Abstract

The effects of axis alignment errors, planetary rotation, and tidal forces on rotating liquid mirrors are analyzed. These produce a surface distortion that decreases exponentially with distance inward from the rim with a characteristic length l=3hf/2, where h is the thickness of the fluid and f is the focal length. Even a small tilt of the rotation axis can produce a significant deformation of the optical surface. The maximum surface height error is 3εl, where ε is the tilt angle and is typically of the order of 1.5  μm for a 1  arc  sec tilt. The main optical effect of the wave is to produce a ring, with angular diameter 6ε, offset by half of the diameter in the direction opposite the tilt. This diamond ring aberration can be avoided by accurate alignment of the rotation axis or by masking the outer few centimeters of the mirror. Planetary rotation produces a small deformation of the order of 100  nm for a 10 m telescope at low latitude on Earth. This deformation can be canceled by a small tilt of the rotation axis. Tidal forces produced by the Moon, or by the Earth in the case of a lunar telescope, produce an inconsequential, subnanometer, surface deformation.

© 2006 Optical Society of America

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  1. E. F. Borra, "The liquid-mirror telescope as a viable astronomical tool," J. R. Astron. Soc. Can. 76, 245-256 (1982).
  2. P. Hickson, E. F. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, "UBC/Laval 2.7-meter liquid-mirror telescope," Astrophys. J. Lett. 436, L201-L204 (1994).
    [CrossRef]
  3. A. Potter and M. K. Mulrooney, "Liquid-metal mirror for optical measurements of orbital debris," Adv. Space Res. 19, 213-219 (1997).
    [CrossRef]
  4. R. J. Sica, S. Sargoytchev, P. S. Argall, E. F. Borra, L. Girard, C. T. Sparrow, and S. Flatt, "Lidar measurements taken with a large-aperture liquid mirror. 1. Rayleigh-scatter system," Appl. Opt. 34, 6925-6936 (1995).
    [CrossRef] [PubMed]
  5. R. Wuerker, Department of Physics, UCLA (personal communication, 1995).
  6. P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."
  7. P. Hickson, "Wide-field tracking with zenith-pointing telescopes," Mon. Not. R. Astron. Soc. 330, 540-546 (2002).
    [CrossRef]
  8. E. F. Borra, Department of Physics, Université Laval (personal communication, 2005).
  9. P. Hickson and K. M. Lanzetta, "Large-aperture mirror array (LAMA): project Overview," in Second Backaskog Workshop on Extremely Large Telescopes, A.L. Ardeberg and T. Andersen, eds., Proc. SPIE 5382,115-125 (2004).
  10. R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
    [PubMed]
  11. R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).
  12. L. Girard and E. F. Borra, "Optical tests of a 2.5-m-diameter liquid mirror: behavior under external perturbations and scattered-light measurements," Appl. Opt. 36, 6278-6288 (1997).
    [CrossRef]
  13. G. Tremblay and E. F. Borra, "Optical tests of a 3.7-m-diameter liquid mirror: behavior under external perturbations," Appl. Opt. 39, 5651-5662 (2000).
    [CrossRef]
  14. M. K. Mulrooney, "A 3.0-meter liquid-mirror telescope," Ph.D. dissertation (Rice University, 2000).
  15. B. K. Gibson and P. Hickson, "Liquid-mirror surface aberrations. I--wavefront analysis," Astrophys. J. 391, 409-417 (1992).
    [CrossRef]
  16. P. Hickson, "Eliminating the coriolis effect in liquid mirrors," Publ. Astron. Soc. Pac. 113, 1511-1514 (2001).
    [CrossRef]
  17. J. P. Vanyo, Rotating Fluids in Engineering and Science (Dover, 1993).
  18. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1987).
  19. R. Wilson, Reflecting Telescope Optics I (Springer, 1996), Section 3.3.2.
  20. A. Maréchal, "Étude des effets combinés de la diffraction et des aberrations géomtriques sur l'image d'un point lumineux," Rev. Opt. 26, 257-277 (1947).

2002 (1)

P. Hickson, "Wide-field tracking with zenith-pointing telescopes," Mon. Not. R. Astron. Soc. 330, 540-546 (2002).
[CrossRef]

2001 (1)

P. Hickson, "Eliminating the coriolis effect in liquid mirrors," Publ. Astron. Soc. Pac. 113, 1511-1514 (2001).
[CrossRef]

2000 (1)

1997 (2)

1995 (1)

1994 (1)

P. Hickson, E. F. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, "UBC/Laval 2.7-meter liquid-mirror telescope," Astrophys. J. Lett. 436, L201-L204 (1994).
[CrossRef]

1992 (1)

B. K. Gibson and P. Hickson, "Liquid-mirror surface aberrations. I--wavefront analysis," Astrophys. J. 391, 409-417 (1992).
[CrossRef]

1982 (1)

E. F. Borra, "The liquid-mirror telescope as a viable astronomical tool," J. R. Astron. Soc. Can. 76, 245-256 (1982).

1947 (1)

A. Maréchal, "Étude des effets combinés de la diffraction et des aberrations géomtriques sur l'image d'un point lumineux," Rev. Opt. 26, 257-277 (1947).

Angel, R.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

Argall, P. S.

Borra, E.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

Borra, E. F.

G. Tremblay and E. F. Borra, "Optical tests of a 3.7-m-diameter liquid mirror: behavior under external perturbations," Appl. Opt. 39, 5651-5662 (2000).
[CrossRef]

L. Girard and E. F. Borra, "Optical tests of a 2.5-m-diameter liquid mirror: behavior under external perturbations and scattered-light measurements," Appl. Opt. 36, 6278-6288 (1997).
[CrossRef]

R. J. Sica, S. Sargoytchev, P. S. Argall, E. F. Borra, L. Girard, C. T. Sparrow, and S. Flatt, "Lidar measurements taken with a large-aperture liquid mirror. 1. Rayleigh-scatter system," Appl. Opt. 34, 6925-6936 (1995).
[CrossRef] [PubMed]

P. Hickson, E. F. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, "UBC/Laval 2.7-meter liquid-mirror telescope," Astrophys. J. Lett. 436, L201-L204 (1994).
[CrossRef]

E. F. Borra, "The liquid-mirror telescope as a viable astronomical tool," J. R. Astron. Soc. Can. 76, 245-256 (1982).

E. F. Borra, Department of Physics, Université Laval (personal communication, 2005).

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

Burge, J.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

Cabanac, R.

P. Hickson, E. F. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, "UBC/Laval 2.7-meter liquid-mirror telescope," Astrophys. J. Lett. 436, L201-L204 (1994).
[CrossRef]

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

Content, R.

P. Hickson, E. F. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, "UBC/Laval 2.7-meter liquid-mirror telescope," Astrophys. J. Lett. 436, L201-L204 (1994).
[CrossRef]

Crotts, A.

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

de Lapparent, V.

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

Eisenstein, D.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

Flatt, S.

Foing, B.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

Gibson, B. K.

P. Hickson, E. F. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, "UBC/Laval 2.7-meter liquid-mirror telescope," Astrophys. J. Lett. 436, L201-L204 (1994).
[CrossRef]

B. K. Gibson and P. Hickson, "Liquid-mirror surface aberrations. I--wavefront analysis," Astrophys. J. 391, 409-417 (1992).
[CrossRef]

Girard, L.

Gosselin, C.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

Gosset, J-L.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

Gromoll, S.

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

Hickson, P.

P. Hickson, "Wide-field tracking with zenith-pointing telescopes," Mon. Not. R. Astron. Soc. 330, 540-546 (2002).
[CrossRef]

P. Hickson, "Eliminating the coriolis effect in liquid mirrors," Publ. Astron. Soc. Pac. 113, 1511-1514 (2001).
[CrossRef]

P. Hickson, E. F. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, "UBC/Laval 2.7-meter liquid-mirror telescope," Astrophys. J. Lett. 436, L201-L204 (1994).
[CrossRef]

B. K. Gibson and P. Hickson, "Liquid-mirror surface aberrations. I--wavefront analysis," Astrophys. J. 391, 409-417 (1992).
[CrossRef]

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

P. Hickson and K. M. Lanzetta, "Large-aperture mirror array (LAMA): project Overview," in Second Backaskog Workshop on Extremely Large Telescopes, A.L. Ardeberg and T. Andersen, eds., Proc. SPIE 5382,115-125 (2004).

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

Johnson, B.

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

Josset, J.-L.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1987).

Lanzetta, K. M.

P. Hickson and K. M. Lanzetta, "Large-aperture mirror array (LAMA): project Overview," in Second Backaskog Workshop on Extremely Large Telescopes, A.L. Ardeberg and T. Andersen, eds., Proc. SPIE 5382,115-125 (2004).

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1987).

Ma, K. B.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

Maréchal, A.

A. Maréchal, "Étude des effets combinés de la diffraction et des aberrations géomtriques sur l'image d'un point lumineux," Rev. Opt. 26, 257-277 (1947).

Mulrooney, M. K.

A. Potter and M. K. Mulrooney, "Liquid-metal mirror for optical measurements of orbital debris," Adv. Space Res. 19, 213-219 (1997).
[CrossRef]

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

M. K. Mulrooney, "A 3.0-meter liquid-mirror telescope," Ph.D. dissertation (Rice University, 2000).

Potter, A.

A. Potter and M. K. Mulrooney, "Liquid-metal mirror for optical measurements of orbital debris," Adv. Space Res. 19, 213-219 (1997).
[CrossRef]

Sargoytchev, S.

Seddiki, O.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

Sica, R. J.

Sivanandam, S.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

Sparrow, C. T.

Thibault, S.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

Tremblay, G.

Van Susante, P.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

Vanyo, J. P.

J. P. Vanyo, Rotating Fluids in Engineering and Science (Dover, 1993).

Walker, G. A. H.

P. Hickson, E. F. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, "UBC/Laval 2.7-meter liquid-mirror telescope," Astrophys. J. Lett. 436, L201-L204 (1994).
[CrossRef]

Wilson, R.

R. Wilson, Reflecting Telescope Optics I (Springer, 1996), Section 3.3.2.

Worden, S. P.

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

Wuerker, R.

R. Wuerker, Department of Physics, UCLA (personal communication, 1995).

Adv. Space Res. (1)

A. Potter and M. K. Mulrooney, "Liquid-metal mirror for optical measurements of orbital debris," Adv. Space Res. 19, 213-219 (1997).
[CrossRef]

Appl. Opt. (3)

Astrophys. J. (1)

B. K. Gibson and P. Hickson, "Liquid-mirror surface aberrations. I--wavefront analysis," Astrophys. J. 391, 409-417 (1992).
[CrossRef]

Astrophys. J. Lett. (1)

P. Hickson, E. F. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, "UBC/Laval 2.7-meter liquid-mirror telescope," Astrophys. J. Lett. 436, L201-L204 (1994).
[CrossRef]

J. R. Astron. Soc. Can. (1)

E. F. Borra, "The liquid-mirror telescope as a viable astronomical tool," J. R. Astron. Soc. Can. 76, 245-256 (1982).

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

P. Hickson, "Wide-field tracking with zenith-pointing telescopes," Mon. Not. R. Astron. Soc. 330, 540-546 (2002).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

P. Hickson, "Eliminating the coriolis effect in liquid mirrors," Publ. Astron. Soc. Pac. 113, 1511-1514 (2001).
[CrossRef]

Rev. Opt. (1)

A. Maréchal, "Étude des effets combinés de la diffraction et des aberrations géomtriques sur l'image d'un point lumineux," Rev. Opt. 26, 257-277 (1947).

Other (10)

J. P. Vanyo, Rotating Fluids in Engineering and Science (Dover, 1993).

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1987).

R. Wilson, Reflecting Telescope Optics I (Springer, 1996), Section 3.3.2.

M. K. Mulrooney, "A 3.0-meter liquid-mirror telescope," Ph.D. dissertation (Rice University, 2000).

E. F. Borra, Department of Physics, Université Laval (personal communication, 2005).

P. Hickson and K. M. Lanzetta, "Large-aperture mirror array (LAMA): project Overview," in Second Backaskog Workshop on Extremely Large Telescopes, A.L. Ardeberg and T. Andersen, eds., Proc. SPIE 5382,115-125 (2004).

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. F. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, and J-L. Gosset, "A deep-field infrared observatory near the lunar pole," in Proceedings of the Seventh International Conference on the Exploration and Utilization of the Moon, Toronto, Canada, 23 September 2005, p. 189.
[PubMed]

R. Angel, D. Eisenstein, S. Sivanandam, S. P. Worden, J. Burge, E. Borra, C. Gosselin, O. Seddiki, P. Hickson, K. B. Ma, B. Foing, J.-L. Josset, S. Thibault, and P. Van Susante, "A Lunar Liquid-Mirror Telescope (LLMT) for deep-field infrared observations near the lunar pole," in Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, J. C. Mather, H. A. MacEwen, and M. W. de Graauw, eds., Proc. SPIE 6265, 62651U (2006).

R. Wuerker, Department of Physics, UCLA (personal communication, 1995).

P. Hickson, R. Cabanac, A. Crotts, S. Gromoll, B. Johnson, V. de Lapparent, K. M. Lanzetta, M. K. Mulrooney, and S. Sivanandam are preparing a manuscript to be called, "The large zenith telescope--a 6-meter mercury-mirror telescope."

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Figures (4)

Fig. 1
Fig. 1

Geometry of a rotating liquid mirror upon a rotating planet.

Fig. 2
Fig. 2

Surface error produced by alignment errors and planetary rotation on an 8 m diameter liquid mirror. The horizontal axes give the position in meters on the surface. The vertical axis shows ζ / ζ max , the ratio of the vertical displacement of the surface to the maximum displacement found at the outer edge. This axis has been magnified by a factor of 20 to emphasize small displacements.

Fig. 3
Fig. 3

Numerical Fourier optics calculation of the image produced by the deformation of Eq. (72) for a 1   arc   sec axis tilt of a 3   m liquid mirror. The fluid thickness is 2   mm and the wavelength is 0.6   μm . The bright central component of the star image, located at the left edge of the ring, has been suppressed to reveal the ring structure.

Fig. 4
Fig. 4

Diamond ring aberration observed with the LZT when the mirror rotation axis was tilted 3   arc   sec from the vertical. The diameter of the ring is approximately 18   arc   sec , in agreement with the theory developed here.

Equations (94)

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ρ t + ( ρ v ) = 0 ,
v t + ( v ) v ν 2 v = F 1 ρ P ,
r 0 = R ( t ) r .
R ( t ) = exp ( t Ω k T k ) ,
[ T k ] i j = ϵ i j k .
[ A × B ] i = ϵ i j k A j B k ,
R ˙ = Ω × .
v 0 r ˙ 0 = v + Ω × r ,
a 0 r ¨ 0 = a + 2 Ω × v + Ω × ( Ω × r ) .
v t + ( v ) v ν 2 v + 2 Ω × v + Ω × ( Ω × r ) = F 1 ρ P .
r 0 = R ( t ) R ( t ) r .
v 0 = R R v + R ˙ R r + R R ˙ r = v + Ω T × r ,
a 0 = R R a + 2 R R ˙ v + 2 R ˙ R v + R R ¨ r + 2 R ˙ R ˙ r + R ¨ R r = a + 2 Ω T × v + Ω × ( Ω × r ) + 2 Ω × ( Ω × r ) + Ω × ( Ω × r ) ,
v t + ( v ) v ν 2 v + 2 Ω T × v = Ω × ( Ω × r ) 2 Ω × ( Ω × r ) Ω × ( Ω × r ) + F 1 ρ P .
a 0 = a + 2 Ω T × v Ω T 2 r ϵ ,
ϵ = 2 ϵ Ω 2 r sin θ cos ( ϕ + Ω t ) z ^ ,
v t + ( v ) v ν 2 v + 2 Ω T × v = Φ e 1 ρ P + ϵ ,
Φ e = Φ 1 2 Ω T 2 r 2 .
Φ e = g z 1 2 Ω T 2 r 2 = P ρ + Φ 0 ,
z = Ω T 2 r 2 2 g .
f = r 2 4 z = g 2 Ω T 2 .
v x t ν 2 v x z 2 = 0 e i ω t .
v x = ( a + b e c z ) e i ω t ,
v x = v 0 [ 1 e z ( 1 + i ) / δ ] ,
h e = 1 v 0 0 h | v x | d z h δ / 2 ,
          x = η ξ cos ϕ , y = η ξ  sin  ϕ , z = ( η 2 ξ 2 ) / 2.
d s 2 = h η 2 d η 2 + h ξ 2 d ξ 2 + h ϕ 2 d ϕ 2 ,
h η = h ξ = ( η 2 + ξ 2 ) 1 / 2 , h ϕ = η ξ .
Φ e = 1 2 [ g ( η 2 ξ 2 ) Ω T 2 η 2 ξ 2 ] .
Φ e = ( g + Ω T 2 η 2 ) ξ h ξ ξ ^ , = g ( 1 + η 2 2 f ) ξ h ξ ξ ^ .
ζ = h ξ ( ξ ξ 0 ) .
v t + 2 Ω × v ν 2 v = 1 ρ P Φ e + ,
v = 0 .
˜ v ˜ + 1 h η h ϕ h ξ ξ ( h η h ϕ v ξ ) = 0 .
v ξ = 1 h η h ϕ h η h ϕ h ξ ˜ v ˜ d ξ .
ζ t = 1 h η h ϕ ξ 0 + h / h ξ ξ 0 ζ / h ξ h η h ϕ h ξ ˜ v ˜ d ξ h ξ ξ 0 ξ 0 + h / h ξ ˜ v ˜ d ξ .
2 Ω × v = 2 Ω ξ v ϕ η ^ 2 Ω η v ϕ ξ ^ .
                  1 h ξ ξ ( P ρ + Φ e ) = ξ v ξ t + 2 Ω η v ϕ + ν 2 v ξ .
P ( ξ ) ρ + Φ e ( ξ ) = ξ 0 ζ / h ξ ξ ( ξ v ξ t + 2 Ω η v ϕ + ν 2 v ξ ) ×  h ξ d ξ + ( P ρ + Φ e ) ξ = ξ 0 ζ / h ξ .
P ( ξ 0 ζ / h ξ ) = P a α ˜ 2 ζ ,
Φ e ( ξ 0 ζ / h ξ ) = Φ e ( ξ 0 ) + g ( 1 + η 2 2 f ) 1 / 2 ζ .
        ˜ ( P ρ + Φ e ) = ( ξ ξ 0 ) h ξ ˜ ξ + g ˜ ζ α ρ ˜ ˜ 2 ζ ,
˜ 2 ( P ρ + Φ e ) = ( ξ ξ 0 ) h ξ ˜ 2 ξ + g ˜ 2 ζ α ρ ˜ 4 ζ .
( t ν ˜ 2 ) ˜ v ˜ = 2 Ω ˜ × v ˜ g ˜ 2 ζ + α ρ ˜ 4 ζ ( ξ ξ 0 ) h ξ ˜ 2 ξ + ˜ ˜ .
t ( ˜ × v ˜ ) = 2 Ω ( ˜ v ˜ ) ˜ × ˜ .
h ξ ξ 0 ξ 0 + h / h ξ t ( ˜ × v ˜ ) d ξ = 2 Ω ζ t h ξ ξ 0 ξ 0 + h / h ξ ˜ × ˜ d ξ .
t { [ 2 t 2 + 4 Ω 2 ( ν t + g h ) ˜ 2 α h ρ ˜ 4 ] ζ h 2 2 ˜ 2 ξ +  h ˜ ˜ } = 2 h Ω ˜ × ˜ .
( 1 + ν g h t ) ˜ 2 ζ + α ρ g ˜ 4 ζ 1 g h ( 2 t 2 + 4 Ω 2 ) ζ = 0 .
      ζ ( η , ϕ , t ) = ζ ( η , ϕ ) e i Ω t , cos ( ϕ + Ω t ) = e i ϕ e i Ω t ,
( 1 + i νΩ g h ) ˜ 2 ζ + α ρ g ˜ 4 ζ 3 Ω 2 g h ζ = 0 .
˜ 2 ζ k 2 ζ = 0 ,
k 2 = 3 Ω 2 g h ( 1 + i νΩ g h ) 1 .
k = [ 3 2 f h 1 + ν 2 / 2 f g h 2 + 1 2 ( 1 + ν 2 / 2 f g h 2 ) ] 1 / 2 × { 1 i [ 1 + ν 2 / 2 f g h 2 1 1 + ν 2 / 2 f g h 2 + 1 ] 1 / 2 } .
k 3 2 f h ,
k ( 1 i ) 3 2 ν ( g f ) 1 / 4
        2 ζ η 2 + 1 η ζ η + ξ 0 2 + η 2 ξ 0 2 η 2 2 ζ ϕ 2 ( ξ 0 2 + η 2 ) k 2 ζ = 0 .
2 ζ η 2 + 1 η ζ η + 1 η 2 2 ζ ϕ 2 ξ 0 2 k 2 ζ = 0 .
            ζ ( η , ϕ ) = m = 0 [ a m I m ( k ξ 0 η ) + b m K m ( k ξ 0 η ) ] e i m ϕ ,
t ( n ^ v ˜ ) + 2 n ^ Ω × v = ( n ^ ) [ g ζ + ( ξ ξ 0 ) h ξ ˜ ξ ] + n ^ ˜ .
              t ( Ω × v ) = 2 ( Ω × v ) Ω + 2 Ω 2 v + Ω × .
( 2 t 2 + 4 Ω 2 ) ( n ^ v ˜ ) = t { ( n ^ ˜ ) [ g ζ + ( ξ ξ 0 ) h ξ ˜ ξ ] + n ^ ˜ } 2 n ^ Ω × .
n ^ ˜ ζ = 1 g n ^ ( ˜ + h 2 ˜ ξ + 2 i z ^ × )
1 h η ( ζ η ) η = R / ξ 0 = [ 2 R ( η ^ z ^ ) h ξ 0 h η ( ξ ^ z ^ ) ] ε Ω 2 g × sin θ e i ( ϕ + Ω t ) ,
= ( 2 R 2 ξ 0 h η h ξ 0 2 h η 2 ) ε 2 f sin θ e i ( ϕ + Ω t ) .
( ζ η ) η = R / ξ 0 = ( R 2 f h 1 + R 2 / 4 f 2 ) ε 2 f sin θ e i ( ϕ + Ω t ) .
          ζ η = k ξ 0 m = 0 [ a m I m ( k r ) + b m K m ( k r ) ] e i ( m ϕ + Ω t ) .
ζ ( r , ϕ ) = Ω sin θ R 2 f h 3 g I 1 ( k r ) I m ( k R ) e i ϕ ,
I m ( x ) e x 2 π x .
I m ( k R ) I m ( k R ) ( 1 1 2 k R ) I m ( k R ) .
ζ ( r , ϕ ) Ω sin θ R 2 f h 3 g e k ( R r ) e i ϕ
= εg x ^ .
1 h η ( ζ η ) η = R / ξ 0 = 3 ε 1 + R 2 / 4 f 2 e i ( ϕ + Ω t ) .
ζ ( r , ϕ ) = ε 6 f h I 1 ( k r ) I 1 ( k R ) e i ϕ .
= 2 G M d 3 [ sin ( θ M ) x + cos ( θ M ) z ] .
1 h η ( ζ η ) η = R / ξ 0 3 sin ( θ M ) G M R g d 3 1 + R 2 / 4 f 2 e 2 i ( ϕ + Ω t ) .
ζ ( r , ϕ ) = 2 3 h f sin ( θ M ) G M R g d 3 I 2 ( k r ) I 2 ( k R ) e i ϕ .
ζ ( r , ϕ ) = γ ( r ) cos ( ϕ ) .
ψ x = 2 ζ x , ψ y = 2 ζ y .
ψ x = 2 cos 2 ϕ [ γ γ r ] 2 γ r
= cos 2 ϕ [ γ γ r ] [ γ + γ r ] ,
ψ y = 2 sin ϕ cos ϕ [ γ γ r ]
= sin 2 ϕ [ γ γ r ] .
( ψ x ψ 0 ) 2 + ψ y 2 = ψ R 2 ,
ψ R ( r ) = [ γ γ r ] ,
ψ 0 ( r ) = [ γ + γ r ] .
γ ( r ) = k ζ ( r )
= 3 ε I 1 ( k r ) I 1 ( k R ) .
ψ R ψ 0 γ ( r ) 3 ε .
S e σ ϕ 2 1 σ ϕ 2 .
σ ϕ 2 = 16 π R 2 λ 2 ζ 2 d 2 r .
σ ϕ 2 ( r ) = 24 π fh [ ε r λ R I 1 ( k R ) ] 2 [ I 1 ( k r ) 2 I 1 ( k r ) I 2 ( k r ) ] .
σ ϕ 2 ( R ) 54 π ε 2 / k 3 R λ 2 .
ψ R ψ 0 ζ ( r ) Ω sin θ R 2 2 g f 3 .
ε = Ω sin θ R 2 3 2 g f 3

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