Band-Limited Masks and Coronagraphic Imaging of Exoplanets Marc Kuchner

1. Band-Limited Masks and Coronagraphic Imaging of Exoplanets Marc Kuchner Exoplanets and Stellar Astrophysics Laboratory NASA Goddard Space Flight Center

2. 水星　Mercury [water star] 金星　Venus [metal star] + 明星 [bright star] 地球　Earth [Earth globe] 火星　Mars [fire star] 木星　Jupiter [wood star] 土星　Saturn [earth (soil) star] 天王星　Uranus [heaven-king (Uranus) star] 海王星　Neptune [sea-king (Neptune) star] 冥王星　Pluto [netherworld-king (Pluto)

3. Crepp et al. 2009 Krist et al. 2007 Balasubramanian 2008

4. Krist et al. 2007 Krist et al. 2007 Balasubramanian 2008

5. Balasubramanian 2008

7. A Entrance Aperturre M Image Mask Lyot Stop L

8. Martinez 2009

9. Incoming field F A F x A FA M M(F A) M  (F xA) L L(M (F xA))

10. Try to solve this in 1-D given: A L 1/2 1/2-/2 Set F=1 to represent on-axis light. What can M be such that L (M A)=0 ?

11. Not physical Notch Filter Masks Kuchner 2005 Complete solution: M(x) = Cj(x-j) + G(x) j

12. /2 M(u) du = 0 2) 0 Notch Filter Masks M(u)=0 here 1) M(u) 1-/2 /2 u M(u) = Fourier Transform of mask

13. /2 M(u) du = 0 2) 0 For a subset of Notch Filter Masks, M(u)=0 here and also here 1) M(u) 1-/2 /2 u We call these masks Band-Limited Masks.

14. Notch Filter (And Band-Limited) Notch Filter Krist et al. 2009 Crepp et al. 2009 Balasubramanian 2008

15. /2 M(u) du = 0 /2 2) M(u) u2 du = 0 0 3) 0 We call these masks Eighth-Order Masks. For a different, overlapping subset of Notch Filter Masks, M(u)=0 here 1) M(u) 1-/2 /2 u

16. 1.0 0.8 0.6 0.4 0.2 0.0 Kuchner, Crepp & Ge 2004 Eighth Order Mask Crepp et al. 2006 1 - sinc2 Mask Transmissivity Eighth Order Mask 0 1 2 3 4 5 distance to optical axis (/D)

17. Aberration Sensitivity 4th Order 8th Order Contrast Waves (RMS) Waves (RMS) Shaklan and Green 2005

18. HCIT RESULTS WITH BAND LIMITED MASKS Variable thickness nickel masks on a glass substrate 1-D sinc2 profile Central wavelength 800 nm Electric Field Conjugation algorithms for single and dual DM control Trauger & Traub 2007 Contrast Achieved: 6e-10 @ 4l/D with 10% bandpass 1.2e-9 @ 3 l/D with 10% bandpass 2.7e-9 @ 3 l/D with 20% bandpass

19. Contrast On HCIT Kern et al. 2008

20. Nickel Mask Moody et al 2008

21. Hybrid Mask: Nickel + Dielectric Band-limited function Moody et al 2008

22. First On-sky Demonstration of a Band-limited Mask • NGS AO at Palomar 200-inch • Installed in PHARO • Use well-corrected subaperture • to achieve ExAO Strehl ratios with • current DM (Serabyn et al. 2007) Mask Design Microscope image before mask was cut from substrate and cleaned in ultrasonic bath • linear 4th-order • smooth binary • IWA = 880 mas • optimized for Kshort Crepp et al. 2009, in prep. Aluminum Fastener

23. After PSF Subtraction Epsilon Eridani Calibrator: Delta Eridani

24. High-Contrast Imaging of Binaries Candidate Tertiary • Hide two stars behind • mask simultaneously • Place additional constrains • on formation theories • compared to single stars x x Crepp et al. 2009, in prep. ~ 230 MJup

25. HWHMc = 0.58” (4l/D @ 4.6 mm) HWHMc = 0.27” (4l/D @ 2.1 mm) Planet Imaging @ 2.4-5.0 μm Planet Imaging @ 2.1 μm NIRCam Occulter Layout 5” x 5” ND Square (OD = 3) 20 arcsec 60 mm 12 mm HWHM = 0.40” (6l/D @ 2.1 mm) HWHM = 0.64” (6l/D @ 3.35 mm) HWHM = 0.82” (6l/D @ 4.3 mm) Disk Imaging @ 4.3 μm Disk Imaging @ 3.4 μm Disk Imaging @ 2.1 μm

26. Pupil Intensity at Lyot Stopfor an Occulted Point Source Using 4l/D wedge occulter Using 6l/D spot occulter 1/5th root intensity stretches

27. NIRCam Lyot StopsMask Openings (white) Superposed on Pupil Lyot stop for 6l/D spot occulters Lyot stop for 4l/D wedge occulters Effective Throughput = 19% Stops are metal coatings on the pupil wedges

28. NIRCAM Predicted Contrast Gl 876b 20 nm RMS wavefront difference between rolls Krist et al. 2007

29. Levine et al. 2009

33. F460M Contrast Coronagraph 4l/D Sinc2 Wedge Coronagraph 6l/D Sombrero2 Spot No Coronagraph Raw Image Roll Subtraction 131 nm RMS wavefront error at occulter 40 nm RMS wavefront change between rolls

34. Kern et al. 2009 Use Lyot stop to eliminateDM effect on some wavelengths DM 768 nm 800 nm 832 nm e=0.47 all lsame ±16 l/D 4 radP-V 1.00 1.00 1.00 No DMeffect on shortest l 105 radP-V 0.00 0.132 1.00 No DMeffect on shortest ls 106 radP-V 0.00 0.00 1.00

35. Imaging Known RV Planets

36. Achievable Contrast for a M0V Star at 4 pc (F460M) Planet Contrasts

37. Without & With the Coronagraph Without Coronagraph With Coronagraph

38. Epsilon Eridani After PSF Subtraction Calibrator: Delta Eridani

39. /2 M(u) du = 0 2) 0 For a different, overlapping subset of Notch Filter Masks, M(u)=0 here 1) M(u) 1-/2 /2 u /2 M(u) u2 du = 0 3) 0 We call these masks Eighth-Order Masks.

40. /2 M(u) du = 0 2) 0 M(u) = constant translates into two requirements on M(u) : M(u)=0 here 1) M(u) 1-/2 /2 u We call masks that meet these criteria Notch Filter Masks.

41. What can M be such that L (M A)=0 ? Define M(u): d/du M(u) = M(u) Then the above equation has the following solution: M(u) = M(u+1) for /2 < u < 1- /2

42. For example, take M(u) = constant. (There are other possibilities but they are all unpleasantly chromatic, like Fresnel lenses.)

43. Notch Filter Functions G(u) u G(u) = 0

44. Eighth Order Notch Filter Image Masks G(u)  u  G(u) du = 0 Bandwidth 0  G(u) u2 du = 0 0

45. 1 1 cos x 1/2 1/2 1 1 sin2 x = - cos x 2 2 1/2 -1/4 -1/4 Fourier Transforms 

46. Fourier Transforms  multiplication convolution

47. convolution 

48. 1/2 -1/4 -1/4 Simplest Possible Band-Limited Mask 1 1 1-D sin2 x = - cos x 2 2  2-D

49. On-axis point source F F x A FA M(F A) M  (F xA) L(M (F xA))

50. M (F xA)  1/2 1/4 1/4 = = + =0 + M  (F xA)