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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 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 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 Proc. of SPIE Vol. 7440 744005-2 Downloaded from SPIE Digital Library on 17 Oct 2009 to 140.180.23.37. Terms of Use: http://spiedl.org/terms 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 Proc. of SPIE Vol. 7440 744005-3 Downloaded from SPIE Digital Library on 17 Oct 2009 to 140.180.23.37. Terms of Use: http://spiedl.org/terms 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 Proc. of SPIE Vol. 7440 744005-4 Downloaded from SPIE Digital Library on 17 Oct 2009 to 140.180.23.37. Terms of Use: http://spiedl.org/terms 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 Proc. of SPIE Vol. 7440 744005-5 Downloaded from SPIE Digital Library on 17 Oct 2009 to 140.180.23.37. Terms of Use: http://spiedl.org/terms 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. Proc. of SPIE Vol. 7440 744005-6 Downloaded from SPIE Digital Library on 17 Oct 2009 to 140.180.23.37. Terms of Use: http://spiedl.org/terms 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. Proc. of SPIE Vol. 7440 744005-7 Downloaded from SPIE Digital Library on 17 Oct 2009 to 140.180.23.37. Terms of Use: http://spiedl.org/terms 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. Proc. of SPIE Vol. 7440 744005-8 Downloaded from SPIE Digital Library on 17 Oct 2009 to 140.180.23.37. Terms of Use: http://spiedl.org/terms