occulter design for theia - princeton universityhcil/papers/kasdinetal_spie2009.pdfdistance. we...

Occulter Design for THEIA

N. Jeremy Kasdina, Eric J. Cadya, Philip J. Dumontb, P. Douglas Lismanb, Stuart B.Shaklanb, Remi Soummerc, David N. Spergela, Robert J. Vanderbeia

aPrinceton University, Princeton, NJ, USAbJet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109

cSpace Telescope Science Institute, Baltimore, MD, USA

ABSTRACT

An occulter is an instrument designed to suppress starlight by diffraction from its edges; most are designedto be circular, with a set of identical “petals” running around the outside. Proposed space-based occultersare lightweight, deployed screens tens of meters in diameter with challenging accuracy requirements. Inthis paper we describe the design of an occulter for the THEIA mission concept. THEIA consists of a4-meter telescope diffraction limited to 300 nm, and a 40-meter external occulter to provide high-contrastimaging. Operating from 250 to 1000 nm, it will provide a rich family of science projects, including exoplanetcharacterization, ultraviolet spectroscopy, and very wide-field imaging. Originally conceived of as a hybridsystem employing both an occulter and internal coronagraph, THEIA now uses a single occulter to achieveall of the starlight suppression but at two different distances from the telescope in order to minimize size anddistance. We describe the basic design principles of the THEIA occulter, its final configuration, performance,and sensitivity.

1. INTRODUCTION

Over the past 25 years, the Hubble Space Telescope has revolutionized our view of the universe, excited andengaged the general public with its compelling images, and has been a workhorse for astrophysics. Over thepast 2 years we have been studying a worthy successor to HST and companion to the James Webb SpaceTelescope (JWST), THEIA, Telescope for Habitable Exoplanets and Interstellar/Intergalactic Astronomy,a flagship 4-meter on-axis optical/UV telescope. With a wide-field imager, an ultraviolet spectrograph, aplanet imager/spectrograph and a companion occulter, THEIA is capable of addressing many of the mostimportant questions in astronomy: Are we alone? Are there other habitable planets? How frequently dosolar systems form and survive? How do stars and galaxies form and evolve? How is dark matter distributedin galaxies and in the filaments? Where are most of the atoms in the universe? How were the heavy elementsnecessary for life created and distributed through cosmic time?

The THEIA observatory∗ is an on-axis three-mirror anastigmat telescope with a 4-meter Al/MgF2-coated primary, an Al/LiF-coated secondary and diffraction-limited performance to 300 nm. It has threemain instruments: the Star Formation Camera (SFC), a dual-channel wide-field UV/optical imager covering19’ x 15’ on the sky with 18 mas pixels; the UltraViolet Spectrograph (UVS), a multi-purpose spectrometeroptimized for high sensitivity observations of faint astronomical sources at spectral resolutions, λ/Δλ, of30,000 to 100,000 in the 100-300 nm wavelength range; and the eXtrasolar Planet Characterizer (XPC),which consists of three narrow-field cameras (250-400 nm; 400-700 nm; 700-1000 nm) and two R/70 integralfield spectrographs (IFS).

Exoplanets are difficult to image directly both because they are faint compared to their host stars, andbecause they are at very small angular separations. For Earth-like planets in habitable zones, the differencein flux between the star and planet is estimated to be 1010.1 There are many approaches to suppressing thestarlight for exoplanet exploration, most of which use either an internal coronagraph or an external occulter.Both have the potential to yield similar exoplanet science (measured in number of planets discovered and

∗In Greek mythology, Theia is the Titan goddess of sight (thea), also called the “far-seeing one”. She is the motherof the Sun, the Moon and Dawn.

Techniques and Instrumentation for Detection of Exoplanets IV, edited by Stuart B. Shaklan, Proc. of SPIE Vol. 7440, 744005 · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.826518

Proc. of SPIE Vol. 7440 744005-1

Downloaded from SPIE Digital Library on 17 Oct 2009 to 140.180.23.37. Terms of Use: http://spiedl.org/terms

Figure 1. (Left) The SFC Optical Layout. (Center) The UVS Optical Layout. (Right) The XPC Optical Layout.

Figure 2. The occulter for the THEIA observatory.

characterized) with a 4-meter telescope, yet each has different technical challenges. For this study wefocused on an external occulter as a demonstration that a suitable mission architecture exists that can bebuilt in the next decade. This choice allows an on-axis telescope without wavefront control, relaxes stabilityrequirements, and simplifies the optical design and packaging for all of the instruments.

THEIA’s companion occulter is 40 meters in diameter and stationkeeps at 55,000 km from the telescopefor imaging from 400-700 nm and at 35,000 km to characterize from 700-1000 nm. It can be seen in Figure2. While the occulter is on target (25% of mission time), XPC detects and characterizes extrasolar planetsand SFC does deep field science. While the occulter moves, THEIA conducts a rich program of generalastrophysics. In the remainder of this paper we discuss the approach we took to reaching this design, itsimplications on the mission, and the resulting manufacturing requirement.

2. OCCULTER DESIGN

The design of the THEIA occulter is based on the fact that a smoothly apodized screen can create asufficient shadow to remove enough stellar photons that a dim companion planet can be seen.2–4 Whilethere are a number of approaches to finding this smooth apodization using scalar diffraction theory, it isvirtually impossible to manufacture with real materials. We therefore approximate such a screen with abinary occulter, which allows either all or none of the light through at any point. The resulting shape has



a series of structures along the edge, called petals, which vary their width with radius so that if a circle isdrawn at a radius r, the fraction of the that circle which is blocked by petals is A(r), the desired apodizationfunction. It can be shown5 that the resulting electric field is then the same as that of a smooth apodization,with a series of additional perturbation terms from the scattering.

We have shown previously5 that optimization tools can be used to design an apodization that results inthe smallest and closest possible occulter while still achieving the starlight suppression requirements over adesired wide spectral band. Nevertheless, in order to achieve our goal of planet characterization from 250 to1000 nm, we find that the starlight has to be suppressed by twelve orders of magnitude at the inner workingangle and beyond in the image plane. This is 100 times more than the ratio between the star and the planet,but is necessary to provide tolerance to errors in the occulter shape and placement. (See6 for more detail.)To accomplish this, a very large occulter flying quite far from the telescope is required (51.2 m in diameterat 70,400 km). Not only is this difficult to build and fit into a launch vehicle, the larger size and distancehas significant impact on the science yield because of the time needed to transfer a larger and more distantocculter between targets. We thus placed a premium on finding the smallest possible occulter. This makes iteasier to manufacture and handle, reduces the size of the launch vehicle and fairing, increases the potentialscience yield, and, hopefully, relaxes requirements on the tolerances.

One approach to achieving a smaller and more nimble occulter is to pursue a hybrid design where a smallerocculter, achieving less than the needed 12 orders of magnitude contrast, is combined with an internal occulterto accomplish the rest. This has a certain appeal as it makes both the occulter and coronagraph less difficult,still relaxes the need for wavefront control, and potentially allows a belt and suspenders approach to meetingrequirements that can reduce risk and increase flexibility. There are a number of approaches one might taketo such a design, but all rely on the electric field at the telescope pupil being flat or symmetric. Unfortunately,after much investigation, none resulted in a robust, implementable design. While most coronagraph designsto date assume a flat electric field at the entrance pupil of the telescope, the presence of the occulter resultsin a spatially varying field, with significant differences across the waveband. Only coronagraphs that relyon symmetry, such as the AIC, can be made to work. However, combining them with an occulter resultsin unreasonable requirements on the stationkeeping of the telescope/occulter combination. Extremely smalldeviations of the occulter from the line of sight (less than 10 mm) break the electric field symmetry at thetelescope and destroy the contrast at the planet location in the image. These unreasonable requirements ledus to search for a different approach.

Fig. 3 shows the effect of the occulter on coronagraph performance. The top figure shows the PSFs ofa star and planet at the telescope image plane, after having been passed through an APLC. The incidentwavefront is a plane wave with a median intensity equal to that of the occulter’s shadow across the telescopeaperture. The bottom figure shows the same, with the occulter shadow itself incident. Sufficient light isdiffracted into the location of the planet at the image plane to reduce the effectiveness of the coronagraphby two orders of magnitude, down to the level that the occulter could provide without the coronagraph’sassistance.

Rather than combine the occulter with a coronagraph, we chose instead to look at operational scenariosthat would allow for a smaller, easier-to-manufacture occulter. Here, we take advantage of certain invariancesin the Fresnel propagation integral used for occulter design.5 Considering only the continuous apodizationfor simplicity, the electric field at the telescope location after an occulter of radius R and apodization A(r)is given by,

Eapod(ρ) = E0e2πiz/λ

(1− 2π

iλz

∫ R

0

A(r)J0

(2πrρ

λz

)e

iπλz (r2+ρ2)rdr

)(1)

where ρ is the radial position in the shadow, λ is the wavelength of light, and z is the occulter/telescopeseparation.

For our occulter design, we use the fact that intensity is invariant under simultaneous scalings of thewavelength and distance. That is, if we scale the distance by a constant c (z → zc) and inverse scale thewavelength by the same constant (λ → λ/c), then we have the same electric field (and thus shadow) at the



Figure 3. (Top) plane wave incident, (Bottom) occulter shadow incident. Star is in blue, planet is in red.

1-dist. Occulter 2-dist. OcculterOcculter radius (m) 25.6 20

Occulter nominal distance (km) 70400 55000Occulter moved-in distance (km) - 35000

Occulter nominal IWA (mas) 75 75Occulter moved-in IWA (mas) - 118

Telescope diameter (m) 4 4Number of petals 20 20Petal length (m) 19 10

Minimum gap between petals (mm) 0.12 1.0Minimum width of petal tip (mm) 1.62 1.0

Table 1. Design parameters for a single distance and multi-distance occulter meeting THEIA requirements. Thetwo-distance occulter is smaller, closer, has shorter petals, and larger gaps.

telescope to within a phase factor, which disappears when intensity is calculated. We thus design an occulterto operate over a band of shorter wavelengths, allowing for a smaller and easier-to-manufacture design, andthen move the occulter closer to the telescope for the band of longer wavelengths.

We show our resulting occulter design for THEIA in Table 1 compared to a single occulter system, wherethe occulter was designed to meet the contrast requirements from 250 to 700 nm at the further distance(55,000 km) and from 700 to 1000 nm at the closer separation (35,000 km). The resulting occulter is smaller(40 m), closer (allowing for shorter slews), has significantly shorter petals (eliminating the need for extrahinge lines and allowing it to fit into a smaller fairing), and 10x larger gaps between petals (making it mucheasier to manufacture). For this design, we have chosen a scaling factor c = 7/11.

There are two drawbacks of such an approach. The first is that it now requires two long integrations inseries to fully characterize the planet over the entire band. For some systems, there may not be enough timebefore the planet leaves the visible zone. The second is that the inner working angle has increased by thesame factor c for the closer observations. Thus, for our occulter designed for an inner working angle of 75



Figure 4. Simulated images of a close in companion planet (red) and the residual starlight (blue) for the hybridTHEIA occulter design. Note that we leave two orders of magnitude margin in contrast to allow for tolerance toerrors.

Petal Position or Shape Error Allocation

r.m.s shape (1/f2 power law) 100 m

Proportional shape 80 m at max width

Length clipping at tip 1 cm

Azimuthal position 0.003 deg (1 mm at tip)

Radial position 1 mm

In-plane rotation about base 0.06 deg (1 cm at tip)

In-plane bending (r2 deviation) 5 cm

Out-plane bending (r2 deviation) 50 cm

Cross-track occulter position 75 cm

Table 2. Requirements on occulter manufacturing to meet a contrast of 10−12 at the planet location.

mas at the shorter wavelengths, we are only able to characterize planets at separations larger than 118 masfor the redder wavelengths. Again, this means the loss of some science on the closest planets. In the nextsection we describe the optical performance of this system, its impact on science yield, and the requirementson manufacturing.

3. SYSTEM PERFORMANCE

Fig. 4 shows the image plane point spread function of a close in planet overlaid on the residual starlight PSFfor three different wavelengths. In each case, a contrast of 10−12 is achieved at the planet location. Notethat while the planet we model only has a contrast of 10−10 relative to the star, we allow a two order ofmagnitude margin in our design to account of various errors on the occulter and telescope. Until a detailedsimulation is completed, a conservative error budget needs to allocate a certain amount of contrast to eacherror. For example, in Table 2 we list some of the largest error sources and the resulting requirements inorder to keep the contribution from each below 10−12. (See Dumont et al. 20096 for further detail.)

Fig. 5 shows the impact on overall science yield from using a two distance occulter vs. a single distanceocculter. While there is no reduction in the number of planets detected, there is some loss in the abilityto characterize them, both because of the inner working angle loss and the added time. However, thatreduction is not large and there is still substantial science obtained. We felt the tradeoff favored the two-distance occulter because of the significant gains in implementation.

4. MECHANICAL DESIGN

The resulting THEIA occulter system, shown in Fig. 6 consists of a 40-meter starshade attached to aspacecraft bus equipped for repositioning, stationkeeping, and pointing. The solar array is sized for 15 kW



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

5

10

15

20

25

30

35

40

Unique Planet Detections

Coronagraph

Occulter

THEIA

THEIA Extended

(a)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

5

10

15

20

25

30

35

40

45Spectral Characterizations to at least 700nm

Coronagraph

Occulter

THEIA

THEIA Extended

(b)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

Spectral Characterizations between 250 and 1000nm

Coronagraph

Occulter

THEIA

THEIA Extended

(c)

Figure 5. Expected science yield from four planet-finding architectures with a 4m telescope: a 2λ/D coronagraph, anocculter at one distance, an occulter at two distances, and an occulter at two distances with an extended mission.(Left) Number of unique planets found. (Center) Number of planets with spectral characterization (to S/N = 11) atthe location of the planet for λ in 250-700nm. (Right) Number of planets with spectral characterization (to S/N =11) at the location of the planet for λ in 250-1000nm.

of end of life power to accommodate 2 NEXT-Ion thrusters firing simultaneously at maximum power (whichcan be adjusted in flight) plus 1 kW for other bus equipment. This thruster subsystem consists of 6 totalthrusters with 3-for-2 redundancy on each side of the starshade. During exoplanet observations, the occultersystem is held on targets constrained to lie between 45 and 85 degrees from the sun line to avoid stellarleak into the telescope or reflections off the starshade. Stationkeeping does not employ electric thrustersbecause they produce a bright plume potentially contaminating the observations. The spacecraft is thusalso equipped with a set of on/off hydrazine thrusters that control position to within ±75 cm. A shutter isemployed during the short, infrequent hydrazine pulses to avoid light contamination from the plume.

After a retargeting slew, the observatory/occulter formation is acquired in 4 overlapping stages of positionsensing: 1) Conventional RF Ground tracking (±100 km), 2) Observatory angle sensing of a Ka-Band beaconfrom the occulter spacecraft (±16 km), 3) XPC IR imaging of a laser beacon (±70 m) and 4) XPC IR imagingof light leaking around the occulter (±35 cm). The Observatory measures occulter range via the S-Bandlink. The occulter system has a maximum expected mass of 5,700 kg as compared to a launch mass capacityof 6,300 kg. The remaining mass margin will be used for additional fuel for extended operations.

The occulter design uses a modular construction approach employing petals deployed around a fabriccore. The starshade is comprised of 2 major subsections, a 19.46 m diameter inner core composed of 3layers of Kapton and an outer section of twenty 10.27 meter tall and 3.7 meter wide petals. Together, whendeployed they form an occulting mask 40 meters in diameter from tip-to-tip. The precision shaped petaledge, defined for maximum light suppression, is machined into an extremely low CTE graphite epoxy sheet.The sheet is bonded to a petal perimeter graphite epoxy box frame to provide structural support. In thestowed configuration, the central core and petals mount to a graphite composite deployment deck, whichin turn mounts to the spacecraft. A central opening accommodates the recessed mounting of propulsivethrusters, antennas and laser beacons.

The stowed configuration fits inside a 5 m launch fairing with margin. A truss structure supports thestowed petals and is jettisoned after launch. Deployment is initiated by extending the entire stowed petalstack on two deployable booms. This linear action unfolds the center-blanket assembly. Once fully extended,the booms begin a rotation that initiates sequential deployment of the petals. All petal hinge lines arecontrolled by redundantly actuated, passively damped, high accuracy hinges. A simple sequencing cambetween the primary hinge-lines of the petals also controls deployment. As the booms rotate, the petalsunfold. The final position is controlled by stops designed into each hinge line. Careful optical analysis wasused to design the hinges and gaps to maintain the needed starlight suppression.



Figure 6. The deployed and stowed occulter and attached spacecraft.

5. THE THEIA MISSION

Design reference missions for THEIA are created using a Monte Carlo mission generator described in Savran-sky et al. 2009.7 In this method, the list of potential targets is populated with planets, and a mission designis created using a set of selection rules designed to maximize total science return over the course of themission, taking into account technical limitations, fuel usage, and realistic optical performance. The list oftargets is then given a new set of planets, and the sequence is repeated to build up a distribution of sciencereturn for a given architecture. The planet populations can be varied to examine different frequencies ofEarth-like planets. Plots of science return for four planet-finding architectures with a 4m telescope are givenin Fig. 5:

1. A 2λ/D coronagraph

2. An occulter operating at a single distance

3. An occulter operating at two distances (THEIA baseline)

4. Total science return if the THEIA occulter is allowed to continue in an extended mission until it runsout of fuel

The science return for the one- and two-distance occulters is similar; however, the smaller occulter posedfewer technical difficulties, which gave it the edge over the larger single distance occulter. In addition, theadditional fuel used to slew the larger occulter means that none remained to run an extended mission. (Theocculters are the ones described in Table 1.)

The THEIA observatory is designed to be placed in a halo orbit around the Earth-Sun L2 point. Theocculter is then slewed around as necessary to place itself between the star and the telescope. The missiondesign assumed a two-week slew between targets; the occulter turned out to spend the majority of its timein transit. 25% of the telescope time was earmarked for observations with the occulter; while these aregoing on, the SFC will also be doing deep field science. The remainder of the mission time will be dedicatedto general astrophysics programs. This percentage is a reasonable assumption with respect to the missiondesign; the DRMs were run assuming that all the time when the occulter was in position would be dedicatedto planet-finding, and this turned out to be between 20% and 30% of the available time, depending on theplanet distribution in the simulated universe.



6. CONCLUSIONS

We have presented the design for the occulter for the THEIA observatory, and its associated observingmission. This system would be able to find Earth-like planets beyond 75mas around nearby stars. Combininga coronagraph with an occulter proves to be an ineffective way to get the occulter smaller and closer to thetelescope; instead, the occulter is made smaller by operating at two different locations with respect to thetelescope.

6.1 Acknowledgments

The work upon which this white paper is based was performed under contract to the National Aeronauticsand Space Administration (NASA), contract number NNX08AL58G. The project was managed by the JetPropulsion Laboratory (JPL), California Institute of Technology, under contract with the National Aero-nautics and Space Administration. Portions of the work were performed at the various university partners,the Goddard Space Flight Center (GSFC), Lockheed Martin Missiles and Space, ITT Space Systems LLC,and Ball Aerospace.

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