Abstract

Off-axis observations made with adaptive optics are severely limited by anisoplanatism errors. However, conjugating the deformable mirror to an optimal altitude can reduce these errors; it is then necessary to control, through extrapolation, actuators that are not measured by the wave-front sensor (unilluminated actuators). In this study various common extrapolation schemes are investigated, and an optimal method that achieves a significantly better performance is proposed. This extrapolation method involves a simple matrix multiplication and will be implemented in ALTAIR, the Gemini North Telescope adaptive optics system located on Mauna Kea, Hawaii. With this optimal method, the relative H-band Strehl reduction due to extrapolation errors is only 5%, 16%, and 30% when the angular distance between the guide source and the science target is 20, 40 and 60 arc sec, respectively. For a site such as Mauna Kea, these errors are largely outweighed by the increase in the size of the isoplanatic field.

© 2000 Optical Society of America

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References

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  1. R. Racine, B. Ellerbroek, “Profiles of night-time turbulence above Mauna Kea and isoplanatism extension in adaptive optics,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 248–257 (1995).
    [CrossRef]
  2. G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
    [CrossRef]
  3. B. R. Oppenheimer, D. Palmer, R. Dekany, A. Sivaramakrishnan, M. Ealey, T. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–579 (1997).
    [CrossRef]
  4. W. Wild, “Innovative wavefront estimators for zonal adaptive optics. II,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 1164–1173 (1998).
    [CrossRef]
  5. A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. 26, 257–277 (1947).
  6. G. Herriot, National Research Council of Canada, Herzberg Institute of Astrophysics, Victoria, British Columbia V8X 4M6, Canada (personal communication, 1998).
  7. E. Gendron, “Optimisation de la commande modale en optique adaptive: application à l’astronomie,” Ph.D. dissertation (Université de Paris VII–Denis Diderot, Paris, 1995).

1947

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. 26, 257–277 (1947).

Dekany, R.

B. R. Oppenheimer, D. Palmer, R. Dekany, A. Sivaramakrishnan, M. Ealey, T. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–579 (1997).
[CrossRef]

Ealey, M.

B. R. Oppenheimer, D. Palmer, R. Dekany, A. Sivaramakrishnan, M. Ealey, T. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–579 (1997).
[CrossRef]

Ellerbroek, B.

R. Racine, B. Ellerbroek, “Profiles of night-time turbulence above Mauna Kea and isoplanatism extension in adaptive optics,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 248–257 (1995).
[CrossRef]

Fletcher, M.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Gendron, E.

E. Gendron, “Optimisation de la commande modale en optique adaptive: application à l’astronomie,” Ph.D. dissertation (Université de Paris VII–Denis Diderot, Paris, 1995).

Herriot, G.

G. Herriot, National Research Council of Canada, Herzberg Institute of Astrophysics, Victoria, British Columbia V8X 4M6, Canada (personal communication, 1998).

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Maréchal, A.

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. 26, 257–277 (1947).

Morris, S.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Oppenheimer, B. R.

B. R. Oppenheimer, D. Palmer, R. Dekany, A. Sivaramakrishnan, M. Ealey, T. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–579 (1997).
[CrossRef]

Palmer, D.

B. R. Oppenheimer, D. Palmer, R. Dekany, A. Sivaramakrishnan, M. Ealey, T. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–579 (1997).
[CrossRef]

Price, T.

B. R. Oppenheimer, D. Palmer, R. Dekany, A. Sivaramakrishnan, M. Ealey, T. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–579 (1997).
[CrossRef]

Racine, R.

R. Racine, B. Ellerbroek, “Profiles of night-time turbulence above Mauna Kea and isoplanatism extension in adaptive optics,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 248–257 (1995).
[CrossRef]

Richardson, H.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Roberts, S.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Saddlemyer, L.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Singh, G.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Sivaramakrishnan, A.

B. R. Oppenheimer, D. Palmer, R. Dekany, A. Sivaramakrishnan, M. Ealey, T. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–579 (1997).
[CrossRef]

Véran, J.-P.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Wild, W.

W. Wild, “Innovative wavefront estimators for zonal adaptive optics. II,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 1164–1173 (1998).
[CrossRef]

Rev. Opt.

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. 26, 257–277 (1947).

Other

G. Herriot, National Research Council of Canada, Herzberg Institute of Astrophysics, Victoria, British Columbia V8X 4M6, Canada (personal communication, 1998).

E. Gendron, “Optimisation de la commande modale en optique adaptive: application à l’astronomie,” Ph.D. dissertation (Université de Paris VII–Denis Diderot, Paris, 1995).

R. Racine, B. Ellerbroek, “Profiles of night-time turbulence above Mauna Kea and isoplanatism extension in adaptive optics,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 248–257 (1995).
[CrossRef]

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, G. Singh, J.-P. Véran, H. Richardson, “Innovations in Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

B. R. Oppenheimer, D. Palmer, R. Dekany, A. Sivaramakrishnan, M. Ealey, T. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–579 (1997).
[CrossRef]

W. Wild, “Innovative wavefront estimators for zonal adaptive optics. II,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 1164–1173 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Effect of the altitude conjugation on the object (ST) pupil and on the GS (reference star) pupil.

Fig. 2
Fig. 2

Diagram of a super DM. The dotted lines limit Pdm. The large and small solid circles limit Pgs. The large and small dashed circles limit Pob.

Fig. 3
Fig. 3

H-band long-exposure Strehl ratio of the ST for the early extrapolation approaches, as a function of the angle between the ST and the guide star. Asterisks, no extrapolation; diamonds, nearest-neighbor slaving; triangles, Zernike extrapolation (Z2-Z3); plus signs, Zernike extrapolation (Z2-Z4); squares, Zernike extrapolation (Z2-Z6); multiplication signs, Zernike extrapolation (Z2-Z8). Solid curve, conjugation to the ground.

Fig. 4
Fig. 4

H-band long-exposure Strehl ratio of the ST for the optimal linear extrapolation approaches, as a function of the angle between the ST and the guide star. Asterisks, no extrapolation; diamonds, nearest-neighbor slaving; triangles, optimal linear extrapolation. Solid curve, conjugation to the ground.

Equations (13)

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

Pgs(r)=1insidePgs0outsidePgs.
(ϕ1|ϕ2)dm=1Sdm Pdm(r)ϕ1(r)ϕ2(r)dr,
(ϕ1|ϕ2)dm=a1Δdma2t.
ϕa(r, t)=φa(r, t)-1Sgs Pgs(r)φa(r, t)dr.
ϕm(r, t)=i=1Ndm(mdm)i(t)Ii(r),
ϕ(r, t)=ϕa(r, t)-ϕm(r, t).
mgs(t)=Δgs-1(ϕa|I1)(t)(ϕa|INgs)(t).
mdm(t)=Δdm-1(ϕa|I1)(t)(ϕa|INdm)(t).
K(u, t)|F{Pob(r)exp [iϕ(r, t)]}|2.
σout2=(mout-m^out)tΔout(mout-m^out).
ϕ(r, t)=ϕa(r+hα, t)-ϕm(r, t).
σout2=(mout-Emgs)tΔout(mout-Emgs)t.
E=moutmgstmgsmgst-1.

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