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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
b Jet
a Princeton
University, Princeton, NJ, USA
Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109
c Space Telescope Science Institute, Baltimore, MD, USA
ABSTRACT
An occulter is an instrument designed to suppress starlight by diffraction from its edges; most are designed
to be circular, with a set of identical “petals” running around the outside. Proposed space-based occulters
are lightweight, deployed screens tens of meters in diameter with challenging accuracy requirements. In
this paper we describe the design of an occulter for the THEIA mission concept. THEIA consists of a
4-meter telescope diffraction limited to 300 nm, and a 40-meter external occulter to provide high-contrast
imaging. Operating from 250 to 1000 nm, it will provide a rich family of science projects, including exoplanet
characterization, ultraviolet spectroscopy, and very wide-field imaging. Originally conceived of as a hybrid
system employing both an occulter and internal coronagraph, THEIA now uses a single occulter to achieve
all of the starlight suppression but at two different distances from the telescope in order to minimize size and
distance. 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 and
engaged the general public with its compelling images, and has been a workhorse for astrophysics. Over the
past 2 years we have been studying a worthy successor to HST and companion to the James Webb Space
Telescope (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, a
planet imager/spectrograph and a companion occulter, THEIA is capable of addressing many of the most
important questions in astronomy: Are we alone? Are there other habitable planets? How frequently do
solar systems form and survive? How do stars and galaxies form and evolve? How is dark matter distributed
in galaxies and in the filaments? Where are most of the atoms in the universe? How were the heavy elements
necessary 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 three
main instruments: the Star Formation Camera (SFC), a dual-channel wide-field UV/optical imager covering
19’ x 15’ on the sky with 18 mas pixels; the UltraViolet Spectrograph (UVS), a multi-purpose spectrometer
optimized for high sensitivity observations of faint astronomical sources at spectral resolutions, λ/Δλ, of
30,000 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 integral
field spectrographs (IFS).
Exoplanets are difficult to image directly both because they are faint compared to their host stars, and
because they are at very small angular separations. For Earth-like planets in habitable zones, the difference
in flux between the star and planet is estimated to be 1010 .1 There are many approaches to suppressing the
starlight 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 mother
of 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
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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 we
focused on an external occulter as a demonstration that a suitable mission architecture exists that can be
built in the next decade. This choice allows an on-axis telescope without wavefront control, relaxes stability
requirements, 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 telescope
for imaging from 400-700 nm and at 35,000 km to characterize from 700-1000 nm. It can be seen in Figure
2. While the occulter is on target (25% of mission time), XPC detects and characterizes extrasolar planets
and SFC does deep field science. While the occulter moves, THEIA conducts a rich program of general
astrophysics. In the remainder of this paper we discuss the approach we took to reaching this design, its
implications 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 a
sufficient shadow to remove enough stellar photons that a dim companion planet can be seen.2–4 While
there are a number of approaches to finding this smooth apodization using scalar diffraction theory, it is
virtually impossible to manufacture with real materials. We therefore approximate such a screen with a
binary occulter, which allows either all or none of the light through at any point. The resulting shape has
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a series of structures along the edge, called petals, which vary their width with radius so that if a circle is
drawn at a radius r, the fraction of the that circle which is blocked by petals is A(r), the desired apodization
function. 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 in
the smallest and closest possible occulter while still achieving the starlight suppression requirements over a
desired wide spectral band. Nevertheless, in order to achieve our goal of planet characterization from 250 to
1000 nm, we find that the starlight has to be suppressed by twelve orders of magnitude at the inner working
angle 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 diameter
at 70,400 km). Not only is this difficult to build and fit into a launch vehicle, the larger size and distance
has significant impact on the science yield because of the time needed to transfer a larger and more distant
occulter between targets. We thus placed a premium on finding the smallest possible occulter. This makes it
easier to manufacture and handle, reduces the size of the launch vehicle and fairing, increases the potential
science 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 smaller
occulter, achieving less than the needed 12 orders of magnitude contrast, is combined with an internal occulter
to 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 meeting
requirements that can reduce risk and increase flexibility. There are a number of approaches one might take
to 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 designs
to date assume a flat electric field at the entrance pupil of the telescope, the presence of the occulter results
in a spatially varying field, with significant differences across the waveband. Only coronagraphs that rely
on symmetry, such as the AIC, can be made to work. However, combining them with an occulter results
in unreasonable requirements on the stationkeeping of the telescope/occulter combination. Extremely small
deviations of the occulter from the line of sight (less than 10 mm) break the electric field symmetry at the
telescope and destroy the contrast at the planet location in the image. These unreasonable requirements led
us to search for a different approach.
Fig. 3 shows the effect of the occulter on coronagraph performance. The top figure shows the PSFs of
a star and planet at the telescope image plane, after having been passed through an APLC. The incident
wavefront is a plane wave with a median intensity equal to that of the occulter’s shadow across the telescope
aperture. The bottom figure shows the same, with the occulter shadow itself incident. Sufficient light is
diffracted into the location of the planet at the image plane to reduce the effectiveness of the coronagraph
by two orders of magnitude, down to the level that the occulter could provide without the coronagraph’s
assistance.
Rather than combine the occulter with a coronagraph, we chose instead to look at operational scenarios
that would allow for a smaller, easier-to-manufacture occulter. Here, we take advantage of certain invariances
in the Fresnel propagation integral used for occulter design.5 Considering only the continuous apodization
for simplicity, the electric field at the telescope location after an occulter of radius R and apodization A(r)
is given by,
iπ
2πrρ
2π R
r 2 +ρ2 )
2πiz/λ
(
λz
rdr
(1)
Eapod (ρ) = E0 e
A(r)J0
1−
e
iλz 0
λz
where ρ is the radial position in the shadow, λ is the wavelength of light, and z is the occulter/telescope
separation.
For our occulter design, we use the fact that intensity is invariant under simultaneous scalings of the
wavelength and distance. That is, if we scale the distance by a constant c (z → zc) and inverse scale the
wavelength by the same constant (λ → λ/c), then we have the same electric field (and thus shadow) at the
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Figure 3. (Top) plane wave incident, (Bottom) occulter shadow incident. Star is in blue, planet is in red.
Occulter radius (m)
Occulter nominal distance (km)
Occulter moved-in distance (km)
Occulter nominal IWA (mas)
Occulter moved-in IWA (mas)
Telescope diameter (m)
Number of petals
Petal length (m)
Minimum gap between petals (mm)
Minimum width of petal tip (mm)
1-dist. Occulter
25.6
70400
75
4
20
19
0.12
1.62
2-dist. Occulter
20
55000
35000
75
118
4
20
10
1.0
1.0
Table 1. Design parameters for a single distance and multi-distance occulter meeting THEIA requirements. The
two-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 occulter
to operate over a band of shorter wavelengths, allowing for a smaller and easier-to-manufacture design, and
then 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, where
the 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 extra
hinge lines and allowing it to fit into a smaller fairing), and 10x larger gaps between petals (making it much
easier 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 in
series to fully characterize the planet over the entire band. For some systems, there may not be enough time
before the planet leaves the visible zone. The second is that the inner working angle has increased by the
same factor c for the closer observations. Thus, for our occulter designed for an inner working angle of 75
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Figure 4. Simulated images of a close in companion planet (red) and the residual starlight (blue) for the hybrid
THEIA occulter design. Note that we leave two orders of magnitude margin in contrast to allow for tolerance to
errors.
Petal Position or Shape Error
r.m.s shape (1/f2 power law)
Proportional shape
Length clipping at tip
In-plane bending (r2 deviation)
Out-plane bending
100 m
80 m at max width
1 cm
Azimuthal position
Radial position
In-plane rotation about base
(r2
Allocation
deviation)
Cross-track occulter position
0.003 deg (1 mm at tip)
1 mm
0.06 deg (1 cm at tip)
5 cm
50 cm
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 mas
for the redder wavelengths. Again, this means the loss of some science on the closest planets. In the next
section we describe the optical performance of this system, its impact on science yield, and the requirements
on manufacturing.
3. SYSTEM PERFORMANCE
Fig. 4 shows the image plane point spread function of a close in planet overlaid on the residual starlight PSF
for three different wavelengths. In each case, a contrast of 10−12 is achieved at the planet location. Note
that while the planet we model only has a contrast of 10−10 relative to the star, we allow a two order of
magnitude margin in our design to account of various errors on the occulter and telescope. Until a detailed
simulation is completed, a conservative error budget needs to allocate a certain amount of contrast to each
error. For example, in Table 2 we list some of the largest error sources and the resulting requirements in
order 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 distance
occulter. While there is no reduction in the number of planets detected, there is some loss in the ability
to characterize them, both because of the inner working angle loss and the added time. However, that
reduction is not large and there is still substantial science obtained. We felt the tradeoff favored the twodistance 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 a
spacecraft bus equipped for repositioning, stationkeeping, and pointing. The solar array is sized for 15 kW
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Spectral Characterizations to at least 700nm
Unique Planet Detections
Spectral Characterizations between 250 and 1000nm
45
40
Coronagraph
40
35
Occulter
THEIA
35
30
Coronagraph
25
Occulter
THEIA
THEIA Extended
THEIA Extended
20
30
25
15
25
20
20
10
15
15
Coronagraph
Occulter
10
10
5
THEIA
5
5
THEIA Extended
0.1
0.2
0.3
0.4
0.5
(a)
0.6
0.7
0.8
0.9
1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(b)
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
(c)
Figure 5. Expected science yield from four planet-finding architectures with a 4m telescope: a 2λ/D coronagraph, an
occulter 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) at
the 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 (which
can be adjusted in flight) plus 1 kW for other bus equipment. This thruster subsystem consists of 6 total
thrusters with 3-for-2 redundancy on each side of the starshade. During exoplanet observations, the occulter
system is held on targets constrained to lie between 45 and 85 degrees from the sun line to avoid stellar
leak into the telescope or reflections off the starshade. Stationkeeping does not employ electric thrusters
because they produce a bright plume potentially contaminating the observations. The spacecraft is thus
also equipped with a set of on/off hydrazine thrusters that control position to within ±75 cm. A shutter is
employed 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 position
sensing: 1) Conventional RF Ground tracking (±100 km), 2) Observatory angle sensing of a Ka-Band beacon
from the occulter spacecraft (±16 km), 3) XPC IR imaging of a laser beacon (±70 m) and 4) XPC IR imaging
of light leaking around the occulter (±35 cm). The Observatory measures occulter range via the S-Band
link. The occulter system has a maximum expected mass of 5,700 kg as compared to a launch mass capacity
of 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 fabric
core. The starshade is comprised of 2 major subsections, a 19.46 m diameter inner core composed of 3
layers of Kapton and an outer section of twenty 10.27 meter tall and 3.7 meter wide petals. Together, when
deployed they form an occulting mask 40 meters in diameter from tip-to-tip. The precision shaped petal
edge, 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 the
stowed configuration, the central core and petals mount to a graphite composite deployment deck, which
in turn mounts to the spacecraft. A central opening accommodates the recessed mounting of propulsive
thrusters, antennas and laser beacons.
The stowed configuration fits inside a 5 m launch fairing with margin. A truss structure supports the
stowed petals and is jettisoned after launch. Deployment is initiated by extending the entire stowed petal
stack 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 are
controlled by redundantly actuated, passively damped, high accuracy hinges. A simple sequencing cam
between the primary hinge-lines of the petals also controls deployment. As the booms rotate, the petals
unfold. The final position is controlled by stops designed into each hinge line. Careful optical analysis was
used to design the hinges and gaps to maintain the needed starlight suppression.
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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 Savransky et al. 2009.7 In this method, the list of potential targets is populated with planets, and a mission design
is created using a set of selection rules designed to maximize total science return over the course of the
mission, taking into account technical limitations, fuel usage, and realistic optical performance. The list of
targets is then given a new set of planets, and the sequence is repeated to build up a distribution of science
return for a given architecture. The planet populations can be varied to examine different frequencies of
Earth-like planets. Plots of science return for four planet-finding architectures with a 4m telescope are given
in 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 runs
out of fuel
The science return for the one- and two-distance occulters is similar; however, the smaller occulter posed
fewer technical difficulties, which gave it the edge over the larger single distance occulter. In addition, the
additional fuel used to slew the larger occulter means that none remained to run an extended mission. (The
occulters 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. The
occulter is then slewed around as necessary to place itself between the star and the telescope. The mission
design assumed a two-week slew between targets; the occulter turned out to spend the majority of its time
in transit. 25% of the telescope time was earmarked for observations with the occulter; while these are
going on, the SFC will also be doing deep field science. The remainder of the mission time will be dedicated
to general astrophysics programs. This percentage is a reasonable assumption with respect to the mission
design; the DRMs were run assuming that all the time when the occulter was in position would be dedicated
to planet-finding, and this turned out to be between 20% and 30% of the available time, depending on the
planet distribution in the simulated universe.
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6. CONCLUSIONS
We have presented the design for the occulter for the THEIA observatory, and its associated observing
mission. This system would be able to find Earth-like planets beyond 75mas around nearby stars. Combining
a coronagraph with an occulter proves to be an ineffective way to get the occulter smaller and closer to the
telescope; instead, the occulter is made smaller by operating at two different locations with respect to the
telescope.
6.1 Acknowledgments
The work upon which this white paper is based was performed under contract to the National Aeronautics
and Space Administration (NASA), contract number NNX08AL58G. The project was managed by the Jet
Propulsion Laboratory (JPL), California Institute of Technology, under contract with the National Aeronautics 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.
REFERENCES
1. D.J. Des Marais, M.O. Harwit, K.W. Jucks, J.F. Kasting, D.N. Lin, J.I. Lunine, J. Schneider, S. Seager,
W.A. Traub, and N.J. Woolf. Remote sensing of planetary properties and biosignatures on extrasolar
terrestrial planets. Astrobiology, 2(2):153–181, 2002.
2. C.J. Copi and G.D. Starkman. The Big Occulting Steerable Satellite [BOSS]. Astrophysical Journal,
532:581–592, 2000.
3. W. Cash. Detection of earth-like planets around nearby stars using a petal-shaped occulter. Nature,
442:51–53, 2006.
4. R.J. Vanderbei, E.J. Cady, and N.J. Kasdin. Optimal occulter design for finding extrasolar planets.
Astrophysical Journal, 665:794–798, 2007.
5. R.J. Vanderbei, D. Spergel, and N.J. Kasdin. Circularly symmetric apodization via star-shaped masks.
Astrophysical Journal, 599:686–694, 2003.
6. P. Dumont, S. Shaklan, E. Cady, J. Kasdin, and R. Vanderbei. Analysis of external occulters in the
presence of defects. volume 7440. SPIE, 2009.
7. Dmitry Savransky, N. Jeremy Kasdin, and David N. Spergel. Results from the automated design reference
mission constructor for exoplanet imagers. volume 7440. SPIE, 2009.
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