Abstract

The signal measured with a curvature sensor is analyzed. At the outset, we derive the required minimum number of sensing elements at the pupil edges, depending on the total number of sensing elements. The distribution of the sensor signal is further characterized in terms of its mean, variance, kurtosis, and skewness. It is established that while the approximation in terms of a Gaussian distribution is correct down to fairly low photon numbers, much higher numbers are required to obtain meaningful sensor measurements for small wavefront distortions. Finally, we indicate a closed expression for the error propagation factor and for the photon-noise-induced Strehl loss.

© 2010 Optical Society of America

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References

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    [CrossRef] [PubMed]
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  3. 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,” Proc. SPIE 3353, 34–43 (1998).
    [CrossRef]
  4. M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
    [CrossRef]
  5. R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
    [CrossRef]
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    [CrossRef]
  7. N. Roddier, “Curvature sensing for adaptive optics: a computer simulation,” M.Sci. thesis (University of Arizona, 1989).
  8. O. Lai and T. V. Craven-Bartle, “Simulations of high order curvature adaptive optics,” Proc. SPIE 4860, 334–342 (2003).
    [CrossRef]
  9. Q. Yang, C. Ftaclas, and M. Chun, “Wavefront correction with high-order curvature adaptive optics systems,” J. Opt. Soc. Am. A 23, 1375–1381 (2006).
    [CrossRef]
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2008 (2)

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

2006 (1)

2003 (2)

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

O. Lai and T. V. Craven-Bartle, “Simulations of high order curvature adaptive optics,” Proc. SPIE 4860, 334–342 (2003).
[CrossRef]

1998 (1)

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,” Proc. SPIE 3353, 34–43 (1998).
[CrossRef]

1991 (1)

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astronomical Society of the Pacific Publications (ISSN (Astronomical Society of the Pacific, 1991), Vol. 103, pp. 131–149.

1989 (1)

N. Roddier, “Curvature sensing for adaptive optics: a computer simulation,” M.Sci. thesis (University of Arizona, 1989).

1988 (1)

1987 (1)

F. Roddier, “Curvature sensing: a diffraction theory,” NOAO Advanced Development Program, No. 87-3 (1987).

1977 (2)

Arsenault, R.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Artigau, E.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

Biller, B.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

Bonnet, H.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Brynnel, J.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Chun, M.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

Q. Yang, C. Ftaclas, and M. Chun, “Wavefront correction with high-order curvature adaptive optics systems,” J. Opt. Soc. Am. A 23, 1375–1381 (2006).
[CrossRef]

Close, L.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

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,” Proc. SPIE 3353, 34–43 (1998).
[CrossRef]

Colley, S.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Craven-Bartle, T. V.

O. Lai and T. V. Craven-Bartle, “Simulations of high order curvature adaptive optics,” Proc. SPIE 4860, 334–342 (2003).
[CrossRef]

Delabre, B.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Delplancke, F.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Dinkins, M.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Donaldson, R.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Dupuy, C.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Eldred, M.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Farinato, J.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Fedrigo, E.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Fried, D.

Ftaclas, C.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

Q. Yang, C. Ftaclas, and M. Chun, “Wavefront correction with high-order curvature adaptive optics systems,” J. Opt. Soc. Am. A 23, 1375–1381 (2006).
[CrossRef]

Gigan, P.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Golota, T.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Graves, J. E.

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,” Proc. SPIE 3353, 34–43 (1998).
[CrossRef]

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astronomical Society of the Pacific Publications (ISSN (Astronomical Society of the Pacific, 1991), Vol. 103, pp. 131–149.

Guyon, O.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Hartung, M.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

Hattori, M.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Hayano, Y.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Hayward, T.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

Hubin, N.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Hudgin, R.

Ito, M.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Ivanescu, L.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Iye, M.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Jaime, A.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Kasper, M.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Lai, O.

O. Lai and T. V. Craven-Bartle, “Simulations of high order curvature adaptive optics,” Proc. SPIE 4860, 334–342 (2003).
[CrossRef]

Liu, M.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

Lizon, J. L.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Minowa, Y.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Murakami, N.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Northcott, M.

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astronomical Society of the Pacific Publications (ISSN (Astronomical Society of the Pacific, 1991), Vol. 103, pp. 131–149.

Northcott, M. 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,” Proc. SPIE 3353, 34–43 (1998).
[CrossRef]

Oya, S.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Paufique, J.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Quattri, M.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Reiss, R.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Rigaut, F.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[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,” Proc. SPIE 3353, 34–43 (1998).
[CrossRef]

Roddier, F.

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astronomical Society of the Pacific Publications (ISSN (Astronomical Society of the Pacific, 1991), Vol. 103, pp. 131–149.

F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225 (1988).
[CrossRef] [PubMed]

F. Roddier, “Curvature sensing: a diffraction theory,” NOAO Advanced Development Program, No. 87-3 (1987).

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,” Proc. SPIE 3353, 34–43 (1998).
[CrossRef]

Roddier, N.

N. Roddier, “Curvature sensing for adaptive optics: a computer simulation,” M.Sci. thesis (University of Arizona, 1989).

Rossi, S.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Saito, Y.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Silber, A.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Stroebele, S.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Takami, H.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Toomey, D.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

Tordo, S.

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

Wahhaj, Z.

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

Watanabe, M.

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

Yang, Q.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

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

Proc. SPIE (4)

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,” Proc. SPIE 3353, 34–43 (1998).
[CrossRef]

M. Chun, D. Toomey, Z. Wahhaj, B. Biller, E. Artigau, T. Hayward, M. Liu, L. Close, M. Hartung, F. Rigaut, and C. Ftaclas, “Performance of the near-infrared coronagraphic imager on Gemini-South,” Proc. SPIE 7015, 70151V–70151V-9 (2008).
[CrossRef]

R. Arsenault, A. Jaime, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J. L. Lizon, P. Gigan, F. Delplancke, A. Silber, M. Quattri, and R. Reiss, “MACAO-VLTI: an adaptive optics system for the ESO VLT interferometer,” Proc. SPIE 4839, 174–185 (2003).
[CrossRef]

M. Watanabe, S. Oya, Y. Hayano, H. Takami, M. Hattori, Y. Minowa, Y. Saito, M. Ito, N. Murakami, M. Iye, O. Guyon, S. Colley, M. Eldred, T. Golota, and M. Dinkins, “Implementation of 188-element curvature-based wavefront sensor and calibration source unit for the subaru LGSAO system,” Proc. SPIE 7015, 701564–701564-8 (2008).
[CrossRef]

SPIE (1)

O. Lai and T. V. Craven-Bartle, “Simulations of high order curvature adaptive optics,” Proc. SPIE 4860, 334–342 (2003).
[CrossRef]

Other (4)

www.maumae.net/yao/.

N. Roddier, “Curvature sensing for adaptive optics: a computer simulation,” M.Sci. thesis (University of Arizona, 1989).

F. Roddier, “Curvature sensing: a diffraction theory,” NOAO Advanced Development Program, No. 87-3 (1987).

F. Roddier, M. Northcott, and J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Astronomical Society of the Pacific Publications (ISSN (Astronomical Society of the Pacific, 1991), Vol. 103, pp. 131–149.

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Figures (7)

Fig. 1
Fig. 1

Minimum number of sensing elements at the aperture edge required to sense the N lowest Zernike modes.

Fig. 2
Fig. 2

Standard deviation and kurtosis of v dependent on Z for V = 0 : The approximation in terms of the Gaussian distribution is justified down to fairly low photon values (right panel), but much higher photon numbers are required to obtain meaningful measurements at small values of V, i.e., for small wavefront distortions (left panel).

Fig. 3
Fig. 3

Standard deviation (solid curve), skewness (dashed curve), and kurtosis (dotted curve) of v dependent on V for Z = 100 . The decrease in the standard error is not substantial in the [0,0.2] range representative of closed-loop AO observations. At the large photon numbers that are thus required, the Gaussian approximation remains valid despite the increase of the skewness and kurtosis.

Fig. 4
Fig. 4

Need for large photon numbers: percent standard error dependent on the measured value v for photon numbers Z = X + Y = 100 (solid curve), 10 3 (dashed curve), 10 4 (dotted curve), and 10 5 (dashed–dotted curve).

Fig. 5
Fig. 5

Configurations of two of the simulated sensors: the wavefront is sampled over 25 and 225 elements. Dashed curve, pupil edge.

Fig. 6
Fig. 6

Error propagation term, G, dependent on the number of subapertures. Solid curve, in terms of the iterative method for the parameters values listed in the second column of Table 2 (square pupil). Dotted curve, in terms of the AO simulation package Yao for the parameter values listed in the third column of Table 2 (circular pupil). G 0 is defined by Eq. (46).

Fig. 7
Fig. 7

Decrease of the instantaneous Strehl ratio due to photon noise dependent on the number of sensing elements, N, and on the average number of photons, Z, received by the sensor during the acquisition of the two extra-focal images. Other parameter values are l = 0.05 N [m], D = 8 m , f = 120 m , and λ = 0.7 μ m .

Tables (2)

Tables Icon

Table 1 Laplacian of Zernike Polynomials: 2 Z ( r , θ ) = 1 r r ( r Z r ) + 1 r 2 2 Z θ 2

Tables Icon

Table 2 Parameter Values for the Computation of the Error Propagation Term

Equations (50)

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v ( r ) = λ f ( f l ) 2 π l [ ( P ( f l r ) ) ( ϕ ( f l r ) ) + P ( f l r ) 2 ϕ ( f l r ) ] ,
ϕ = n 0 m = n n a n m Z n m ,
n ( n + 1 ) 2 1 < K ( n + 1 ) ( n + 2 ) 2 1.
N e = 2 1 2 ( 8 K + 9 1 ) ,
κ 1 = 2 k 1 1 ,
κ 2 = 4 k 2 ,
κ 3 = 8 k 3 ,
κ 4 = 16 k 4 .
f ( x , z ) = p ( z , Z ) b ( x ; z , p ) .
( x z ) i = z > 0 ( x = 0 z x i b ( x ; z , p ) ) z i p ( z , Z ) 1 e z ,
= z > 0 μ i ( z , p ) z i p ( z , Z ) 1 e z ,
μ 1 z = p ,
μ 2 z 2 = ( p p 2 ) z + p 2 ,
μ 3 z 3 = ( p 3 p 2 + 2 p 3 ) z 2 + 3 ( p 2 p 3 ) z + p 3 ,
μ 4 z 4 = ( p 7 p 2 + 12 p 3 6 p 4 ) z 3 + ( 7 p 2 18 p 3 + 11 p 4 ) z 2 + 6 ( p 3 p 4 ) z + p 4 .
ρ i = z i Z i ,
= Z i z > 0 z i p ( z , Z ) 1 e z ,
= Z i z > 0 z i e Z Z z z ! 1 1 e z .
k 1 = u 1 ,
k 2 = u 2 u 1 2 ,
k 3 = u 3 3 u 2 u 1 + 2 u 1 3 ,
k 4 = u 4 4 u 3 u 1 + 6 u 2 u 1 2 3 u 1 4 u 3 + 3 u 2 u 1 2 u 1 3 .
κ 1 = 2 p 1 ,
κ 2 = 4 ( p p 2 ) ρ 1 Z ,
κ 3 = 8 ( p 3 p 2 + 2 p 3 ) ρ 2 Z 2 ,
κ 4 = 16 ( p 7 p 2 + 12 p 3 6 p 4 ) Z 2 + 16 ( 3 p 2 6 p 3 + 3 p 4 ) ( ρ 2 ρ 1 2 ) Z 2 .
κ 1 = V ,
κ 2 = ( 1 V 2 ) ρ 1 Z ,
κ 3 = 2 V ( 1 V 2 ) ρ 2 Z 2 ,
κ 4 = ( 2 + 8 V 2 6 V 4 ) ρ 3 Z 3 + 3 ( 1 V 2 ) 2 ( ρ 2 ρ 1 2 ) Z 2 .
v = V ,
σ v 2 = ( 1 V 2 ) ρ 1 Z ,
sk v = 2 V 1 V 2 ρ 2 ρ 1 1.5 1 Z ,
kur v = ( 4 V 2 1 V 2 2 ) ρ 3 ρ 1 2 1 Z + 3 ( ρ 2 ρ 1 2 1 ) .
σ v 2 = ( 1 V 2 ) Z ,
sk v = 2 V 1 V 2 1 Z ,
kur v = ( 4 V 2 1 V 2 + 1 ) 1 Z .
G = σ ϕ 2 σ v 2 ,
ϕ ( l , n ) = ( ϕ ( l 1 , n ) + d ϕ x ( l 1 , n ) + ϕ ( l + 1 , n ) d ϕ x ( l , n ) + ϕ ( l , n 1 ) + d ϕ y ( l , n 1 ) + ϕ ( l , n + 1 ) d ϕ y ( l , n ) ) 4 .
ϕ ( l , n ) ( ϕ ( l 1 , n ) + d ϕ x ( l 1 , n ) + ϕ ( l + 1 , n ) d ϕ x ( l , n ) + ϕ ( l , n 1 ) + d ϕ y ( l , n 1 ) + ϕ ( l , n + 1 ) d ϕ y ( l , n ) ) 4 .
d 2 ϕ ( l , n ) = ( d ϕ x ( l 1 , n ) d ϕ x ( l , n ) + d ϕ y ( l , n 1 ) d ϕ y ( l , n ) ) 4 .
ϕ ( l , n ) ( ϕ ( l 1 , n ) + ϕ ( l + 1 , n ) + ϕ ( l , n 1 ) + ϕ ( l , n + 1 ) ) 4 + d 2 ϕ ( l , n ) ,
d 2 ϕ ( l , n ) = 2 ϕ ( l , n ) a 2 4 = π l a 2 2 λ f ( f l ) v ( l , n ) ,
G = ( 2.20 ± 0.05 ) 10 3 N ( 2.03 ± 0.05 ) 10 4 .
G = σ ϕ 2 σ v 2 = G 0 [ ( 0.85 ± 0.05 ) ( 6.0 ± 0.5 ) N ] ,
G 0 = ( l N ) 2 ( D f ) 4 1 λ 2 .
G = 1 1000 i = 1 1000 σ ϕ 2 ( i ) σ v 2 .
G = σ ϕ 2 σ v 2 = ( l N ) 2 ( D f ) 4 1 λ 2 [ ( 0.64 ± 0.04 ) ( 2.7 ± 0.3 ) N ] .
S 1 S 0 = exp ( σ ϕ 2 ) = exp ( G N Z ) ,
S 1 S 0 = exp ( G 0 Z [ ( 0.64 ± 0.04 ) N ( 2.7 ± 0.3 ) ] ) ,

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