Modeling low order aberrations in laser guide star adaptive optics systems

Richard M. Clare; Marcos A. van Dam; Antonin H. Bouchez

doi:10.1364/OE.15.004711

Modeling low order aberrations in laser guide star adaptive optics systems

Richard M. Clare, Marcos A. van Dam, and Antonin H. Bouchez

Optics Express
Vol. 15,
Issue 8,
pp. 4711-4725
(2007)
•https://doi.org/10.1364/OE.15.004711

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Richard M. Clare, Marcos A. van Dam, and Antonin H. Bouchez, "Modeling low order aberrations in laser guide star adaptive optics systems," Opt. Express 15, 4711-4725 (2007)

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Related Topics
Table of Contents Category
- Adaptive Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Active or adaptive optics (010.1080)
- Wave-front sensing (010.7350)

About this Article
History
- Original Manuscript: January 24, 2007
- Revised Manuscript: March 19, 2007
- Manuscript Accepted: March 29, 2007
- Published: April 3, 2007

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Open Access

Abstract

When using a laser guide star (LGS) adaptive optics (AO) system, quasi-static aberrations are observed between the measured wavefronts from the LGS wavefront sensor (WFS) and the natural guide star (NGS) WFS. These LGS aberrations, which can be as much as 1200 nm RMS on the Keck II LGS AO system, arise due to the finite height and structure of the sodium layer. The LGS aberrations vary significantly between nights due to the difference in sodium structure. In this paper, we successfully model these LGS aberrations for the Keck II LGS AO system. We use this model to characterize the LGS aberrations as a function of pupil angle, elevation, sodium structure, uplink tip/tilt error, detector field of view, the number of detector pixels, and seeing. We also employ the model to estimate the LGS aberrations for the Palomar LGS AO system, the planned Keck I and the Thirty Meter Telescope (TMT) LGS AO systems. The LGS aberrations increase with increasing telescope diameter, but are reduced by central projection of the laser compared to side projection.

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References

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Year
|
Author
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Publication

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York1998).
C. E. Max, “Laser guide star operational issues,” in Laser Guide Star Adaptive Optics for Astronomy, N. Ageorges and C. Dainty, eds. (Kluwer, Dordrecht, 1997), 89–106.
D. L. Fried and J. F. Belsher, “Analysis of fundamental limits to artificial-guide-star adaptive-optics-system performance for astronomical imaging,” J. Opt. Soc. Am A 11, 277–287 (1994).
[Crossref]
M. A. van Dam, A. H. Bouchez, D. Le Mignant, and P. L. Wizinowich “Quasi-static aberrations induced by laser guide stars in adaptive optics,” Opt. Express 14, 7535–7540 (2006).
[Crossref] [PubMed]
P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” PASP 118, 297–309 (2006).
[Crossref]
M. A. van Dam, A. H. Bouchez, D. Le Mignant, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, E. M. Johansson, R. Lafon, P. J. Stomski Jr., D. M. Summers, and P. L. Wizinowich, “The W. M. Keck Observatory laser guide star adaptive optics system: performance characterization,” PASP 118, 310–318 (2006).
[Crossref]
D. Summers, A. H. Bouchez, J. Chin, A. Contos, S. Hartman, E. Johansson, R. Lafon, D. Le Mignant, P. Stomski, M. A. van Dam, and P. L. Wizinowich, “Focus and pointing adjustments necessary for laser guide star adaptive optics at the W.M. Keck Observatory,” in Advancements in Adaptive Optics, D. Bonaccini Calia, B. L. Ellerbroek, and R. Ragazzoni, eds, Proc. SPIE 5490, 1117–1128 (2004).
[Crossref]
G. Herriot, P. Hickson, B. L. Ellerbroek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. M. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Vran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia eds., Proc. SPIE 6272, 62720Q (2006).
[Crossref]
R. M. Clare, B. L. Ellerbroek, G. Herriot, and J. P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[Crossref] [PubMed]
P. L. Wizinowich, J. Chin, E. Johansson, S. Kellner, R. Lafon, D. Le Mignant, C. Neyman, P. Stomski, D. Summers, R. Sumner, and M. van Dam,“Adaptive Optics Developements at Keck Observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia eds., Proc. SPIE 6272, 627209 (2006).
[Crossref]
R. Dekany, V. Velur, H. Petrie, A. Bouchez, M. Britton, A. Morrissett, R. Thicksten, M. Troy, C. Shelton, T. Troung, J. Roberts, G. Brack, T. Trinh, S. Bikkannavar, S. Guiwits, J. Angione, F. Shi, and E. Kibblewhite “Laser Guide Star Adaptive Optics on the 5.1 Meter Telescope at Palomar Observatory,” AMOS Technical Conference Proceedings (2005).
R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
[Crossref]
P. S. Argall, O. N. Vassiliev, R. J. Sica, and M. M. Mwangi,“Lidar Measurements Taken With a Large-Aperture Liquid Mirror. 2. Sodium Resonance-Fluorescence System,” Appl. Opt., 39, 2393–2400 (2000).
[Crossref]
A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 3651235–1242 (2006).
[Crossref]
L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. 42, 5807–5815 (2003).
[Crossref] [PubMed]
L. Gilles and B. L. Ellerbroek, “Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering,” Appl. Opt. 45, 6568–6576 (2006).
[Crossref] [PubMed]
J. Nelson and G. H. Sanders, “TMT status report,”in Ground-based and Airborne Telescopes, L. M. Stepp ed., Proc. SPIE 6267, 745–761 (2006).
J. W. Beletic, “Follow the yellow-orange rabbit: a CCD optimized for wavefront sensing a pulsed sodium laser guide star,” in Optical and Infrared Detectors for AstronomyJ. D. Garnett and J. W. Beletic; eds., Proc. SPIE 5499, 302–309 (2004)
[Crossref]

2006 (9)

M. A. van Dam, A. H. Bouchez, D. Le Mignant, and P. L. Wizinowich “Quasi-static aberrations induced by laser guide stars in adaptive optics,” Opt. Express 14, 7535–7540 (2006).
[Crossref] [PubMed]

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” PASP 118, 297–309 (2006).
[Crossref]

M. A. van Dam, A. H. Bouchez, D. Le Mignant, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, E. M. Johansson, R. Lafon, P. J. Stomski Jr., D. M. Summers, and P. L. Wizinowich, “The W. M. Keck Observatory laser guide star adaptive optics system: performance characterization,” PASP 118, 310–318 (2006).
[Crossref]

G. Herriot, P. Hickson, B. L. Ellerbroek, D. A. Andersen, T. Davidge, D. A. Erickson, I. P. Powell, R. M. Clare, L. Gilles, C. Boyer, M. Smith, L. Saddlemyer, and J.-P. Vran, “NFIRAOS: TMT narrow field near-infrared facility adaptive optics,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia eds., Proc. SPIE 6272, 62720Q (2006).
[Crossref]

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J. P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[Crossref] [PubMed]

P. L. Wizinowich, J. Chin, E. Johansson, S. Kellner, R. Lafon, D. Le Mignant, C. Neyman, P. Stomski, D. Summers, R. Sumner, and M. van Dam,“Adaptive Optics Developements at Keck Observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia eds., Proc. SPIE 6272, 627209 (2006).
[Crossref]

A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 3651235–1242 (2006).
[Crossref]

L. Gilles and B. L. Ellerbroek, “Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering,” Appl. Opt. 45, 6568–6576 (2006).
[Crossref] [PubMed]

J. Nelson and G. H. Sanders, “TMT status report,”in Ground-based and Airborne Telescopes, L. M. Stepp ed., Proc. SPIE 6267, 745–761 (2006).

2005 (1)

R. Dekany, V. Velur, H. Petrie, A. Bouchez, M. Britton, A. Morrissett, R. Thicksten, M. Troy, C. Shelton, T. Troung, J. Roberts, G. Brack, T. Trinh, S. Bikkannavar, S. Guiwits, J. Angione, F. Shi, and E. Kibblewhite “Laser Guide Star Adaptive Optics on the 5.1 Meter Telescope at Palomar Observatory,” AMOS Technical Conference Proceedings (2005).

2004 (2)

D. Summers, A. H. Bouchez, J. Chin, A. Contos, S. Hartman, E. Johansson, R. Lafon, D. Le Mignant, P. Stomski, M. A. van Dam, and P. L. Wizinowich, “Focus and pointing adjustments necessary for laser guide star adaptive optics at the W.M. Keck Observatory,” in Advancements in Adaptive Optics, D. Bonaccini Calia, B. L. Ellerbroek, and R. Ragazzoni, eds, Proc. SPIE 5490, 1117–1128 (2004).
[Crossref]

J. W. Beletic, “Follow the yellow-orange rabbit: a CCD optimized for wavefront sensing a pulsed sodium laser guide star,” in Optical and Infrared Detectors for AstronomyJ. D. Garnett and J. W. Beletic; eds., Proc. SPIE 5499, 302–309 (2004)
[Crossref]

2003 (1)

L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. 42, 5807–5815 (2003).
[Crossref] [PubMed]

2000 (1)

P. S. Argall, O. N. Vassiliev, R. J. Sica, and M. M. Mwangi,“Lidar Measurements Taken With a Large-Aperture Liquid Mirror. 2. Sodium Resonance-Fluorescence System,” Appl. Opt., 39, 2393–2400 (2000).
[Crossref]

1994 (1)

D. L. Fried and J. F. Belsher, “Analysis of fundamental limits to artificial-guide-star adaptive-optics-system performance for astronomical imaging,” J. Opt. Soc. Am A 11, 277–287 (1994).
[Crossref]

1976 (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
[Crossref]

Andersen, D. A.

Angione, J.

Argall, P. S.

Beletic, J. W.

Belsher, J. F.

Bikkannavar, S.

Bouchez, A.

Bouchez, A. H.

Boyer, C.

Brack, G.

Britton, M.

Brown, C. G.

Campbell, R. D.

Chin, J.

Chin, J. C. Y.

Clare, R. M.

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J. P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[Crossref] [PubMed]

Contos, A.

Contos, A. R.

Danforth, P. M.

Davidge, T.

Dekany, R.

Ellerbroek, B. L.

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J. P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[Crossref] [PubMed]

Erickson, D. A.

Fried, D. L.

Gilles, L.

Guiwits, S.

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York1998).

Hartman, S.

Hartman, S. K.

Herriot, G.

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J. P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[Crossref] [PubMed]

Hickson, P.

Johansson, E.

Johansson, E. M.

Kellner, S.

Kibblewhite, E.

Lafon, R.

Lafon, R. E.

Le Mignant, D.

Lewis, H.

Max, C. E.

C. E. Max, “Laser guide star operational issues,” in Laser Guide Star Adaptive Optics for Astronomy, N. Ageorges and C. Dainty, eds. (Kluwer, Dordrecht, 1997), 89–106.

Morrissett, A.

Mwangi, M. M.

Nelson, J.

J. Nelson and G. H. Sanders, “TMT status report,”in Ground-based and Airborne Telescopes, L. M. Stepp ed., Proc. SPIE 6267, 745–761 (2006).

Neyman, C.

Noll, R. J.

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
[Crossref]

Pennington, D. M.

Petrie, H.

Powell, I. P.

Poyneer, L. A.

L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. 42, 5807–5815 (2003).
[Crossref] [PubMed]

Roberts, J.

Saddlemyer, L.

Sanders, G. H.

J. Nelson and G. H. Sanders, “TMT status report,”in Ground-based and Airborne Telescopes, L. M. Stepp ed., Proc. SPIE 6267, 745–761 (2006).

Shelton, C.

Shi, F.

Sica, R. J.

Smith, M.

Stomski, P.

Stomski, P. J.

Stomski Jr., P. J.

Summers, D.

Summers, D. M.

Sumner, R.

Thicksten, R.

Tokovinin, A.

A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 3651235–1242 (2006).
[Crossref]

Travouillon, T.

A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 3651235–1242 (2006).
[Crossref]

Trinh, T.

Troung, T.

Troy, M.

van Dam, M.

van Dam, M. A.

Vassiliev, O. N.

Velur, V.

Véran, J. P.

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J. P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[Crossref] [PubMed]

Vran, J.-P.

Wizinowich, P. L.

AMOS Technical Conference Proceedings (1)

Appl. Opt. (4)

L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. 42, 5807–5815 (2003).
[Crossref] [PubMed]

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J. P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[Crossref] [PubMed]

J. Opt. Soc. Am A (1)

J. Opt. Soc. Am. (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 3651235–1242 (2006).
[Crossref]

Opt. Express (1)

PASP (2)

Proc. SPIE (5)

J. Nelson and G. H. Sanders, “TMT status report,”in Ground-based and Airborne Telescopes, L. M. Stepp ed., Proc. SPIE 6267, 745–761 (2006).

Other (2)

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York1998).

C. E. Max, “Laser guide star operational issues,” in Laser Guide Star Adaptive Optics for Astronomy, N. Ageorges and C. Dainty, eds. (Kluwer, Dordrecht, 1997), 89–106.

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Fig. 1. The measured LGS aberrations as a function of pupil angle near zenith for the night of (a) 26 January 2005, and (b) 20 July 2006. The curves are, 0° astigmatism (red), 45° astigmatism (black), y-coma (green), x-coma (dark blue) and spherical aberration (light blue).

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Fig. 2. The total low order LGS aberrations for the night of 26 January 2005 at a pupil angle of (a) 0°, (b) 30°, (c) 60°, and (d) 90°. The yellow diamond indicates the approximate position of the laser.

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Fig. 3. The geometrical model of the pupil, laser, detector pixel and laser guide star.

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Fig. 4. The normalized sodium profiles: (a) best-fit sum of 2 Gaussians for the night of January 26 2005, (b) best-fit single Gaussian for the night of January 26 2005, and (c) median profile from the University of Western Ontario LIDAR.

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Fig. 5. The modeled LGS aberrations as a function of pupil angle at zenith for using the sum of two Gaussians sodium profile assuming (a) no UTT error, and (b) a UTT error of (0.1″ , -0.1″). The curves are 0° astigmatism (red), 45° astigmatism (black), y-coma (green), x-coma (dark blue) and spherical aberration (light blue).

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Fig. 6. The modeled LGS aberrations as a function of pupil angle at zenith for (a) the Gaussian sodium profile and (b) the median LIDAR profile. The curves are, 0° astigmatism (red), 45° astigmatism (black), y-coma (green) and x-coma (dark blue) and spherical aberration (light blue).

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Fig. 7. (a) The modeled total magnitude of the LGS low order aberrations (nm) for Keck II versus frame number of the LIDAR profile. The frames are sampled 72 seconds apart. (b) The difference in the LGS aberrations (nm) between consecutive frames.

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Fig. 8. The total simulated LGS aberration as a function of zenith angle (deg) for the Keck II system at 0° pupil angle.

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Fig. 9. The weighting over the FOV for a 3.0″ spot with a center-of-mass centroid for (a) a quad-cell, and (b) 8×8 pixels.

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Fig. 10. The total low-order LGS aberration for 2×2 (black), 4×4 (red) and 8×8 (green) pixels for (a) a FOV of 4.2″ and (b) a FOV of 8.4″.

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Fig. 11. The total simulated LGS aberration for the Keck II system at 0° pupil angle and at zenith as a function of (a) the FOV, and (b) the atmospheric seeing.

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Fig. 12. The simulated total low order LGS aberration for the centrally projected Keck I at 0° pupil angle and at zenith.

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Fig. 13. The Zernike polynomials corresponding to non-zero LGS aberration coefficients for a centrally projected laser: (a) Z₁₁, (b) Z₁₄, (c) Z₂₂, and (d) Z₂₆.

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Tables (2)

Table 1. LGS aberrations in Zernike polynomials for the Palomar, Keck I and TMT LGS AO systems for the sum of two Gaussians sodium profile.

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Table 2. LGS aberrations in Zernike polynomials for TMT for different sodium profiles.

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Equations (10)

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

η = \frac{\cos (ζ) bt}{h^{2}},

ϕ = \sum_{i = 5}^{11} a_{i} Z_{i}

g (i; x, y) = \int_{z_{0} (i; x, y)}^{z_{1} (i; x, y)} \frac{n (z)}{\cos (θ (i, x, y)) \cos (ζ)} dz,

p (i, x, y) = g (i, x, y) ⊙ s (x, y) ⊙ m (x, y) .

c_{x} (i) = \frac{∑xp (i, x, y)}{∑p (i, x, y)}

c_{y} (i) = \frac{\sum yp (i; x, y)}{∑p (i; x, y)}

\sum c_{x} = \sum c_{y} = 0 .

p' (i, x, y) = ℱ^{- 1} (ℱ (p (i, x, y)) \exp [j 2 π (d_{x} (i) x + d_{y} (i) y)])

a = {(H^{T} H)}^{- 1} H^{T} d,

ε (ζ) = ε (0) \sec {(ζ)}^{\frac{3}{5}},

Zernike polynomial	Coefficient of LGS aberration (nm)
Zernike polynomial	Gaussian profile	Sum of 2 Gaussians	Median profile
Z₁₁	260	834	-163
Z₁₄	100	338	-50
Z₂₂	-8	42	9
Z₂₆	29	158	-23
Total	281	915	173

Zernike polynomial	Coefficient of LGS aberration (nm)
Zernike polynomial	Gaussian profile	Sum of 2 Gaussians	Median profile
Z₁₁	260	834	-163
Z₁₄	100	338	-50
Z₂₂	-8	42	9
Z₂₆	29	158	-23
Total	281	915	173

Zernike polynomial	Coefficient of LGS aberration (nm)
Zernike polynomial	Palomar	Keck I	TMT
Z₁₁	5	34	834
Z₁₄	0	25	338
Z₂₂	0	4	42
Z₂₆	0	7	158
Total	5	43	915