Abstract

High contrast imaging from space relies on coronagraphs to limit diffraction and a wavefront control systems to compensate for imperfections in both the telescope optics and the coronagraph. The extreme contrast required (up to 10-10 for terrestrial planets) puts severe requirements on the wavefront control system, as the achievable contrast is limited by the quality of the wavefront. This paper presents a general closed loop correction algorithm for high contrast imaging coronagraphs by minimizing the energy in a predefined region in the image where terrestrial planets could be found. The estimation part of the algorithm reconstructs the complex field in the image plane using phase diversity caused by the deformable mirror. This method has been shown to achieve faster and better correction than classical speckle nulling.

© 2007 Optical Society of America

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References

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  1. W. A. Traub, ed. Proceedings of Coronagraph Workshop2006. JPL Publication 07-02.
  2. R.K. TysonIntroduction to Adaptive Optics. SPIE Press, 2000.
    [CrossRef]
  3. L.A. Poyneer and B. Macintosh “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21(5), 810–819 (2004).
    [CrossRef]
  4. A. Give’on, N. J. Kasdin, R. J. Vanderbei, and Y. Avitzour “On representing and correcting wavefront errors in high-contrast imaging systems,” J. Opt. Soc. Am. A 23 (2006).
  5. J. T. Trauger, C. Burrows, and B. Gordon et al, “Coronagraph contrast demonstration with the high-contrast imagaing testbed,” Proc. SPIE 5487, 1330–1336 (2004).
    [CrossRef]
  6. R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).
  7. P. J. Borde and W. A. Traub, “High-contrast imaging from space: Speckle nulling in a low aberration regime,” Astrophys. J. 638 (2006).
  8. F. Malbet, J.W. Yu, and M Shao, “High dynamic range imaging using a deformable mirror for space coronography”, PASP,  107, pp. 386 (1995).
    [CrossRef]
  9. N. J. Kasdin, R. J. Vanderbei, D. N. Spergel, and M. G. Littman “Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs” Astrophys. J. 582(2), 1147–1161, (2003).
    [CrossRef]
  10. M. J. Kuchner, J. Crepp, J. Ge, and Astrophys.“Eighth-Order Image Masks for Terrestrial Planet Finding,”  J. 628(1), 466–473 (2005).
  11. N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

2006 (3)

A. Give’on, N. J. Kasdin, R. J. Vanderbei, and Y. Avitzour “On representing and correcting wavefront errors in high-contrast imaging systems,” J. Opt. Soc. Am. A 23 (2006).

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

P. J. Borde and W. A. Traub, “High-contrast imaging from space: Speckle nulling in a low aberration regime,” Astrophys. J. 638 (2006).

2005 (2)

M. J. Kuchner, J. Crepp, J. Ge, and Astrophys.“Eighth-Order Image Masks for Terrestrial Planet Finding,”  J. 628(1), 466–473 (2005).

N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

2004 (2)

L.A. Poyneer and B. Macintosh “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21(5), 810–819 (2004).
[CrossRef]

J. T. Trauger, C. Burrows, and B. Gordon et al, “Coronagraph contrast demonstration with the high-contrast imagaing testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

2003 (1)

N. J. Kasdin, R. J. Vanderbei, D. N. Spergel, and M. G. Littman “Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs” Astrophys. J. 582(2), 1147–1161, (2003).
[CrossRef]

1995 (1)

F. Malbet, J.W. Yu, and M Shao, “High dynamic range imaging using a deformable mirror for space coronography”, PASP,  107, pp. 386 (1995).
[CrossRef]

Astrophys.,

M. J. Kuchner, J. Crepp, J. Ge, and Astrophys.“Eighth-Order Image Masks for Terrestrial Planet Finding,”  J. 628(1), 466–473 (2005).

Avitzour, Y.

A. Give’on, N. J. Kasdin, R. J. Vanderbei, and Y. Avitzour “On representing and correcting wavefront errors in high-contrast imaging systems,” J. Opt. Soc. Am. A 23 (2006).

Balasubramanian, K.

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

Beall, J.

N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

Belikov, R.

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

Borde, P. J.

P. J. Borde and W. A. Traub, “High-contrast imaging from space: Speckle nulling in a low aberration regime,” Astrophys. J. 638 (2006).

Burrows, C.

J. T. Trauger, C. Burrows, and B. Gordon et al, “Coronagraph contrast demonstration with the high-contrast imagaing testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Carr, M.

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

Crepp, J.

M. J. Kuchner, J. Crepp, J. Ge, and Astrophys.“Eighth-Order Image Masks for Terrestrial Planet Finding,”  J. 628(1), 466–473 (2005).

Ge, J.

M. J. Kuchner, J. Crepp, J. Ge, and Astrophys.“Eighth-Order Image Masks for Terrestrial Planet Finding,”  J. 628(1), 466–473 (2005).

Give’on, A.

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

A. Give’on, N. J. Kasdin, R. J. Vanderbei, and Y. Avitzour “On representing and correcting wavefront errors in high-contrast imaging systems,” J. Opt. Soc. Am. A 23 (2006).

N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

Gordon, B.

J. T. Trauger, C. Burrows, and B. Gordon et al, “Coronagraph contrast demonstration with the high-contrast imagaing testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Kasdin, N. J.

A. Give’on, N. J. Kasdin, R. J. Vanderbei, and Y. Avitzour “On representing and correcting wavefront errors in high-contrast imaging systems,” J. Opt. Soc. Am. A 23 (2006).

N. J. Kasdin, R. J. Vanderbei, D. N. Spergel, and M. G. Littman “Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs” Astrophys. J. 582(2), 1147–1161, (2003).
[CrossRef]

Kasdin, N.J.

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

Kuchner, M. J.

M. J. Kuchner, J. Crepp, J. Ge, and Astrophys.“Eighth-Order Image Masks for Terrestrial Planet Finding,”  J. 628(1), 466–473 (2005).

Kuhnert, A.

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

Littman, M. G.

N. J. Kasdin, R. J. Vanderbei, D. N. Spergel, and M. G. Littman “Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs” Astrophys. J. 582(2), 1147–1161, (2003).
[CrossRef]

Littman, M.G.

N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

Macintosh, B.

L.A. Poyneer and B. Macintosh “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21(5), 810–819 (2004).
[CrossRef]

Malbet, F.

F. Malbet, J.W. Yu, and M Shao, “High dynamic range imaging using a deformable mirror for space coronography”, PASP,  107, pp. 386 (1995).
[CrossRef]

Poyneer, L.A.

L.A. Poyneer and B. Macintosh “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21(5), 810–819 (2004).
[CrossRef]

Shao, M

F. Malbet, J.W. Yu, and M Shao, “High dynamic range imaging using a deformable mirror for space coronography”, PASP,  107, pp. 386 (1995).
[CrossRef]

Shi, F.

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

Spergel, D. N.

N. J. Kasdin, R. J. Vanderbei, D. N. Spergel, and M. G. Littman “Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs” Astrophys. J. 582(2), 1147–1161, (2003).
[CrossRef]

Traub, W. A.

P. J. Borde and W. A. Traub, “High-contrast imaging from space: Speckle nulling in a low aberration regime,” Astrophys. J. 638 (2006).

Trauger, J. T.

J. T. Trauger, C. Burrows, and B. Gordon et al, “Coronagraph contrast demonstration with the high-contrast imagaing testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

Trauger, J.T.

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

Tyson, R.K.

R.K. TysonIntroduction to Adaptive Optics. SPIE Press, 2000.
[CrossRef]

Vanderbei, R. J.

A. Give’on, N. J. Kasdin, R. J. Vanderbei, and Y. Avitzour “On representing and correcting wavefront errors in high-contrast imaging systems,” J. Opt. Soc. Am. A 23 (2006).

N. J. Kasdin, R. J. Vanderbei, D. N. Spergel, and M. G. Littman “Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs” Astrophys. J. 582(2), 1147–1161, (2003).
[CrossRef]

Vanderbei, R.J.

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

Yu, J.W.

F. Malbet, J.W. Yu, and M Shao, “High dynamic range imaging using a deformable mirror for space coronography”, PASP,  107, pp. 386 (1995).
[CrossRef]

Astrophys. (2)

P. J. Borde and W. A. Traub, “High-contrast imaging from space: Speckle nulling in a low aberration regime,” Astrophys. J. 638 (2006).

N. J. Kasdin, R. J. Vanderbei, D. N. Spergel, and M. G. Littman “Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs” Astrophys. J. 582(2), 1147–1161, (2003).
[CrossRef]

J. Opt. Soc. Am. (2)

L.A. Poyneer and B. Macintosh “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21(5), 810–819 (2004).
[CrossRef]

A. Give’on, N. J. Kasdin, R. J. Vanderbei, and Y. Avitzour “On representing and correcting wavefront errors in high-contrast imaging systems,” J. Opt. Soc. Am. A 23 (2006).

PASP (1)

F. Malbet, J.W. Yu, and M Shao, “High dynamic range imaging using a deformable mirror for space coronography”, PASP,  107, pp. 386 (1995).
[CrossRef]

Proc. SPIE (3)

J. T. Trauger, C. Burrows, and B. Gordon et al, “Coronagraph contrast demonstration with the high-contrast imagaing testbed,” Proc. SPIE 5487, 1330–1336 (2004).
[CrossRef]

R. Belikov, A. Give’on, J.T. Trauger, M. Carr, N.J. Kasdin, R.J. Vanderbei, F. Shi, K. Balasubramanian, and A. Kuhnert, “Toward 1010 contrast for terrestrial exoplanet detection: demonstration of wavefront correction in a shaped-pupil coronagraph,” Proc. SPIE 6265, pp. 626–518 (2006).

N.J. Kasdin, R. Belikov, J. Beall, R.J. Vanderbei, M.G. Littman, M. Carr, and A. Give’on, “Shaped pupil coronagraphs for planet finding: optimization, manufacturing, and experimental results,” Proc. SPIE 5905, 128–136 (2005).

Other (3)

M. J. Kuchner, J. Crepp, J. Ge, and Astrophys.“Eighth-Order Image Masks for Terrestrial Planet Finding,”  J. 628(1), 466–473 (2005).

W. A. Traub, ed. Proceedings of Coronagraph Workshop2006. JPL Publication 07-02.

R.K. TysonIntroduction to Adaptive Optics. SPIE Press, 2000.
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

CCD images. Left: Before correction. Average contrast across (5-14λ/D) is about 10-5. Center: After Classical Speckle Nulling correction bottoms out. Contrast across (6-14 λ/D) is about 10-6. Right: After Energy Minimization bottoms out. Contrast across (6-14 λ/D) is about 6×10-7.

Fig. 2.
Fig. 2.

A log-log plot of average contrast in the control region vs. number of images taken by the estimation and control algorithms.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

E f = C { E 0 }
E 0 = A e α + i β e i ψ ,
E f = C { A e α + i β e i ψ } C { A ( 1 + Φ ) ( 1 + i ψ ) }
= C { A ( 1 + Φ + i ψ + i ψ Φ ) } C { A ( 1 + Φ + i ψ ) }
= C { A e α + i β } + i C { A ψ }
𝓔 = C { A e α + i β } + i C { A ψ } , C { A e α + i β } + i C { A ψ }
ψ = k = 1 N dm l = 1 N dm a k , l f k , l ,
m = 1 N dm n = 1 N dm a m , n { C { A f k , l } , C { A f m , n } } = { C { A f k , l } , C { A e α + i β } } ,
[ G 1 , 1 G 1 , N dm 2 G N dm 2 , 1 G N dm 2 , N dm 2 ] [ a 1 a N dm 2 ] = [ H 1 H N dm 2 ] ,
E k C { A e α + i β } + C { A Ψ k }
I k = C { A e α + i β } + C { A Ψ k } 2 .
I 0 = C { A e α + i β } 2 .
I k I 0 C { A Ψ k } 2 = ( C { A e α + i β } ) * C { A Ψ k } + C { A e α + i β } ( C { A Ψ k } ) * .
[ I 1 I 0 C { A Ψ 1 } 2 I k I 0 C { A Ψ k } 2 ] = 2 [ { C { A Ψ 1 } } { C { A Ψ 1 } } { C { A Ψ k } } { C { A Ψ k } } ] [ { C { A e α + i β } } { C { A e α + i β } } ]
[ { C { A e α + i β } } { C { A e α + i β } } ] = 1 2 [ { C { A Ψ 1 } } { C { A Ψ 1 } } { C { A Ψ k } } { C { A Ψ k } } ] [ I 1 I 0 C { A Ψ 1 } 2 I k I 0 C { A Ψ k } 2 ]
{ C { A Ψ m } } { C { A Ψ n } } { C { A Ψ m } } { C { A Ψ n } } 0

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