Abstract

The objective of the present study is to estimate the ability of conventional adaptive optics (AO) to correct for a wavefront created by static errors randomly distributed over the population of a multisegmented primary mirror for an extremely large telescope (ELT). The criterion for the performance of AO is a correction factor: a ratio between two root-mean-square (RMS) values of the phase before and after the AO correction. We define a best value for the correction factor as the one obtained in an AO model described as a hard-edge high-pass filter applied to phase aberrations of the telescope pupil. We compare the results of other AO models with this best value. The relation between RMS and the power spectral density helps us evaluate the initial requirements of segment aberration for optimistic and pessimistic cases without need of specifying the type of AO. This work develops a tool that can be used for segment manufacturing specifications, for defining the requirements on an active optics system controlling segment shape, and for designing a high-contrast imaging instrument for an ELT.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. E. Vernet, L. Jochum, P. La Penna, N. Hubin, and R. Muradore, “The field stabilization and adaptive optics mirrors for the European Extremely Large Telescope,” Proc. SPIE 7015, 70150s (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008 (4)

E. Vernet, L. Jochum, P. La Penna, N. Hubin, and R. Muradore, “The field stabilization and adaptive optics mirrors for the European Extremely Large Telescope,” Proc. SPIE 7015, 70150s (2008).
[CrossRef]

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

N. Yaitskova, “Diffraction halo by a segmented telescope,” Proc. SPIE 7012, 701215 (2008).
[CrossRef]

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

2007 (2)

2006 (2)

M. Troy, I. Crossfield, G. Chanan, P. Dumont, J. Green, and B. Macintosh, “Effects of diffraction and static wavefront errors on high-contrast imaging from the Thirty Meter Telescope,” Proc. SPIE 6267, 626722C (2006).

N. Yaitskova and C. Verinaud, “Adaptive optics correction of the wavefront distortions induced by segments misalignment in extremely large telescope,” Proc. SPIE 6267, 62672N (2006).
[CrossRef]

2003 (3)

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

M. Troy and G. Chanan, “Diffraction effects from giant segmented-mirror telescopes,” Appl. Opt. 42, 3745-3753 (2003).
[CrossRef] [PubMed]

N. Yaitskova, K. Dohlen, and P. Dierickx, “Analytical study of diffraction effects in extremely large segmented telescopes,” J. Opt. Soc. Am. A 20, 1563-1575 (2003).
[CrossRef]

2002 (1)

1998 (1)

F. Rigaut, J.-P. Veran, and O. Lai, “An analytical model of Shack-Hartmann-based adaptive optics system,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

1993 (1)

N. Hubin and L. Noethe, “Active optics, adaptive optics, and laser guide stars,” Science 262, 1390-1394 (1993).
[CrossRef] [PubMed]

1990 (1)

1982 (1)

1978 (1)

J. E. Harvey and G. M. Callahan, “Wavefront error compensation capabilities of multi-actuator deformable mirrors,” Proc. Soc. Photo-Opt. Instrum. Eng. 141, 50-57 (1978).

1953 (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229-236 (1953).
[CrossRef]

Arsenault, R.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229-236 (1953).
[CrossRef]

Baudoz, P.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Beuzit, J.-L.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Boccaletti, A.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Callahan, G. M.

J. E. Harvey and G. M. Callahan, “Wavefront error compensation capabilities of multi-actuator deformable mirrors,” Proc. Soc. Photo-Opt. Instrum. Eng. 141, 50-57 (1978).

Chanan, G.

M. Troy, I. Crossfield, G. Chanan, P. Dumont, J. Green, and B. Macintosh, “Effects of diffraction and static wavefront errors on high-contrast imaging from the Thirty Meter Telescope,” Proc. SPIE 6267, 626722C (2006).

M. Troy and G. Chanan, “Diffraction effects from giant segmented-mirror telescopes,” Appl. Opt. 42, 3745-3753 (2003).
[CrossRef] [PubMed]

Charton, J.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Crossfield, I.

M. Troy, I. Crossfield, G. Chanan, P. Dumont, J. Green, and B. Macintosh, “Effects of diffraction and static wavefront errors on high-contrast imaging from the Thirty Meter Telescope,” Proc. SPIE 6267, 626722C (2006).

Crossfield, I. J.

Dierickx, P.

Dohlen, K.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

N. Yaitskova, K. Dohlen, and P. Dierickx, “Analytical study of diffraction effects in extremely large segmented telescopes,” J. Opt. Soc. Am. A 20, 1563-1575 (2003).
[CrossRef]

N. Yaitskova and K. Dohlen, “Tip-tilt error for extremely large segmented telescope: detail theoretical analysis and numerical simulation,” J. Opt. Soc. Am. A 19, 1274-1285 (2002).
[CrossRef]

Dumont, P.

M. Troy, I. Crossfield, G. Chanan, P. Dumont, J. Green, and B. Macintosh, “Effects of diffraction and static wavefront errors on high-contrast imaging from the Thirty Meter Telescope,” Proc. SPIE 6267, 626722C (2006).

Ellerbroek, B.

B. Ellerbroek, (personal communication, 2006, brente@caltech.edu).

Feautrier, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Feldt, M.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Fusco, T.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Gendron, E.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Gigan, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Gilmozzi, R.

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1986).

Gratton, R.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Green, J.

M. Troy, I. Crossfield, G. Chanan, P. Dumont, J. Green, and B. Macintosh, “Effects of diffraction and static wavefront errors on high-contrast imaging from the Thirty Meter Telescope,” Proc. SPIE 6267, 626722C (2006).

Hansen, R.

C. Lawson and R. Hansen, Solving Least Square Problems (Prentice Hall, 1979).

Harvey, J. E.

J. E. Harvey and G. M. Callahan, “Wavefront error compensation capabilities of multi-actuator deformable mirrors,” Proc. Soc. Photo-Opt. Instrum. Eng. 141, 50-57 (1978).

Hubin, N.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

E. Vernet, L. Jochum, P. La Penna, N. Hubin, and R. Muradore, “The field stabilization and adaptive optics mirrors for the European Extremely Large Telescope,” Proc. SPIE 7015, 70150s (2008).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

N. Hubin and L. Noethe, “Active optics, adaptive optics, and laser guide stars,” Science 262, 1390-1394 (1993).
[CrossRef] [PubMed]

Jochum, L.

E. Vernet, L. Jochum, P. La Penna, N. Hubin, and R. Muradore, “The field stabilization and adaptive optics mirrors for the European Extremely Large Telescope,” Proc. SPIE 7015, 70150s (2008).
[CrossRef]

Kasper, M.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Kerber, F.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Kern, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

La Penna, P.

E. Vernet, L. Jochum, P. La Penna, N. Hubin, and R. Muradore, “The field stabilization and adaptive optics mirrors for the European Extremely Large Telescope,” Proc. SPIE 7015, 70150s (2008).
[CrossRef]

Lacombe, F.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Lagrange, A.-M.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Lai, O.

F. Rigaut, J.-P. Veran, and O. Lai, “An analytical model of Shack-Hartmann-based adaptive optics system,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

Lawrence, G. N.

Lawson, C.

C. Lawson and R. Hansen, Solving Least Square Problems (Prentice Hall, 1979).

Macintosh, B.

M. Troy, I. Crossfield, G. Chanan, P. Dumont, J. Green, and B. Macintosh, “Effects of diffraction and static wavefront errors on high-contrast imaging from the Thirty Meter Telescope,” Proc. SPIE 6267, 626722C (2006).

Madec, P.-Y.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Moor, K. E.

Mouillet, D.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Muradore, R.

E. Vernet, L. Jochum, P. La Penna, N. Hubin, and R. Muradore, “The field stabilization and adaptive optics mirrors for the European Extremely Large Telescope,” Proc. SPIE 7015, 70150s (2008).
[CrossRef]

Noethe, L.

N. Hubin and L. Noethe, “Active optics, adaptive optics, and laser guide stars,” Science 262, 1390-1394 (1993).
[CrossRef] [PubMed]

Puget, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Rabaud, D.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Rabou, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Rigaut, F.

F. Rigaut, J.-P. Veran, and O. Lai, “An analytical model of Shack-Hartmann-based adaptive optics system,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

F. Rigaut, (personal communication, 2008, frigaut@gemini.edu).

Roelfsema, R.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Rousset, G.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Schmid, H. M.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Spyromilio, J.

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Stadler, E.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Swat, A.

A. Swat (personal communication, 2007, aswat@eso.org).

Thatte, N.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

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I. J. Crossfield and M. Troy, “Segment aberration effect on contrast,” Appl. Opt. 46, 4533-4540 (2007).
[CrossRef] [PubMed]

M. Troy, I. Crossfield, G. Chanan, P. Dumont, J. Green, and B. Macintosh, “Effects of diffraction and static wavefront errors on high-contrast imaging from the Thirty Meter Telescope,” Proc. SPIE 6267, 626722C (2006).

M. Troy and G. Chanan, “Diffraction effects from giant segmented-mirror telescopes,” Appl. Opt. 42, 3745-3753 (2003).
[CrossRef] [PubMed]

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Venema, L.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Veran, J.-P.

F. Rigaut, J.-P. Veran, and O. Lai, “An analytical model of Shack-Hartmann-based adaptive optics system,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

Verinaud, C.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

N. Yaitskova and C. Verinaud, “Adaptive optics correction of the wavefront distortions induced by segments misalignment in extremely large telescope,” Proc. SPIE 6267, 62672N (2006).
[CrossRef]

Vernet, E.

E. Vernet, L. Jochum, P. La Penna, N. Hubin, and R. Muradore, “The field stabilization and adaptive optics mirrors for the European Extremely Large Telescope,” Proc. SPIE 7015, 70150s (2008).
[CrossRef]

Wolf, S.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

Yaitskova, N.

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

N. Yaitskova, “Diffraction halo by a segmented telescope,” Proc. SPIE 7012, 701215 (2008).
[CrossRef]

N. Yaitskova, “Influence of irregular gaps between primary mirror segments on telescope image quality,” J. Opt. Soc. Am. A 24, 2558-2567 (2007).
[CrossRef]

N. Yaitskova and C. Verinaud, “Adaptive optics correction of the wavefront distortions induced by segments misalignment in extremely large telescope,” Proc. SPIE 6267, 62672N (2006).
[CrossRef]

N. Yaitskova, K. Dohlen, and P. Dierickx, “Analytical study of diffraction effects in extremely large segmented telescopes,” J. Opt. Soc. Am. A 20, 1563-1575 (2003).
[CrossRef]

N. Yaitskova and K. Dohlen, “Tip-tilt error for extremely large segmented telescope: detail theoretical analysis and numerical simulation,” J. Opt. Soc. Am. A 19, 1274-1285 (2002).
[CrossRef]

Zins, G.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

Appl. Opt. (4)

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Proc. Soc. Photo-Opt. Instrum. Eng. (1)

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Proc. SPIE (8)

M. Kasper, J.-L. Beuzit, C. Verinaud, N. Yaitskova, P. Baudoz, A. Boccaletti, R. Gratton, N. Hubin, F. Kerber, R. Roelfsema, H. M. Schmid, N. Thatte, K. Dohlen, M. Feldt, L. Venema, and S. Wolf, “EPICS: the exoplanet imager for EELT,” Proc. SPIE 701570151s, (2008).
[CrossRef]

M. Troy, I. Crossfield, G. Chanan, P. Dumont, J. Green, and B. Macintosh, “Effects of diffraction and static wavefront errors on high-contrast imaging from the Thirty Meter Telescope,” Proc. SPIE 6267, 626722C (2006).

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140-149 (2003).
[CrossRef]

E. Vernet, L. Jochum, P. La Penna, N. Hubin, and R. Muradore, “The field stabilization and adaptive optics mirrors for the European Extremely Large Telescope,” Proc. SPIE 7015, 70150s (2008).
[CrossRef]

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

N. Yaitskova, “Diffraction halo by a segmented telescope,” Proc. SPIE 7012, 701215 (2008).
[CrossRef]

N. Yaitskova and C. Verinaud, “Adaptive optics correction of the wavefront distortions induced by segments misalignment in extremely large telescope,” Proc. SPIE 6267, 62672N (2006).
[CrossRef]

F. Rigaut, J.-P. Veran, and O. Lai, “An analytical model of Shack-Hartmann-based adaptive optics system,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

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A. Swat (personal communication, 2007, aswat@eso.org).

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Figures (6)

Fig. 1
Fig. 1

Normalized PSD of segmentation error for aberrations from piston to coma Y.

Fig. 2
Fig. 2

Same as in Fig. 1 but for aberrations from the first spherical to the second spherical.

Fig. 3
Fig. 3

Correction factor: comparison among the best case (thick solid curve), a least-square fit (circles), and the results of simulations (triangles and stars). The dashed and dotted–dashed curves are the best cases degraded by 10% and 20%, respectively. Aberrations: from piston to astigmatism Y.

Fig. 4
Fig. 4

Same as in Fig. 3 but for aberrations from the coma X to the second astigmatism X.

Fig. 5
Fig. 5

Same as in Fig. 3 but for aberrations from the second astigmatism Y to the second sphere.

Fig. 6
Fig. 6

Initial and residual phase maps from the simulation with global least-square fitting. Images show one-quarter of the EELT primary mirror.

Tables (2)

Tables Icon

Table 1 Zernike Polynomials

Equations (44)

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φ ( x ) = j = 1 N a j n Z n ( x r j ) θ ( x r j ) .
F ( x ) = j = 1 N θ ( x r j ) exp [ a j n Z n ( x r j ) ] .
PSF ( w ) = 1 N 2 A 2 j = 1 N k = 1 N d 2 ξ θ ( ξ ) d 2 ξ θ ( ξ ) exp [ i 2 π λ w ( ξ ξ ) ] exp [ i a j n Z n ( ξ ) ] exp [ i a k n Z n ( ξ ) ] exp [ i 2 π λ w ( r j r k ) ] .
exp [ i a j n Z n ( ξ ) ] exp [ i a k l Z k ( ξ ) ] = { exp { i a n [ Z n ( ξ ) Z n ( ξ ) ] } for j = k exp [ i a n Z n ( ξ ) ] exp [ i a n Z n ( ξ ) ] for j k } .
GF ( w ) = 1 N j = 1 N exp [ i 2 π λ w r j ] 2 ,
B ( w ) = 1 A exp [ i a n Z n ( ξ ) ] θ ( ξ ) exp ( i 2 π λ w ξ ) d 2 ξ 2 ,
D ( w ) = 1 A 2 exp { i a n [ Z n ( ξ ) Z n ( ξ ) ] } exp [ i 2 π λ w ( ξ ξ ) ] θ ( ξ ) θ ( ξ ) d 2 ξ d 2 ξ ,
PSF ( w ) = GF ( w ) B ( w ) + D ( w ) B ( w ) N .
exp [ i a n Z n ( ξ ) ] exp [ i a n Z n ( ξ ) ] 1 1 2 σ n 2 [ Z n 2 ( ξ ) + Z n 2 ( ξ ) ] ,
exp { i a n [ Z n ( ξ ) Z n ( ξ ) ] } 1 1 2 σ n 2 [ Z n 2 ( ξ ) + Z n 2 ( ξ ) ] + σ n 2 Z n ( ξ ) Z n ( ξ ) .
D ( w ) B ( w ) N σ n 2 N t n ( w ) 2 ,
t n ( w ) = 1 A Z n ( ξ ) θ ( ξ ) exp ( i 2 π λ w ξ ) d 2 ξ .
PSD ( w ) = 1 A N φ ( x ) exp ( i 2 π λ w x ) d 2 x 2 .
PSD ( w ) = 1 N 2 j = 1 N k = 1 N a j n a k n exp [ i 2 π λ w ( r j r k ) ] × 1 A Z n ( ξ ) θ ( ξ ) exp ( 2 π λ ξ ) d 2 ξ 2 .
PSD ( w ) = σ n 2 N t n ( w ) 2 .
α = π d w x 2 λ , β = π d w y 2 λ ,
x = 3 ξ x d , y = 3 ξ y d ,
t n ( α , β ) = 2 3 3 3 2 3 2 d y 1 + y 3 1 y 3 d x Z n ( x , y ) exp [ i ( α x + β y ) 4 3 ] .
RMS 2 = 1 A N φ 2 ( x ) d 2 x .
RMS 2 = A N λ 2 PSD ( w ) d 2 w .
RMS ini 2 = A N λ 2 G AO PSD ini ( w ) d 2 w + A N λ 2 G AO c PSD ini ( w ) d 2 w ,
RMS fin 2 = A N λ 2 G AO PSD fin ( w ) d 2 w + A N λ 2 G AO c PSD ini ( w ) d 2 w ,
RMS fin , ult 2 = A N λ 2 G AO c PSD ini ( w ) d 2 w .
γ AO , n ult = RMS fin , ult RMS ini .
γ AO , n ult = [ 1 2 3 π 2 τ n π d 4 d a π d 4 d a π d 4 d a π d 4 d a t n ( α , β ) 2 d α d β ] 1 2 .
φ res ( x ) = j = 1 N a j n [ Z n ( x r j ) θ ( x r j ) m θ j κ m n I F ( x x m ) ] .
RMS fin 2 = σ n 2 N j = 1 N 1 A [ Z n ( ξ ) θ ( ξ ) I F s j n ( ξ ) ] 2 d 2 ξ .
I F s j n ( ξ ) = m θ j κ m n I F ( ξ ξ m ) .
γ AO , n = RMS fin 2 RMS ini 2 = RMS fin 2 τ n σ n 2 = { 1 N j = 1 N 1 A τ n [ Z n ( ξ ) θ ( ξ ) I F s j n ( ξ ) ] 2 d 2 ξ } 1 2 .
e j 2 = [ Z n ( ξ ) θ ( ξ ) m θ j κ m n I F ( ξ ξ m ) ] 2 d 2 ξ min
κ = ( H t H ) 1 H t B .
e j 2 = B I H ( H t H ) 1 H t B t ,
γ AO , n fit = 1 N j = 1 n e j 2 τ n A ̃ ,
I F ( x ) = 1 ( 2 c + 1 ) { 1 + ( 4 c 2.5 ) x 2 + ( 3 c + 1.5 ) x 3 0 < x < d a ( 2 c 0.5 ) ( 2 x ) 2 + ( c + 0.5 ) ( 2 x ) 3 d a < x < 2 d a , 0 x > 2 d a }
I F ( x ) = { 1 x 3.805 + 3.74 ln ( x ) x 2.451 0 < x < d a . 0 x > d a }
1 γ AO , n good = 0.9 ( 1 γ AO , n ult ) ,
1 γ AO , n medium = 0.8 ( 1 γ AO , n ult ) .
PSD ¯ fin = [ γ AO , n 2 ( γ AO , n ult ) 2 ] RMS ini 2 N 2 3 1 ( d d a ) 2 .
PSD ¯ fin good = 2 3 [ 0.01 + 0.18 γ AO , n ult 0.19 ( γ AO , n ult ) 2 ] RMS ini 2 N 1 ( d d a ) 2 ,
PSD ¯ fin medium = 2 3 [ 0.04 + 0.32 γ AO , n ult 0.36 ( γ AO , n ult ) 2 ] RMS ini 2 N 1 ( d d a ) 2 .
RMS 2 = 1 A N j = 1 N a n j 2 θ ( x r j ) Z 2 ( x r j ) d 2 x = 1 A θ ( ξ ) Z 2 ( ξ ) d 2 ξ 1 N j = 1 N a n j 2 .
τ n 1 A θ ( ξ ) n 2 Z n 2 ( ξ ) d 2 ξ = 2 3 3 3 2 3 2 d y 1 + y 3 1 y 3 d x Z n 2 ( x , y ) .
RMS 2 = τ n 1 N j = 1 N a n j 2 = τ n σ n 2 .
RMS 2 τ n σ n 2 .

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