Abstract

We demonstrate the existence of higher-order curvature adaptive optics (AO) systems and compare their performance with the current 85-element system being built at the Institute for Astronomy at the University of Hawaii. Simulation results show that systems with in excess of 500 actuators are possible with actuator patterns that are simple extensions of the 85-element design. The attenuation of residual phase error within the Nyquist frequency of the deformable mirror (DM) satisfies the (56) power law. A high-order system is also analyzed in which the pattern of wavefront sensor is synthesized from square pixels and the curvature actuators of the DM are also rectangular. The Strehl performance is 2% worse than its annular analog.

© 2006 Optical Society of America

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  1. F. Roddier, M. J. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared applications," Publ. Astron. Soc. Pac. 103, 131-149 (1991).
    [Crossref]
  2. F. Roddier, "Curvature sensing and compensation: a new concept in adaptive optics," Appl. Opt. 27, 1223-1225 (1988).
    [Crossref] [PubMed]
  3. S. A. Kokorowski, "Analysis of adaptive optical elements made from piezoelectric bimorphs," J. Opt. Soc. Am. 69, 181-187 (1979).
    [Crossref]
  4. C. Schwartz, E. Ribak, and S. G. Lipson, "Bimorph adaptive mirrors and curvature sensing," J. Opt. Soc. Am. A 11, 895-902 (1994).
    [Crossref]
  5. J. C. Dainty, A. V. Koryabin, and A. V. Kudryashov, "Low-order adaptive deformable mirror," Appl. Opt. 37, 4663-4668 (1998).
    [Crossref]
  6. F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, 1999), p. 72.
  7. F. Roddier, C. Roddier, J. E. Graves, and M. J. Northcott, "Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle," Astrophys. J. 443, 249-260 (1995).
    [Crossref]
  8. J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, and L. M. Close, "First light for Hokupa'a: 36-element curvature AO system at UH," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 34-43 (1998).
  9. J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).
  10. D. J. O'Connor, J. E. Graves, M. J. Northcott, D. W. Toomey, R. D. Joseph, and J. C. Shelton, "Curvature-based adaptive optics for the NASA IRTF," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 180-185 (2000).
  11. H. Takami, N. Takato, M. Otsubo, T. Kanzawa, Y. Kamata, K. Nakashima, and M. Iye, "Adaptive optics system for Cassegrain focus of Subaru 8.2-m telescope," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 500-507 (1998).
  12. C. B. Hogge and R. R. Butts, "Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence," IEEE Trans. Antennas Propag. AP-24, 144-154 (1976).
    [Crossref]
  13. J. M. Conan, G. Rousset, and P. Y. Madec, "Wavefront temporal spectra in high resolution imaging through turbulence," J. Opt. Soc. Am. A 12, 1559-1570 (1995).
    [Crossref]
  14. R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976).
    [Crossref]
  15. F. Roddier and F. Rigaut, "The UH-CFHT systems," in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge U. Press, 1999), pp. 205-234.
    [Crossref]
  16. C. Ftaclas and A. Kostinski, "Curvature sensors, adaptive optics, and Neumann boundary conditions," Appl. Opt. 40, 435-438 (2001).
    [Crossref]
  17. W. C. Young, Roark's Formulas for Stress and Strain, 7th ed. (McGraw-Hill, 2001), p. 767.
  18. O. Lai, "High order curvature adaptive optics revisited," in Beyond Conventional Adaptive Optics, R.Ragazzoni, S.Esposito, and N.Hubin, eds., Proceedings of the European Southern Observatory Conference, Venice, Italy (European Southern Observatory, 2001), pp. 343-348.
  19. O. Lai and T. C. Bartle, "Simulations of high order curvature adaptive optics," in High-Contrast Imaging for Exo-Planet Detection, A.B.Schultz and R.G.Lyon, eds., Proc. SPIE 4860, 334-342 (2002).
  20. M. J. Northcott, J. E. Graves, F. J. Roddier, and F. J. Rigaut, "Design and performance of an 85-actuator curvature system," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 126-130 (2000).

2001 (1)

1998 (1)

1995 (2)

J. M. Conan, G. Rousset, and P. Y. Madec, "Wavefront temporal spectra in high resolution imaging through turbulence," J. Opt. Soc. Am. A 12, 1559-1570 (1995).
[Crossref]

F. Roddier, C. Roddier, J. E. Graves, and M. J. Northcott, "Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle," Astrophys. J. 443, 249-260 (1995).
[Crossref]

1994 (1)

1991 (1)

F. Roddier, M. J. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared applications," Publ. Astron. Soc. Pac. 103, 131-149 (1991).
[Crossref]

1988 (1)

1979 (1)

1976 (2)

R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976).
[Crossref]

C. B. Hogge and R. R. Butts, "Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence," IEEE Trans. Antennas Propag. AP-24, 144-154 (1976).
[Crossref]

Bartle, T. C.

O. Lai and T. C. Bartle, "Simulations of high order curvature adaptive optics," in High-Contrast Imaging for Exo-Planet Detection, A.B.Schultz and R.G.Lyon, eds., Proc. SPIE 4860, 334-342 (2002).

Butts, R. R.

C. B. Hogge and R. R. Butts, "Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence," IEEE Trans. Antennas Propag. AP-24, 144-154 (1976).
[Crossref]

Chun, M. R.

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).

Close, L. M.

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, and L. M. Close, "First light for Hokupa'a: 36-element curvature AO system at UH," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 34-43 (1998).

Conan, J. M.

Dainty, J. C.

Ftaclas, C.

Graves, J. E.

F. Roddier, C. Roddier, J. E. Graves, and M. J. Northcott, "Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle," Astrophys. J. 443, 249-260 (1995).
[Crossref]

F. Roddier, M. J. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared applications," Publ. Astron. Soc. Pac. 103, 131-149 (1991).
[Crossref]

M. J. Northcott, J. E. Graves, F. J. Roddier, and F. J. Rigaut, "Design and performance of an 85-actuator curvature system," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 126-130 (2000).

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, and L. M. Close, "First light for Hokupa'a: 36-element curvature AO system at UH," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 34-43 (1998).

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).

D. J. O'Connor, J. E. Graves, M. J. Northcott, D. W. Toomey, R. D. Joseph, and J. C. Shelton, "Curvature-based adaptive optics for the NASA IRTF," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 180-185 (2000).

Hogge, C. B.

C. B. Hogge and R. R. Butts, "Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence," IEEE Trans. Antennas Propag. AP-24, 144-154 (1976).
[Crossref]

Iye, M.

H. Takami, N. Takato, M. Otsubo, T. Kanzawa, Y. Kamata, K. Nakashima, and M. Iye, "Adaptive optics system for Cassegrain focus of Subaru 8.2-m telescope," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 500-507 (1998).

Joseph, R. D.

D. J. O'Connor, J. E. Graves, M. J. Northcott, D. W. Toomey, R. D. Joseph, and J. C. Shelton, "Curvature-based adaptive optics for the NASA IRTF," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 180-185 (2000).

Kamata, Y.

H. Takami, N. Takato, M. Otsubo, T. Kanzawa, Y. Kamata, K. Nakashima, and M. Iye, "Adaptive optics system for Cassegrain focus of Subaru 8.2-m telescope," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 500-507 (1998).

Kanzawa, T.

H. Takami, N. Takato, M. Otsubo, T. Kanzawa, Y. Kamata, K. Nakashima, and M. Iye, "Adaptive optics system for Cassegrain focus of Subaru 8.2-m telescope," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 500-507 (1998).

Kokorowski, S. A.

Koryabin, A. V.

Kostinski, A.

Kudryashov, A. V.

Lai, O.

O. Lai, "High order curvature adaptive optics revisited," in Beyond Conventional Adaptive Optics, R.Ragazzoni, S.Esposito, and N.Hubin, eds., Proceedings of the European Southern Observatory Conference, Venice, Italy (European Southern Observatory, 2001), pp. 343-348.

O. Lai and T. C. Bartle, "Simulations of high order curvature adaptive optics," in High-Contrast Imaging for Exo-Planet Detection, A.B.Schultz and R.G.Lyon, eds., Proc. SPIE 4860, 334-342 (2002).

Lipson, S. G.

Madec, P. Y.

Nakashima, K.

H. Takami, N. Takato, M. Otsubo, T. Kanzawa, Y. Kamata, K. Nakashima, and M. Iye, "Adaptive optics system for Cassegrain focus of Subaru 8.2-m telescope," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 500-507 (1998).

Noll, R. J.

Northcott, M. J.

F. Roddier, C. Roddier, J. E. Graves, and M. J. Northcott, "Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle," Astrophys. J. 443, 249-260 (1995).
[Crossref]

F. Roddier, M. J. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared applications," Publ. Astron. Soc. Pac. 103, 131-149 (1991).
[Crossref]

M. J. Northcott, J. E. Graves, F. J. Roddier, and F. J. Rigaut, "Design and performance of an 85-actuator curvature system," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 126-130 (2000).

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, and L. M. Close, "First light for Hokupa'a: 36-element curvature AO system at UH," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 34-43 (1998).

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).

D. J. O'Connor, J. E. Graves, M. J. Northcott, D. W. Toomey, R. D. Joseph, and J. C. Shelton, "Curvature-based adaptive optics for the NASA IRTF," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 180-185 (2000).

O'Connor, D. J.

D. J. O'Connor, J. E. Graves, M. J. Northcott, D. W. Toomey, R. D. Joseph, and J. C. Shelton, "Curvature-based adaptive optics for the NASA IRTF," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 180-185 (2000).

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).

Otsubo, M.

H. Takami, N. Takato, M. Otsubo, T. Kanzawa, Y. Kamata, K. Nakashima, and M. Iye, "Adaptive optics system for Cassegrain focus of Subaru 8.2-m telescope," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 500-507 (1998).

Potter, D.

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).

Ribak, E.

Rigaut, F.

F. Roddier and F. Rigaut, "The UH-CFHT systems," in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge U. Press, 1999), pp. 205-234.
[Crossref]

Rigaut, F. J.

M. J. Northcott, J. E. Graves, F. J. Roddier, and F. J. Rigaut, "Design and performance of an 85-actuator curvature system," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 126-130 (2000).

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).

Roddier, C.

F. Roddier, C. Roddier, J. E. Graves, and M. J. Northcott, "Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle," Astrophys. J. 443, 249-260 (1995).
[Crossref]

Roddier, C. A.

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, and L. M. Close, "First light for Hokupa'a: 36-element curvature AO system at UH," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 34-43 (1998).

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).

Roddier, F.

F. Roddier, C. Roddier, J. E. Graves, and M. J. Northcott, "Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle," Astrophys. J. 443, 249-260 (1995).
[Crossref]

F. Roddier, M. J. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared applications," Publ. Astron. Soc. Pac. 103, 131-149 (1991).
[Crossref]

F. Roddier, "Curvature sensing and compensation: a new concept in adaptive optics," Appl. Opt. 27, 1223-1225 (1988).
[Crossref] [PubMed]

F. Roddier and F. Rigaut, "The UH-CFHT systems," in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge U. Press, 1999), pp. 205-234.
[Crossref]

F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, 1999), p. 72.

Roddier, F. J.

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, and L. M. Close, "First light for Hokupa'a: 36-element curvature AO system at UH," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 34-43 (1998).

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).

M. J. Northcott, J. E. Graves, F. J. Roddier, and F. J. Rigaut, "Design and performance of an 85-actuator curvature system," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 126-130 (2000).

Rousset, G.

Schwartz, C.

Shelton, J. C.

D. J. O'Connor, J. E. Graves, M. J. Northcott, D. W. Toomey, R. D. Joseph, and J. C. Shelton, "Curvature-based adaptive optics for the NASA IRTF," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 180-185 (2000).

Takami, H.

H. Takami, N. Takato, M. Otsubo, T. Kanzawa, Y. Kamata, K. Nakashima, and M. Iye, "Adaptive optics system for Cassegrain focus of Subaru 8.2-m telescope," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 500-507 (1998).

Takato, N.

H. Takami, N. Takato, M. Otsubo, T. Kanzawa, Y. Kamata, K. Nakashima, and M. Iye, "Adaptive optics system for Cassegrain focus of Subaru 8.2-m telescope," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 500-507 (1998).

Toomey, D. W.

D. J. O'Connor, J. E. Graves, M. J. Northcott, D. W. Toomey, R. D. Joseph, and J. C. Shelton, "Curvature-based adaptive optics for the NASA IRTF," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 180-185 (2000).

Young, W. C.

W. C. Young, Roark's Formulas for Stress and Strain, 7th ed. (McGraw-Hill, 2001), p. 767.

Appl. Opt. (3)

Astrophys. J. (1)

F. Roddier, C. Roddier, J. E. Graves, and M. J. Northcott, "Adaptive optics imaging of proto-planetary nebulae: Frosty Leo and the Red Rectangle," Astrophys. J. 443, 249-260 (1995).
[Crossref]

IEEE Trans. Antennas Propag. (1)

C. B. Hogge and R. R. Butts, "Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence," IEEE Trans. Antennas Propag. AP-24, 144-154 (1976).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Publ. Astron. Soc. Pac. (1)

F. Roddier, M. J. Northcott, and J. E. Graves, "A simple low-order adaptive optics system for near-infrared applications," Publ. Astron. Soc. Pac. 103, 131-149 (1991).
[Crossref]

Other (10)

F. Roddier and F. Rigaut, "The UH-CFHT systems," in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge U. Press, 1999), pp. 205-234.
[Crossref]

W. C. Young, Roark's Formulas for Stress and Strain, 7th ed. (McGraw-Hill, 2001), p. 767.

O. Lai, "High order curvature adaptive optics revisited," in Beyond Conventional Adaptive Optics, R.Ragazzoni, S.Esposito, and N.Hubin, eds., Proceedings of the European Southern Observatory Conference, Venice, Italy (European Southern Observatory, 2001), pp. 343-348.

O. Lai and T. C. Bartle, "Simulations of high order curvature adaptive optics," in High-Contrast Imaging for Exo-Planet Detection, A.B.Schultz and R.G.Lyon, eds., Proc. SPIE 4860, 334-342 (2002).

M. J. Northcott, J. E. Graves, F. J. Roddier, and F. J. Rigaut, "Design and performance of an 85-actuator curvature system," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 126-130 (2000).

F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, 1999), p. 72.

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, and L. M. Close, "First light for Hokupa'a: 36-element curvature AO system at UH," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 34-43 (1998).

J. E. Graves, M. J. Northcott, F. J. Roddier, C. A. Roddier, D. Potter, D. J. O'Connor, F. J. Rigaut, and M. R. Chun, "First light for Hokupa'a 36 on Gemini North," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 26-31 (2000).

D. J. O'Connor, J. E. Graves, M. J. Northcott, D. W. Toomey, R. D. Joseph, and J. C. Shelton, "Curvature-based adaptive optics for the NASA IRTF," in Adaptive Optical Systems Technology, P.L.Wizinowich, ed., Proc. SPIE 4007, 180-185 (2000).

H. Takami, N. Takato, M. Otsubo, T. Kanzawa, Y. Kamata, K. Nakashima, and M. Iye, "Adaptive optics system for Cassegrain focus of Subaru 8.2-m telescope," in Adaptive Optical Systems Technologies, D.Bonaccini and R.K.Tyson, eds., Proc. SPIE 3353, 500-507 (1998).

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Figures (7)

Fig. 1
Fig. 1

Four bimorph mirrors with different number of actuators. Subfigure (a) has 85 actuators, subfigure (b) has 157 actuators, subfigure (c) has 259 actuators, and subfigure (d) has 535 actuators. The dashed circles are the pupils of each DM that is imaged to the 8 m primary mirror.

Fig. 2
Fig. 2

Scaled singular values from the four curvature AO systems.

Fig. 3
Fig. 3

Input and output phase power spectral densities for the four electrode configurations analyzed.

Fig. 4
Fig. 4

For each power spectrum in Fig. 3 we have calculated the phase transfer functions plotted above as the ratio of output to input power spectra. In each case the Nyquist frequency is indicated by the corresponding vertical line with label f H 85 , f H 157 , f H 259 , or f H 535 .

Fig. 5
Fig. 5

Phase transfer functions for a range of cases are plotted against spatial frequency normalized to the Nyquist frequency for each case.

Fig. 6
Fig. 6

Residual phase standard deviation as a function of f N . The regression line fit is consistent with ideal scaling with a single transfer function.

Fig. 7
Fig. 7

Rectangular patterns of DM (a) and lenslet (b) for a 540-actuator curvature system. The curvature electrodes are designed as a rectangular pattern by which commercial lenslets can be implemented directly. The slope signals on the pupil edge are synthesized by co-adding the relevant pixels with appropriate weights according to the fraction of the pixel in the sensed region. The dashed circles in subfigure (a) indicates the pupil of the DM. Each squared area surrounded by the faint dotted lines in subfigure (b) indicates a lenslet subaperture contributing to the WFS slope signals, and each squared area surrounded by the solid lines indicates a lenslet subaperture contributing to the WFS curvature signals.

Tables (3)

Tables Icon

Table 1 Required Radii of Curvature for Different DMs

Tables Icon

Table 2 Parameters for the AO Simulation Systems

Tables Icon

Table 3 Attenuation of H-535 Performance with the Brightness of the Guide Star

Equations (14)

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

a 4 , a 4 = 0.023 ( S r 0 ) 5 3 ,
d = D 4 π N ,
Δ f f = 0.023 ( d r 0 ) 5 3 ,
f p = 2 3 Δ f f λ 2 π ,
R curv = d 2 8 f p ,
R curv 1.3 D 2 λ N 7 12 ( D r 0 ) 5 6 .
R DM = ( D DM D ) 2 R curv .
2 u = k V t 2 ,
R = t 2 2 d 31 V ,
R DM = R min ( D DM D ) 2 .
α C = ( D 2 2 d 31 E max R min ) ( t D DM 2 ) .
f 0 = κ ( τ Δ 2 ) ,
α C = ( f 0 D 2 2 κ d 31 E max R min ) ( Δ D DM ) 2 .
σ 2 ( r 0 f N ) 5 3 ( f f N ) 11 3 F ( f f N ) 2 π ( f f N ) d ( f f N ) .

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