New Worlds Occulters Webster Cash University of Colorado September 29, 2006.

New Worlds New Worlds OccultersOcculters

Webster CashWebster CashUniversity of University of

ColoradoColoradoSeptember 29, September 29,

20062006

New Worlds ContributorsNew Worlds ContributorsWebster Cash University of ColoradoJim GreenEric SchindhelmJeremy Kasdin Princeton UniversityBob VanderbeiDavid SpergelSara Seager Carnegie Institution – WashingtonAlan Stern Southwest Research Institute – BoulderSteve Kilston Ball AerospaceTom BankCharlie NoeckerJim LeitchJon Arenberg Northrop GrummanRon PolidanChuck LillieAmy LoGlenn Starkman Case WesternSally Heap Goddard Space Flight CenterMarc KuchnerKeith Gendreau

and growing…

Important CaveatsImportant Caveats New Worlds is an emerging mission conceptNew Worlds is an emerging mission concept

Rapidly developing with a small teamRapidly developing with a small team Recent emphasis was on Discovery proposal, Recent emphasis was on Discovery proposal,

not a TPF-C class missionnot a TPF-C class mission TPF mission under very active studyTPF mission under very active study There is no mission design or final conceptThere is no mission design or final concept

We have found no obvious impediments to such a We have found no obvious impediments to such a missionmission

It is a major goal of this talk to inform the It is a major goal of this talk to inform the audience on how occulters do and do not audience on how occulters do and do not workwork

Given the limited time here, the results are Given the limited time here, the results are sample of the work that has been donesample of the work that has been done

Overview of the Occulter Overview of the Occulter HourHour

Development and performance of the Development and performance of the occulter (Cash-CU)occulter (Cash-CU)

Occulter modeling (Lyon-GSFC)Occulter modeling (Lyon-GSFC) Overview of architecture trades Overview of architecture trades

(Arenberg-NGST)(Arenberg-NGST) Alignment (Noecker-Ball)Alignment (Noecker-Ball) Summary (Arenberg-NGST)Summary (Arenberg-NGST)

Origin: 2002-2003Origin: 2002-2003 Maxim was stalledMaxim was stalled

Still isStill is Maxim was outgrowth of 1999-2001 NIACMaxim was outgrowth of 1999-2001 NIAC

Was there a way to apply Maxim technology to a Was there a way to apply Maxim technology to a more immediate problem?more immediate problem?

Noticed that TPF and Maxim were both driven by the Noticed that TPF and Maxim were both driven by the need for high performance opticsneed for high performance optics

Personally, the only thing I find as exciting as Personally, the only thing I find as exciting as imaging a black hole is finding and imaging Earth-imaging a black hole is finding and imaging Earth-like planetslike planets

Decided to try my hand at the exo-planet gameDecided to try my hand at the exo-planet game

June 2003June 2003

Came up with the Pinhole camera ideaCame up with the Pinhole camera idea

It was not MAXIM, but a rather a refusion It was not MAXIM, but a rather a refusion and reapplication of the Maxim approachand reapplication of the Maxim approach

A Pinhole Camera Meets The Requirements:Perfect TransmissionNo Phase ErrorsScatter only from edges – can be very low

Large Distance Set by 0.01 arcsec requirementdiffraction: /D = .01” D = 10m

@500nmgeometric: F = D/tan(.01”) = 180,000km

““Standard” Observatory Views Standard” Observatory Views StarshadeStarshade

~1” resolution or somewhat better (not diffraction limited!)

High efficiency, low noise spectrograph (e.g. COS)

View Back Toward View Back Toward StarshadeStarshade

Background Stars & Zodiacal Light

Starshade

Diffracted Starlightaround edge fallsoutside slit

SpectrographEntrance Slit(Projected)

Planet Light

Background Stars & Zodiacal Light

Starshade

Diffracted Starlightaround edge fallsoutside slit

SpectrographEntrance Slit(Projected)

Planet Light

Starshade Aperture ShapesStarshade Aperture Shapes

Focal Plane Focal Plane

View Dark Side of StarshadeView Dark Side of Starshade

Planet Finding ModePlanet Finding ModeSolar System at 10pc

Survey to 7AU Survey Habitable Zone

Jupiter

Earth

Venus

Mars

Venus

Earth

Why Pinhole Why Pinhole Camera?Camera?

Why Not Occulter?Why Not Occulter?

Because Because

Everybody knows that Everybody knows that diffraction around an diffraction around an occulter is too severeocculter is too severe

OccultersOcculters Several previous programs have looked at occultersSeveral previous programs have looked at occulters

First look by Spitzer (1962)First look by Spitzer (1962) Marchal (1985) Used simple petal shapesMarchal (1985) Used simple petal shapes

Achieved 10Achieved 10-5-5 suppression across a broad spectral band suppression across a broad spectral band With transmissive shadesWith transmissive shades

Achieved only 10Achieved only 10-5-5 suppression despite scatter problem suppression despite scatter problem

http://umbras.org/BOSS Starkman (TRW ca 2000)

Extinguishing Extinguishing

Poisson’s SpotPoisson’s Spot SimpleSimple Occulters Have Very Poor Diffraction Performance Occulters Have Very Poor Diffraction Performance

The 1818 Prediction of Fresnel led to the famous episode of:The 1818 Prediction of Fresnel led to the famous episode of: Poisson’s Spot (variously Arago’s Spot)Poisson’s Spot (variously Arago’s Spot) Occulters Often Concentrate Light!Occulters Often Concentrate Light!

Must satisfy Fresnel Equation, Not Just the Fraunhoffer EquationMust satisfy Fresnel Equation, Not Just the Fraunhoffer Equation

Must Create a Zone That Is:Must Create a Zone That Is: Deep Deep Below 10Below 10-10-10 diffraction diffraction Wide Wide A couple meters minimumA couple meters minimum Broad Broad Suppress across at least one octave of spectrumSuppress across at least one octave of spectrum

Must Be PracticalMust Be Practical Binary Binary Non-transmitting to avoid scatterNon-transmitting to avoid scatter Size Size Below 150m DiameterBelow 150m Diameter Tolerance Tolerance Insensitive to microscopic errorsInsensitive to microscopic errors

The Vanderbei FlowerThe Vanderbei Flower Developed for Aperture in TPF focal planeDeveloped for Aperture in TPF focal plane Was to be only millimeters acrossWas to be only millimeters across Vanderbei had determined it would work for Vanderbei had determined it would work for

the pinhole camera but did not necessarily the pinhole camera but did not necessarily work for occulter.work for occulter.

Agreement that it was worth a lookAgreement that it was worth a look

BreakthroughBreakthrough

From 11/17/04 to 4/12/05 worked on diffraction codesFrom 11/17/04 to 4/12/05 worked on diffraction codes Put the problem out there for whomever to solvePut the problem out there for whomever to solve

At one point had 3 professors, 2 engineers and 4 studentsAt one point had 3 professors, 2 engineers and 4 students On April 12 last year (after Phase I, before Phase II On April 12 last year (after Phase I, before Phase II

due)due) Had working codeHad working code Was trying functions (as opposed to VDB generalized forms)Was trying functions (as opposed to VDB generalized forms) Tried OFFSET gaussianTried OFFSET gaussian Ten minutes later had a solutionTen minutes later had a solution

In June discovered hyper-gaussians even betterIn June discovered hyper-gaussians even better

The Apodization The Apodization FunctionFunction

0A a

a 1

na

bA e

for

for

and

Found this in April. Extended in June.This Function Extinguishes Poisson’s Spot to High Precision

PerformancePerformanceA 50m diameter occulter at 50,000km will reveal Earths at 10pcA 50m diameter occulter at 50,000km will reveal Earths at 10pc

a=b=12.5mn=6F=50,000km

Arenberg and Cash (2005)

Occulters Are Occulters Are Fundamentally FresnelFundamentally Fresnel

(Never Ever Fraunhoffer)(Never Ever Fraunhoffer)

The central Fresnel zone and the eight inner half zones are The central Fresnel zone and the eight inner half zones are shown schematically. The dark star in the centre represents a shown schematically. The dark star in the centre represents a mask that is confined to the region where the Fraunhoffer mask that is confined to the region where the Fraunhoffer approximation can be used. It is clear that such a mask will approximation can be used. It is clear that such a mask will

integrate out to a net positive contribution in the focal plane.integrate out to a net positive contribution in the focal plane.

Suppression of Edge Diffraction Suppression of Edge Diffraction Can Be UnderstoodCan Be Understood

Using Fresnel Zones and GeometryUsing Fresnel Zones and Geometry

The occulter is a true binary opticThe occulter is a true binary optic Transmission is unity or nilTransmission is unity or nil

Edge diffraction from solid disk is Edge diffraction from solid disk is suppressed by cancellation suppressed by cancellation The power in the even zones cancels The power in the even zones cancels

the power in the odd zonesthe power in the odd zones Need enough zones to give good deep Need enough zones to give good deep

cancellationcancellation Sets the length of the petals Sets the length of the petals

Petal shape is exponential Petal shape is exponential b is scale of petal shapeb is scale of petal shape n is an index of petal shapen is an index of petal shape a is the diameter of the central circlea is the diameter of the central circle

ab

Huygens-Fresnel PrincipleHuygens-Fresnel Principle

0 ikrEE Ae dS

i r

F

s

F

s

Fresnel ApproximationFresnel Approximation

2

2 2 cos20 2

0 0

,

iksik ik sikF F

F FE e e

E e A e d di F

2

22

0 20

0

iksikikF F

FE ke e k s

E e A J diF F

Then, if circularly symmetric:

Babinet’s PrincipleBabinet’s PrincipleNecessary for Integration Across ShadeNecessary for Integration Across Shade

0 1 2E E E

We seek E2=0 or:

2 1ikFE e E

1ikFE e

2

2

0

ikikF ikFF

ke A e d e

iF

2

2

0

1ik

Fk

A e diF

or

To simplify math we concentrate on the center of the shadow (s=0)

We seek A() such that:

or

Now, Evaluate Candidate Now, Evaluate Candidate Apodization FunctionApodization Function

n

a

bA e

1A

22

22

0

n

n

a ika ikFbF

a

k kE e d e d

iF iF

Dimensionless Natural UnitsDimensionless Natural Units

ka

F

kb

F

k

F

Electric Field at Center:Electric Field at Center:

22

22

0

1 1n

ii

E e d e di i

22

221

1

nii

E e e di

Integrate by PartsIntegrate by Parts

2 1

2

nni

R n e e d

Yields E = 1+R where R is small as desiredAnd

This closed-form integral represents the electric fieldat the center of the shadow

Continue Integrating by Continue Integrating by PartsParts

1! 1 1 !

n

n n n

n nR

Drop Small Terms

Dominant Term

If 2 >> n

Binary ApodizationBinary Apodization

a

b

b

a a

b

b

a

2 2 cos cos

2

0

,2

ik ik s ik s

F F F

a

kR e A e A e d d

F

Difference between petalsand circularly symmetric

apodization.

Tolerance AnalysisTolerance Analysis

Procedes by perturbation analysisProcedes by perturbation analysis Pitch or Yaw error – Pitch or Yaw error – foreshortened to 1-foreshortened to 1- in one dimension in one dimension

2

12

0

ni y

y nR n e e y dy

csRR

Reduces to:

Proving

2 2 2

22 2222

(1 )

2 2

11

2 2

(1 )

2

1

n

iky ikz

F F

ikF

y z aikziky b

F F

e e dydz

kE e

iF

e e e dydz

Where z=x/(1-)

Starshade Starshade TolerancesTolerances

PositionPosition LateralLateral Several MetersSeveral Meters DistanceDistance Many KilometersMany Kilometers

AngleAngle RotationalRotational NoneNone Pitch/YawPitch/Yaw Many DegreesMany Degrees

ShapeShape TruncationTruncation 1mm1mm ScaleScale 10%10% BlobBlob 3cm3cm22 or greater or greater

HolesHoles Single HoleSingle Hole 3cm3cm22

PinholesPinholes 3cm3cm22 total total

E II x , y ie ikz

zE I x, y e

iz

x x 2 y y 2 dxdy

E I x,y E0 1 M x, y

E II x , y E0eikz 1

i

ze

iz

x 2 y 2 M x,y e

iz

x 2 y 2 e i

2z

x x y y dxdy

Fresnel Propagation from External Occulter

• Parallel “C/MPI” code to (512 node Beowulf): - Model occulter - Fresnel propagate to telescope • Current grids 32768 x 32768• Don’t yet get theorectical limit• Aliasing from small structure ? - No aliasing from Fresnel ripples (low Fresnel #) - from small scale structure ?

Core radius a 6.25 m Inner (Solid) starshadePetal Length b 6.25 m Petal characteristic lengthPetal Taper n 6 Petal shape parameter# of Petals p 12 Number of petalsDiameter d 25 m to 1/e transmission ptDiameter D 30 m tip-to-tipDistance z 18,000 km distance to TelescopeWavelength 0.5 um

-20 -16 -12 -8 -4 0 4 8 12 16 20

1e-10

1e-08

1e-06

1e-04

1e-02

1e+00

Meters

Intensity at Telescope

45 meters

LOGO.049

R. Lyon09/29/06

100,000 km 50,000 km

25,000 km 18,000 km

Real part of field at mask

Copyright 2006 Northrop Grumman Corporation

Occulter Systems Terrestrial Planet Finding

Jon Arenberg

Amy Lo

Chuck Lillie

Richard Malmstrom

Ron Polidan


Occulter Based TPF Missions are Viable

Occulter 101 Sufficient suppression of star light

at the same time as achieving small IWA

Sizing and spacing of the occulter

How does the occulter handle challenges to performance

What would a mission look like? How is occulter telescope

alignment established and maintained (Charley Noecker)

Experimental Results; Leviton and Cash (In Prep)


The Basic NWO Architecture Occulters blocks on-axis star light Telescope looks at off-axis star light to observe

companion

planet

Target Star NWO OcculterTelescope


The Occulter Parameters

Parameter Symbol Affects….

solid disk radius a IWA, stellar suppression

Gaussian radius parameter b IWA, stellar suppression

the petal shape parameter n Observation wavelength

Occulter separation F IWA, stellar suppression

number of petals P Minimum needed


Two Effects of the Occulter

Image at aperture:Diffraction pattern produced by occulter, color indicates the achievable stellar suppression

Image at focal plane, the Occulter’s “PSF”, note that outside of the IWA, it’s dark!

star occulter telescope

LOG Scale

LOG Scale

R


The Occulter PSF

Occulter acts as an optical element and focuses incident starlight to the entrance pupil

The intensity of the starlight is greatly decreased, and the phase is distorted by the destructive interference caused by the occulter petals

The telescope optics therefore produces a defocused residual stellar image at the focal plane, here called the stellar leakage

Inside a certain radius on the focal plane, defined as the IWA, the stellar leakage is bright, and can be thought of as the occulter’s “PSF”

IWA

These four points are artifacts of diffraction calculated with a square grid

LOG Scale


The Occulter PSF

Incomplete destructive interference produces gradual roll off of the residual stellar leakage

The leakages decreases with radial distance from the occulter center, and is the chief source of the “background” signal OUTSIDE of the IWA

Planet light compete with this background signal

The correct figure of merit used to judge the NWO occulter is to measure the signal to noise of this background with incident, off-axis planet light

IWA

These four points are artifacts of diffraction calculated with a square grid

LOG Scale


NWO Only Needs 10-8 Suppression

In order for the planet light to be above the background, the occulter only needs to achieve 10-8 stellar suppression between the star and the planet

We are in fact measuring the planet signals inside the wings of the stellar PSF, which gives us the extra factor of 100 reduction

10-10 Suppression 10-9 Suppression 10-8 Suppression

Linear Scale


“Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

0 mas

LOG Scale Linear Scale



50 mas




70 mas




75 mas




80 mas




85 mas




90 mas




100 mas




110 mas



Occulters Capable of 10-10 Suppression

Occulters that achieve the desired suppression

Occulters that do NOT achieve desired suppression

The following were generated using 1-D FrFT simulation

All numbers shown are real results, no approximations have been made

4 m telescope (on axis)

Maximum wavelength 800 nm

Order 6 occulter


Occulters IWA Less Than 100 mas

Occulters with IWA smaller than 100 mas

Occulters with IWA larger than 100 mas


Intersection Identifies Viable Parameter Space

There is a minimum size occulter for a given set of requirements

Different plot for hypergaussian order and maximum wavelength

This size does not account for known liens on performance

Smallest Possible Occulter, 28m

Occulters with both suppression better than 10-10

and IWA smaller than 100 mas

SPIE Astronomical and Instrumentation 2006, Orlando, FL

Paper 6265-67

Requirements Flow for Test Case• Contrast ratio of 10-10,

IWA of 100 mas• 4 m diffraction limited

telescope• Maximum =800 nm• Each source gets

O(10-11)

a, b, n, P, F, edge width, reflectance,Instrument

a, b, n, P

Operationalconstraint

a, b, n, P, F

a, b, n, P, F

Operationalconstraint

a, b, n, P, F

SPIE Astronomical and Instrumentation 2006, Orlando, FL

Paper 6265-67

Design Space Construction

10 15 20 25 30 35 40 45 50 55 6010

20

30

40

50

60

70

80

90

100Occulter Log CR < -10, and IWA < 90 mas

Occulter Diameter [m]

Occ

ulte

r S

ep

ara

tion

[10

00

km

]

Occulter Too Far Away

Occu

lter To

o L

arge

•The allowed design space is continuous

10-5

10-4

10-3

10-2

10-2

100

102

104

106

108

wo [m]

Co

ntr

ast

LO

SS

4 cycles

8 cycles

12 cycles16 cycles

22 cycles

32 cycles

-15 -10 -5 0 5 10 15

10-12

10-10

10-8

10-6

10-4

10-2

100

Telescope Plane Size [m]


Occulter Systems are Flexible

An occulter can be located at any separation distance

Allows the system to mix and match suppression and IWA


Full Scale Mission: 1 Telescope, 2 Occulters

4 meter VIS/UV ordinary space telescope Smaller telescope does allow the TPF-C science program to

be accomplished 50% planet hunting duty cycle, 50% general astrophysics

Survey occulter: quickly scan and discovery signatures of planets

IWA = 100 mas, Stellar suppression = 10-10 @ 800 nm Occulter size (theory) 28 m and separation 30 Mm

Big Occulter: aligns with target star and provides deep integration

IWA = 50 mas, Stellar suppression = 10-11 @ 800 nm Occulter size (theory) 50m and separation 80 Mm


Reference Mission Month


Sample Full-Mission Orbit and V

Lissajous orbit at Sun-Earth L2 point 1.2M km wide Launch to C3 = −.68 km²/s²

Telescope ∆V required: 70 m/s injection ~ 2 m/s/yr stationkeeping

Survey occulter Drift rate: 7.6 x 10-6 m/s2

1 m/s stationkeeping [1 day] 40 m/s slewing [25°, 6 days] Total V = 304*41 = 12.5 km/s

Big occulter Drift rate: 1.7 x 10-5 m/s2

7.5 m/s stationkeeping [5 days] 70 m/s slewing [25°, 12 days] Total V = 80*77.5 = 6.2 km/s

SEP is necessary for both the small and large occulters

New Worlds ObserverAlignment Sensing Concepts

Charley Noecker

The challenge

Target star, telescope, and star-shade must be collinear within1. About 60-100 mas for the onset of occultation2. About 4 mas (TBR) during the observation

During on-orbit checkout, allow alignment acquisition and calibration to take telescope time

During normal operations, try to minimize telescope participation in alignment acquisition

The Problem

Four steps:– (01) Find partner s/c on sky– (2) Acquire occultation on new target ( accuracy)– (23) Optimize alignment before observation ( calibration)– (3) Maintain alignment during observation ( stability)

1

Uncertainty in bearing (rad)

DSN Find partner Astrometry Occult’n

10-2 10-6 10-8 10-4

CC retro ground calib? Calibr

3210

Sensor options under consideration

Telescope

Antipode field stars

Brighttarget

star

Target star

Target star

Telescope & field stars

Retro

Retro

Occulter Telescope

Red leak of occulter illuminates aperture

edges; guide telescope to a minimum

TelescopeLaser or sunlight

Starlight

Acquisition

Target acquisition requires accuracy

Bearing vector (telescope starshade) aligned with line of sight (LOS) within – Arcsecond or more (close range) during initial checkout and calibration– 60-100 mas accuracy operationally

• Bonus points: minimize telescope participation, for minimum impact on observing schedule

Techniques– On starshade, observe light from telescope against antipode stars

• Hipparcos limit ~30-50 mas (antipode vs. nearby stars)– On starshade, observe light from telescope against retroreflected target star

(camera/telescope with cubecorner in front)• CC calibration pre-launch• On-orbit calibration after first acquisition

– On telescope, observe light from starshade against target star Light sources:

– Scattered sunlight from other spacecraft– Laser beacon

Optimize alignment before observation

Observe stellar occultation depth with telescope andsimultaneously watch the alignment sensor

Map out target star’s occultation depth vs. alignment offsets– Calibrate alignment sensor vs. peak occultation– Hold the peak for the duration of an observation– Maybe the detected image of diffracted starlight will help

This calibration, carried from star to star, reduces the setup time needed to reach deep occultation

Maintaining alignment during observation only requires stability

Nominal control tolerance ~4 mas (TBR)– 1 meter / 50,000km = 4 mas = 20 nrad– For a 2 µrad pixel 20 nrad = 1%

Stable for 4-16 hours (TBR) with few recalibrations

During science observation, sensing of diffractive leakage at longer wavelengths (out of band) can help maintain centering and calibration without interruption

Other spacecraft may be faint

If telescope has 1 m2 total of lambertian scattering surface in direct sunlight, this gives 14 mag apparent brightness seen from 50,000 km

Active source (laser) would need small divergence angle to keep optical power requirement low

Large surfaces (starshade’s near side) could be turned deliberately into sunlight to boost visibility during acquisition


Occulters Are Viable for TPF A mission design is being developed based on external occulters

No special telescope needed with multiple occulters Occulter sizes and distances reasonable

Design space smooth System can be aligned Provide for flexible operations Can handle finite stellar size Are broadband

Upper wavelength is the design parameter No outer working angle

Engineering challenges to implementation exist, but technologies are of high TRL

External occulters need to be described by figures of merit that are different than other candidates

Current work continuing the rapid development of occulter based missions for exoplanetary science

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New Worlds Occulters Webster Cash University of Colorado September 29, 2006.

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