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

2. New Worlds Contributors Webster CashUniversity of Colorado Jim Green Eric Schindhelm Jeremy KasdinPrinceton University Bob Vanderbei David Spergel Sara SeagerCarnegie Institution – Washington Alan SternSouthwest Research Institute – Boulder Steve KilstonBall Aerospace Tom Bank Charlie Noecker Jim Leitch Jon ArenbergNorthrop Grumman Ron Polidan Chuck Lillie Amy Lo Glenn StarkmanCase Western Sally HeapGoddard Space Flight Center Marc Kuchner Keith Gendreau and growing…

3. Important Caveats New Worlds is an emerging mission concept New Worlds is an emerging mission concept Rapidly developing with a small team Rapidly developing with a small team Recent emphasis was on Discovery proposal, not a TPF-C class mission Recent emphasis was on Discovery proposal, not a TPF-C class mission TPF mission under very active study TPF mission under very active study There is no mission design or final concept There is no mission design or final concept We have found no obvious impediments to such a mission We have found no obvious impediments to such a mission It is a major goal of this talk to inform the audience on how occulters do and do not work It is a major goal of this talk to inform the audience on how occulters do and do not work Given the limited time here, the results are sample of the work that has been done Given the limited time here, the results are sample of the work that has been done

4. Overview of the Occulter Hour Development and performance of the occulter (Cash-CU) Development and performance of the occulter (Cash-CU) Occulter modeling (Lyon-GSFC) Occulter modeling (Lyon-GSFC) Overview of architecture trades (Arenberg-NGST) Overview of architecture trades (Arenberg-NGST) Alignment (Noecker-Ball) Alignment (Noecker-Ball) Summary (Arenberg-NGST) Summary (Arenberg-NGST)

5. Origin: 2002-2003 Maxim was stalled Maxim was stalled Still is Still is Maxim was outgrowth of 1999-2001 NIAC Maxim was outgrowth of 1999-2001 NIAC Was there a way to apply Maxim technology to a more immediate problem? Was there a way to apply Maxim technology to a more immediate problem? Noticed that TPF and Maxim were both driven by the need for high performance optics Noticed that TPF and Maxim were both driven by the need for high performance optics Personally, the only thing I find as exciting as imaging a black hole is finding and imaging Earth- like planets Personally, the only thing I find as exciting as imaging a black hole is finding and imaging Earth- like planets Decided to try my hand at the exo-planet game Decided to try my hand at the exo-planet game

6. June 2003 Came up with the Pinhole camera idea Came up with the Pinhole camera idea It was not MAXIM, but a rather a refusion and reapplication of the Maxim approach It was not MAXIM, but a rather a refusion and reapplication of the Maxim approach

7. A Pinhole Camera Meets The Requirements: Perfect Transmission No Phase Errors Scatter only from edges – can be very low Large Distance Set by 0.01 arcsec requirement diffraction: /D =.01”  D = 10m @500nm geometric: F = D/tan(.01”) = 180,000km

9. “Standard” Observatory Views Starshade ~1” resolution or somewhat better (not diffraction limited!) High efficiency, low noise spectrograph (e.g. COS)

10. View Back Toward Starshade

11. Starshade Aperture Shapes

12. Focal Plane

13. View Dark Side of Starshade

14. Planet Finding Mode Solar System at 10pc Survey to 7AUSurvey Habitable Zone Jupiter Earth Venus Mars Venus Earth

15. Why Pinhole Camera? Why Not Occulter? Because  Because  Everybody knows that diffraction around an occulter is too severe Everybody knows that diffraction around an occulter is too severe

16. Occulters Several previous programs have looked at occulters Several previous programs have looked at occulters First look by Spitzer (1962) First look by Spitzer (1962) Marchal (1985) Used simple petal shapes Marchal (1985) Used simple petal shapes Achieved 10 -5 suppression across a broad spectral band Achieved 10 -5 suppression across a broad spectral band With transmissive shades With transmissive shades Achieved only 10 -5 suppression despite scatter problem Achieved only 10 -5 suppression despite scatter problem http://umbras.org/ BOSS Starkman (TRW ca 2000)

17. Extinguishing Poisson’s Spot Simple Occulters Have Very Poor Diffraction Performance Simple 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 Equation Must satisfy Fresnel Equation, Not Just the Fraunhoffer Equation Must Create a Zone That Is: Must Create a Zone That Is: Deep Below 10 -10 diffraction Deep Below 10 -10 diffraction Wide A couple meters minimum Wide A couple meters minimum Broad Suppress across at least one octave of spectrum Broad Suppress across at least one octave of spectrum Must Be Practical Must Be Practical Binary Non-transmitting to avoid scatter Binary Non-transmitting to avoid scatter Size Below 150m Diameter Size Below 150m Diameter Tolerance Insensitive to microscopic errors Tolerance Insensitive to microscopic errors

18. The Vanderbei Flower Developed for Aperture in TPF focal plane Developed for Aperture in TPF focal plane Was to be only millimeters across Was to be only millimeters across Vanderbei had determined it would work for the pinhole camera but did not necessarily work for occulter. Vanderbei had determined it would work for the pinhole camera but did not necessarily work for occulter. Agreement that it was worth a look Agreement that it was worth a look

19. Breakthrough From 11/17/04 to 4/12/05 worked on diffraction codes From 11/17/04 to 4/12/05 worked on diffraction codes Put the problem out there for whomever to solve Put the problem out there for whomever to solve At one point had 3 professors, 2 engineers and 4 students At one point had 3 professors, 2 engineers and 4 students On April 12 last year (after Phase I, before Phase II due) On April 12 last year (after Phase I, before Phase II due) Had working code Had working code Was trying functions (as opposed to VDB generalized forms) Was trying functions (as opposed to VDB generalized forms) Tried OFFSET gaussian Tried OFFSET gaussian Ten minutes later had a solution Ten minutes later had a solution In June discovered hyper-gaussians even better In June discovered hyper-gaussians even better

20. The Apodization Function for and Found this in April. Extended in June. This Function Extinguishes Poisson’s Spot to High Precision

21. Performance A 50m diameter occulter at 50,000km will reveal Earths at 10pc a=b=12.5m n=6 F=50,000km Arenberg and Cash (2005)

22. Occulters Are Fundamentally Fresnel (Never Ever Fraunhoffer) The central Fresnel zone and the eight inner half zones are shown schematically. The dark star in the centre represents a mask that is confined to the region where the Fraunhoffer approximation can be used. It is clear that such a mask will integrate out to a net positive contribution in the focal plane.

23. Suppression of Edge Diffraction Can Be Understood Using Fresnel Zones and Geometry The occulter is a true binary optic The occulter is a true binary optic Transmission is unity or nil Transmission is unity or nil Edge diffraction from solid disk is suppressed by cancellation Edge diffraction from solid disk is suppressed by cancellation The power in the even zones cancels the power in the odd zones The power in the even zones cancels the power in the odd zones Need enough zones to give good deep cancellation Need enough zones to give good deep cancellation 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 shape b is scale of petal shape n is an index of petal shape n is an index of petal shape a is the diameter of the central circle a is the diameter of the central circle a b

24. Huygens-Fresnel Principle

25. Fresnel Approximation Then, if circularly symmetric:

26. Babinet’s Principle Necessary for Integration Across Shade We seek E 2 =0 or: or To simplify math we concentrate on the center of the shadow (s=0) We seek A(  ) such that: or

27. Now, Evaluate Candidate Apodization Function

28. Dimensionless Natural Units

29. Electric Field at Center:

30. Integrate by Parts Yields E = 1+R where R is small as desired And This closed-form integral represents the electric field at the center of the shadow

31. Continue Integrating by Parts Drop Small Terms Dominant Term If  2 >> n

32. Binary Apodization Difference between petals and circularly symmetric apodization.

33. Tolerance Analysis Procedes by perturbation analysis Procedes by perturbation analysis Pitch or Yaw error – foreshortened to 1-  in one dimension Pitch or Yaw error – foreshortened to 1-  in one dimension Reduces to: Proving Where z=x/(1-  )

34. Starshade Tolerances Position Position LateralSeveral Meters LateralSeveral Meters DistanceMany Kilometers DistanceMany Kilometers Angle Angle RotationalNone RotationalNone Pitch/YawMany Degrees Pitch/YawMany Degrees Shape Shape Truncation1mm Truncation1mm Scale10% Scale10% Blob3cm 2 or greater Blob3cm 2 or greater Holes Holes Single Hole3cm 2 Single Hole3cm 2 Pinholes3cm 2 total Pinholes3cm 2 total

35. 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 ? 45 meters R. Lyon 09/29/06 100,000 km 50,000 km 25,000 km 18,000 km Real part of field at mask

36. Copyright 2006 Northrop Grumman Corporation Occulter Systems Terrestrial Planet Finding Jon Arenberg Amy Lo Chuck Lillie Richard Malmstrom Ron Polidan

37. Copyright 2006 Northrop Grumman Corporation 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)

38. Copyright 2006 Northrop Grumman Corporation The Basic NWO Architecture  Occulters blocks on-axis star light  Telescope looks at off-axis star light to observe companion planet Target Star NWO Occulter Telescope

39. Copyright 2006 Northrop Grumman Corporation The Occulter Parameters ParameterSymbolAffects…. solid disk radius aIWA, stellar suppression Gaussian radius parameterbIWA, stellar suppression the petal shape parameternObservation wavelength Occulter separationFIWA, stellar suppression number of petalsPMinimum needed

40. Copyright 2006 Northrop Grumman Corporation 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 occultertelescope LOG Scale LOG Scale R

41. Copyright 2006 Northrop Grumman Corporation 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

42. Copyright 2006 Northrop Grumman Corporation 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

43. Copyright 2006 Northrop Grumman Corporation 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

44. Copyright 2006 Northrop Grumman Corporation “Movie” of Planet moving Off-Axis Suppression at Suppression = 10 -10 0 mas LOG Scale Linear Scale

45. Copyright 2006 Northrop Grumman Corporation “Movie” of Planet moving Off-Axis Suppression at Suppression = 10 -10 50 mas LOG Scale Linear Scale

46. Copyright 2006 Northrop Grumman Corporation “Movie” of Planet moving Off-Axis Suppression at Suppression = 10 -10 70 mas LOG Scale Linear Scale

47. Copyright 2006 Northrop Grumman Corporation “Movie” of Planet moving Off-Axis Suppression at Suppression = 10 -10 75 mas LOG Scale Linear Scale

48. Copyright 2006 Northrop Grumman Corporation “Movie” of Planet moving Off-Axis Suppression at Suppression = 10 -10 80 mas LOG Scale Linear Scale

49. Copyright 2006 Northrop Grumman Corporation “Movie” of Planet moving Off-Axis Suppression at Suppression = 10 -10 85 mas LOG Scale Linear Scale

50. Copyright 2006 Northrop Grumman Corporation “Movie” of Planet moving Off-Axis Suppression at Suppression = 10 -10 90 mas LOG Scale Linear Scale

51. Copyright 2006 Northrop Grumman Corporation “Movie” of Planet moving Off-Axis Suppression at Suppression = 10 -10 100 mas LOG Scale Linear Scale

52. Copyright 2006 Northrop Grumman Corporation “Movie” of Planet moving Off-Axis Suppression at Suppression = 10 -10 110 mas LOG Scale Linear Scale

53. Copyright 2006 Northrop Grumman Corporation 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

54. Copyright 2006 Northrop Grumman Corporation Occulters IWA Less Than 100 mas Occulters with IWA smaller than 100 mas Occulters with IWA larger than 100 mas

55. Copyright 2006 Northrop Grumman Corporation 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

56. Paper 6265-67 SPIE Astronomical and Instrumentation 2006, Orlando, FL 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 Operational constraint a, b, n, P, F Operational constraint a, b, n, P, F

57. Paper 6265-67 SPIE Astronomical and Instrumentation 2006, Orlando, FL Design Space Construction Occulter Too Far Away Occulter Too Large The allowed design space is continuous

58. Copyright 2006 Northrop Grumman Corporation Occulter Systems are Flexible  An occulter can be located at any separation distance  Allows the system to mix and match suppression and IWA

59. Copyright 2006 Northrop Grumman Corporation 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

60. Copyright 2006 Northrop Grumman Corporation Reference Mission Month

61. Copyright 2006 Northrop Grumman Corporation Sample Full-Mission Orbit and  V  Lissajous orbit at Sun-Earth L 2 point  1.2M km wide  Launch to C 3 = −.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/s 2  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/s 2  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

62. New Worlds Observer Alignment Sensing Concepts Charley Noecker

63. The challenge Target star, telescope, and star-shade must be collinear within 1.About 60-100 mas for the onset of occultation 2.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

64. The Problem Four steps: –(0  1) Find partner s/c on sky –(2) Acquire occultation on new target(  accuracy) –(2  3) Optimize alignment before observation(  calibration) –(3) Maintain alignment during observation(  stability) 1 Uncertainty in bearing (rad) DSNFind partnerAstrometryOccult’n 10 -2 10 -6 10 -8 10 -4 CC retro ground calib? Calibr 3210

65. Sensor options under consideration Telescope Antipode field stars Bright target star Target star Telescope & field stars Retro Occulter Telescope Red leak of occulter illuminates aperture edges; guide telescope to a minimum Telescope Laser or sunlight Starlight Acquisition

66. 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

67. Optimize alignment before observation Observe stellar occultation depth with telescope and simultaneously 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

68. 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

69. Other spacecraft may be faint If telescope has 1 m 2 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

70. Copyright 2006 Northrop Grumman Corporation 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