Abstract

Multiconjugate adaptive optics (MCAO) is a technique for correcting turbulence-induced phase distortions in three dimensions instead of two, thereby greatly expanding the corrected field of view of an adaptive optics system. This is accomplished with use of multiple deformable mirrors conjugate to distinct ranges in the atmosphere, with actuator commands computed from wave-front sensor (WFS) measurements from multiple guide stars. Laser guide stars (LGSs) must be used (at least for the forseeable future) to achieve a useful degree of sky coverage in an astronomical MCAO system. Much as a single LGS cannot be used to measure overall wave-front tilt, a constellation of multiple LGSs at a common range cannot detect tilt anisoplanatism. This error alone will significantly degrade the performance of a MCAO system based on a single tilt-only natural guide star (NGS) and multiple tilt-removed LGSs at a common altitude. We present a heuristic, low-order model for the principal source of tilt anisoplanatism that suggests four possible approaches to eliminating this defect in LGS MCAO: (i) tip/tilt measurements from multiple NGS, (ii) a solution to the LGS tilt uncertainty problem, (iii) additional higher-order WFS measurements from a single NGS, or (iv) higher-order WFS measurements from both sodium and Rayleigh LGSs at different ranges. Sample numerical results for one particular MCAO system configuration indicate that approach (ii), if feasible, would provide the highest degree of tilt anisoplanatism compensation. Approaches (i) and (iv) also provide very useful levels of performance and do not require unrealistically low levels of WFS measurement noise. For a representative set of parameters for an 8-m telescope, the additional laser power required for approach (iv) is on the order of 2 W per Rayleigh LGS.

© 2001 Optical Society of America

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References

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  1. J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in ESO Conference on Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), Vol. 2, pp. 693–703.
  2. B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783–805 (1994).
    [CrossRef]
  3. E. Viard, N. N. Hubin, M. Le Louarn, A. A. Tokovinin, “Concept and performance of multiple laser guide stars for 8m class telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 94–105 (2000).
    [CrossRef]
  4. R. Flicker, B. L. Ellerbroek, F. J. Rigaut, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8m telescope,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000).
    [CrossRef]
  5. F. J. Rigaut, B. L. Ellerbroek, R. Flicker, “Principles, limitations, and performance of multi-conjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1022–1031 (2000).
    [CrossRef]
  6. R. Ragazzoni, “Adaptive optics for 100m class telescopes: New challenges require new solutions,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1076–1087 (2000).
    [CrossRef]
  7. B. L. Ellerbroek, F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
    [CrossRef]
  8. D. L. Fried, “Artificial-guide-star tilt-anisoplanatism: its magnitude and (limited) amelioration,” in Adaptive Optics, M. Cullum, ed., Vol. 23 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 363–369.
  9. J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).
  10. B. L. Ellerbroek, D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North telescope,” Proc. Astron. Soc. Pac. 110, 165–185 (1998).
    [CrossRef]
  11. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]

1998 (1)

B. L. Ellerbroek, D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North telescope,” Proc. Astron. Soc. Pac. 110, 165–185 (1998).
[CrossRef]

1994 (1)

1976 (1)

Agabi, A.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

Avila, R.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

Azouit, M.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

Beckers, J. M.

J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in ESO Conference on Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), Vol. 2, pp. 693–703.

Conan, R.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

Ellerbroek, B. L.

B. L. Ellerbroek, D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North telescope,” Proc. Astron. Soc. Pac. 110, 165–185 (1998).
[CrossRef]

B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783–805 (1994).
[CrossRef]

F. J. Rigaut, B. L. Ellerbroek, R. Flicker, “Principles, limitations, and performance of multi-conjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1022–1031 (2000).
[CrossRef]

B. L. Ellerbroek, F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
[CrossRef]

R. Flicker, B. L. Ellerbroek, F. J. Rigaut, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8m telescope,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000).
[CrossRef]

Flicker, R.

R. Flicker, B. L. Ellerbroek, F. J. Rigaut, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8m telescope,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000).
[CrossRef]

F. J. Rigaut, B. L. Ellerbroek, R. Flicker, “Principles, limitations, and performance of multi-conjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1022–1031 (2000).
[CrossRef]

Fried, D. L.

D. L. Fried, “Artificial-guide-star tilt-anisoplanatism: its magnitude and (limited) amelioration,” in Adaptive Optics, M. Cullum, ed., Vol. 23 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 363–369.

Hubin, N. N.

E. Viard, N. N. Hubin, M. Le Louarn, A. A. Tokovinin, “Concept and performance of multiple laser guide stars for 8m class telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 94–105 (2000).
[CrossRef]

Le Louarn, M.

E. Viard, N. N. Hubin, M. Le Louarn, A. A. Tokovinin, “Concept and performance of multiple laser guide stars for 8m class telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 94–105 (2000).
[CrossRef]

Martin, F.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

Masciadri, E.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

Noll, R. J.

Ragazzoni, R.

R. Ragazzoni, “Adaptive optics for 100m class telescopes: New challenges require new solutions,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1076–1087 (2000).
[CrossRef]

Rigaut, F. J.

R. Flicker, B. L. Ellerbroek, F. J. Rigaut, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8m telescope,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000).
[CrossRef]

B. L. Ellerbroek, F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
[CrossRef]

F. J. Rigaut, B. L. Ellerbroek, R. Flicker, “Principles, limitations, and performance of multi-conjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1022–1031 (2000).
[CrossRef]

Sanchez, L.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

Tokovinin, A. A.

E. Viard, N. N. Hubin, M. Le Louarn, A. A. Tokovinin, “Concept and performance of multiple laser guide stars for 8m class telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 94–105 (2000).
[CrossRef]

Tyler, D. W.

B. L. Ellerbroek, D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North telescope,” Proc. Astron. Soc. Pac. 110, 165–185 (1998).
[CrossRef]

Vernin, J.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

Viard, E.

E. Viard, N. N. Hubin, M. Le Louarn, A. A. Tokovinin, “Concept and performance of multiple laser guide stars for 8m class telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 94–105 (2000).
[CrossRef]

Ziad, A.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

J. Opt. Soc. Am. (1)

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

Proc. Astron. Soc. Pac. (1)

B. L. Ellerbroek, D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North telescope,” Proc. Astron. Soc. Pac. 110, 165–185 (1998).
[CrossRef]

Other (8)

J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in ESO Conference on Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), Vol. 2, pp. 693–703.

E. Viard, N. N. Hubin, M. Le Louarn, A. A. Tokovinin, “Concept and performance of multiple laser guide stars for 8m class telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 94–105 (2000).
[CrossRef]

R. Flicker, B. L. Ellerbroek, F. J. Rigaut, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8m telescope,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000).
[CrossRef]

F. J. Rigaut, B. L. Ellerbroek, R. Flicker, “Principles, limitations, and performance of multi-conjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1022–1031 (2000).
[CrossRef]

R. Ragazzoni, “Adaptive optics for 100m class telescopes: New challenges require new solutions,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1076–1087 (2000).
[CrossRef]

B. L. Ellerbroek, F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
[CrossRef]

D. L. Fried, “Artificial-guide-star tilt-anisoplanatism: its magnitude and (limited) amelioration,” in Adaptive Optics, M. Cullum, ed., Vol. 23 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 363–369.

J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, A. Ziad, “1998 Gemini site testing campaign: Cerro Pachon and Cerro Tololo,” (Gemini Observatory, Hilo, Hawaii, 2000).

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Figures (4)

Fig. 1
Fig. 1

Altitude weighting of atmospheric focus aberrations for a differential focus measurement between a pair of guide stars at different altitudes. Owing to the cone effect, the first altitude moment of the focus component of atmospheric turbulence, μ1(b), may be estimated by differencing the focus terms of the wave-front measurements from a pair of guide stars at two different ranges. This figure plots the value of the differential focus measurement b(θ, H1)-b(θ, H2) as a function of the altitude h of a single-layer focus aberration of unit amplitude. The lower solid curve is for the guide-star ranges H1=90 km and H2=, and the upper solid curve corresponds to the case H1=15 km, H2=90 km. The dashed curves describe linear approximations 2(H1-1-H2-1)h. If the difference between this linear approximation and the actual value of b(θ, H1)-b(θ, H2) is small, the focus moment μ1(b) may be estimated as [b(θ, H2)-b(θ, H1)][2(H1-1-H2-1)]-1 with acceptable accuracy, independently of the vertical distribution of the atmospheric turbulence layers. If the slope of the linear approximation is large, this estimate will be more robust with respect to WFS measurement noise and the spatial aliasing of higher-order wave-front modes.

Fig. 2
Fig. 2

Strehl versus NGS WFS noise for a MCAO system with five sodium LGS and four tip/tilt NGS WFS. These results correspond to the MCAO system parameters, the field-of-view, and the atmospheric turbulence profile of row 4 of Table 2. WFS measurement noise is expressed as a one-axis, one-sigma value.

Fig. 3
Fig. 3

Strehl versus NGS WFS measurement noise for a system with five sodium LGS and one high-order NGS WFS. This figure is analogous to Fig. 2, except that the MCAO system parameters correspond to line 8 of Table 2. The order of the NGS WFS is 4×4 subapertures.

Fig. 4
Fig. 4

Strehl versus Rayleigh WFS measurement noise for a system with five sodium LGSs and five Raleigh LGSs. This figure is analogus to Fig. 3, except that the MCAO system parameters correspond to line 11 of Table 2. The order of the Rayleigh LGS WFSs is 4×4 subapertures, and the range of the Rayleigh beacons is 15 km.

Tables (2)

Tables Icon

Table 1 Cerro Pachon Cn2(h) Profile for Sample Calculationsa

Tables Icon

Table 2 Sample Results for MCAO Systems with a 68.72 arc sec FoVa

Equations (34)

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

si(x)=aix+bix2.
ϕ(x; θ, H)=hi<Hsiθhi+1-hiHx=a(θ, H)x+b(θ, H)x2+c(θ, H).
a(θ, H)=hi<H1-hiH(ai+2θhibi),
b(θ, H)=hi<H1-hiH2bi,
a(θ, )=μ0(a)+2θμ1(b),
b(θ, )=μ0(b),
μn(x)=ihinxi.
μ0(a)=[a(θ, )+a(-θ, )]/2,
μ1(b)=[a(θ, )-a(-θ, )]/(4θ).
b(θ, H2)-b(θ, H1)=2(H1-1-H2-1)μ1(b)+ifibi,
fi=hi2(H2-2-H1-2)ifhiH11-2hiH1-1+hi2H2-2ifH1hiH2.2hi(H2-1-H1-1)otherwise
σθ=0.57(λ/r0)SNR,
σθ=θB/SNR,
Npde=Npτt(τa)2τrη(ζ0δz)exp[-(z+zo)/z0]As/(4πz2)
Np=Pnλhc.
Npde=130.
ϕ1(x, y)=i=1aiZi(x/R, y/R),
ϕ1(x, y)=i=1aiZi[x/R+(hθ)/R, y/R],
ϕ2(x, y)-ϕ1(x, y)=i=1ai{Zi[x/R+(hθ)/R, y/R]-Zi(x/R, y/R)}.
Z4(x/R, y/R)=32xR2+2yR2-1,
a4{Z4[x/R+(hθ)/R, y/R]-Z4(x/R, y/R)}
=a443hθRxR+c,
Z5(x/R, y/R)=26xRyR,
a5{Z5[x/R+(hθ)/R, y/R]-Z5(x/R, y/R)]
=a526hθRyR,
Z6(x/R, y/R)=6xR2-yR2,
a6{Z6[x/R+(hθ)/R, y/R]-Z6(x/R, y/R)}
=a66hθRxR+c.
σ22=hθR2[12a42+6a52+6a62],
σ22=0.55(D/r0)5/3hθR2,
σ32=1.32(D/r0)5/3hθR4,
σ32σ22=1.55hθR2,
hθ0.65R.
hθ¯=0.23R.

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