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 Balasubramanian 2008

5. Balasubramanian 2008

7. L Lyot Stop MImage Mask A Entrance Aperturre

8. Martinez 2009

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

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

11. Complete solution: M(x) =  C j  (x-j) + G(x) Notch Filter MasksNot physical Kuchner 2005 j

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

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

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

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

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

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

18. HCIT RESULTS WITH BAND LIMITED MASKS –Variable thickness nickel masks on a glass substrate –1-D sinc 2 profile –Central wavelength 800 nm –Electric Field Conjugation algorithms for single and dual DM control Contrast Achieved : 6e-10 @ 4 /D with 10% bandpass 1.2e-9 @ 3 /D with 10% bandpass 2.7e-9 @ 3 /D with 20% bandpass Trauger & Traub 2007

19. Kern et al. 2008 Contrast On HCIT

20. Nickel Mask Moody et al 2008

21. Hybrid Mask: Nickel + Dielectric Band-limited function

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) Crepp et al. 2009, in prep. Mask Design linear 4 th -order smooth binary IWA = 880 mas optimized for K short Aluminum Fastener Microscope image before mask was cut from substrate and cleaned in ultrasonic bath

23. Epsilon Eridani After PSF Subtraction Calibrator: Delta Eridani

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

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

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

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

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

29. Levine et al. 2009

33. F460M Contrast No Coronagraph Coronagraph 4 /D Sinc 2 Wedge Coronagraph 6 /D Sombrero 2 Spot Raw Image Roll Subtraction 131 nm RMS wavefront error at occulter 40 nm RMS wavefront change between rolls

34. Use Lyot stop to eliminate DM effect on some wavelengths  =0.47 768 nm800 nm832 nm 1.00 all same 0.000.13 2 1.00 0.00 1.00 4 rad P-V 10 5 rad P-V 10 6 rad P-V No DM effect on shortest No DM effect on shortest s ±16 /D DM Kern et al. 2009

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

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

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

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

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

44. Notch Filter Image Masks  u G(u) Bandwidth  G(u) du = 0  0  G(u) u 2 du = 0  0 Eighth Order

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

46. Fourier Transforms multiplication convolution 

47. 

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

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

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

51. F F x A M  (F x A) L(M  (F x A)) M(F  A) F  AF  A

52. = 0 L(M  (F x A)) L x M  (F x A)

53. Lyot Stop

54. sin 2 u M(u)

55. b M(u)=0 for |u| > b  M(u) du = 0 Band- Limited Functions

56. b M(u) M(u)  0 for |u| > b  M(u) du = 0 Classical Lyot Coronagraph e.g. HST ACS Band- Limited Functions

57. 0 1 2 3 4 /(  D) M Useful Band-Limited Functions Kuchner & Kasdin 1010

58. Band-limited masks in the JPL High Contrast Imaging Testbed

59. Kuchner & Spergel 2003 Debes et al. 2004 Binary Band-Limited Masks

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

61. M(x) = - e 2  iux + - e -2  iux 1 4 1 4 1 4 - 1 4 - 1/2 1 2

62. M(x) = - e 2  iux + - e -2  iux Fourier Transform 1/2 -1/4 Mask 1 2 1 4 1 4

63. M(x) = sin 2 ux Fourier Transform 1/2 -1/4 Mask

64. M(x) = - e 2  iux + - e -2  iux u < D/ 1 4 1 4 1 2

65. M image mask L Lyot stop A entrance aperture

66. M image mask L Lyot stop A entrance aperture

67. Band-limited Image Masks  u M(u) Bandwidth  M(u) du = 0

68. linear 8th order 3 /D mask 2.4mm x 8mm linear 8th order 4 /D mask 2.4mm x 8mm linear 8th order optimized mask 2.054mm x 8mm calibration pinholes linear 4th order 1-sinc2 4 /D mask 2.4mm x 8mm Microscope Photos of Newly Completed JPL Binary Masks

70. Other Competitive Coronagraph Schemes: Shaped Pupils Pupil PSF Kasdin, Vanderbei, Spergel et al.

71. Other Competitive Coronagraph Schemes: Continuous Pupil Mapping (PIAA) Guyon, Traub, Vanderbei et al.

73. Kuchner, Crepp & Ge 2004 1 - sinc 2 Mask Eighth Order Mask |M(x)| 2 ^

74. Entrance Aperture A Image Mask M Lyot Stop L

75. Band-Limited masks in the JPL testbed Trauger et al. 2005

76. 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) Crepp et al. 2009, in prep. linear 4 th -order IWA = 880 mas optimized for K short Aluminum Fastener