Abstract

End-to-end simulation of adaptive optics (AO) systems allows high-fidelity modeling of system performance, but at the cost of long computation time. Analytical modeling, on the other hand, can provide much faster first-order performance estimates for a rapid exploration of the AO parameter space. In this paper, we present the foundations of a modeling method for the AO optical transfer function, based on an analytical description of the residual phase spatial power spectrum. The method has been implemented in an IDL-based code, PAOLA, and comparison with end-to-end simulations demonstrates the validity of the analytical approach.

© 2006 Optical Society of America

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  6. L. Jolissaint, J.-P. Véran, and J. A. Stoesz, "Wide field adaptive optics upper limit performances," in Proc. SPIE 5382, 468-477 (2004).
    [Crossref]
  7. L. Jolissaint and J.-F. Lavigne, "An analytic model for the study of the impact of mirror segmentation on AO performance, and application to a 30 m segmented telescope," in Proc. SPIE 5497, 1038-1048 (2004).
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    [Crossref]
  12. J. A. Stoesz, D. Andersen, and L. Jolissaint, "GLAO feasibility study report for Gemini telescopes." Tech. Rep. GLAO-PRD-001 (Herzberg Institute of Astrophysics, National Research Council of Canada, 2005).
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  24. C. Verinaud, "On the nature of the measurements provided by a pyramid wave-front sensor," Opt. Commun.233, (2004).
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    [Crossref]
  27. A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
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  28. L. A. Poyneer and B. Macintosh, "Spatially filtered wave-front sensor for high-order adaptive optics," J. Opt. Soc. Am. A 21, 810-819 (2004).
    [Crossref]

2005 (1)

B. L. Ellerbroek, "Linear systems modeling of adaptive optics in the spatial-frequency domain," J. Opt. Soc. Am. A 22, 300-322 (2005).
[Crossref]

2004 (10)

C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. 612, L85-L88 (2004).
[Crossref]

O. Lardiere, P. Salinari, L. Jolissaint, M. Carbillet, A. Riccardi, and S. Esposito, "Adaptive optics and site requirements for the search of earth-like planets with ELTs," in Proc. SPIE 5382, 550-559 (2004).
[Crossref]

T. Travouillon, J. S. Lawrence, and L. Jolissaint, "Ground layer adaptive optics performance in Antarctica," in Proc. SPIE 5497, 934-942 (2004).
[Crossref]

M. Le Louarn, "Parallel simulation tools for AO on ELTs," in Proc. SPIE 5490, 705-712 (2004).
[Crossref]

T. Fusco and J.-M. Conan, "On- and off-axis statistical behavior of adaptive-optics-corrected short-exposure Strehl ratio," J. Opt. Soc. Am. A 21, 1277-1289 (2004).
[Crossref]

A. Tokovinin, "Seeing improvement with ground-layer adaptive optics," Publ. Astron. Soc. Pac. 116, 941-951 (2004).
[Crossref]

L. Jolissaint, J.-P. Véran, and J. A. Stoesz, "Wide field adaptive optics upper limit performances," in Proc. SPIE 5382, 468-477 (2004).
[Crossref]

L. Jolissaint and J.-F. Lavigne, "An analytic model for the study of the impact of mirror segmentation on AO performance, and application to a 30 m segmented telescope," in Proc. SPIE 5497, 1038-1048 (2004).

C. Innocenti and A. Consortini, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).
[Crossref]

L. A. Poyneer and B. Macintosh, "Spatially filtered wave-front sensor for high-order adaptive optics," J. Opt. Soc. Am. A 21, 810-819 (2004).
[Crossref]

2003 (2)

B. L. Ellerbroek and R. A. Buchroeder, "Near-infrared AO coronagraph design for giant telescopes," in Proc. SPIE 4840, 404-411 (2003).
[Crossref]

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
[Crossref]

1998 (1)

F. Rigaut, J.-P. Véran, and O. Lai, "An analytic model for Shack-Hartmann based adaptive optics systems," in Proc. SPIE 3353, 1038-1048 (1998).
[Crossref]

1997 (1)

J.-P. Véran, F. Rigaut, H. Maître, and D. Rouan, "Estimation of the adaptive optics long-exposure point spread function using control loop data," J. Opt. Soc. Am. A 14, 2957-3069 (1997).
[Crossref]

1994 (1)

R. J. Sasiela, "Wave-front correction by one or more synthetic beacons," J. Opt. Soc. Am. A 11, 389-393 (1994).
[Crossref]

1966 (1)

Abraham, L.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Aime, C.

C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. 612, L85-L88 (2004).
[Crossref]

Andersen, D.

J. A. Stoesz, D. Andersen, and L. Jolissaint, "GLAO feasibility study report for Gemini telescopes." Tech. Rep. GLAO-PRD-001 (Herzberg Institute of Astrophysics, National Research Council of Canada, 2005).

Bloemhof, E. E.

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
[Crossref]

Bohlender, D.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Buchroeder, R. A.

B. L. Ellerbroek and R. A. Buchroeder, "Near-infrared AO coronagraph design for giant telescopes," in Proc. SPIE 4840, 404-411 (2003).
[Crossref]

Carbillet, M.

O. Lardiere, P. Salinari, L. Jolissaint, M. Carbillet, A. Riccardi, and S. Esposito, "Adaptive optics and site requirements for the search of earth-like planets with ELTs," in Proc. SPIE 5382, 550-559 (2004).
[Crossref]

Carlberg, R.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Conan, J.-M.

T. Fusco and J.-M. Conan, "On- and off-axis statistical behavior of adaptive-optics-corrected short-exposure Strehl ratio," J. Opt. Soc. Am. A 21, 1277-1289 (2004).
[Crossref]

J.-M. Conan, Etude de la Correction Partielle en Optique Adaptative (Office National d'Etude et de Recherche Aérospatiale, Paris, 1995).

Consortini, A.

C. Innocenti and A. Consortini, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).
[Crossref]

Crabtree, D.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Davidge, T.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Ellerbroek, B. L.

B. L. Ellerbroek, "Linear systems modeling of adaptive optics in the spatial-frequency domain," J. Opt. Soc. Am. A 22, 300-322 (2005).
[Crossref]

B. L. Ellerbroek and R. A. Buchroeder, "Near-infrared AO coronagraph design for giant telescopes," in Proc. SPIE 4840, 404-411 (2003).
[Crossref]

Esposito, S.

O. Lardiere, P. Salinari, L. Jolissaint, M. Carbillet, A. Riccardi, and S. Esposito, "Adaptive optics and site requirements for the search of earth-like planets with ELTs," in Proc. SPIE 5382, 550-559 (2004).
[Crossref]

Fried, D. L.

Fulbright, K.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Fusco, T.

Gillespie, B.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Hodge, P. E.

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
[Crossref]

Hudson, M.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Innocenti, C.

C. Innocenti and A. Consortini, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).
[Crossref]

Jolissaint, L.

O. Lardiere, P. Salinari, L. Jolissaint, M. Carbillet, A. Riccardi, and S. Esposito, "Adaptive optics and site requirements for the search of earth-like planets with ELTs," in Proc. SPIE 5382, 550-559 (2004).
[Crossref]

T. Travouillon, J. S. Lawrence, and L. Jolissaint, "Ground layer adaptive optics performance in Antarctica," in Proc. SPIE 5497, 934-942 (2004).
[Crossref]

L. Jolissaint and J.-F. Lavigne, "An analytic model for the study of the impact of mirror segmentation on AO performance, and application to a 30 m segmented telescope," in Proc. SPIE 5497, 1038-1048 (2004).

L. Jolissaint, J.-P. Véran, and J. A. Stoesz, "Wide field adaptive optics upper limit performances," in Proc. SPIE 5382, 468-477 (2004).
[Crossref]

L. Jolissaint and J.-P. Véran, "Fast computation and morphologic interpretation of the adaptive optics point spread function," in Beyond Conventional Adaptive Optics, E.Vernet, R.Ragazzoni, S.Esposito, and N.Hubin, eds., Vol. 58 of European Southern Observatory Conference and Workshop Proceedings, 201-208 (ESO, 2001).

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

J. A. Stoesz, D. Andersen, and L. Jolissaint, "GLAO feasibility study report for Gemini telescopes." Tech. Rep. GLAO-PRD-001 (Herzberg Institute of Astrophysics, National Research Council of Canada, 2005).

Kavelaars, J. J.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Lai, O.

F. Rigaut, J.-P. Véran, and O. Lai, "An analytic model for Shack-Hartmann based adaptive optics systems," in Proc. SPIE 3353, 1038-1048 (1998).
[Crossref]

Lardiere, O.

O. Lardiere, P. Salinari, L. Jolissaint, M. Carbillet, A. Riccardi, and S. Esposito, "Adaptive optics and site requirements for the search of earth-like planets with ELTs," in Proc. SPIE 5382, 550-559 (2004).
[Crossref]

Lavigne, J.-F.

L. Jolissaint and J.-F. Lavigne, "An analytic model for the study of the impact of mirror segmentation on AO performance, and application to a 30 m segmented telescope," in Proc. SPIE 5497, 1038-1048 (2004).

Lawrence, J. S.

T. Travouillon, J. S. Lawrence, and L. Jolissaint, "Ground layer adaptive optics performance in Antarctica," in Proc. SPIE 5497, 934-942 (2004).
[Crossref]

Le Louarn, M.

M. Le Louarn, "Parallel simulation tools for AO on ELTs," in Proc. SPIE 5490, 705-712 (2004).
[Crossref]

Lloyd, J. P.

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
[Crossref]

Macintosh, B.

Maître, H.

J.-P. Véran, F. Rigaut, H. Maître, and D. Rouan, "Estimation of the adaptive optics long-exposure point spread function using control loop data," J. Opt. Soc. Am. A 14, 2957-3069 (1997).
[Crossref]

Makidon, R. B.

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
[Crossref]

Morbey, C.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Oke, B.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Oppenheimer, B. R.

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
[Crossref]

Perrin, M. D.

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
[Crossref]

Poyneer, L. A.

Riccardi, A.

O. Lardiere, P. Salinari, L. Jolissaint, M. Carbillet, A. Riccardi, and S. Esposito, "Adaptive optics and site requirements for the search of earth-like planets with ELTs," in Proc. SPIE 5382, 550-559 (2004).
[Crossref]

Rigaut, F.

F. Rigaut, J.-P. Véran, and O. Lai, "An analytic model for Shack-Hartmann based adaptive optics systems," in Proc. SPIE 3353, 1038-1048 (1998).
[Crossref]

J.-P. Véran, F. Rigaut, H. Maître, and D. Rouan, "Estimation of the adaptive optics long-exposure point spread function using control loop data," J. Opt. Soc. Am. A 14, 2957-3069 (1997).
[Crossref]

Roddier, F.

F. Roddier, "The effect of atmospheric turbulence in optical astronomy," in Progress in Optics, Vol. XIX, E.Wolf, ed. (North-Holland, 1981), pp. 281-376.
[Crossref]

Rouan, D.

J.-P. Véran, F. Rigaut, H. Maître, and D. Rouan, "Estimation of the adaptive optics long-exposure point spread function using control loop data," J. Opt. Soc. Am. A 14, 2957-3069 (1997).
[Crossref]

Rousset, G.

G. Rousset, "Wavefront sensing," in NATO ASIC Proc. 423: Adaptive Optics for Astronomy (1994), p. 115.

Salinari, P.

O. Lardiere, P. Salinari, L. Jolissaint, M. Carbillet, A. Riccardi, and S. Esposito, "Adaptive optics and site requirements for the search of earth-like planets with ELTs," in Proc. SPIE 5382, 550-559 (2004).
[Crossref]

Sasiela, R. J.

R. J. Sasiela, "Wave-front correction by one or more synthetic beacons," J. Opt. Soc. Am. A 11, 389-393 (1994).
[Crossref]

Sivaramakrishnan, A.

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
[Crossref]

Soummer, R.

C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. 612, L85-L88 (2004).
[Crossref]

Stetson, P.

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

Stoesz, J. A.

L. Jolissaint, J.-P. Véran, and J. A. Stoesz, "Wide field adaptive optics upper limit performances," in Proc. SPIE 5382, 468-477 (2004).
[Crossref]

J. A. Stoesz, D. Andersen, and L. Jolissaint, "GLAO feasibility study report for Gemini telescopes." Tech. Rep. GLAO-PRD-001 (Herzberg Institute of Astrophysics, National Research Council of Canada, 2005).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium, (Dover, 1961), translated by R. A. Silverman.

Tokovinin, A.

A. Tokovinin, "Seeing improvement with ground-layer adaptive optics," Publ. Astron. Soc. Pac. 116, 941-951 (2004).
[Crossref]

Travouillon, T.

T. Travouillon, J. S. Lawrence, and L. Jolissaint, "Ground layer adaptive optics performance in Antarctica," in Proc. SPIE 5497, 934-942 (2004).
[Crossref]

Véran, J.-P.

L. Jolissaint, J.-P. Véran, and J. A. Stoesz, "Wide field adaptive optics upper limit performances," in Proc. SPIE 5382, 468-477 (2004).
[Crossref]

F. Rigaut, J.-P. Véran, and O. Lai, "An analytic model for Shack-Hartmann based adaptive optics systems," in Proc. SPIE 3353, 1038-1048 (1998).
[Crossref]

J.-P. Véran, F. Rigaut, H. Maître, and D. Rouan, "Estimation of the adaptive optics long-exposure point spread function using control loop data," J. Opt. Soc. Am. A 14, 2957-3069 (1997).
[Crossref]

J.-P. Véran, "Estimation de la réponse impulsionelle et restauration d'image en optique adaptative," Ph.D. thesis (Ecole Nationale Supérieure des Télécommunications, Paris, 1997).

L. Jolissaint and J.-P. Véran, "Fast computation and morphologic interpretation of the adaptive optics point spread function," in Beyond Conventional Adaptive Optics, E.Vernet, R.Ragazzoni, S.Esposito, and N.Hubin, eds., Vol. 58 of European Southern Observatory Conference and Workshop Proceedings, 201-208 (ESO, 2001).

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

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Astrophys. J. (1)

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

Proc. SPIE (8)

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[Crossref]

A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," in Proc. SPIE 4860, 161-176 (2003).
[Crossref]

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[Crossref]

M. Le Louarn, "Parallel simulation tools for AO on ELTs," in Proc. SPIE 5490, 705-712 (2004).
[Crossref]

L. Jolissaint, J.-P. Véran, and J. A. Stoesz, "Wide field adaptive optics upper limit performances," in Proc. SPIE 5382, 468-477 (2004).
[Crossref]

L. Jolissaint and J.-F. Lavigne, "An analytic model for the study of the impact of mirror segmentation on AO performance, and application to a 30 m segmented telescope," in Proc. SPIE 5497, 1038-1048 (2004).

O. Lardiere, P. Salinari, L. Jolissaint, M. Carbillet, A. Riccardi, and S. Esposito, "Adaptive optics and site requirements for the search of earth-like planets with ELTs," in Proc. SPIE 5382, 550-559 (2004).
[Crossref]

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L. Jolissaint and J.-P. Véran, "Fast computation and morphologic interpretation of the adaptive optics point spread function," in Beyond Conventional Adaptive Optics, E.Vernet, R.Ragazzoni, S.Esposito, and N.Hubin, eds., Vol. 58 of European Southern Observatory Conference and Workshop Proceedings, 201-208 (ESO, 2001).

B. Gillespie, R. Carlberg, T. Davidge, J. J. Kavelaars, D. Crabtree, M. Hudson, B. Oke, C. Morbey, L. Abraham, L. Jolissaint, J.-P. Véran, K. Fulbright, P. Stetson, and D. Bohlender, "The science case and instrumentation for extra large telescopes," Report for the Extra Large Telescope Canadian Project, Tech. Rep. (Herzberg Institute of Astrophysics, National Research Council of Canada, 2001).

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[Crossref]

V. I. Tatarski, Wave Propagation in a Turbulent Medium, (Dover, 1961), translated by R. A. Silverman.

E. Weisstein, "Jensen's Inequality," http://mathworld.wolfram.com/JensensInequality.html.

J.-P. Véran, "Estimation de la réponse impulsionelle et restauration d'image en optique adaptative," Ph.D. thesis (Ecole Nationale Supérieure des Télécommunications, Paris, 1997).

C. Verinaud, "On the nature of the measurements provided by a pyramid wave-front sensor," Opt. Commun.233, (2004).

G. Rousset, "Wavefront sensing," in NATO ASIC Proc. 423: Adaptive Optics for Astronomy (1994), p. 115.

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Figures (13)

Fig. 1
Fig. 1

Aniso–servo power spectrum ( 1 8 power-law scaling) within the LF domain; see parameters in Table 1.

Fig. 2
Fig. 2

Aliasing power spectrum ( 1 8 power-law scaling) within the LF domain; see parameters in Table 1.

Fig. 3
Fig. 3

WFS noise power spectrum ( 1 8 power-law scaling) within the LF domain; see parameters in Table 1.

Fig. 4
Fig. 4

Total phase power spectrum ( 1 8 power-law scaling). Spatial frequency domain has been extended to twice the LF boundary to show the fitting error power spectrum. Note the square boundary between the low (corrected) and the high spatial frequency domains. See parameters in Table 1.

Fig. 5
Fig. 5

f x -cut across the total phase power spectrum shown in Fig. 4. Dashed curve shows the turbulent, uncorrected phase power spectrum.

Fig. 6
Fig. 6

Fitting error and LF phase structure functions. Horizontal dashed–dotted lines represent twice the fitting error and LF variances. See parameters in Table 1.

Fig. 7
Fig. 7

Long exposure OTFs for the telescope, the telescope with an AO corrected phase (associated with the structure functions shown in the Fig. 6), and the telescope with an uncorrected turbulent phase. See parameters in Table 1.

Fig. 8
Fig. 8

Long exposure PSF profiles associated with the OTFs shown in Fig. 7.

Fig. 9
Fig. 9

Strehl ratio versus WFS sampling frequency. NGS magnitude from 10 (top curve) to 13 (bottom). See other parameters in Table 1.

Fig. 10
Fig. 10

Strehl ratio versus DM actuator density. NGS magnitudes from 10 (top curve) to 13 (bottom). See other parameters in Table 1.

Fig. 11
Fig. 11

50% encircled energy diameter versus NGS off-axis angle. NGS magnitude from 10 (bottom curve) to 13. Horizontal dashed lines: top, seeing-limited case; bottom, diffraction-limited case.

Fig. 12
Fig. 12

Monte Carlo end-to-end extreme AO simulation: instantaneous PSF (log scale). Telescope diameter 7.9 m , wavelength 1.65 μ m , 44 actuators across the DM, seeing 0.95 , outer scale 30 m , Strehl ratio 95%. WFS aliasing has been optically filtered (courtesy of B. Macintosh and L. Poyneer, poyneer@llnl.gov).

Fig. 13
Fig. 13

PAOLA extreme AO simulation; same conditions as Fig. 12. The PSF has been calculated from an AO-corrected phase screen that was built using a phase power spectrum calculated with the code PAOLA (courtesy of R. Soummer, soummer @stsci.edu).

Tables (1)

Tables Icon

Table 1 Atmosphere, Telescope, and Adaptive Optics System Parameters

Equations (51)

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φ ( r , t ) = φ ¯ ( r ) + δ φ ( r , t ) .
OTF sys ( f ) = 1 S p R 2 exp { i [ δ φ ( r , t ) δ φ ( r + ρ , t ) ] } t × exp { i [ φ ¯ ( r ) φ ¯ ( r + ρ ) ] } P ( r ) P ( r + ρ ) d 2 r ,
OTF sys ( f ) = 1 S p R 2 exp [ 1 2 F φ 2 ( r , ρ , t ) t ] × exp { i [ φ ¯ ( r ) φ ¯ ( r + ρ ) ] } P ( r ) P ( r + ρ ) d 2 r ,
D φ ( ρ ) F φ 2 ( ρ , t ) t ,
D φ ( ρ ) = 6.883877 ( ρ r 0 ) 5 3 ,
OTF sys ( f ) = exp [ D φ ( λ f ) 2 ] 1 S p R 2 exp { i [ φ ¯ ( r ) φ ¯ ( r + λ f ) ] } P ( r ) P ( r + λ f ) d 2 r = OTF atm ( f ) OTF tsc ( f ) ,
OTF sys ( f ) exp [ D φ ( λ f ) 2 ] 1 S p R 2 exp { i [ φ ¯ ( r ) φ ¯ ( r + λ f ) ] } P ( r ) P ( r + λ f ) d 2 r = OTF ado ( f ) OTF tsc ( f ) .
D φ ( ρ ) = 2 R 2 [ 1 cos ( 2 π f ρ ) ] Ξ { δ φ } ( f ) d 2 f ,
δ φ r ( r , θ , t ) = δ φ a ( r , θ , t ) δ φ a ˜ ( r , 0 , t ) ,
m ( r , t ) = M { 1 Δ t Δ t 2 Δ t 2 δ φ a ( r , 0 , t + t t l ) d t } + ν ( r , t ) = M { δ φ a ¯ ( r , 0 , t ) } + ν { r , t } ,
δ φ a ˜ ( r , 0 , t ) = R { M [ δ φ a ¯ ( r , 0 , t ) ] } + R { ν ( r , t ) } .
δ φ ( r , t ) = R 2 δ φ ̂ ( f , t ) exp [ 2 π i ( x f x + y f y ) ] d 2 f .
δ φ = δ φ LF + δ φ HF .
δ φ r ( r , θ , t ) = δ φ LF , a ( r , θ , t ) + δ φ HF , a ( r , θ , t ) R { M [ ( δ φ LF , a + δ φ HF , a ) ¯ ( r , 0 , t ) ] } R { ν ( r , t ) } .
R ( m LF ) = R { M [ δ φ LF ] } = δ φ LF .
Ξ ( δ φ r ) ( f ) = δ φ ̂ r ( f , θ , t ) 2 = δ φ ̂ HF , a ( f , θ , t ) 2 + δ φ ̂ LF , θ ( f , θ , t ) 2 + δ φ ̂ LF , s ( f , 0 , t ) 2 + δ φ ̂ LF , HF ( f , 0 , t ) 2 + δ φ ̂ LF , n ( f , t ) 2 + CS .
CS = δ φ ̂ LF , θ ( f , θ , t ) δ φ ̂ LF , s * ( f , 0 , t ) + δ φ ̂ LF , θ * ( f , θ , t ) δ φ ̂ LF , s ( f , 0 , t ) ,
Ξ K { δ φ a } ( f ) = 0.0229 r 0 5 3 f 11 3 ,
Ξ HA { δ φ a } ( f ) = 0.0229 r 0 5 3 ( f 2 + 1 L 0 2 ) 11 6 [ 1 + 3.43 f l 0 + 0.538 ( f l 0 ) 7 6 ] exp ( 3.625 f 2 l 0 2 ) .
F p ( f ) = 1 [ 2 J 1 ( π D f ) π D f ] 2 ,
Ξ { δ φ HF , a } ( f ) = μ HF ( f ) F p ( f ) M Ξ { δ φ a } ( f ) ,
δ φ a ( r , θ , t ) = n = 1 N δ φ a [ h n ] ( r + h n θ , t ) .
δ φ ̂ LF , θ ( f , θ , t ) = n = 1 N δ φ ̂ LF , a [ h n ] ( f , t ) [ exp ( 2 π i h n f θ ) 1 ] ,
Ξ { δ φ LF , θ } ( f , θ ) = 2 μ LF ( f ) F p ( f ) n = 1 N Ξ M { δ φ a [ h n ] } ( f ) [ 1 cos ( 2 π h n f θ ) ] ,
δ φ a ( r , t + τ ) = n = 1 N δ φ a [ h n ] ( r v [ h n ] τ , t ) .
δ φ ̂ LF , s ( f , t ) = δ φ ̂ LF , a ( f , t ) F { δ φ LF , a ¯ ( r , t ) } .
F { δ φ LF , a ¯ ( r , t ) } = n = 1 N δ φ ̂ LF , a [ h n ] ( f , t ) Δ t 2 Δ t 2 exp [ 2 π i ( t t l ) f v ( h n ) ] d t .
F { δ φ LF , a ¯ ( r , t ) } = n = 1 N δ φ ̂ LF , a [ h n ] ( f , t ) sinc [ Δ t f v ( h n ) ] exp [ 2 π i t l f v ( h n ) ] .
δ φ ̂ LF , s ( f , t ) = n = 1 N δ φ ̂ LF , a [ h n ] ( f , t ) { 1 sinc [ Δ t f v ( h n ) ] exp [ 2 π i t l f v ( h n ) ] } ,
Ξ { δ φ LF , s } ( f ) = μ LF ( f ) F p ( f ) n = 1 N Ξ M { δ φ a [ h n ] } ( f ) × { 1 2 cos [ 2 π t l f v ( h n ) ] sinc [ Δ t f v ( h n ) ] + sinc 2 [ Δ t f v ( h n ) ] } .
Ξ { δ φ θ , s } ( f ) = δ φ ̂ LF , a ( f , θ , t ) 2 + δ φ ¯ ̂ LF , a ( f , 0 , t ) 2 2 Re { δ φ ̂ LF , a ( f , θ , t ) δ φ ¯ ̂ LF , a * ( f , 0 , t ) } .
Ξ { δ φ θ , s } ( f ) = μ LF ( f ) F p ( f ) n = 1 N Ξ M { δ φ a [ h n ] } ( f ) × ( 1 2 cos { 2 π f [ h n θ t l v ( h n ) ] } sinc [ Δ t f v ( h n ) ] + sinc 2 [ Δ t f v ( h n ) ] ) .
m x ( r ) = M { δ φ ( r , t ) } x = { δ φ x ( r , t ) 1 Λ 2 [ Π ( x Λ ) Π ( y Λ ) ] } III ( r Λ ) .
m ̂ x ( f , t ) = Λ 2 2 π i [ f x δ φ ̂ ( f , t ) sinc ( Λ f x ) sinc ( Λ f y ) ] III ( Λ f ) ,
M ̂ Λ 2 2 π i [ f sinc ( Λ f x ) sinc ( Λ f y ) ] III ( Λ f ) .
ϵ 2 = { m x ( r , t ) M [ δ φ ˜ a ( r , 0 , t ) ] x } 2 + { m y ( r , t ) M [ δ φ ˜ a ( r , 0 , t ) ] y } 2 .
δ φ ̃ ̂ a ( f , t ) = m ̂ x ( f , t ) f x + m ̂ y ( f , t ) f y 2 π i f 2 sinc ( Λ f x ) sinc ( Λ f y ) = R ̂ [ m ̂ x ( r , t ) ; m ̂ y ( r , t ) ] ,
R ̂ f [ 2 π i f 2 sinc ( Λ f x ) sinc ( Λ f y ) ] .
δ φ ̂ LF , HF ( f , t ) = n = 1 N F { R M [ δ φ HF , a [ h n ] ( r , t ) ] } sinc [ Δ t f v ( h n ) ] exp [ 2 π i t l f v ( h n ) ] ,
F { R M [ δ φ HF , a [ h n ] ] } = [ 2 π i f 2 sinc ( Λ f x ) sinc ( Λ f y ) ] 1 ( Λ 2 { [ f x δ φ ̂ HF , a sinc ( Λ f x ) sinc ( Λ f y ) ] III ( Λ f ) } f x + Λ 2 { [ f y δ φ ̂ HF , a sinc ( Λ f x ) sinc ( Λ f y ) ] III ( Λ f ) } f y ) .
III ( Λ f ) = 1 Λ 2 k , l = + δ ( f x k Λ , f y l Λ )
sinc [ Λ f ( x , y ) ( k , l ) ] sinc ( Λ f ( x , y ) ) = ( 1 ) ( k , l ) Λ f ( x , y ) Λ f ( x , y ) ( k , l ) ,
δ φ ̂ LF , HF ( f , t ) = μ LF ( f ) f x f y f 2 n = 1 N { sinc [ Δ t f v ( h n ) ] exp [ 2 π i t l f v ( h n ) ] k , l = k + l > 0 + [ ( 1 ) k + 1 ( f x f y l Λ + f y f x k Λ ) δ φ ̂ HF , a [ h n ] ( f x k Λ , f y l Λ , t ) ] } ,
Ξ ( δ φ LF , HF ) ( f ) = μ LF ( f ) f x 2 f y 2 f 4 n = 1 N ( sinc 2 [ Δ t f v ( h n ) ] k , l = k + l > + { ( f x f y l Λ + f y f x k Λ ) 2 F p ( f x k Λ , f y l Λ ) Ξ M { δ φ a [ h n ] } ( f x k Λ , f y 1 Λ ) } ) ,
Ξ { δ φ LF , HF } ( 0 , f y ) = μ LF ( 0 , f y ) n = 1 N { sinc 2 [ Δ t f y v y ( h n ) ] l = l 0 + F p ( 0 , f y l Λ ) Ξ M { δ φ a [ h n ] } ( 0 , f y l Λ ) } ,
Ξ { δ φ LF , HF } ( f x , 0 ) = μ LF ( f x , 0 ) n = 1 N { sinc 2 [ Δ t f x v x ( h n ) ] k = k 0 + F p ( f x k Λ , 0 ) Ξ M { δ φ a [ h n ] } ( f x k Λ , 0 ) } ,
Ξ ( δ φ LF , HF ) ( 0 , 0 ) = μ LF ( 0 , 0 ) n = 1 N k = k 0 + F p ( k Λ , 0 ) Ξ M { δ φ a [ h n ] } ( k Λ , 0 ) ,
= μ LF ( 0 , 0 ) n = 1 N l = l 0 + F p ( 0 , l Λ ) Ξ M { δ φ a [ h n ] } ( 0 , l Λ ) .
δ φ ̂ LF , n ( f , t ) = R ̂ n ̂ s ( f , t ) = f x n ̂ s , x ( f , t ) + f y n ̂ s , y ( f , t ) 2 π i f 2 sinc ( Λ f x ) sinc ( Λ f y ) ,
Ξ { δ φ LF , n } ( f ) = μ LF ( f ) N ( f ) 4 π 2 f 2 sinc 2 ( Λ f x ) sinc 2 ( Λ f y ) ,
σ n 2 = f x , f y < f WFS N ( f ) d 2 f = N Λ 2 .

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