geetal. 2006 ).Throughoutgraduateschool,Ispent40nightsatKittPeakNationalObservatoryusingthesingleobjectExoplanetTracker(ET)RVinstrumentand31nightsatApachePointObservatoryusingthemulti-objectKeck-ETRVinstrument.Ithoughtitwouldbeinterestingtotargetthisstarandplacelimitsonthepresenceofsubstellarcompanions.HD102195alsoappearstoberelativelyyoung,althoughuncertaintiesstillremainregardingitsage.ItsphysicalparametersandrelevantobservationaldataareshowninTable 6-3 SensitivitywaslimitedbyAOlatencyerrorsasisindicatedbytheblurringpatternseensurroundingthemaskinFig. 6-19 .TheDMrefreshratewasagainsettoonly200Hz,inordertocollectsucientuxineachwavefrontsensorsubaperture.ThefaintesttargetforwhichtherelayopticswillprovideasubstantialboostinStrehlisVmag=9. Wewereabletoruleoutsubstellarcompanionsorbitingexteriorto50AUdowntothelevelsshowninFig. 6-21 .Therearenobrowndwarfsmoremassivethan:25MJupiterandyoungerthan100Myrsoutsideof125AU;50MJupiterandyoungerthan500Myrsoutsideof150AU;and70MJupiterandyoungerthan1Gyrsoutsideof150AU( Baraeetal. 2003 )at5abovethenoiseoor. Table6-3. PhysicalparametersandobservationalinformationforET-1. SAO=119033distance=29.0pcsage=0.6-4.2Gyrsairmass=1.19RA=114542.3sp.type=K0Vtsource=595sseeing=1.2"DEC=+024917.34Vmag=8.1tsky=297sStrehl=75:40:7 123

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FullyprocessedcoronagraphicimagesofET-1. Figure6-20. ET-1coronagraphsensitivityaboveandbelowmaskinmagnitudes. 124

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ET-1coronagraphsensitivityinJupitermassesasafunctionofage. 125

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Tokovinin 2004 ; Duquennoy&Mayor 1991 ).Todate,however,theyhavebeenquitepurposefullyavoidedbyhigh-contrastimaginginstrumentsduetoaninabilitytosuppressthelightfrombothstarssimultaneously.Dependingontheseparation,nearbystellarcompanionswilleither:(i)addunnecessarypointingerrors,or(ii)completelyoverwhelmaportionofthenalimage.ThecartooninFig. 7-1 depictsthesituationforaground-basedtelescopewithperfectAOandacoronagraph.Resolvingthestellarpairresultsinsignicantcontrastdegradationanddramaticallyreducestheprospectsfordiscoveringfainttertiarycompanions. Suchcongurationsoccurfrequentlyatnear-IRwavelengthswithlargeaperturetelescopes.Forexample,thereexistsadistinctpeakintheorbitalperioddistributionofbinarystarswithG-typeprimariesat104:8days( Duquennoy&Mayor 1991 ).Thisnumbercorrespondstoanangularspacingof0.5"ontheskyifwetake75pcsasacharacteristicdistancetotargetsinthesolarneighborhood.Thespatialresolutionofadiraction-limited5mtelescopeat2.0micronsis0:1".Thus,themajorityofnearbyintermediate-spectral-typebinarystarsareseparatedbyseveraldiractionwidths. 7-1 indicatesthepotentiallocationofacompanionexecutingap-typeorbitaroundabinarystarsystemthathasalargeinclinationrelativetotheplaneofthesky. 126

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Qualitativesimulationimagescomparingcirculartolinearmasks.(a)Binarystarsseparatedbyseveral=D.Thepointingerrorsaresignicant.(b)Alinearmaskalignedtobothstarssimultaneously.(c)Binarystarsseparatedbymany=D.Thesearch-spaceisseverelylimited.(d)Alinearmaskcanaccommodateanysuchgeometry.Theseimagesweregeneratedusingperfectwavefronts,equallyluminousstars,hard-edgemaskswithhightransmission(0.05),andnoLyotstop.Intensityisshownonalogarithmicscale. Numericalsimulationshaveshownthatcompanionsarestableinsuchcongurationsoverawiderangeofseparations,massratios,andorbitaleccentricities( Holman&Wiegert 1999 ).Moreover,recentSpitzerobservationshavedetectedseveralcircumbinarydebrisdisks( Trillingetal. 2007 ),lendingcredencetopotentiallow-masscompanionformationinthesedynamicallymorecomplexenvironments,and20%ofshortperiodplanetsorbitasinglememberofabinarysystem( Mugraueretal. 2007 ).Giventhisinformation,itishardlyjustiabletomakeconclusionsregardingthefrequencyofsubstellarcompanionswithoutconsideringbinarystars. Inadditiontosearchinganewparameterspace,otherpoignantreasonsfortargetingbinariesare: Marcy&Butler 2000 ).Subsequentimagingsurveysshowthatthisso-called\brown-dwarfdesert"extendsasfaras1000AU( McCarthy&Zuckerman 2004 ; Carsonetal. 2006 ).Theexistenceofasimilardesertwithbinary 127

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Duch^eneetal. 2007 )predictsthatlarge-separationbrown-dwarfsshouldbeslightlymorecommonaroundbinariesthansinglestars,basedsolelyonargumentsofbinding-energy.Suchobservationscantestthisprediction. Basedonthesescienticjustications,wewereawardedon-skytimeatPalomartoconductthersthigh-contrastimagingobservationsofvisualbinarystarsusingthecoronagraphicmasksfromx .Theremainderofthischapterdescribestargetselectioncriterionandresultsfromour\mini-pilot-survey". AdistancecutisincludedtomaintainaclosephysicalIWAandremoveintrinsicallybrightstarsthatmeettheapparentmagnitudecriterion.Theangularseparationbetweenstars,,shouldbelargeenoughthatan8-10mtelescoperesolvesthebinary,butsmallenoughthatcircumbinaryorbitsinthesearchareaarereasonablystable.[Noticethatwecouldusethesmallaperturetoouradvantageagainbytargetingstarsthatwedonotresolve(50.mas.300)butthosethatalargetelescopewould{specically,situation(a)inFig. 7-1 .Inthiscase,acircularmaskisideal.] Themostrestrictivecriterionisthepositionangle.Theslit-wheelrangeofmotionwithinthePHAROFOV,withtherelayopticsinplace,isonly7:5o.Ifweinclude 128

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.Inotherwords,wedonotknowwithcertaintywhetheraparticularbinaryisobservableuntilwegoon-sky(!) Intotal,690targets(0
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. ManyoftheindividualK-bandapparentmagnitudesarenotavailablesince2MASSisseeinglimited.Itis,however,possibletousethecombineduxrecordedby2MASSwithourdiraction-limitedcalibrationimagestoobtaintheapparentK-bandmagnitudes: (7{1) (7{2) whereK2MASSisthecombined(unresolved)apparentK-bandmagnitudemeasuredby2MASS( Skrutskieetal. 2006 )andF1andF2aretheuxesmeasuredfromourcalibrationimagesinarbitraryunits.ApparentmagnitudesarethenconvertedtoabsolutemagnitudesinordertocalculatecontrastinJupiter-massesusingthe Girardietal. ( 2002 )and Baraeetal. ( 2003 )atmosphericmodels,whichareconsistentwithoneanothernearthebrown-dwarf{stellarboundaryforagesgreaterthan50Myrs. Makarov 2003 ).Table 7-1 listsitsphysicalparametersandrelevantobservationalinformation.SeeingmeasurementsusuallyrecordedbythePalomarMASS-DIMMsystem( Thomsenetal. 2007 )arenotavailableforthisrunduetoinconsistentweatherconditions.Wedidnotmeasuretheseeingdirectlyonaccountofthesetimeconstraints. Table7-1. PhysicalparametersandobservationalinformationforHIP88637. SAO=85723distance=37.7pcsage<150Myrsairmass=1.05RA=180549.7sep/PAa=0.49"/91.4otsource=991sseeing=unav.DEC=+212645.2Vmag=7.6/8.4tsky=991sStrehl=89:80:9

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Calibrationandhigh-passFourier-lteredcoronagraphimagesofHIP88637. ResultsareshowninFigs. 7-2 7-3 ,and 7-4 .Reectionsfromaneutral-densitylterarevisibleforeachstarinthecalibrationimage,butnotseeninthecoronagraphimagesincethelterisremovedoncethemaskisaligned.Therearenoweightwae-modepeaks.Thecontrastiscomparabletolevelsachievedaroundsinglestarsinx (see Figure7-3. HIP88637coronagraphsensitivityinmagnitudes.Theasymmetryinuxaboveandbelowthemaskisaresultofmechanicalexure. 131

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HIP88637coronagraphsensitivityinJupitermassesforanageof100Myrs. below).Wewereabletogeneratesensitivitiestobrown-dwarfsandmassiveextrasolarplanetsorbitingexteriorto50AUand275AUrespectivelyatthe5level.Notertiarycompanionsweredetected. Haywardetal. 2001 ),thatsuppressesthenon-common-patherrorsshowninFig. 6-9 .Italsohashigherthroughputandspatialresolution,althoughthedesigninx ,whichwasusedforallobservationsinApril2007,shouldworkbestintheidealcase. Table7-2. PhysicalparametersandobservationalinformationforHIP82510inApril2007. SAO=84655distance=56.9pcsage=unknownairmass=1.02RA=165150.1sep/PA=1.36"/102.5otsource=297sseeing=0.9"DEC=+283959.0Vmag=7.0/8.5tsky=149sStrehl=85:90:3% 132

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CalibrationimagesofHIP82510inApril2007andMay2008.SpatialresolutionandthroughputareimprovedonaccountofawiderLyotstop. Figure7-6. CoronagraphimagesofHIP82510inApril2007andMay2008. WeobservedthebinarystarsystemHIP82510on2007-4-29and2008-5-26(UT)usingthehard-edgemaskandBLMrespectively..Table 7-2 displaysitsphysical 133

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HIP82510coronagraphsensitivityinmagnitudesin2007and2008. Figure7-8. HIP82510coronagraphsensitivityinJupitermassesin2007and2008.Althoughdierentmaskswereused,theenhancedperformanceistheresultofswitchingtoaLyotstopbettersuitedtohandlenon-common-patherrors. 134

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ThepositionanglerelativetoPHAROchangedby11.4oinbetweenruns,butonly0.5oisduetoorbitalmotion(PA=103oinMay2008),implyingthattheCass-ringanglechangedby10.9o.Thisisasignicantamountandaectstargetselectionsincetheslit-wheelrangeofmotionisonly15o(x ).TheeectwillbeaccountedforinthefuturebycompilinglistsoftargetsthatspantherangeofpositionanglessurroundingtheCass-ring\sweet-spots"(i.e.whereanunobscuredquadrantofthetelescopeaperturecanbeselected)orbybuildingmasksthatarenotparalleltooneanother(x ). Thedierenceinrelativepositionanglemadeitmandatorytousedierentmasksforthetworuns.AlthoughtheBLMhasthepotentialtooutperformthehard-edgemask(x ),theimprovedsensitivityshowninFigs. 7-7 and 7-8 isaresultofblockingnon-common-patherrorsandpassingmoreo-axislightwiththemediumcrossLyotstop.Thescatteredlightoordropsjustenoughtodetectmassivebrown-dwarfs.WenotethattheK-banduxratio,F2=F1,wasmeasuredtobe0.319in2007and0.318in2008. 7-3 displaysitsphysicalparametersandrelevantobservationalinformation.ResultsareshowninFigs. 7-9 7-10 ,and 7-11 .TheDMoperatedat500HZ,whichisfasterthanmostoftheobservationspresentedhereusingtherelayoptics.Frequenciesapproaching2kHzareidealforminimizingAOlag-timeerrors. Table7-3. PhysicalparametersandobservationalinformationforHIP88964. SAO=123187distance=50.1pcsage=unknownairmass=1.18RA=180933.9sep/PA=0.62"/288.2otsource=977sseeing=unav.DEC=+035935.8Vmag=6.1/7.4tsky=489sStrehl=88:81:5% Mass-sensitivitydependsstronglyonageonlybelowthebrowndwarf{starboundary(.80MJupiter).Thisistheresultofcoolingsincesubstellarbodiesareunabletosustain 135

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CalibrationandcoronagraphimagesofHIP88964. Figure7-10. HIP88964coronagraphsensitivityinmagnitudes. 136

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HIP88964coronagraphsensitivityinJupitermassesforvariousages. hydrogenfusionreactions.Thecontrastreaches40MJupiteratanageof500Myrs.Nocompanionsweredetected. 7-4 )on2008-5-26(UT)usingtheBLM.Impendingcloudspreventedacquisitionofacalibrationimage.Nevertheless,wewereabletocalculatetheK-bandmagnitudesviaEqu. 7{2 fromthewae-modepeaks(!) Severalpoint-sourcesarevisibleaboveandbelowthemask(Fig. 7-12 ).Symmetriesintheimagesuggestthepresenceoflong-livedspeckles(so-called\super-speckles"),whicharetheresultofquasi-staticerrors,butnotallofthesourceshaveasymmetricoranti-symmetricpartner,whichmightbetheresultofslightlydierentmaskalignmentsforeachstar.Follow-upobservationsarerequiredtodiscriminatespecklesfromcompanions.Theevidenceinthiscaseis,however,likelytooweaktowarrantaproposal. 137

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PhysicalparametersandobservationalinformationforHIP66458. SAO=63648distance=58.8pcsage=unknownairmass=1.05RA=133727.6sep/PA=1.74"/96.9otsource=942sseeing=unav.DEC=+361741.6Vmag=5.0/7.1tsky=248sStrehl=unav. Figure7-12. CoronagraphimageofHIP66458. Figure7-13. HIP66458coronagraphsensitivityinmagnitudes. 138

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HIP66458coronagraphsensitivityinJupitermassesforvariousages. 7-5 )on2008-5-26(UT)usingthehard-edgemask.TheDMwasoperatingat500Hz.ResultsareshowninFigs. 7-15 7-16 ,and 7-17 .Sensitivitiessucienttodetectmassivebrowndwarfsweregeneratedatprojectedseparationsgreaterthan250AU.Nonearbypointsourcesweredetected. Table7-5. PhysicalparametersandobservationalinformationforHIP76952. SAO=83958distance=44.5pcsage=unknownairmass=1.01RA=154244.6sep/PA=0.72"/112.4otsource=439sseeing=unav.DEC=+261744.3Vmag=4.1/5.6tsky=439sStrehl=92:31:7% 7-6 )on2007-4-29(UT)usingtheBLM.TheDMwasoperatingat500Hz.ResultsareshowninFigs. 7-18 7-19 ,and 7-20 .Wewereunabletogeneratesensitivitiestobrowndwarfsindependentofage.Notertiariesweredetected. Table7-6. PhysicalparametersandobservationalinformationforHIP82898. SAO=17285distance=67.1pcsage=unknownairmass=1.18RA=165625.3sep/PA=1.29"/67.7otsource=142sseeing=0.9"DEC=+650220.8Vmag=7.1/7.4tsky=71sStrehl=89:50:3% 139

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CalibrationandcoronagraphimagesofHIP76952. Figure7-16. HIP76952coronagraphsensitivityinmagnitudes. 140

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HIP76952coronagraphsensitivityinJupitermassesforvariousages. Figure7-18. CalibrationandunlteredcoronagraphicimagesofHIP82898. 141

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HIP82898coronagraphsensitivityaboveandbelowmaskinmagnitudes. Figure7-20. HIP82898coronagraphsensitivityinJupitermassesforanageof5Gyrs. 142

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Inanycase,wehavelearnedalot.TheBLMclearlyworksandwehaveidentiedtheeectsthatcanlimitsensitivity.Theex-camerawillsoonoperatesmoothlyandcorrectforthedriftsseenwithHIP83389andHIP88637.WenowhaveahandleonthepreferredCass-cageringanglesandhowtheytranslatetoon-skymeasurementsrelativetoourmaskwithinPHARO.Combiningthisinformationwithmoreon-skytimewillpermitobservationsthatbetterfavoryoungsystems.Moreover,weexpectsignicantgainsinsensitivity(seex )byremovingthenon-common-patherrorsshowninFig. 6-9 .Onceenoughsourcesareobservedandtheabovehardwareadjustmentsaremade,itwillbepossibletomakeapple-to-applecomparisonsofthehard-edgemaskversustheBLMandtothefullapertureusingdataobtainedpreviouslybyJoeCarson. Weanticipateanexperimentinthenear-termwhereaverybrightsource,likeVega,isimagedontoaquadrantofthearray.Thiswillreducetheread-timeandallowforbetterspeckletracking.Wealsoplantofullycharacterizeboththehard-edgemaskandBLMbymovingthewhitelightsourcedowntheirlongaxis(x ).Ifnon-common-patherrorsassociatedwithvisualbinarystars,whichlandondierentlocationsofthemask(seex ),canbeneglected,oratleastminimizedusinganoptimalDMsetting,itmaybepossibletoperformhigh-delityPSFsubtraction(x ),bymodelingthespecklepattern. Asensitiveandstatisticallysignicantsurveyofvisualbinarystarswillplacenewconstraintsonthepopulationofsubstellartertiarycompanions,whichisimportantforthe 143

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.ItisinterestingtoconsiderhowthesearchareaofalinearmaskaectstheresultsofaMonteCarlosimulationwherearticialbrowndwarfsareinserted.Ofcourse,afewdetectionswouldbemostexciting. Iamalsonaturallycuriousaboutcircumbinaryplanets.Iftheyaremoremassive(onaverage)comparedtoplanetsorbitingsinglestars,duetoasurplusofmaterialfromwhichtheycanform,oriftheirorbitsaremoreeccentric(onaverage),duetostochasticprocesses,theywillbeeasiertoimage! 144

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ThissectionreiteratesthemainconclusionsfromChapters2-7andbrieydescribestheproject'slikelypathoverthenextfewyears. Insummary,wendthat: Thebasicpremiseofthisworkisstraightforward:contrastismostimportantinthegameofhigh-contrastimaging,especiallywiththeeldinitscurrentstate:oneormaybetwoimagesofextrasolarplanetsthusfarthatdidnotevenrequireacoronagraphtodetect(!)Simultaneousdierentialimagingtechniqueshavegeneratedthedeepestsensitivitiestodate,buttheycanalwaysbeappliedaftertheinstrumentscatteredlighthasbeenexplicitlyremovedusinghardware.Sincestar-planetseparationsspanseveralordersofmagnitude(0.018AU-275AU,HD41004BbandABPicrespectively),thereshouldbeanabundantnumberofcompanionswith>0:5"separations.Forexample,EpsilonEridanibwillreachitsgreatestelongationof1.6"intheyear2010( Benedictetal. 2006 ).Itisthusquitereasonabletosacricespatialresolutiontohelpovercomefundamentallychallengingproblems,suchastheexquisitepositioningofnumerous,closely-spacedactuatorstocorrectfortheatmospherewhileremovinginstrumentscatteredlight.RelayopticscanaddresstheseissuesseveralyearsbeforethenextgenerationofAOsystems 145

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Thisprojecthasalotofpotentialandthereareseveralobviousnextstepstotake: and/orbypokingindividualactuatorsandlookingattheresultintheLyotpupilplane. Dekanyetal. 2007 ). Figure 8-1 showspredictionsforbrightsinglestarsusingrelayopticswithandwithoutcompensationfornon-common-patherrorsandthenwiththeupgradetoPALM-3k.Instantaneouscontrastlevelsoforder106arepossible.Anintegral-eld-unitshouldbecapableofdiscriminatingbetweenspecklesandcompanionsusingcolorinformationtoimprovetheeectivesensitivitybyanotherorderofmagnitude. Theremaybeinsucientuxforall64x64wavefrontsensorsubaperturesusingtherelayoptics,but,aswehaveshowninx ,itisnotnecessarytocorrectneartheouter-mostedgesofthedark-hole.Thissacriceinsearchareapermitsuseoflesssubapertureswhileimprovingthedark-holedepth.Laser-guidestarAOmaybeanotheralternativeinthissituationsincethe`cone-eect'associatedwithilluminatinganearbylayeroftheatmosphere(i.e.,thefactthatthelaserdoesnotcreateaperfectpointsource)isrelativelysmallfora1.5mtelescope. 146

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ContrastasafunctionofangularseparationfortheHaletelescopeusingrelayoptics.Itispossibletoremove(quasi-static)scatteredlight(createdbynon-common-patherrors)downtothenoiseoorsetbytheatmosphereat7106intheK-band(redcurve).ThesemethodsmaythenbeappliedtotehPALM-3ksystemintheJ-bandandwithanewBLM(bluecurve).TheIWAwillimprovefrom880masto510masandthecontrastwilldropto2106andextendto5400mas.Sacricesoftheoutersearchareamaydroptheinstantaneousnoiseoorevenfurther.Thefullaperturecanprobesmallerseparationsbutcannotmatchthesensitivity.Withpost-processingtechniques,theeectivecontrastmayreach107.Youngmassiveexoplanetsaredetectablewiththistechnology. 147

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JustinRobertCreppwasborninEllwoodCity,Pennsylvania,USAin1979toparentsRobertandJennieCrepp.Hehasayoungerbrother,Adam,andalargefamilywithmanyaunts,uncles,andcousins.JustingraduatedfromPennStateErie-TheBehrendCollege,withabachelorsdegreeinphysicsandminorinmathematicsinDecember2002.OnOctober16th,2006,hemarriedAmyLynnSlozatonHolmesBeachneartheTampaBay.Theirrstchild,AaronJustin,wasbornjustdaysbeforethenalversionofthisworkwassubmittedtotheUniversityofFloridaDepartmentofAstronomy. 159