New Worlds Observer tolerance overview ABSTRACT 1. INTRODUCTION STARSHADE

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1 New Worlds Observer tolerance overview Ann Shipley a, Webster Cash a, Jonathan W. Arenberg b, Amy S. Lo b a University of Colorado, Center for Astrophysics and Space Astronomy b Northrop Grumman Space Technology ABSTRACT New Worlds Observer (NWO) is a formation flying mission that combines a starshade with a telescope to study Earthlike exoplanets around neighboring stars. The general architecture consists of a telescope and detector that share one spacecraft platform pointed toward a nearby solar system. Planets in the solar system are revealed by blocking the bright star with a starshade, on its own spacecraft, positioned between the telescope and its target. Questions arise regarding the type of precision, tolerances, and diffraction control required when considering the practicality of such an endeavor. We address the generalities here by presenting an overview of requirements necessary for this type of system. Basic tolerances are described at both the mission and starshade level. Keywords: contrast, diffraction, exoplanet, New Worlds, occulter, starshade, starshield, suppression, tolerance 1. INTRODUCTION An earth-like planet viewed from 1 parsecs away is about 1 billion times fainter and only 1/1 of an arcsecond from its host star. Interestingly, the difficulty in imaging such an exoplanet doesn t lie in making an extremely high-quality or very large telescope, but rather in suppressing the light from the nearby star. Once rid of the extraneous light, new methods of observation become available. Not only can we identify other planetary systems, we can analyze their atmospheres and surfaces, characterize their basic nature, and open the search for signs of simple life. 1, The NWO concept consists of two spacecraft flying at Earth-Sun L or in a drift-away solar orbit. One craft carries a diffraction-limited telescope optimized to work in the visible band, and the other is a starshade craft. The starshade is maneuvered to block the telescope s line-of-sight to a nearby star, thus revealing the off-axis planet light. See figure 1.,_-_ STARSHADE TELESCOPE Figure 1. NWO throws a deep shadow over the telescope, but allows planet light past Although, the idea of using external starshades is not new, our recent investigation of petal-shaped starshades has enabled a fresh understanding of apodization in the Fresnel limit 3. The starshade s perimeter is specifically shaped to cancel out positive and negative electric field zones as incident plane waves from a star pass across it, see Figure. The diameter of the starshade and its distance from the telescope define the size of the suppressed shadow in which the telescope must reside to view a nearby planet. UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts III edited by Howard A. MacEwen, James B. Breckinridge Proc. of SPIE Vol. 6687, 66871A, (7) X/7/$18 doi: / Proc. of SPIE Vol A-1

2 b b a a Figure. Layout of a 1-petal starshade for NWO. The gray rings represent Fresnel zones (see text). The family of apodization profiles is given by. for ρ a n A( ρ ) = ρ a. (1) 1 exp for ρ > a b The parameter a represents the radius of a fully opaque circular center to the shade and b represents the distance from the edge of the central disk to the point at which the transmission rises to (1-1/e). It has been shown that if there are enough zones (a ~b >>nλf/π) covered by the shade, the amount of diffraction in the center of the shadow is given by λf R= ( n! ) π ab The shadow at the center of this type of starshade is extremely dark over the entire spectral band from.4 to 1.1µm, and is of large enough diameter to accommodate a telescope with margin for alignment. The starshade may be made of any dark, opaque, deployable material. Then, for example, a starshade 5 meters tip-to-tip and positioned 7, km from the telescope can observe to within an inner working angle (IWA) of 7 milli-arcseconds from the star. n. ANALYSIS SOFTWARE Computer models are used to represent both an image and the electric field at the focal plane. The starshade perimeter is modeled with a line integral representing the hyper-gaussian petal shapes. Light transmission is treated in a binary fashion as either unity outside the starshade s shadow or nil inside its shadow. Edge diffraction zone power is suppressed along the length of the starshade petals using an apodization function. Codes for this work exist at the University of Colorado, Princeton, Goddard Space Flight Center and Northrop Grumman Space Technology. 4 Tolerances and analysis presented in this paper were run using Colorado s line integral code for true -D analysis of the hyper-gaussian petal shapes. 5 Figure 3 below shows predicted diffraction patterns surrounding suppression at ten orders of magnitude. () Proc. of SPIE Vol A

3 Starshade position, angle, and shape can be changed in the computer code to predict the effect of various types of errors. Current designs indicate lateral position on-orbit may vary by several meters, angle by many degrees, and distance between the starshade and telescope by many kilometers. Performance will not be significantly impaired by petal profile anomalies at the 1mm level, or holes and blobs that add up to about 3cm. The Colorado code is currently being upgraded to handle error budgeting in diffraction analysis. See figure 3 below. fle 1Ua Figure 3. The new code can map detailed performance of diffraction. To the left is the shadow of a starshade shown on a linear scale. To the right is the same shadow shown on a logarithmic scale. The bottom of the shadow is ten orders of magnitude lower than the surrounding, unshadowed region. 3. TOLERANCES We predict imaging performance and a tolerance range by manipulating parameters in our computer code. The ability to see an earth-like planet requires that diffracted light from its parent star (noise) be suppressed to a level well below the planet signal. This suppressed shadow must be large enough to contain a telescope of adequate size to image the planet, with a small enough inner working angle (IWA) to see a planet within 1 milli-arcseconds of its star. Two important parameters that set the basis for performance are a starshade s size and its distance from the telescope. Other parameters that define starshade shape can also affect the level of diffraction control, shadow size, and IWA. Table 1 below defines nominal parameters we vary with computer code to simulate a modified hyper-gaussian petal shape. We begin with a starshade design of nominal values, and change one parameter at a time in each tolerance evaluation to demonstrate the direct effect on system performance. Table 1. Nominal Parameters for a typical Starshade Core radius a 1.5 m Inner (solid) starshade Petal Length b 1.5 m Petal characteristic length Petal Taper n 6 Petal shape parameter Number of Petals p 16 Number of petals Diameter d 5 m to 1/e transmission point Diameter D 6 m tip to tip Distance F 7, km distance to telescope Wavelength λ.5µm.4µm - 1.1µm broadband Proc. of SPIE Vol A-3

4 3.1 Off-axis Figure 4 below shows diffraction suppression for a nominal starshade located 7, km from its telescope. The shadow radius represents an area in which a telescope must reside to maintain a given level of suppression. Full transmission of the planet around the edge of the starshade is just outside a 7 milli-arcsecond inner working angle (IWA). Thus, a diffraction limited four meter diameter telescope could vary in lateral position up to a meter in any direction and still remain in an area of 1-1 suppression to view a planet 1 milli-arcseconds away from its host star. Alternatively, a smaller telescope could be used with looser positioning or a larger telescope with tighter lateral tolerances. As the telescope moves off-axis the suppression level degrades quickly. For instance, the same four-meter telescope two meters off-axis would degrade the suppression level to 1. Here, a planet may still be detectable, but its light must compete with exozodiacal light scattered within the planetary system. The residual light that is not fully suppressed by the starshade at the center of the shadow will be re-imaged by the telescope and appear as a ring of light centered on the position of the target star. Because this light is coherent, a spot of light can even appear near the center of the starshade. But some of the light will be diffracted outward to the position of the inner planets. In a typical situation, only 1% of the residual starlight will appear in the resolution element that contains the planet a 1 suppression level of the star will yield a noise level of 1-1 at the exoplanet. Coincidentally, the total contribution from exozodiacal light will be at about the 1 level and will have an effect quite similar to residual diffracted starlight. It is clear that if suppression is allowed to climb significantly above 1, then there will be degradation of sensitivity. There is little point in suppressing below 1-1 because that will gain us very little in the way of sensitivity Log Figure 4. Log 1 Suppression of a nominal starshade vs. telescope shadow radius and IWA Proc. of SPIE Vol A

5 3. Focal distance Focal distance between a starshade and its telescope may fluctuate by many kilometers without hindering the ability to see exoplanets and their systems. Such a loose requirement can be very valuable having the potential to greatly simplify formation flying, station keeping, and fuel requirements. Figure 5 below shows a plot of the IWA of a nominal 5 meter diameter starshade at various focal distances from its telescope. Suppression curves at matching focal distances are plotted against the starshade s shadow diameter at the focal plane on the right vertical axis. The desired 7 milli-arcsecond limit corresponds with a focal distance of 7, km. At this distance a suppression level of 1-1 can be maintained for a four meter telescope (or smaller) over a focal range of 1,km. At 1, the shadow diameter at the focal plane range goes from 5 meters, and focal distance may vary by more than 1,km IWA 7 mas Shadow diameter (m) F (Mm) Figure 5. Allowable focal distance range (in Mega-meters, 1 6 meters) between starshade and telescope. Proc. of SPIE Vol A-5

6 3.3 Wavelength New Worlds Observer is designed to work over a broad spectral band from.4 to 1.1µm. Suppression level and shadow radius both degrade as wavelength increases as shown in figure 6 below and as expected from (). The suppression area becomes quite deep and wide at shorter wavelengths. The resulting broadband image will be a composite of contributions from each color in the visible spectrum and is expected to vary among target planetary systems. A broad spectral response is desirable to support both imaging and spectroscopy of exoplanets. Filters may be used to isolate the desired bandpass for a given type of observation. At Colorado, we have performed simulations of the inner solar system as viewed from 1 parsecs. Results show an Earth that actually appears blue, while Venus looks white. Cleverly filtered New Worlds images might also produce similarly colored exoplanets that would not be possible without broadband light. Alternately, even though suppression levels are somewhat degraded above 8nm, there are spectroscopic signatures of interest. New Worlds Observer will also have the capability of observing an exoplanet for signature lines such as molecular oxygen (76nm) and water (96nm). The presence of one or both lines establishes compelling arguments for simple life. Figure 6 shows that our nominal starshade produces a shadow of adequate depth and diameter to accommodate a four meter telescope working across the desired bandpass Log λ=nm λ=4nm λ=6nm λ=8nm λ=1micron λ=1.microns Figure 6. Wavelength affects both suppression levels and shadow radius. Proc. of SPIE Vol A

7 3.4 Starshade tilt Since we rely on the hyper-gaussian nature of the starshade s perimeter to effectively extinguish Fresnel zones, it is natural to question how precisely the shape must be controlled. A starshade viewed from a perpendicular line of sight will have a symmetrical shape and represents the nominal case. However, if one side of the starshade is tilted away from the line of sight, the starshade s on-axis profile will appear slightly distorted. The effects of tilting a starshade on-orbit are much less imposing than one might imagine. Figure 7 below shows suppression and shadow radius for a nominal starshade tilted at different angles off-axis from telescope line of sight. Here we can see our nominal starshade may be tilted nearly º and still provide the desired suppression level with a four meter telescope. The relaxed nature of this requirement also lends itself to ease of formation flying tolerances Log 1-1 deg 5 deg 1 deg deg 3 deg 4 deg Figure 7. A nominal starshade is tilted away from line of sight with its telescope. degrees represents the case where the starshade is perpendicular to the line of sight. Proc. of SPIE Vol A-7

8 3.5 Number of petals The number of petals on a starshade affects the shadow radius at the focal plane more dramatically than the on axis suppression, as shown in figure 8. A starshade with fewer petals is easier to fabricate, launch, and deploy, not to mention more economical. On the other hand, more petals seem to improve performance consistently up to around P=4. Additional petals beyond that will likely contribute more to cost (and mass) than performance. Our nominal starshade used in this study has 16 petals and allows for ample telescope position error in the focal plane shadow, however, a starshade with as few as 1 petals would also be suitable. Of course, looser station-keeping tolerances or a much larger telescope could be accommodated by increasing the number of petals to Log 1-1 P=4 P=6 P=8 P=1 P=16 P=4 P= Figure 8. The number of petals on a starshade are proportional to shadow radius up to P=4. Proc. of SPIE Vol A

9 3.6 Petal length/truncation The requirement driving a starshade s petal length is actually driven by the width where the petal tip is truncated. The area of the petal from the truncation point outward represents the area of anomaly from the ideal hyper-gaussian shape. So, as the tip becomes very narrow, its contribution to total area of the starshade becomes smaller. There is a maximum allowable tip width that corresponds to a minimum petal length, after which added petal length has little to no effect on starshade performance. In figure 9 below, one can see that higher truncation values correspond with improved suppression up to the value 1.6, after which there is no appreciable change. The truncation value can be used to quantify differences in petal lengths as follows. The distance from the center of a starshade to the tip of a petal is defined as: L = a + b*trunc where: a is the solid inner disc of the starshade b is the distance for the base of a petal to a point 1/e trunc is a ratio that defines the location of the tip of a petal. Our nominal starshade petal lengths are set using a trunc value set at 1.6, where suppression performance converges around 1-1. Longer petals will not improve performance and there is margin for truncations down to about 1.45*b due to deployment or other errors on-orbit. The quantified difference between the nominal and allowable truncated petal length for a 5 meter diameter starshade is 1.8 meters over a total petal length of about meters, or just under 1% Log trunc= Figure 9. Petal truncation vs. log suppression Proc. of SPIE Vol A-9

10 3.7 Petal taper (n, Hyper Gaussian index) The variable, n, represents how rapidly a petal tapers from its base toward its tip. Specifically, a larger n value produces shorter and wider, or stubbier petals. Conversely, a smaller n results in longer and narrower petals. 3 It is an exponential term in the apodization function and not surprisingly has a significant effect on starshade performance, as expected from (). Our nominal starshade has the value n=6. As shown in figure 1, decreasing n degrades suppression level and broadens the shadow at the focal plane. Alternatively, increasing n has the opposite effect Log 1-1 n=6 n=4 n= Figure 1. The effects of petal stubbiness. 4. CONCLUSION We have simulated several types of anomalies that depart from the ideal position and shape of a starshade intended for planet imaging in a NWO configuration. We have discussed how each irregularity affects performance of the system and identified a usable range for each parameter in our computer code. Starshade position requirements have been shown to be relaxed and well within easy formation flying capability. The most challenging parameters are associated with starshade perimeter and shape, but appear to within tractable range. We plan to refine and update our understanding of the requirements as our understanding of diffraction control expands and lab test results become available to validate our calculations. Proc. of SPIE Vol A-1

11 ACKNOWLEDGEMENTS This work was supported by the NASA Institute for Advanced Concepts. REFERENCES 1. Cash, W., Detection of Earth-like planets around nearby stars using a petal-shaped occulter, Nature, 44, 51-53, 6.. W. Cash, E. et al, The New Worlds Observer: using occulters to directly observe planets, Proceedings of the SPIE, 665, (6). 3. Cash, W. et al, "External Occulters for Direct Observation of Exoplanets: An Overview," Proceedings of the SPIE, 6687, (7). 4. Jonathan Arenberg et al, New Worlds Occulter Performance: A First Look, Proceedings of the SPIE, 6687, (7). 5. E. Schindhelm et al., Laboratory Studies of Petal-Shaped Occulters, Proceedings of the SPIE, 6687, (7). Proc. of SPIE Vol A-11