Abstract

We derive the broadband contrast floor in a coronagraphic telescope having nonideal optical surfaces. We consider only fundamental spatial frequencies within the control bandwidth of the coronagraph's deformable mirror. Cross terms arising from the beating of spatial frequencies beyond the deformable mirror control bandwidth will be considered in a second paper. Two wavefront control systems are analyzed:a zero-path difference Michelson interferometer with two deformable mirrors at a pupil image, and a sequential pair of deformable mirrors with one placed at a pupil image. We derive requirements on optical surface figure and reflectivity uniformity for both cases.

© 2006 Optical Society of America

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References

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  1. V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).
  2. F. Malbet, J. Yu, and M. Shao, "High-dynamic range imaging using a deformable mirror for space coronagraphy," Publ. Astron. Soc. Pac. 107, 386 (1995).
  3. M. G. Littman, M. Carr, J. Leighton, E. Burke, D. N. Spergel, and N. J. Kasdin, "Phase and amplitude control ability using spatial light modulation and zero path length difference Michelson interferometer," in Future EUV/UV and Visible Space Missions and Instrumentation, J. C. Blades and O. H. W. Siegmund, eds., Proc. SPIE 4854, 405-412 (2003).
    [CrossRef]
  4. L. Pueyo, M. G. Littman, M. Carr, N. J. Kasdin, D. N. Spergel, and R. J. Vanderbei, "Amplitude and phase control of pupil coronagraph for exoplanet detection using spatial light modulators," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170, 241-249 (2003).
    [CrossRef]
  5. 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, 1063-1073 (2006).
    [CrossRef]
  6. R. A. Brown, "Obscurational completeness," Astrophys. J. 607, 1003-1013 (2004).
    [CrossRef]
  7. W. H. F. Talbot, "Facts relating to optical science, No. IV," Philos. Mag. 9, 401-407 (1836).
  8. L. Pueyo, M. G. Littman, N. J. Kasdin, R. Vanderbei, R. Belikov, and A. Give'on, "Chromaticity effects in adaptive optics:wavelength dependence of amplitude compensation," in Techniques and Instrumentation for Detection of Exolanets II, D. R. Coulter, ed., Proc. SPIE 5903, 190-198 (2005).
  9. J. A. Perreault and A. Wirth, "Survey of adaptive optic techniques," in Focal Plane Arrays for Space Telescopes II, T. J. Grycewicz and C. J. Marshall, eds., Proc. SPIE 5903, 43-50 (2005).
  10. L. Pueyo, Princeton University, Princeton, N.J. 08544 (personal communication, 2005).
  11. P. Z. Mouroulis and S. B. Shaklan, "Optical design of the Terrestrial Planet Finder Coronagraph starlight suppression system," in Current Developments in Lens Design and Optical Engineering VI, P. Z. Mouroulis, W. J. Smith, and R. B. Johnson, eds., Proc. SPIE 5874, 187-197 (2005).
  12. R. P. Linfield, "Wavefront amplitude errors for a TPF Coronagraph: their effects and possible correction," in Optical, Infrared, and Millimeter Space Telescopes, J. C. Mather, ed., Proc. SPIE 5487, 412-422 (2004).
  13. M. A. Ealey and J. T. Trauger, "High density deformable mirrors to enable coronagraphic planet detection," in UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts, H. A. MacEwen, ed., Proc. SPIE 5166, 172-179 (2004).
    [CrossRef]
  14. D. Palacios, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif. 91109 (personal communication, 2005).
  15. J. S. Taylor, "Progress in meeting stringent optical system requirements in EUV lithography," presented at SPIE's 26th Symposium on Microlithography and Emerging Lithographies V, Santa Clara, Calif., 25 February-2 March, 2001.

2006 (1)

2005 (3)

L. Pueyo, M. G. Littman, N. J. Kasdin, R. Vanderbei, R. Belikov, and A. Give'on, "Chromaticity effects in adaptive optics:wavelength dependence of amplitude compensation," in Techniques and Instrumentation for Detection of Exolanets II, D. R. Coulter, ed., Proc. SPIE 5903, 190-198 (2005).

J. A. Perreault and A. Wirth, "Survey of adaptive optic techniques," in Focal Plane Arrays for Space Telescopes II, T. J. Grycewicz and C. J. Marshall, eds., Proc. SPIE 5903, 43-50 (2005).

P. Z. Mouroulis and S. B. Shaklan, "Optical design of the Terrestrial Planet Finder Coronagraph starlight suppression system," in Current Developments in Lens Design and Optical Engineering VI, P. Z. Mouroulis, W. J. Smith, and R. B. Johnson, eds., Proc. SPIE 5874, 187-197 (2005).

2004 (3)

R. P. Linfield, "Wavefront amplitude errors for a TPF Coronagraph: their effects and possible correction," in Optical, Infrared, and Millimeter Space Telescopes, J. C. Mather, ed., Proc. SPIE 5487, 412-422 (2004).

M. A. Ealey and J. T. Trauger, "High density deformable mirrors to enable coronagraphic planet detection," in UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts, H. A. MacEwen, ed., Proc. SPIE 5166, 172-179 (2004).
[CrossRef]

R. A. Brown, "Obscurational completeness," Astrophys. J. 607, 1003-1013 (2004).
[CrossRef]

2003 (3)

V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).

M. G. Littman, M. Carr, J. Leighton, E. Burke, D. N. Spergel, and N. J. Kasdin, "Phase and amplitude control ability using spatial light modulation and zero path length difference Michelson interferometer," in Future EUV/UV and Visible Space Missions and Instrumentation, J. C. Blades and O. H. W. Siegmund, eds., Proc. SPIE 4854, 405-412 (2003).
[CrossRef]

L. Pueyo, M. G. Littman, M. Carr, N. J. Kasdin, D. N. Spergel, and R. J. Vanderbei, "Amplitude and phase control of pupil coronagraph for exoplanet detection using spatial light modulators," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170, 241-249 (2003).
[CrossRef]

1836 (1)

W. H. F. Talbot, "Facts relating to optical science, No. IV," Philos. Mag. 9, 401-407 (1836).

Avitzour, Y.

Belikov, R.

L. Pueyo, M. G. Littman, N. J. Kasdin, R. Vanderbei, R. Belikov, and A. Give'on, "Chromaticity effects in adaptive optics:wavelength dependence of amplitude compensation," in Techniques and Instrumentation for Detection of Exolanets II, D. R. Coulter, ed., Proc. SPIE 5903, 190-198 (2005).

Brown, R. A.

R. A. Brown, "Obscurational completeness," Astrophys. J. 607, 1003-1013 (2004).
[CrossRef]

Burke, E.

M. G. Littman, M. Carr, J. Leighton, E. Burke, D. N. Spergel, and N. J. Kasdin, "Phase and amplitude control ability using spatial light modulation and zero path length difference Michelson interferometer," in Future EUV/UV and Visible Space Missions and Instrumentation, J. C. Blades and O. H. W. Siegmund, eds., Proc. SPIE 4854, 405-412 (2003).
[CrossRef]

Carr, M.

M. G. Littman, M. Carr, J. Leighton, E. Burke, D. N. Spergel, and N. J. Kasdin, "Phase and amplitude control ability using spatial light modulation and zero path length difference Michelson interferometer," in Future EUV/UV and Visible Space Missions and Instrumentation, J. C. Blades and O. H. W. Siegmund, eds., Proc. SPIE 4854, 405-412 (2003).
[CrossRef]

L. Pueyo, M. G. Littman, M. Carr, N. J. Kasdin, D. N. Spergel, and R. J. Vanderbei, "Amplitude and phase control of pupil coronagraph for exoplanet detection using spatial light modulators," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170, 241-249 (2003).
[CrossRef]

Cohen, E. J.

V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).

Ealey, M. A.

M. A. Ealey and J. T. Trauger, "High density deformable mirrors to enable coronagraphic planet detection," in UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts, H. A. MacEwen, ed., Proc. SPIE 5166, 172-179 (2004).
[CrossRef]

Ford, V. G.

V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).

Give'on, A.

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, 1063-1073 (2006).
[CrossRef]

L. Pueyo, M. G. Littman, N. J. Kasdin, R. Vanderbei, R. Belikov, and A. Give'on, "Chromaticity effects in adaptive optics:wavelength dependence of amplitude compensation," in Techniques and Instrumentation for Detection of Exolanets II, D. R. Coulter, ed., Proc. SPIE 5903, 190-198 (2005).

Hull, A. B.

V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).

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, 1063-1073 (2006).
[CrossRef]

L. Pueyo, M. G. Littman, N. J. Kasdin, R. Vanderbei, R. Belikov, and A. Give'on, "Chromaticity effects in adaptive optics:wavelength dependence of amplitude compensation," in Techniques and Instrumentation for Detection of Exolanets II, D. R. Coulter, ed., Proc. SPIE 5903, 190-198 (2005).

L. Pueyo, M. G. Littman, M. Carr, N. J. Kasdin, D. N. Spergel, and R. J. Vanderbei, "Amplitude and phase control of pupil coronagraph for exoplanet detection using spatial light modulators," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170, 241-249 (2003).
[CrossRef]

M. G. Littman, M. Carr, J. Leighton, E. Burke, D. N. Spergel, and N. J. Kasdin, "Phase and amplitude control ability using spatial light modulation and zero path length difference Michelson interferometer," in Future EUV/UV and Visible Space Missions and Instrumentation, J. C. Blades and O. H. W. Siegmund, eds., Proc. SPIE 4854, 405-412 (2003).
[CrossRef]

Leighton, J.

M. G. Littman, M. Carr, J. Leighton, E. Burke, D. N. Spergel, and N. J. Kasdin, "Phase and amplitude control ability using spatial light modulation and zero path length difference Michelson interferometer," in Future EUV/UV and Visible Space Missions and Instrumentation, J. C. Blades and O. H. W. Siegmund, eds., Proc. SPIE 4854, 405-412 (2003).
[CrossRef]

Levine, M. B.

V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).

Linfield, R. P.

R. P. Linfield, "Wavefront amplitude errors for a TPF Coronagraph: their effects and possible correction," in Optical, Infrared, and Millimeter Space Telescopes, J. C. Mather, ed., Proc. SPIE 5487, 412-422 (2004).

Littman, M. G.

L. Pueyo, M. G. Littman, N. J. Kasdin, R. Vanderbei, R. Belikov, and A. Give'on, "Chromaticity effects in adaptive optics:wavelength dependence of amplitude compensation," in Techniques and Instrumentation for Detection of Exolanets II, D. R. Coulter, ed., Proc. SPIE 5903, 190-198 (2005).

L. Pueyo, M. G. Littman, M. Carr, N. J. Kasdin, D. N. Spergel, and R. J. Vanderbei, "Amplitude and phase control of pupil coronagraph for exoplanet detection using spatial light modulators," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170, 241-249 (2003).
[CrossRef]

M. G. Littman, M. Carr, J. Leighton, E. Burke, D. N. Spergel, and N. J. Kasdin, "Phase and amplitude control ability using spatial light modulation and zero path length difference Michelson interferometer," in Future EUV/UV and Visible Space Missions and Instrumentation, J. C. Blades and O. H. W. Siegmund, eds., Proc. SPIE 4854, 405-412 (2003).
[CrossRef]

Lowman, A. E.

V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).

Malbet, F.

F. Malbet, J. Yu, and M. Shao, "High-dynamic range imaging using a deformable mirror for space coronagraphy," Publ. Astron. Soc. Pac. 107, 386 (1995).

Mouroulis, P. Z.

P. Z. Mouroulis and S. B. Shaklan, "Optical design of the Terrestrial Planet Finder Coronagraph starlight suppression system," in Current Developments in Lens Design and Optical Engineering VI, P. Z. Mouroulis, W. J. Smith, and R. B. Johnson, eds., Proc. SPIE 5874, 187-197 (2005).

Palacios, D.

D. Palacios, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif. 91109 (personal communication, 2005).

Perreault, J. A.

J. A. Perreault and A. Wirth, "Survey of adaptive optic techniques," in Focal Plane Arrays for Space Telescopes II, T. J. Grycewicz and C. J. Marshall, eds., Proc. SPIE 5903, 43-50 (2005).

Pueyo, L.

L. Pueyo, M. G. Littman, N. J. Kasdin, R. Vanderbei, R. Belikov, and A. Give'on, "Chromaticity effects in adaptive optics:wavelength dependence of amplitude compensation," in Techniques and Instrumentation for Detection of Exolanets II, D. R. Coulter, ed., Proc. SPIE 5903, 190-198 (2005).

L. Pueyo, M. G. Littman, M. Carr, N. J. Kasdin, D. N. Spergel, and R. J. Vanderbei, "Amplitude and phase control of pupil coronagraph for exoplanet detection using spatial light modulators," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170, 241-249 (2003).
[CrossRef]

L. Pueyo, Princeton University, Princeton, N.J. 08544 (personal communication, 2005).

Shaklan, S. B.

P. Z. Mouroulis and S. B. Shaklan, "Optical design of the Terrestrial Planet Finder Coronagraph starlight suppression system," in Current Developments in Lens Design and Optical Engineering VI, P. Z. Mouroulis, W. J. Smith, and R. B. Johnson, eds., Proc. SPIE 5874, 187-197 (2005).

V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).

Shao, M.

F. Malbet, J. Yu, and M. Shao, "High-dynamic range imaging using a deformable mirror for space coronagraphy," Publ. Astron. Soc. Pac. 107, 386 (1995).

Spergel, D. N.

L. Pueyo, M. G. Littman, M. Carr, N. J. Kasdin, D. N. Spergel, and R. J. Vanderbei, "Amplitude and phase control of pupil coronagraph for exoplanet detection using spatial light modulators," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170, 241-249 (2003).
[CrossRef]

M. G. Littman, M. Carr, J. Leighton, E. Burke, D. N. Spergel, and N. J. Kasdin, "Phase and amplitude control ability using spatial light modulation and zero path length difference Michelson interferometer," in Future EUV/UV and Visible Space Missions and Instrumentation, J. C. Blades and O. H. W. Siegmund, eds., Proc. SPIE 4854, 405-412 (2003).
[CrossRef]

Talbot, W. H. F.

W. H. F. Talbot, "Facts relating to optical science, No. IV," Philos. Mag. 9, 401-407 (1836).

Taylor, J. S.

J. S. Taylor, "Progress in meeting stringent optical system requirements in EUV lithography," presented at SPIE's 26th Symposium on Microlithography and Emerging Lithographies V, Santa Clara, Calif., 25 February-2 March, 2001.

Trauger, J. T.

M. A. Ealey and J. T. Trauger, "High density deformable mirrors to enable coronagraphic planet detection," in UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts, H. A. MacEwen, ed., Proc. SPIE 5166, 172-179 (2004).
[CrossRef]

Vanderbei, R.

L. Pueyo, M. G. Littman, N. J. Kasdin, R. Vanderbei, R. Belikov, and A. Give'on, "Chromaticity effects in adaptive optics:wavelength dependence of amplitude compensation," in Techniques and Instrumentation for Detection of Exolanets II, D. R. Coulter, ed., Proc. SPIE 5903, 190-198 (2005).

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, 1063-1073 (2006).
[CrossRef]

L. Pueyo, M. G. Littman, M. Carr, N. J. Kasdin, D. N. Spergel, and R. J. Vanderbei, "Amplitude and phase control of pupil coronagraph for exoplanet detection using spatial light modulators," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170, 241-249 (2003).
[CrossRef]

White, M. L.

V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).

Wirth, A.

J. A. Perreault and A. Wirth, "Survey of adaptive optic techniques," in Focal Plane Arrays for Space Telescopes II, T. J. Grycewicz and C. J. Marshall, eds., Proc. SPIE 5903, 43-50 (2005).

Yu, J.

F. Malbet, J. Yu, and M. Shao, "High-dynamic range imaging using a deformable mirror for space coronagraphy," Publ. Astron. Soc. Pac. 107, 386 (1995).

Astrophys. J. (1)

R. A. Brown, "Obscurational completeness," Astrophys. J. 607, 1003-1013 (2004).
[CrossRef]

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

Philos. Mag. (1)

W. H. F. Talbot, "Facts relating to optical science, No. IV," Philos. Mag. 9, 401-407 (1836).

Proc. SPIE (7)

L. Pueyo, M. G. Littman, N. J. Kasdin, R. Vanderbei, R. Belikov, and A. Give'on, "Chromaticity effects in adaptive optics:wavelength dependence of amplitude compensation," in Techniques and Instrumentation for Detection of Exolanets II, D. R. Coulter, ed., Proc. SPIE 5903, 190-198 (2005).

J. A. Perreault and A. Wirth, "Survey of adaptive optic techniques," in Focal Plane Arrays for Space Telescopes II, T. J. Grycewicz and C. J. Marshall, eds., Proc. SPIE 5903, 43-50 (2005).

P. Z. Mouroulis and S. B. Shaklan, "Optical design of the Terrestrial Planet Finder Coronagraph starlight suppression system," in Current Developments in Lens Design and Optical Engineering VI, P. Z. Mouroulis, W. J. Smith, and R. B. Johnson, eds., Proc. SPIE 5874, 187-197 (2005).

R. P. Linfield, "Wavefront amplitude errors for a TPF Coronagraph: their effects and possible correction," in Optical, Infrared, and Millimeter Space Telescopes, J. C. Mather, ed., Proc. SPIE 5487, 412-422 (2004).

M. A. Ealey and J. T. Trauger, "High density deformable mirrors to enable coronagraphic planet detection," in UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts, H. A. MacEwen, ed., Proc. SPIE 5166, 172-179 (2004).
[CrossRef]

M. G. Littman, M. Carr, J. Leighton, E. Burke, D. N. Spergel, and N. J. Kasdin, "Phase and amplitude control ability using spatial light modulation and zero path length difference Michelson interferometer," in Future EUV/UV and Visible Space Missions and Instrumentation, J. C. Blades and O. H. W. Siegmund, eds., Proc. SPIE 4854, 405-412 (2003).
[CrossRef]

L. Pueyo, M. G. Littman, M. Carr, N. J. Kasdin, D. N. Spergel, and R. J. Vanderbei, "Amplitude and phase control of pupil coronagraph for exoplanet detection using spatial light modulators," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170, 241-249 (2003).
[CrossRef]

Techniques and Instrumentation for Detection of Exoplanets (1)

V. G. Ford, A. B. Hull, S. B. Shaklan, M. B. Levine, M. L. White, A. E. Lowman, and E. J. Cohen, "Terrestrial Planet Finder Coronagraph," in Techniques and Instrumentation for Detection of Exoplanets , D. R. Coulter, ed., Proc. SPIE 5170, 1-12 (2003).

Other (4)

F. Malbet, J. Yu, and M. Shao, "High-dynamic range imaging using a deformable mirror for space coronagraphy," Publ. Astron. Soc. Pac. 107, 386 (1995).

D. Palacios, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif. 91109 (personal communication, 2005).

J. S. Taylor, "Progress in meeting stringent optical system requirements in EUV lithography," presented at SPIE's 26th Symposium on Microlithography and Emerging Lithographies V, Santa Clara, Calif., 25 February-2 March, 2001.

L. Pueyo, Princeton University, Princeton, N.J. 08544 (personal communication, 2005).

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Figures (8)

Fig. 1
Fig. 1

(Color online) Collimated light reflects from an optic having a periodic surface deformation of rms height s. The light propagates a distance z to the pupil (or pupil conjugate plane) where the wavefront correction system is located. The system shown is a dual deformable mirror (DM) corrector in a Michelson configuration. The DMs control both amplitude and phase.

Fig. 2
Fig. 2

Wavefront control system now consists of one DM located at a pupil image (DMp) and a second one, DMnp, a distance z DM downstream. DMp controls phase, while DMnp controls amplitude. Both the phase-induced amplitude from the optical surface errors and the amplitude control using DMnp are wavelength independent.

Fig. 3
Fig. 3

Lines show the allowed surface rms value versus spatial frequency for a periodic deformation resulting in a contrast floor of 10−12 per optic. The left panel assumes wavefront control in the Michelson configuration, and the right panel assumes control using the sequential configuration. We use R = 6.3, D = 10 cm, and optics positions z taken from Table 1. For comparison, the dashed line in each panel is the rms surface height achieved in an optic manufactured for EUV lithography.

Fig. 4
Fig. 4

Solid diagonal lines show the allowed rms reflectivity variation versus spatial frequency in the sequential configuration for a periodic deformation resulting in a contrast floor of 10−12 per optic. The requirement for the Michelson configuration is the horizontal line at 3.1e−5. The dashed line shows the allowed reflectivity variation assuming that the DM is limited to 30 nm piston and is at a distance of 3 m from the pupil.

Fig. 5
Fig. 5

Average contrast for fold mirror M4. We assume R = 6.3. The solid curve is for the “Super Fold” WFE PSD (see Table 3). The dashed line is for the measured WFE PSD of an optic manufactured for EUV lithography.

Fig. 6
Fig. 6

Required 2-D PSD of optical surface height in the Michelson and sequential configurations. We also show the surface PSD achieved for EUV optics. The EUV curve is an approximate fit to data provided by Lawrence Livermore National Laboratory of interferometric measurements of two aspherical optics produced for EUV lithography by Tinsley. The rms WFE of the EUV optic for the spatial frequencies shown is 0.30 nm.

Fig. 7
Fig. 7

3-DM fully redundant system. This diagram depicts an unfolded layout that provides for two nonpupil DMs placed z DM = 3 m from the pupil DMp. A unity magnification telescope images the coarse DM pupil plane CDM to DMp (dashed line). The design provides 1 m between CDM-M1 and M2-DMnp,1 to fold the beams at a shallow angle.

Fig. 8
Fig. 8

Michelson configuration passes half the light from incident field EA to each arm. One arm introduces phase θ, the other −θ. The incident field has values between 1 – 2EA and 1. The phase is adjusted so that the output amplitude is equal to the minimum of the periodic amplitude, 1 – 2EA.

Tables (3)

Tables Icon

Table 1 Terrestrial Planet Finder Coronagraph Optical Layout

Tables Icon

Table 2 Summary of Perturbations, Wavelength Dependence, and Compensation

Tables Icon

Table 3 Power Spectral Density Specifications for Terrestrial Planet Finder Coronagraph Optics (Wavefront Specifications)

Equations (33)

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E = ( 1 2 A ) [ 1 + 2 A 1 2 A cos ( 2 π y N / D + ψ ) ] ×   e i 2 α cos ( 2 π y N / D + ϕ ) 1 2 A + 2 A cos ( 2 π y N / D + ψ ) + i 2 α cos ( 2 π y N / D + ϕ ) .
d = z θ 2 2 = z λ 2 N 2 2 D 2 .
E 1 2 r 2 + [ 2 r 2 cos ( 2 π y N / D + ψ ) + i 2 α cos ( 2 π y N / D + ϕ ) ] e i 2 π d / λ .
z T = 2 D 2 λ N 2 = 2 P 2 λ ,
E 1 2 r 2 + [ 2 r 2 cos ( 2 π y N / D + ψ ) + i 2 α cos ( 2 π y N / D + ϕ ) ] ×   [ 1 1 2 ( π z λ N 2 D 2 ) 2 + i π z λ N 2 D 2 ] .
E = [ r 2 ( 1 1 2 ( π z λ N 2 D 2 ) 2 ) α π z λ N 2 D 2 , α ( 1 1 2 ( π z λ N 2 D 2 ) 2 ) + π r z λ N 2 2 D 2 ] .
E = [ r 2 r 4 ( π z λ N 2 D 2 ) 2 4 π 2 s z N 2 D 2 , 4 π s λ 2 π 3 s z 2 λ N 4 D 4 π r z λ N 2 2 D 2 ] = [ E r E r , p 2 E s , p ,   E s E s , p 2 E r , p ] = [ E A ,   E ϕ ] .
4 π s DM λ 0 = k = 1 m ( 4 π s k λ 0 2 π 3 s k z k     2 λ 0 N 4 D 4 π r k z k λ 0 N 2 2 D 2 ) ,
E p = 4 π s p ν 0 c = k = 1 m 2 π 3 s k z k     2 c N 4 D 4 ν 0 + π r k z k c N 2 2 D 2 ν 0 .
E = E p ν ν 0 k = 1 m 2 π 3 s k z k     2 c N 4 D 4 ν + π r k z k c N 2 2 D 2 ν = E p ( ν ν 0 ν 0 ν ) .
C ( ν ) = 1 2 | E p ( ν ν 0 ν 0 ν ) | 2 = C 0 ( ν ν 0 ν 0 ν ) 2 ,
C ¯ = 1 Δ ν C 0 ν Δ ν / 2 ν + Δ ν / 2 ( ν ν 0 ν 0 ν ) 2 d ν = C 0 [ ν 0     2 ν 0     2 Δ ν 2 4 1 + 1 12 ( Δ ν ν 0 ) 2 ] = C 0 ( 1 4 R 2 1 + 1 12 R 2 ) C 0 3 R 2 = 1 6 R 2 ( k = 1 m 2 π 3 s k z k    2 λ 0 N 4 D 4 + π r k z k λ 0 N 2 2 D 2 ) 2 ,
E A = k = 1 m r k 2 r k 4 ( π z k c N 2 D 2 ν 0 ) 2 4 π 2 s k z k N 2 D 2 .
1 2 ( π z λ N 2 D 2 ) 2 1.
θ DM ( ν ) = θ 0 ν ν 0 .
E ( ν ) = E A [ ( ν ν 0 ) 2 1 ] .
C ( ν ) = | E A [ ( ν ν 0 ) 2 1 ] | 2 = C 0 [ ( ν ν 0 ) 2 1 ] 2 ,
C ¯ = 1 Δ ν C 0    ν Δ ν / 2 ν + Δ ν / 2 [ ( ν ν 0 ) 2 1 ] 2 d ν = C 0 [ 1 80 ( Δ ν ν ) 4 + 1 3 ( Δ ν ν ) 2 ] C 0 3 R 2 .
C ¯ = 1 3 R 2 ( k = 1 m r k 2 + 4 π 2 s k z k N 2 D 2 ) 2 .
E A , Tot = E r + E r , p 2 + E s , p = k = 1 m r k 2 r k 4 ( π z k c N 2 D 2 ν 0 ) 2 4 π 2 s k z k N 2 D 2 .
s DM = D 2 4 π 2 z DM N 2 ( E r + E s , p ) .
s k = 6 C ¯ 4 π 2 D 2 R z k N 2 .
r k = 2 R 6 C ¯ .
s k = 6 C ¯ 2 π 3 D 4 R λ 0 z k 2 N 4 .
r k = 2 6 C ¯ π D 2 R λ 0 z k N 2 .
r = 8 π 2 s DM z DM N 2 D 2 .
PSD = A 0 1 + ( k / k 0 ) n ,
E ( ϕ ) = 1 E A + E A cos ( ϕ ) = 1 2 E A sin 2 ( ϕ / 2 ) .
E ( ϕ ) cos ( θ 0 ) = 1 2 E A .
θ 0 2 E A 1 2 E A sin 2 ( ϕ / 2 ) cos ( ϕ / 2 ) .
θ 0 = 4 π s ν 0 c .
E resid = 1 2 E A E ( ϕ ) cos ( θ ) 1 2 E A E ( ϕ ) ( 1 θ 2 / 2 ) = 1 2 E A E ( ϕ ) [ 1 θ 0     2 ( ν ν 0 ) 2 ] .
E resid = 2 E A cos 2 ( ϕ / 2 ) [ ( ν ν 0 ) 2 1 ] .

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