Abstract

We built and tested a 3.7-m-diameter liquid mirror that rotates on a ball bearing. Although the ball bearing is of a poor quality, the mirror is surprisingly good for one that comprises 1-mm-thick mercury layers. We found no evidence of the strong astigmatism that might have been expected from Coriolis forces. We did not detect effects of turbulence might or vibrations for thin mercury layers, illustrating the necessity of using thin layers: Large liquid mirrors would have had unacceptable optical qualities for layers much thicker than 2 mm.

© 2000 Optical Society of America

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References

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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. E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. F. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
    [CrossRef]
  3. L. Girard, 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]
  4. R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
    [CrossRef]
  5. 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, 201–204 (1994).
    [CrossRef]
  6. R. Cabanac, E. F. Borra, M. Beauchemin, “A search for peculiar objects with the NASA Orbital Debris Observatory 3-m liquid mirror telescope,” Astrophys. J. 509, 309–323 (1998).
    [CrossRef]
  7. P. Hickson, M. Mulrooney, “University of British Columbia–NASA Multi-Narrowband Survey. I. Description and photometric properties of the survey,” Astrophys. J. Suppl. 115, 35–42 (1998).
    [CrossRef]
  8. R. J. Sica, S. Sargoytchev, E. F. Borra, L. Girard, S. Argall, C. T. Sarrow, S. Flatt, “Lidar measurements taken with a large aperture liquid mirror. 1. The Rayleigh–scatter system,” Appl. Opt. 34, 6925–6936 (1995).
    [CrossRef] [PubMed]
  9. R. J. Sica, A. T. Russel, “Measurements of the effect of gravity waves in the middle atmosphere using parametric models of density fluctuations. I. Vertical wavenumber and temporal spectra,” J. Atmos. Sci. 56, 1308–1329 (1999).
    [CrossRef]
  10. R. Wuerker, “Bistatic LMT lidar alignment,” Opt. Eng. 36, 1421–1424 (1997).
    [CrossRef]
  11. N. M. Ninane, C. A. Jamar, “Parabolic liquid mirrors in optical shop testing,” Appl. Opt. 35, 6131–6139 (1996).
    [CrossRef] [PubMed]
  12. S. Thibault, E. F. Borra, “Telecentric three-dimensional sensor using a liquid mirror for large object inspection,” Appl. Opt. 38, 5962–5967 (1999).
    [CrossRef]
  13. E. F. Borra, “Liquid mirrors,” Can J. Phys. 73, 109–125 (1995).
    [CrossRef]
  14. G. Tremblay, “Étude des propriétés optiques et mécaniques d’un miroir liquide de 3.7 metres de diamètre,” Ph.D. dissertation (Département de Physique, Université Laval, Quebec, Canada, 1999).
  15. R. Content, “Tests optiques sur un miroir liquide de 1.5 m et développement de la technologie des miroirs liquides,” Ph.D. dissertation (Département de Physique, Université Laval, Québec, Canada, 1992).
  16. S. Thibault, E. F. Borra, “Telecentric three-dimensional sensor using a liquid mirror for large object inspection,” Appl. Opt. 38, 5962–5967 (1999).
    [CrossRef]
  17. P. Hickson, B. K. Gibson, D. W. Hogg, “Large astronomical liquid mirrors,” Publ. Astron. Soc. Pac. 105, 501–508 (1993).
    [CrossRef]
  18. R. V. Shack, G. H. Hopkins, “The Shack interferometer,” Opt. Eng. 18, 226–228 (1979).
    [CrossRef]
  19. C. Roddier, F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1673 (1987).
    [CrossRef] [PubMed]
  20. E. F. Borra, M. Beauchemin, R. Lalande, “Liquid mirror telescopes: observations with a 1-meter diameter prototype and scaling-up considerations,” Astrophys. J. 297, 846–851 (1985).
    [CrossRef]
  21. B. K. Gibson, P. Hickson, “Liquid mirror surface aberrations. 1. Wavefront analysis,” Astrophys. J. 391, 409–417 (1992).
    [CrossRef]
  22. L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1959).
  23. A. P. French, Vibrations and Waves, M.I.T. Introductory Physics Series (Norton, New York, 1971).
  24. F. Biesel, “Calcul de l’amortissement d’une houille dans un liquide visqueux de profondeur finie,” Houille Blanche 5, 630–634 (1949).
    [CrossRef]
  25. R. Kobayashi, Y. Kohama, C. Takamade, “Spiral vortices in boundary layer transition regime on a rotating disk,” Acta Mech. 35, 71–82 (1980).
    [CrossRef]

1999 (3)

R. J. Sica, A. T. Russel, “Measurements of the effect of gravity waves in the middle atmosphere using parametric models of density fluctuations. I. Vertical wavenumber and temporal spectra,” J. Atmos. Sci. 56, 1308–1329 (1999).
[CrossRef]

S. Thibault, E. F. Borra, “Telecentric three-dimensional sensor using a liquid mirror for large object inspection,” Appl. Opt. 38, 5962–5967 (1999).
[CrossRef]

S. Thibault, E. F. Borra, “Telecentric three-dimensional sensor using a liquid mirror for large object inspection,” Appl. Opt. 38, 5962–5967 (1999).
[CrossRef]

1998 (2)

R. Cabanac, E. F. Borra, M. Beauchemin, “A search for peculiar objects with the NASA Orbital Debris Observatory 3-m liquid mirror telescope,” Astrophys. J. 509, 309–323 (1998).
[CrossRef]

P. Hickson, M. Mulrooney, “University of British Columbia–NASA Multi-Narrowband Survey. I. Description and photometric properties of the survey,” Astrophys. J. Suppl. 115, 35–42 (1998).
[CrossRef]

1997 (2)

1996 (1)

1995 (2)

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, 201–204 (1994).
[CrossRef]

1993 (1)

P. Hickson, B. K. Gibson, D. W. Hogg, “Large astronomical liquid mirrors,” Publ. Astron. Soc. Pac. 105, 501–508 (1993).
[CrossRef]

1992 (2)

B. K. Gibson, P. Hickson, “Liquid mirror surface aberrations. 1. Wavefront analysis,” Astrophys. J. 391, 409–417 (1992).
[CrossRef]

E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. F. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

1989 (1)

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

1987 (1)

1985 (1)

E. F. Borra, M. Beauchemin, R. Lalande, “Liquid mirror telescopes: observations with a 1-meter diameter prototype and scaling-up considerations,” Astrophys. J. 297, 846–851 (1985).
[CrossRef]

1982 (1)

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

1980 (1)

R. Kobayashi, Y. Kohama, C. Takamade, “Spiral vortices in boundary layer transition regime on a rotating disk,” Acta Mech. 35, 71–82 (1980).
[CrossRef]

1979 (1)

R. V. Shack, G. H. Hopkins, “The Shack interferometer,” Opt. Eng. 18, 226–228 (1979).
[CrossRef]

1949 (1)

F. Biesel, “Calcul de l’amortissement d’une houille dans un liquide visqueux de profondeur finie,” Houille Blanche 5, 630–634 (1949).
[CrossRef]

Argall, S.

Beauchemin, M.

R. Cabanac, E. F. Borra, M. Beauchemin, “A search for peculiar objects with the NASA Orbital Debris Observatory 3-m liquid mirror telescope,” Astrophys. J. 509, 309–323 (1998).
[CrossRef]

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

E. F. Borra, M. Beauchemin, R. Lalande, “Liquid mirror telescopes: observations with a 1-meter diameter prototype and scaling-up considerations,” Astrophys. J. 297, 846–851 (1985).
[CrossRef]

Biesel, F.

F. Biesel, “Calcul de l’amortissement d’une houille dans un liquide visqueux de profondeur finie,” Houille Blanche 5, 630–634 (1949).
[CrossRef]

Boily, E.

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

Boily, E. F.

E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. F. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

Borra, E. F.

S. Thibault, E. F. Borra, “Telecentric three-dimensional sensor using a liquid mirror for large object inspection,” Appl. Opt. 38, 5962–5967 (1999).
[CrossRef]

S. Thibault, E. F. Borra, “Telecentric three-dimensional sensor using a liquid mirror for large object inspection,” Appl. Opt. 38, 5962–5967 (1999).
[CrossRef]

R. Cabanac, E. F. Borra, M. Beauchemin, “A search for peculiar objects with the NASA Orbital Debris Observatory 3-m liquid mirror telescope,” Astrophys. J. 509, 309–323 (1998).
[CrossRef]

L. Girard, 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]

E. F. Borra, “Liquid mirrors,” Can J. Phys. 73, 109–125 (1995).
[CrossRef]

R. J. Sica, S. Sargoytchev, E. F. Borra, L. Girard, S. Argall, C. T. Sarrow, S. Flatt, “Lidar measurements taken with a large aperture liquid mirror. 1. The 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, 201–204 (1994).
[CrossRef]

E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. F. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

E. F. Borra, M. Beauchemin, R. Lalande, “Liquid mirror telescopes: observations with a 1-meter diameter prototype and scaling-up considerations,” Astrophys. J. 297, 846–851 (1985).
[CrossRef]

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

Cabanac, R.

R. Cabanac, E. F. Borra, M. Beauchemin, “A search for peculiar objects with the NASA Orbital Debris Observatory 3-m liquid mirror telescope,” Astrophys. J. 509, 309–323 (1998).
[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, 201–204 (1994).
[CrossRef]

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, 201–204 (1994).
[CrossRef]

E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. F. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

R. Content, “Tests optiques sur un miroir liquide de 1.5 m et développement de la technologie des miroirs liquides,” Ph.D. dissertation (Département de Physique, Université Laval, Québec, Canada, 1992).

Drinkwater, M. J.

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

Flatt, S.

French, A. P.

A. P. French, Vibrations and Waves, M.I.T. Introductory Physics Series (Norton, New York, 1971).

Gauthier, A.

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

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, 201–204 (1994).
[CrossRef]

P. Hickson, B. K. Gibson, D. W. Hogg, “Large astronomical liquid mirrors,” Publ. Astron. Soc. Pac. 105, 501–508 (1993).
[CrossRef]

B. K. Gibson, P. Hickson, “Liquid mirror surface aberrations. 1. Wavefront analysis,” Astrophys. J. 391, 409–417 (1992).
[CrossRef]

Girard, L.

Hickson, P.

P. Hickson, M. Mulrooney, “University of British Columbia–NASA Multi-Narrowband Survey. I. Description and photometric properties of the survey,” Astrophys. J. Suppl. 115, 35–42 (1998).
[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, 201–204 (1994).
[CrossRef]

P. Hickson, B. K. Gibson, D. W. Hogg, “Large astronomical liquid mirrors,” Publ. Astron. Soc. Pac. 105, 501–508 (1993).
[CrossRef]

B. K. Gibson, P. Hickson, “Liquid mirror surface aberrations. 1. Wavefront analysis,” Astrophys. J. 391, 409–417 (1992).
[CrossRef]

Hogg, D. W.

P. Hickson, B. K. Gibson, D. W. Hogg, “Large astronomical liquid mirrors,” Publ. Astron. Soc. Pac. 105, 501–508 (1993).
[CrossRef]

Hopkins, G. H.

R. V. Shack, G. H. Hopkins, “The Shack interferometer,” Opt. Eng. 18, 226–228 (1979).
[CrossRef]

Jamar, C. A.

Kobayashi, R.

R. Kobayashi, Y. Kohama, C. Takamade, “Spiral vortices in boundary layer transition regime on a rotating disk,” Acta Mech. 35, 71–82 (1980).
[CrossRef]

Kohama, Y.

R. Kobayashi, Y. Kohama, C. Takamade, “Spiral vortices in boundary layer transition regime on a rotating disk,” Acta Mech. 35, 71–82 (1980).
[CrossRef]

Lalande, R.

E. F. Borra, M. Beauchemin, R. Lalande, “Liquid mirror telescopes: observations with a 1-meter diameter prototype and scaling-up considerations,” Astrophys. J. 297, 846–851 (1985).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1959).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1959).

Mulrooney, M.

P. Hickson, M. Mulrooney, “University of British Columbia–NASA Multi-Narrowband Survey. I. Description and photometric properties of the survey,” Astrophys. J. Suppl. 115, 35–42 (1998).
[CrossRef]

Ninane, N. M.

Poirier, S.

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

Poisson, E.

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

Roddier, C.

Roddier, F.

Russel, A. T.

R. J. Sica, A. T. Russel, “Measurements of the effect of gravity waves in the middle atmosphere using parametric models of density fluctuations. I. Vertical wavenumber and temporal spectra,” J. Atmos. Sci. 56, 1308–1329 (1999).
[CrossRef]

Sargoytchev, S.

Sarrow, C. T.

Shack, R. V.

R. V. Shack, G. H. Hopkins, “The Shack interferometer,” Opt. Eng. 18, 226–228 (1979).
[CrossRef]

Sica, R. J.

R. J. Sica, A. T. Russel, “Measurements of the effect of gravity waves in the middle atmosphere using parametric models of density fluctuations. I. Vertical wavenumber and temporal spectra,” J. Atmos. Sci. 56, 1308–1329 (1999).
[CrossRef]

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

Szapiel, S.

E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. F. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

Takamade, C.

R. Kobayashi, Y. Kohama, C. Takamade, “Spiral vortices in boundary layer transition regime on a rotating disk,” Acta Mech. 35, 71–82 (1980).
[CrossRef]

Thibault, S.

Tremblay, G.

G. Tremblay, “Étude des propriétés optiques et mécaniques d’un miroir liquide de 3.7 metres de diamètre,” Ph.D. dissertation (Département de Physique, Université Laval, Quebec, Canada, 1999).

Tremblay, L. M.

E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. F. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

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, 201–204 (1994).
[CrossRef]

Wuerker, R.

R. Wuerker, “Bistatic LMT lidar alignment,” Opt. Eng. 36, 1421–1424 (1997).
[CrossRef]

Acta Mech. (1)

R. Kobayashi, Y. Kohama, C. Takamade, “Spiral vortices in boundary layer transition regime on a rotating disk,” Acta Mech. 35, 71–82 (1980).
[CrossRef]

Appl. Opt. (6)

Astron. J. (1)

R. Content, E. F. Borra, M. J. Drinkwater, S. Poirier, E. Poisson, M. Beauchemin, E. Boily, A. Gauthier, L. M. Tremblay, “A search for optical flashes and flares with a liquid mirror telescope,” Astron. J. 97, 917–922 (1989).
[CrossRef]

Astrophys. J. (4)

R. Cabanac, E. F. Borra, M. Beauchemin, “A search for peculiar objects with the NASA Orbital Debris Observatory 3-m liquid mirror telescope,” Astrophys. J. 509, 309–323 (1998).
[CrossRef]

E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. F. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

E. F. Borra, M. Beauchemin, R. Lalande, “Liquid mirror telescopes: observations with a 1-meter diameter prototype and scaling-up considerations,” Astrophys. J. 297, 846–851 (1985).
[CrossRef]

B. K. Gibson, P. Hickson, “Liquid mirror surface aberrations. 1. 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, 201–204 (1994).
[CrossRef]

Astrophys. J. Suppl. (1)

P. Hickson, M. Mulrooney, “University of British Columbia–NASA Multi-Narrowband Survey. I. Description and photometric properties of the survey,” Astrophys. J. Suppl. 115, 35–42 (1998).
[CrossRef]

Can J. Phys. (1)

E. F. Borra, “Liquid mirrors,” Can J. Phys. 73, 109–125 (1995).
[CrossRef]

Houille Blanche (1)

F. Biesel, “Calcul de l’amortissement d’une houille dans un liquide visqueux de profondeur finie,” Houille Blanche 5, 630–634 (1949).
[CrossRef]

J. Atmos. Sci. (1)

R. J. Sica, A. T. Russel, “Measurements of the effect of gravity waves in the middle atmosphere using parametric models of density fluctuations. I. Vertical wavenumber and temporal spectra,” J. Atmos. Sci. 56, 1308–1329 (1999).
[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).

Opt. Eng. (2)

R. Wuerker, “Bistatic LMT lidar alignment,” Opt. Eng. 36, 1421–1424 (1997).
[CrossRef]

R. V. Shack, G. H. Hopkins, “The Shack interferometer,” Opt. Eng. 18, 226–228 (1979).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

P. Hickson, B. K. Gibson, D. W. Hogg, “Large astronomical liquid mirrors,” Publ. Astron. Soc. Pac. 105, 501–508 (1993).
[CrossRef]

Other (4)

L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1959).

A. P. French, Vibrations and Waves, M.I.T. Introductory Physics Series (Norton, New York, 1971).

G. Tremblay, “Étude des propriétés optiques et mécaniques d’un miroir liquide de 3.7 metres de diamètre,” Ph.D. dissertation (Département de Physique, Université Laval, Quebec, Canada, 1999).

R. Content, “Tests optiques sur un miroir liquide de 1.5 m et développement de la technologie des miroirs liquides,” Ph.D. dissertation (Département de Physique, Université Laval, Québec, Canada, 1992).

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Figures (12)

Fig. 1
Fig. 1

Vibration spectrum of the mirror. The amplitudes of the oscillations have been measured with an accelerometer. The figure is somewhat misleading, for it gives the impression that the peak at 33 Hz is more important for the mirror than the peak at 12.6 Hz. Such is not the case (see text for complete explanation).

Fig. 2
Fig. 2

Typical interferogram of the 3.7-m mirror. The two conspicuous dark rings near the edges lie on one of the surfaces of the Shack cube and not on the LM.

Fig. 3
Fig. 3

Wave front obtained from the interferogram of Fig. 2. The spatial resolution on the mirror is 4 cm × 8 cm. OPD, optical path difference.

Fig. 4
Fig. 4

Highly saturated PSF taken with a relatively thick mercury layer (2.3 mm), showing the scattered light within 14 arcsec of the core of the PSF.

Fig. 5
Fig. 5

Part of the out-of-focus PSF of the mirror with 2.3 mm of mercury. White arrow, the outer edge of the mirror; the black arrow points to a bar that encompasses four 7-cm waves.

Fig. 6
Fig. 6

Encircled energy curves for two mercury thicknesses, each with and without a mask.

Fig. 7
Fig. 7

Comparison of the values of the resonant frequencies of the mirror obtained from the type 2 diffraction rings (points with error bars) with those obtained directly from measurements made with an accelerometer (continuous curve).

Fig. 8
Fig. 8

Slopes of the concentric waves on the mirror. The measurements are displayed along with the amplitudes predicted by the theory described in Section 5. Dotted curve, α = 3; solid curve, α = 7.

Fig. 9
Fig. 9

Amplitudes of the waves, predicted by the model in Section 5, for a mercury thickness of 2.3 mm.

Fig. 10
Fig. 10

Amplitudes of the concentric waves, predicted by the model in Section 5, for a mercury thickness of 0.85 mm.

Fig. 11
Fig. 11

Composite of snapshots of mirror surfaces obtained from out-of-focus PSF’s for various mercury thicknesses, qualitatively confirming the damping properties of thin layers.

Fig. 12
Fig. 12

Left, the surface of the 3.7-m mirror with a mercury thickness of 0.85 mm. Spiral-shaped defects can be seen at the right, which shows the surface of the 3.7-m mirror with a mercury thickness of 2.3 mm.

Tables (7)

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Table 1 rms Wave-Front Deviations (632.8-nm units), Strehl Ratios, and Third-Order Aberrations (Seidel coefficients) of Four Series of Measurements Obtained with a Mercury Thickness of 1.15 ± 0.03 mma

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Table 2 Average Wave Fronts for Eight Azimuth Anglesa

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Table 3 Characteristics of Three Individual Wave Frontsa

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Table 4 Statistics of the Wave Fronts of Table 3 after Third-Order Aberrations Are Removed

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Table 5 Parameters of the Principal Diffraction Rings

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Table 6 rms Surface Deviations as a Function of Layer Thickness, Caused by Vibration-Induced Concentric Ringsa

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Table 7 Diameters and Reynolds Numbers at the Onset of Turbulence as a Function of Mercury Thickness

Equations (12)

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Ω2=gk+αk3ρtanh kh,
λ=0.187 h0.42,
ν=12gπl,
Ax=F0/m|ω02-ω2|.
md2xdt2+κx=F0 cos ωt,
Ar=0.05Ac exp-αr-0.05+1.8Ae×exp-α1.8-r/r,
ζr=Arcos2πr/λ,
α=k3β2ncosh4kh+cosh2kh-1cosh4kh-1+β2k sinh2kh,
n=121+2khsinh2kh,
β=ω2ν,
α=15.8h-1.38.
R=r2ω/ν,

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