Abstract

We introduce a new optical vortex coronagraph(OVC) method to determine the angular distance between two sources when the separation is sub-Rayleigh. We have found a direct relationship between the position of the minima and the source angular separation. A priori knowledge about the location of the two sources is not required. The superresolution capabilities of an OVC, equipped with an = 2 N-step spiral phase plate in its optical path, were investigated numerically. The results of these investigations show that a fraction of the light, increasing with N, from the secondary source can be detected with a sub-Rayleigh resolution of at least 0.1 λ/D.

© 2012 OSA

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References

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  1. A. Quirrenbach, “Coronographic Methods for the Detection of Terrestrial Planets,” Arxiv preprint astroph/0502254 (2005).
  2. F. Roddier and C. Roddier, “Stellar coronograph with phase mask,” Publ. Astr. Soc. Pacif. 109, 815–820 (1997).
    [CrossRef]
  3. D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The Four-Quadrant Phase-Mask Coronagraph. I. Principle,” Publ. Astr. Soc. Pacif. 112, 1479–1486 (2000).
    [CrossRef]
  4. D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: Laboratory results and first light at Palomar Observatory,” Astrophys. J. 709, 53–57 (2010).
    [CrossRef]
  5. G. Foo, D. M. Palacios, and G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30, 3308–3310 (2005).
    [CrossRef]
  6. J. Lee, G. Foo, E. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph.” Phys. Rev. Lett. 97(5), 053901 (2006).
    [CrossRef] [PubMed]
  7. E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464(7291), 1018–1020 (2010).
    [CrossRef] [PubMed]
  8. P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
    [CrossRef]
  9. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [CrossRef] [PubMed]
  10. F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97(16), 163903 (2006).
    [CrossRef] [PubMed]
  11. D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
    [CrossRef]
  12. G. A. Swartzlander, “The optical vortex coronagraph,” J. Opt. A Pure Appl. Opt. 11, 094022 (2009).
    [CrossRef]
  13. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  14. E. Mari, G. Anzolin, F. Tamburini, M. Prasciolu, G. Umbriaco, A. Bianchini, C. Barbieri, and F. Romanato, “Fabrication and testing of l = 2 optical vortex phase masks for coronography,” Opt. Express 18, 2339–2344 (2010).
    [CrossRef] [PubMed]
  15. E. Hecht, Optics, 4th ed. (Addison-Wesley Publishing Company, 2001).
  16. H. Müller, S.-W. Chiow, Q. Long, C. Vo, and S. Chu, “Active sub-Rayleigh alignment of parallel or antiparallel laser beams,” Opt. Lett. 30, 3323–3325 (2005).
    [CrossRef]
  17. G. A. Swartzlander, “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497–499 (2001).
    [CrossRef]
  18. M. Pitchumani, H. Hockel, W. Mohammed, and E. Johnson, “Additive lithography for fabrication of diffractive optics,” Appl. Opt. 41(29), 6176–6181 (2002).
    [CrossRef] [PubMed]
  19. G. A. Swartzlander, “Obtaining spatial information from an extremely unresolved source,” Opt. Lett. 36, 4731–4733 (2011).
    [CrossRef] [PubMed]
  20. E. Mari, F. Tamburini, C. Barbieri, and A. Bianchini, “Fabrication and testing of phase masks for optical vortex coronagraph to observe extrasolar planets,” Proceedings of SPIE 7735, 773534 (2010).
    [CrossRef]

2011 (1)

2010 (4)

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464(7291), 1018–1020 (2010).
[CrossRef] [PubMed]

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: Laboratory results and first light at Palomar Observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

E. Mari, F. Tamburini, C. Barbieri, and A. Bianchini, “Fabrication and testing of phase masks for optical vortex coronagraph to observe extrasolar planets,” Proceedings of SPIE 7735, 773534 (2010).
[CrossRef]

E. Mari, G. Anzolin, F. Tamburini, M. Prasciolu, G. Umbriaco, A. Bianchini, C. Barbieri, and F. Romanato, “Fabrication and testing of l = 2 optical vortex phase masks for coronography,” Opt. Express 18, 2339–2344 (2010).
[CrossRef] [PubMed]

2009 (1)

G. A. Swartzlander, “The optical vortex coronagraph,” J. Opt. A Pure Appl. Opt. 11, 094022 (2009).
[CrossRef]

2006 (2)

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97(16), 163903 (2006).
[CrossRef] [PubMed]

J. Lee, G. Foo, E. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph.” Phys. Rev. Lett. 97(5), 053901 (2006).
[CrossRef] [PubMed]

2005 (3)

2002 (1)

2001 (1)

2000 (1)

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The Four-Quadrant Phase-Mask Coronagraph. I. Principle,” Publ. Astr. Soc. Pacif. 112, 1479–1486 (2000).
[CrossRef]

1997 (1)

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

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

1989 (1)

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[CrossRef]

Absil, O.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Anzolin, G.

E. Mari, G. Anzolin, F. Tamburini, M. Prasciolu, G. Umbriaco, A. Bianchini, C. Barbieri, and F. Romanato, “Fabrication and testing of l = 2 optical vortex phase masks for coronography,” Opt. Express 18, 2339–2344 (2010).
[CrossRef] [PubMed]

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97(16), 163903 (2006).
[CrossRef] [PubMed]

Barbieri, C.

E. Mari, G. Anzolin, F. Tamburini, M. Prasciolu, G. Umbriaco, A. Bianchini, C. Barbieri, and F. Romanato, “Fabrication and testing of l = 2 optical vortex phase masks for coronography,” Opt. Express 18, 2339–2344 (2010).
[CrossRef] [PubMed]

E. Mari, F. Tamburini, C. Barbieri, and A. Bianchini, “Fabrication and testing of phase masks for optical vortex coronagraph to observe extrasolar planets,” Proceedings of SPIE 7735, 773534 (2010).
[CrossRef]

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97(16), 163903 (2006).
[CrossRef] [PubMed]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Bianchini, A.

E. Mari, F. Tamburini, C. Barbieri, and A. Bianchini, “Fabrication and testing of phase masks for optical vortex coronagraph to observe extrasolar planets,” Proceedings of SPIE 7735, 773534 (2010).
[CrossRef]

E. Mari, G. Anzolin, F. Tamburini, M. Prasciolu, G. Umbriaco, A. Bianchini, C. Barbieri, and F. Romanato, “Fabrication and testing of l = 2 optical vortex phase masks for coronography,” Opt. Express 18, 2339–2344 (2010).
[CrossRef] [PubMed]

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97(16), 163903 (2006).
[CrossRef] [PubMed]

Boccaletti, A.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The Four-Quadrant Phase-Mask Coronagraph. I. Principle,” Publ. Astr. Soc. Pacif. 112, 1479–1486 (2000).
[CrossRef]

Burruss, R.

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464(7291), 1018–1020 (2010).
[CrossRef] [PubMed]

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: Laboratory results and first light at Palomar Observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

Chiow, S.-W.

Chu, S.

Clénet, Y.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The Four-Quadrant Phase-Mask Coronagraph. I. Principle,” Publ. Astr. Soc. Pacif. 112, 1479–1486 (2000).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Coullet, P.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[CrossRef]

Foo, G.

J. Lee, G. Foo, E. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph.” Phys. Rev. Lett. 97(5), 053901 (2006).
[CrossRef] [PubMed]

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

Gil, L.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley Publishing Company, 2001).

Hickey, J.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: Laboratory results and first light at Palomar Observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

Hockel, H.

Johnson, E.

J. Lee, G. Foo, E. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph.” Phys. Rev. Lett. 97(5), 053901 (2006).
[CrossRef] [PubMed]

M. Pitchumani, H. Hockel, W. Mohammed, and E. Johnson, “Additive lithography for fabrication of diffractive optics,” Appl. Opt. 41(29), 6176–6181 (2002).
[CrossRef] [PubMed]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Labeyrie, A.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The Four-Quadrant Phase-Mask Coronagraph. I. Principle,” Publ. Astr. Soc. Pacif. 112, 1479–1486 (2000).
[CrossRef]

Lee, J.

J. Lee, G. Foo, E. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph.” Phys. Rev. Lett. 97(5), 053901 (2006).
[CrossRef] [PubMed]

Liewer, K.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: Laboratory results and first light at Palomar Observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

Long, Q.

Mari, E.

E. Mari, G. Anzolin, F. Tamburini, M. Prasciolu, G. Umbriaco, A. Bianchini, C. Barbieri, and F. Romanato, “Fabrication and testing of l = 2 optical vortex phase masks for coronography,” Opt. Express 18, 2339–2344 (2010).
[CrossRef] [PubMed]

E. Mari, F. Tamburini, C. Barbieri, and A. Bianchini, “Fabrication and testing of phase masks for optical vortex coronagraph to observe extrasolar planets,” Proceedings of SPIE 7735, 773534 (2010).
[CrossRef]

Mawet, D.

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464(7291), 1018–1020 (2010).
[CrossRef] [PubMed]

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: Laboratory results and first light at Palomar Observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

Mohammed, W.

Müller, H.

Palacios, D. M.

Pitchumani, M.

Prasciolu, M.

Quirrenbach, A.

A. Quirrenbach, “Coronographic Methods for the Detection of Terrestrial Planets,” Arxiv preprint astroph/0502254 (2005).

Riaud, P.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The Four-Quadrant Phase-Mask Coronagraph. I. Principle,” Publ. Astr. Soc. Pacif. 112, 1479–1486 (2000).
[CrossRef]

Rocca, F.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[CrossRef]

Roddier, C.

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

Roddier, F.

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

Romanato, F.

Rouan, D.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The Four-Quadrant Phase-Mask Coronagraph. I. Principle,” Publ. Astr. Soc. Pacif. 112, 1479–1486 (2000).
[CrossRef]

Serabyn, E.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: Laboratory results and first light at Palomar Observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464(7291), 1018–1020 (2010).
[CrossRef] [PubMed]

Shemo, D.

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: Laboratory results and first light at Palomar Observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Surdej, J.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

Swartzlander, G. A.

Tamburini, F.

E. Mari, F. Tamburini, C. Barbieri, and A. Bianchini, “Fabrication and testing of phase masks for optical vortex coronagraph to observe extrasolar planets,” Proceedings of SPIE 7735, 773534 (2010).
[CrossRef]

E. Mari, G. Anzolin, F. Tamburini, M. Prasciolu, G. Umbriaco, A. Bianchini, C. Barbieri, and F. Romanato, “Fabrication and testing of l = 2 optical vortex phase masks for coronography,” Opt. Express 18, 2339–2344 (2010).
[CrossRef] [PubMed]

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97(16), 163903 (2006).
[CrossRef] [PubMed]

Umbriaco, G.

E. Mari, G. Anzolin, F. Tamburini, M. Prasciolu, G. Umbriaco, A. Bianchini, C. Barbieri, and F. Romanato, “Fabrication and testing of l = 2 optical vortex phase masks for coronography,” Opt. Express 18, 2339–2344 (2010).
[CrossRef] [PubMed]

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97(16), 163903 (2006).
[CrossRef] [PubMed]

Vo, C.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Appl. Opt. (1)

Astrophys. J. (2)

D. Mawet, E. Serabyn, K. Liewer, R. Burruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: Laboratory results and first light at Palomar Observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

G. A. Swartzlander, “The optical vortex coronagraph,” J. Opt. A Pure Appl. Opt. 11, 094022 (2009).
[CrossRef]

Nature (1)

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beamwidths from a star,” Nature 464(7291), 1018–1020 (2010).
[CrossRef] [PubMed]

Opt. Commun. (2)

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73(5), 403–408 (1989).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97(16), 163903 (2006).
[CrossRef] [PubMed]

J. Lee, G. Foo, E. Johnson, and G. A. Swartzlander, “Experimental verification of an optical vortex coronagraph.” Phys. Rev. Lett. 97(5), 053901 (2006).
[CrossRef] [PubMed]

Proceedings of SPIE (1)

E. Mari, F. Tamburini, C. Barbieri, and A. Bianchini, “Fabrication and testing of phase masks for optical vortex coronagraph to observe extrasolar planets,” Proceedings of SPIE 7735, 773534 (2010).
[CrossRef]

Publ. Astr. Soc. Pacif. (2)

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

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The Four-Quadrant Phase-Mask Coronagraph. I. Principle,” Publ. Astr. Soc. Pacif. 112, 1479–1486 (2000).
[CrossRef]

Other (2)

E. Hecht, Optics, 4th ed. (Addison-Wesley Publishing Company, 2001).

A. Quirrenbach, “Coronographic Methods for the Detection of Terrestrial Planets,” Arxiv preprint astroph/0502254 (2005).

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Figures (5)

Fig. 1
Fig. 1

Optical scheme of an OVC. T is the objective, L1 the collimating lens, and LS the Lyot stop, placed at the same focal distance as that of L1. The light of the on-axis object, O1, crosses the central dislocation of the SPP and is transformed into a ”ring of fire” in the back focal plane of L1. The ring of light is blocked by a Lyot stop LS placed in the back focal plane of L1. The light emitted by the off-axis source, O2, evades the central dislocation of the SPP and the LS, so it is focused by L2 to be on the detector array CCD.

Fig. 2
Fig. 2

Numerically generated intensity distributions and profiles (a) Two unresolvable point sources with the same intensity separated by 0.1λ/D (b) corresponding intensity profiles (c) Intensity pattern of the off-axis source when crosses an = 2 SPP (see text) and its intensity profile (d).

Fig. 3
Fig. 3

(a): Plot of minima position versus angular separation. points represent numerically calculated examples. (b): Numerically generated intensity profile of one of two unresolvable point sources with the same intensity. Arrow indicate the minimum position θmin for the angular separation 0.2λ/D′. (c) Enlargement of the minimum zone of the profile (b). The minimum occur exactly at the angular separation 0.2λ/D′.

Fig. 4
Fig. 4

Power measured in the dark vortex core region when the sources subtend a fixed angle Δθ′ = 0.3λ/D′ and when the telescope is swept through an angle, ΔθSPP (along a line defined by the two sources). The position ΔθSPP = Δθ′ corresponds to an alignment of the SPP axis and the primary star.

Fig. 5
Fig. 5

Simulated coronagraphic image in 2D and 3D for an ideal SPP (upper panels) and a stepped SPP with 8 levels(lower panels), when the two sources have an intensity ratio of 10−8 and 10−2, respectively. Angular distances between two objects: 0.5λ/D′ and 3λ/D′.

Tables (1)

Tables Icon

Table 1 The percentage of the light of the secondary source passing through the LS with a diameter 0.7 times that of the exit pupil of the telescope. It depends on the number of the steps N used to build the total phase gap and on the angular distance Δθ in units of λ/D.

Metrics