Abstract

There are different techniques for sensing wavefront phase distortions due to atmospheric turbulence. Curvature sensors are practical because their sensitivity is adjustable to the prevailing atmospheric conditions. Even at the best sites, the turbulence intensity has been found to vary at times over only a few minutes and regularly over longer periods. Two methods to automatically adjust the sensitivity of a curvature sensor are proposed: First, the defocus distance can be adjusted prior to the adaptive-optics (AO) loop through the acquisition of a long-exposure image and can then be kept constant. Second, the defocus distance can be changed during the AO loop, based on the voltage values sent to the deformable mirror. We demonstrate that the performance increase—assessed in terms of the image Strehl ratio—can be significant.

© 2010 Optical Society of America

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References

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2008 (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 (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 (2008).
[CrossRef]

M. Sarazin, J. Melnick, J. Navarrete, and G. Lombardi, “Seeing is believing: new facts about the evolution of seeing on Paranal,” ESO Messenger 132, 11–17 (2008).

C. Torti, S. Gruppetta, and L. Diaz-Santana, “Wavefront curvature sensing for the human eye,” J. Mod. Opt. 55, 691 (2008).
[CrossRef]

2006 (1)

2004 (1)

M. Glanc, E. Gendron, F. Lacombe, D. Lafaille, J. F. Le Gargasson, and P. Léna, “Towards wide-field retinal imaging with adaptive optics,” Opt. Commun. 230, 225–238 (2004).
[CrossRef]

2003 (2)

V. Kornilov, A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. Potanin, and M. Sarazin, “MASS: a monitor of the vertical turbulence distribution,” Proc. SPIE 4839, 837–845 (2003).
[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]

2001 (4)

B. C. Platt and R. Shack, “History and principles of Shack Hartmann wave-front sensing,” J. Refract. Surg. 17, s573–s577 (2001).
[PubMed]

J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18, 1793–1803 (2001).
[CrossRef]

H. Hofer, P. Artal, B. Singer, J. L. Aragon, and D. R. Williams, “Dynamics of the eye’s wave aberration,” J. Opt. Soc. Am. A 18, 497–506 (2001).
[CrossRef]

E. Moreno-Barriuso, S. Marcos, R. Navarro, and S. A. Burns, “Comparing laser ray tracing, the spatially resolved refractometer, and the Hartmann-Shack sensor to measure the ocular wave aberration,” Optom. Vision Sci. 78, 152–156(2001).
[CrossRef]

2000 (1)

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]

1997 (1)

J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

1995 (1)

F. Roddier, “Error propagation in a closed loop adaptive optics system: a comparison between Shack-Hartmann and curvature wave-front sensor,” Opt. Commun. 113, 357–359 (1995).
[CrossRef]

1994 (1)

F. Rigaut, R. Arsenault, J. Kerr, D. Salmon, M. Northcott, Y. Dutil, and C. Boyer, “The Canada France Hawaii adaptive optics bonnette II: simulations and control,” Proc. SPIE 2201, 149–160 (1994).
[CrossRef]

1991 (1)

F. Roddier, M. 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]

1990 (1)

M. Sarazin and F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).

1988 (1)

Aragon, J. L.

Arjona, M.

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]

F. Rigaut, R. Arsenault, J. Kerr, D. Salmon, M. Northcott, Y. Dutil, and C. Boyer, “The Canada France Hawaii adaptive optics bonnette II: simulations and control,” Proc. SPIE 2201, 149–160 (1994).
[CrossRef]

Artal, P.

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 (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 (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]

Boyer, C.

F. Rigaut, R. Arsenault, J. Kerr, D. Salmon, M. Northcott, Y. Dutil, and C. Boyer, “The Canada France Hawaii adaptive optics bonnette II: simulations and control,” Proc. SPIE 2201, 149–160 (1994).
[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]

Burns, S. A.

E. Moreno-Barriuso, S. Marcos, R. Navarro, and S. A. Burns, “Comparing laser ray tracing, the spatially resolved refractometer, and the Hartmann-Shack sensor to measure the ocular wave aberration,” Optom. Vision Sci. 78, 152–156(2001).
[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 (2008).
[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 (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 (2008).
[CrossRef]

Cox, I. G.

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]

Diaz-Douton, F.

Diaz-Santana, L.

C. Torti, S. Gruppetta, and L. Diaz-Santana, “Wavefront curvature sensing for the human eye,” J. Mod. Opt. 55, 691 (2008).
[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 (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]

Dutil, Y.

F. Rigaut, R. Arsenault, J. Kerr, D. Salmon, M. Northcott, Y. Dutil, and C. Boyer, “The Canada France Hawaii adaptive optics bonnette II: simulations and control,” Proc. SPIE 2201, 149–160 (1994).
[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 (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]

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 (2008).
[CrossRef]

Gendron, E.

M. Glanc, E. Gendron, F. Lacombe, D. Lafaille, J. F. Le Gargasson, and P. Léna, “Towards wide-field retinal imaging with adaptive optics,” Opt. Commun. 230, 225–238 (2004).
[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]

Glanc, M.

M. Glanc, E. Gendron, F. Lacombe, D. Lafaille, J. F. Le Gargasson, and P. Léna, “Towards wide-field retinal imaging with adaptive optics,” Opt. Commun. 230, 225–238 (2004).
[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 (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,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Gruppetta, S.

C. Torti, S. Gruppetta, and L. Diaz-Santana, “Wavefront curvature sensing for the human eye,” J. Mod. Opt. 55, 691 (2008).
[CrossRef]

Guirao, A.

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 (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 (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 (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 (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 (2008).
[CrossRef]

Hofer, H.

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]

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 (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 (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]

Kerr, J.

F. Rigaut, R. Arsenault, J. Kerr, D. Salmon, M. Northcott, Y. Dutil, and C. Boyer, “The Canada France Hawaii adaptive optics bonnette II: simulations and control,” Proc. SPIE 2201, 149–160 (1994).
[CrossRef]

Kornilov, V.

V. Kornilov, A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. Potanin, and M. Sarazin, “MASS: a monitor of the vertical turbulence distribution,” Proc. SPIE 4839, 837–845 (2003).
[CrossRef]

Lacombe, F.

M. Glanc, E. Gendron, F. Lacombe, D. Lafaille, J. F. Le Gargasson, and P. Léna, “Towards wide-field retinal imaging with adaptive optics,” Opt. Commun. 230, 225–238 (2004).
[CrossRef]

Lafaille, D.

M. Glanc, E. Gendron, F. Lacombe, D. Lafaille, J. F. Le Gargasson, and P. Léna, “Towards wide-field retinal imaging with adaptive optics,” Opt. Commun. 230, 225–238 (2004).
[CrossRef]

Lai, O.

O. Lai, “L’optique adaptative du Telescope Canada-France-Hawaii et son utilisation pour l’etude des coeurs de galaxies a flambee d’etoiles,” Ph. D. dissertation, University Paris VII (1996).

Le Gargasson, J. F.

M. Glanc, E. Gendron, F. Lacombe, D. Lafaille, J. F. Le Gargasson, and P. Léna, “Towards wide-field retinal imaging with adaptive optics,” Opt. Commun. 230, 225–238 (2004).
[CrossRef]

Léna, P.

M. Glanc, E. Gendron, F. Lacombe, D. Lafaille, J. F. Le Gargasson, and P. Léna, “Towards wide-field retinal imaging with adaptive optics,” Opt. Commun. 230, 225–238 (2004).
[CrossRef]

Liang, J.

J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[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 (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]

Lombardi, G.

M. Sarazin, J. Melnick, J. Navarrete, and G. Lombardi, “Seeing is believing: new facts about the evolution of seeing on Paranal,” ESO Messenger 132, 11–17 (2008).

Luque, S. O.

Marcos, S.

E. Moreno-Barriuso, S. Marcos, R. Navarro, and S. A. Burns, “Comparing laser ray tracing, the spatially resolved refractometer, and the Hartmann-Shack sensor to measure the ocular wave aberration,” Optom. Vision Sci. 78, 152–156(2001).
[CrossRef]

Melnick, J.

M. Sarazin, J. Melnick, J. Navarrete, and G. Lombardi, “Seeing is believing: new facts about the evolution of seeing on Paranal,” ESO Messenger 132, 11–17 (2008).

Miller, D. T.

J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[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 (2008).
[CrossRef]

Moreno-Barriuso, E.

E. Moreno-Barriuso, S. Marcos, R. Navarro, and S. A. Burns, “Comparing laser ray tracing, the spatially resolved refractometer, and the Hartmann-Shack sensor to measure the ocular wave aberration,” Optom. Vision Sci. 78, 152–156(2001).
[CrossRef]

E. Moreno-Barriuso and R. Navarro, “Laser ray tracing versus Hartmann-Shack sensor for measuring optical aberrations in the human eye,” J. Opt. Soc. Am. A 17, 974–985 (2000).
[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 (2008).
[CrossRef]

Navarrete, J.

M. Sarazin, J. Melnick, J. Navarrete, and G. Lombardi, “Seeing is believing: new facts about the evolution of seeing on Paranal,” ESO Messenger 132, 11–17 (2008).

Navarro, R.

E. Moreno-Barriuso, S. Marcos, R. Navarro, and S. A. Burns, “Comparing laser ray tracing, the spatially resolved refractometer, and the Hartmann-Shack sensor to measure the ocular wave aberration,” Optom. Vision Sci. 78, 152–156(2001).
[CrossRef]

E. Moreno-Barriuso and R. Navarro, “Laser ray tracing versus Hartmann-Shack sensor for measuring optical aberrations in the human eye,” J. Opt. Soc. Am. A 17, 974–985 (2000).
[CrossRef]

Northcott, M.

F. Rigaut, R. Arsenault, J. Kerr, D. Salmon, M. Northcott, Y. Dutil, and C. Boyer, “The Canada France Hawaii adaptive optics bonnette II: simulations and control,” Proc. SPIE 2201, 149–160 (1994).
[CrossRef]

F. Roddier, M. 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]

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 (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]

J. Paufique, European Southern Observatory, June 2010 (personal communication).

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack Hartmann wave-front sensing,” J. Refract. Surg. 17, s573–s577 (2001).
[PubMed]

Porter, J.

Potanin, S.

V. Kornilov, A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. Potanin, and M. Sarazin, “MASS: a monitor of the vertical turbulence distribution,” Proc. SPIE 4839, 837–845 (2003).
[CrossRef]

Pujol, J.

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 (2008).
[CrossRef]

F. Rigaut, R. Arsenault, J. Kerr, D. Salmon, M. Northcott, Y. Dutil, and C. Boyer, “The Canada France Hawaii adaptive optics bonnette II: simulations and control,” Proc. SPIE 2201, 149–160 (1994).
[CrossRef]

F. Rigaut and M. Sarazin, “Seeing constraints in adaptive optics calibrations,” Astronomy with Adaptive Optics: Present Results and Future Programs, Vol. 56 of ESO Conference and Workshop Proceedings (1999), pp. 383–388.

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, “Error propagation in a closed loop adaptive optics system: a comparison between Shack-Hartmann and curvature wave-front sensor,” Opt. Commun. 113, 357–359 (1995).
[CrossRef]

F. Roddier, M. 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. Sarazin and F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).

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 Program87-3 (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]

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 (2008).
[CrossRef]

Salmon, D.

F. Rigaut, R. Arsenault, J. Kerr, D. Salmon, M. Northcott, Y. Dutil, and C. Boyer, “The Canada France Hawaii adaptive optics bonnette II: simulations and control,” Proc. SPIE 2201, 149–160 (1994).
[CrossRef]

Sarazin, M.

M. Sarazin, J. Melnick, J. Navarrete, and G. Lombardi, “Seeing is believing: new facts about the evolution of seeing on Paranal,” ESO Messenger 132, 11–17 (2008).

V. Kornilov, A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. Potanin, and M. Sarazin, “MASS: a monitor of the vertical turbulence distribution,” Proc. SPIE 4839, 837–845 (2003).
[CrossRef]

M. Sarazin and F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).

F. Rigaut and M. Sarazin, “Seeing constraints in adaptive optics calibrations,” Astronomy with Adaptive Optics: Present Results and Future Programs, Vol. 56 of ESO Conference and Workshop Proceedings (1999), pp. 383–388.

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack Hartmann wave-front sensing,” J. Refract. Surg. 17, s573–s577 (2001).
[PubMed]

Shatsky, N.

V. Kornilov, A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. Potanin, and M. Sarazin, “MASS: a monitor of the vertical turbulence distribution,” Proc. SPIE 4839, 837–845 (2003).
[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]

Singer, B.

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 (2008).
[CrossRef]

Tokovinin, A.

V. Kornilov, A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. Potanin, and M. Sarazin, “MASS: a monitor of the vertical turbulence distribution,” Proc. SPIE 4839, 837–845 (2003).
[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 (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]

Torti, C.

C. Torti, S. Gruppetta, and L. Diaz-Santana, “Wavefront curvature sensing for the human eye,” J. Mod. Opt. 55, 691 (2008).
[CrossRef]

Vozyakova, O.

V. Kornilov, A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. Potanin, and M. Sarazin, “MASS: a monitor of the vertical turbulence distribution,” Proc. SPIE 4839, 837–845 (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 (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 (2008).
[CrossRef]

Williams, D. R.

Zaitsev, A.

V. Kornilov, A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. Potanin, and M. Sarazin, “MASS: a monitor of the vertical turbulence distribution,” Proc. SPIE 4839, 837–845 (2003).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. (1)

M. Sarazin and F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).

ESO Messenger (1)

M. Sarazin, J. Melnick, J. Navarrete, and G. Lombardi, “Seeing is believing: new facts about the evolution of seeing on Paranal,” ESO Messenger 132, 11–17 (2008).

J. Mod. Opt. (1)

C. Torti, S. Gruppetta, and L. Diaz-Santana, “Wavefront curvature sensing for the human eye,” J. Mod. Opt. 55, 691 (2008).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Refract. Surg. (1)

B. C. Platt and R. Shack, “History and principles of Shack Hartmann wave-front sensing,” J. Refract. Surg. 17, s573–s577 (2001).
[PubMed]

Opt. Commun. (2)

F. Roddier, “Error propagation in a closed loop adaptive optics system: a comparison between Shack-Hartmann and curvature wave-front sensor,” Opt. Commun. 113, 357–359 (1995).
[CrossRef]

M. Glanc, E. Gendron, F. Lacombe, D. Lafaille, J. F. Le Gargasson, and P. Léna, “Towards wide-field retinal imaging with adaptive optics,” Opt. Commun. 230, 225–238 (2004).
[CrossRef]

Opt. Lett. (1)

Optom. Vision Sci. (1)

E. Moreno-Barriuso, S. Marcos, R. Navarro, and S. A. Burns, “Comparing laser ray tracing, the spatially resolved refractometer, and the Hartmann-Shack sensor to measure the ocular wave aberration,” Optom. Vision Sci. 78, 152–156(2001).
[CrossRef]

Proc. SPIE (6)

V. Kornilov, A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. Potanin, and M. Sarazin, “MASS: a monitor of the vertical turbulence distribution,” Proc. SPIE 4839, 837–845 (2003).
[CrossRef]

F. Rigaut, R. Arsenault, J. Kerr, D. Salmon, M. Northcott, Y. Dutil, and C. Boyer, “The Canada France Hawaii adaptive optics bonnette II: simulations and control,” Proc. SPIE 2201, 149–160 (1994).
[CrossRef]

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 (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 (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]

Publ. Astron. Soc. Pac. (1)

F. Roddier, M. 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 (5)

Users Manual for the CFHT Adaptive Optics Bonnette, http://www.cfht.hawaii.edu/Instruments/Imaging/AOB/.

F. Rigaut and M. Sarazin, “Seeing constraints in adaptive optics calibrations,” Astronomy with Adaptive Optics: Present Results and Future Programs, Vol. 56 of ESO Conference and Workshop Proceedings (1999), pp. 383–388.

J. Paufique, European Southern Observatory, June 2010 (personal communication).

F. Roddier, “Curvature sensing: a diffraction theory,” NOAO Advanced Development Program87-3 (1987).

O. Lai, “L’optique adaptative du Telescope Canada-France-Hawaii et son utilisation pour l’etude des coeurs de galaxies a flambee d’etoiles,” Ph. D. dissertation, University Paris VII (1996).

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Figures (6)

Fig. 1
Fig. 1

Configuration of the simulated sensor: the wavefront is sampled over 80 subapertures. Dashed curves, pupil inner and outer edges.

Fig. 2
Fig. 2

Strehl ratio and defocus distance versus seeing for a curvature sensor under various seeing conditions (See left column of Table 1 for the parameter values). Triangles, sequences with different defocus values are simulated and the defocus that yields the highest Strehl is kept. Dashed curve (respectively, dotted and dashed-dotted), the minimum (respectively, the average and maximum) defocus distance obtained with the former procedure is kept for all turbulence intensities. Solid curve, the defocus value is determined from a long-exposure image, acquired prior to the AO loop.

Fig. 3
Fig. 3

Seeing at 0.5 μm , recorded by the DIMM (dots) and MASS (squares) on the Mauna Kea observatory. The monitors are installed next to the Canada–France–Hawaii telescope, which accommodates the curvature AO system PUEO. DIMM and MASS acquire a measurement about every 2 min . MASS is insensitive to the lowest turbulent layers and generally measures smaller seeing values than DIMM. Credit: http://mkwc.ifa.hawaii.edu/.

Fig. 4
Fig. 4

70 s AO sequence, during which the seeing, θ 0 , is incremented by 0.05 every 1000th iteration. Left panel: solid curve, average Strehl when the defocus is adjusted during the sequence; dotted curve, the defocus is determined prior to the AO loop when θ 0 = 0.2 ; circles, θ 0 / 2 . Right panel: defocus values; circles, θ 0 . (Parameter values: see right column of Table 1).

Fig. 5
Fig. 5

70 s AO sequence, during which the seeing, θ 0 , is modified every 1000th iteration. Left panel: solid curve, average Strehl when the defocus is adjusted during the sequence; dotted curve, the defocus is determined prior to the AO loop when θ 0 = 0.15 ; circles, θ 0 / 2 . Right panel: defocus values; circles, θ 0 . (Parameter values: see right column of Table 1).

Fig. 6
Fig. 6

70 s AO sequence, during which the seeing, θ 0 , is modified every 1000th iteration between 0.1 and 1.8 . Solid curves, average Strehl when the defocus is adjusted during the sequence; dotted curves, the defocus is determined prior to the AO loop when θ 0 = 1.6 . The magnitude of the reference star varies among 5 (black), 9 (magenta) and 11 (blue). Circles, θ 0 / 2 . (Further parameter values: see right column of Table 1.)

Tables (1)

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Table 1 Parameter Values of the Numerical Simulations, if Not Otherwise Specified in the Text

Equations (5)

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v ( r ) = λ S f ( f l ) π l [ ( P ( f l r ) ) · ( ϕ ( f l r ) ) + P ( f l r ) · 2 ϕ ( f l r ) ] .
l 0 = k 1 · λ S f 2 N D r 0 ( λ S ) ,
l 0 = k 2 · ( λ I λ S ) 1 / 5 · f 2 N D · θ 50 ( λ I ) ,
σ ϕ 2 = 1 K · 1 M 2 k = 1 K m , n = 1 M ϕ k ( m , n ) 2 = κ · ( D r 0 ( λ S ) ) 5 / 3 ,
l 0 = k 3 · λ S ( f D ) 2 N σ ϕ 6 / 5 .

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