Abstract

We introduce a stellar coronagraph that uses a coronagraphic mask described by a Hermite function or a combination of them. It allows the detection of exoplanets providing both deep starlight extinction and high angular resolution. This angular resolution depends on the order of the Hermite function used. An analysis of the coronagraph performance is carried out for different even order masks. Numerical simulations of the ideal case, with no phase errors and perfect telescope pointing, show that on-axis starlight is reduced to very low intensity levels corresponding to a gain of at least 25 magnitudes (10−10 light intensity reduction). The coronagraphic throughput depends on the Hermite function or combination selected. The proposed mask series presents the same advantages of band limited masks along with the benefit of reducing the light diffracted by the mask border thanks to its particular shape. Nevertheless, for direct detection of Earth-like exoplanets it requires the use of adaptive optics facilities for compensating the perturbations introduced by the atmosphere and by the optical system.

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  1. N. Woolf and J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36(1), 507–537 (1998).
    [CrossRef]
  2. A. Beichman, N. J. Wolf, and C. A. Lindensmith, eds., Terrestrial Planet Finder (TPF) (JPL Publications 99–003, Jet Propulsion Laboratory, Pasadena, 1999).
  3. O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar planets detection with coronagraphs,” Astrophys. J. Suppl. Ser. 167(1), 81–99 (2006).
    [CrossRef]
  4. C. Aime, “Radon approach to shaped and apodized apertures for imaging exoplanets,” Astron. Astrophys. 434(2), 785–794 (2005).
    [CrossRef]
  5. O. Guyon, E. A. Pluzhnik, R. Galicher, F. Martinache, S. T. Ridgway, and R. A. Woodruff, “Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle,” Astrophys. J. 622(1), 744–758 (2005).
    [CrossRef]
  6. F. Roddier and C. Roddier, “Stellar Coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
    [CrossRef]
  7. P. Baudoz, Y. Rabbia, and J. Gay, “Achromatic interfero coronagraphy,” Astron. Astrophys. Suppl. Ser. 141(2), 319–329 (2000).
    [CrossRef]
  8. D. Rouan, D. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph,” Publ. Astron. Soc. Pac. 112(777), 1479–1486 (2000).
    [CrossRef]
  9. G. Foo, D. M. Palacios, and G. A. Swartzlander., “Optical vortex coronagraph,” Opt. Lett. 30(24), 3308–3310 (2005).
    [CrossRef]
  10. M. J. Kuchner and W. A. Traub, “A Coronagraph with a Band-limited Mask for Finding Terrestrial Planets,” Astrophys. J. 570(2), 900–908 (2002).
    [CrossRef]
  11. M. P. Cagigal and V. F. Canales, “Exoplanet detection using a nulling interferometer,” Opt. Express 9(1), 36–41 (2001).
    [CrossRef] [PubMed]
  12. M. P. Cagigal and V. F. Canales, “Speckle statistics in partially corrected wave fronts,” Opt. Lett. 23(14), 1072–1074 (1998).
    [CrossRef]
  13. V. F. Canales and M. P. Cagigal, “Photon statistics in partially compensated wave fronts,” J. Opt. Soc. Am. A 16(10), 2550–2554 (1999).
    [CrossRef]
  14. A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552(1), 397–408 (2001).
    [CrossRef]
  15. J. E. Oti, V. F. Canales, and M. P. Cagigal, “Pure amplitude masks for exoplanet detection with the optical differentiation coronagraph,” Astrophys. J. 662(1), 738–743 (2007).
    [CrossRef]
  16. P. J. Borde and W. A. Traub, “High-contrast imaging from space: speckle nulling in a low-aberration regime,” Astrophys. J. 638(1), 488–498 (2006).
    [CrossRef]

2007 (1)

J. E. Oti, V. F. Canales, and M. P. Cagigal, “Pure amplitude masks for exoplanet detection with the optical differentiation coronagraph,” Astrophys. J. 662(1), 738–743 (2007).
[CrossRef]

2006 (2)

P. J. Borde and W. A. Traub, “High-contrast imaging from space: speckle nulling in a low-aberration regime,” Astrophys. J. 638(1), 488–498 (2006).
[CrossRef]

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar planets detection with coronagraphs,” Astrophys. J. Suppl. Ser. 167(1), 81–99 (2006).
[CrossRef]

2005 (3)

C. Aime, “Radon approach to shaped and apodized apertures for imaging exoplanets,” Astron. Astrophys. 434(2), 785–794 (2005).
[CrossRef]

O. Guyon, E. A. Pluzhnik, R. Galicher, F. Martinache, S. T. Ridgway, and R. A. Woodruff, “Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle,” Astrophys. J. 622(1), 744–758 (2005).
[CrossRef]

G. Foo, D. M. Palacios, and G. A. Swartzlander., “Optical vortex coronagraph,” Opt. Lett. 30(24), 3308–3310 (2005).
[CrossRef]

2002 (1)

M. J. Kuchner and W. A. Traub, “A Coronagraph with a Band-limited Mask for Finding Terrestrial Planets,” Astrophys. J. 570(2), 900–908 (2002).
[CrossRef]

2001 (2)

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552(1), 397–408 (2001).
[CrossRef]

M. P. Cagigal and V. F. Canales, “Exoplanet detection using a nulling interferometer,” Opt. Express 9(1), 36–41 (2001).
[CrossRef] [PubMed]

2000 (2)

P. Baudoz, Y. Rabbia, and J. Gay, “Achromatic interfero coronagraphy,” Astron. Astrophys. Suppl. Ser. 141(2), 319–329 (2000).
[CrossRef]

D. Rouan, D. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph,” Publ. Astron. Soc. Pac. 112(777), 1479–1486 (2000).
[CrossRef]

1999 (1)

1998 (2)

M. P. Cagigal and V. F. Canales, “Speckle statistics in partially corrected wave fronts,” Opt. Lett. 23(14), 1072–1074 (1998).
[CrossRef]

N. Woolf and J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36(1), 507–537 (1998).
[CrossRef]

1997 (1)

F. Roddier and C. Roddier, “Stellar Coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[CrossRef]

Aime, C.

C. Aime, “Radon approach to shaped and apodized apertures for imaging exoplanets,” Astron. Astrophys. 434(2), 785–794 (2005).
[CrossRef]

Angel, J. R.

N. Woolf and J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36(1), 507–537 (1998).
[CrossRef]

Baudoz, P.

P. Baudoz, Y. Rabbia, and J. Gay, “Achromatic interfero coronagraphy,” Astron. Astrophys. Suppl. Ser. 141(2), 319–329 (2000).
[CrossRef]

Berkefeld, T.

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552(1), 397–408 (2001).
[CrossRef]

Boccaletti, A.

D. Rouan, D. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph,” Publ. Astron. Soc. Pac. 112(777), 1479–1486 (2000).
[CrossRef]

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(1), 488–498 (2006).
[CrossRef]

Cagigal, M. P.

Canales, V. F.

Clénet, Y.

D. Rouan, D. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph,” Publ. Astron. Soc. Pac. 112(777), 1479–1486 (2000).
[CrossRef]

Collins, B.

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar planets detection with coronagraphs,” Astrophys. J. Suppl. Ser. 167(1), 81–99 (2006).
[CrossRef]

Foo, G.

Galicher, R.

O. Guyon, E. A. Pluzhnik, R. Galicher, F. Martinache, S. T. Ridgway, and R. A. Woodruff, “Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle,” Astrophys. J. 622(1), 744–758 (2005).
[CrossRef]

Gay, J.

P. Baudoz, Y. Rabbia, and J. Gay, “Achromatic interfero coronagraphy,” Astron. Astrophys. Suppl. Ser. 141(2), 319–329 (2000).
[CrossRef]

Guyon, O.

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar planets detection with coronagraphs,” Astrophys. J. Suppl. Ser. 167(1), 81–99 (2006).
[CrossRef]

O. Guyon, E. A. Pluzhnik, R. Galicher, F. Martinache, S. T. Ridgway, and R. A. Woodruff, “Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle,” Astrophys. J. 622(1), 744–758 (2005).
[CrossRef]

Koresko, C. D.

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552(1), 397–408 (2001).
[CrossRef]

Kuchner, M. J.

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar planets detection with coronagraphs,” Astrophys. J. Suppl. Ser. 167(1), 81–99 (2006).
[CrossRef]

M. J. Kuchner and W. A. Traub, “A Coronagraph with a Band-limited Mask for Finding Terrestrial Planets,” Astrophys. J. 570(2), 900–908 (2002).
[CrossRef]

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552(1), 397–408 (2001).
[CrossRef]

Labeyrie, A.

D. Rouan, D. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph,” Publ. Astron. Soc. Pac. 112(777), 1479–1486 (2000).
[CrossRef]

Makidon, R. B.

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552(1), 397–408 (2001).
[CrossRef]

Martinache, F.

O. Guyon, E. A. Pluzhnik, R. Galicher, F. Martinache, S. T. Ridgway, and R. A. Woodruff, “Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle,” Astrophys. J. 622(1), 744–758 (2005).
[CrossRef]

Oti, J. E.

J. E. Oti, V. F. Canales, and M. P. Cagigal, “Pure amplitude masks for exoplanet detection with the optical differentiation coronagraph,” Astrophys. J. 662(1), 738–743 (2007).
[CrossRef]

Palacios, D. M.

Pluzhnik, E. A.

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar planets detection with coronagraphs,” Astrophys. J. Suppl. Ser. 167(1), 81–99 (2006).
[CrossRef]

O. Guyon, E. A. Pluzhnik, R. Galicher, F. Martinache, S. T. Ridgway, and R. A. Woodruff, “Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle,” Astrophys. J. 622(1), 744–758 (2005).
[CrossRef]

Rabbia, Y.

P. Baudoz, Y. Rabbia, and J. Gay, “Achromatic interfero coronagraphy,” Astron. Astrophys. Suppl. Ser. 141(2), 319–329 (2000).
[CrossRef]

Riaud, D.

D. Rouan, D. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph,” Publ. Astron. Soc. Pac. 112(777), 1479–1486 (2000).
[CrossRef]

Ridgway, S. T.

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar planets detection with coronagraphs,” Astrophys. J. Suppl. Ser. 167(1), 81–99 (2006).
[CrossRef]

O. Guyon, E. A. Pluzhnik, R. Galicher, F. Martinache, S. T. Ridgway, and R. A. Woodruff, “Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle,” Astrophys. J. 622(1), 744–758 (2005).
[CrossRef]

Roddier, C.

F. Roddier and C. Roddier, “Stellar Coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[CrossRef]

Roddier, F.

F. Roddier and C. Roddier, “Stellar Coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[CrossRef]

Rouan, D.

D. Rouan, D. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph,” Publ. Astron. Soc. Pac. 112(777), 1479–1486 (2000).
[CrossRef]

Sivaramakrishnan, A.

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552(1), 397–408 (2001).
[CrossRef]

Swartzlander, G. A.

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(1), 488–498 (2006).
[CrossRef]

M. J. Kuchner and W. A. Traub, “A Coronagraph with a Band-limited Mask for Finding Terrestrial Planets,” Astrophys. J. 570(2), 900–908 (2002).
[CrossRef]

Woodruff, R. A.

O. Guyon, E. A. Pluzhnik, R. Galicher, F. Martinache, S. T. Ridgway, and R. A. Woodruff, “Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle,” Astrophys. J. 622(1), 744–758 (2005).
[CrossRef]

Woolf, N.

N. Woolf and J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36(1), 507–537 (1998).
[CrossRef]

Annu. Rev. Astron. Astrophys. (1)

N. Woolf and J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36(1), 507–537 (1998).
[CrossRef]

Astron. Astrophys. (1)

C. Aime, “Radon approach to shaped and apodized apertures for imaging exoplanets,” Astron. Astrophys. 434(2), 785–794 (2005).
[CrossRef]

Astron. Astrophys. Suppl. Ser. (1)

P. Baudoz, Y. Rabbia, and J. Gay, “Achromatic interfero coronagraphy,” Astron. Astrophys. Suppl. Ser. 141(2), 319–329 (2000).
[CrossRef]

Astrophys. J. (5)

O. Guyon, E. A. Pluzhnik, R. Galicher, F. Martinache, S. T. Ridgway, and R. A. Woodruff, “Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle,” Astrophys. J. 622(1), 744–758 (2005).
[CrossRef]

M. J. Kuchner and W. A. Traub, “A Coronagraph with a Band-limited Mask for Finding Terrestrial Planets,” Astrophys. J. 570(2), 900–908 (2002).
[CrossRef]

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552(1), 397–408 (2001).
[CrossRef]

J. E. Oti, V. F. Canales, and M. P. Cagigal, “Pure amplitude masks for exoplanet detection with the optical differentiation coronagraph,” Astrophys. J. 662(1), 738–743 (2007).
[CrossRef]

P. J. Borde and W. A. Traub, “High-contrast imaging from space: speckle nulling in a low-aberration regime,” Astrophys. J. 638(1), 488–498 (2006).
[CrossRef]

Astrophys. J. Suppl. Ser. (1)

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar planets detection with coronagraphs,” Astrophys. J. Suppl. Ser. 167(1), 81–99 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Opt. Lett. (2)

Publ. Astron. Soc. Pac. (2)

F. Roddier and C. Roddier, “Stellar Coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997).
[CrossRef]

D. Rouan, D. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph,” Publ. Astron. Soc. Pac. 112(777), 1479–1486 (2000).
[CrossRef]

Other (1)

A. Beichman, N. J. Wolf, and C. A. Lindensmith, eds., Terrestrial Planet Finder (TPF) (JPL Publications 99–003, Jet Propulsion Laboratory, Pasadena, 1999).

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Figures (3)

Fig. 1
Fig. 1

Set-up of the proposed stellar coronagraph. It is composed of 3 lenses, L1, L2 and L3, the Lyot stop, LS, the mask, HFM, placed at the common focal plane of L1 and L2, and an imaging system like a CCD camera.

Fig. 2
Fig. 2

Design of the HFM required in our instrument. a) Amplitude transmittance of the MC 4 mask (blue curve), MC 6 mask (red curve), MC 8 (black solid curve) and MC (dashed curve).

Fig. 3
Fig. 3

Radial intensity profile obtained for the mask MC 4 (dotted curve), MC 6 (dashed-dotted curve), MC 8 (solid curve) and M C (dashed curve) in the perfect wavefront case. For comparison, the dashed-dotted-dotted curve shows the no-filter profile (with the stop).

Equations (5)

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Mn(x,v)=1n!2nπexp(x22v)Hn(x)
Hn(x)=(1)nex2ddxnex2
FT  [Mn(x,v)](u)=2πv(2v1)n/2inMn(2πv2v1u,v2v1)
Mc(x)=kakMnk(x,vk)nk  even
MC2(x,v)=M2(x,v)+12M0(x,v)=12!22πexp(x22v)[H2(x)+2H0(x)]

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