Abstract

A parabolic liquid mirror obtained by the rotation of a mercury bath around a vertical axis has been built and its optical surface characteristics measured to demonstrate that it can be used in optical shop testing as a reference surface. A linear Hartmann test allowed us to check that the focal length is well related to the rotation velocity, following the theory, and that no spherical aberration is present, as assumed by previous authors. The spherical aberration has been found to be smaller than λ/50 at 633 nm. An interferometric test of the mirror compared with a null lens gave information about the quality of the optical surface for which the rms wave-front error, when the random errors are averaged, is ∼λ./25. Because modifying the mirror diameter is cheap and fast and adjusting its focal length within a large range is straightforward, the parabolic liquid mirror can become a highly adaptable tool in optical metrology. In particular, it can be used in optical shop testing as a reference surface to test null correctors, to check any system developed to control the shape of large parabolic or quasiparabolic top-quality solid-state mirrors, or to make holographic references of such surfaces.

© 1996 Optical Society of America

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References

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  1. Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
    [CrossRef]
  2. D. A. Kestelsen, D. S. Anderson, “Optical testing with large liquid flats,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 365–371 (1988).
  3. E. F. Borra, “The liquid mirror telescope as a viable astronomical tool,” J. R. Astron. Soc. Can. 76, 245–256 (1982).
  4. E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. Boily, “Liquid mirrors: optical shop tests and contribution to the technology,” Astrophys. J. 393, 829–847 (1992).
    [CrossRef]
  5. P. Hickson, E. Borra, R. Cabanac, R. Content, B. K. Gibson, G. A. H. Walker, “UBC/Laval 2.7-meter liquid mirror telescope,” Astrophys. J. 436, L201–L204 (1994).
    [CrossRef]
  6. R. J. Sica, S. Sargoytchev, P. S. Argall, E. F. Borra, L. Girard, C. T. Sparrow, S. Flatt, “Lidar measurements taken with a large-aperture liquid mirror. 1. Rayleigh-scatter system,” Appl. Opt. 34, 6925–6936 (1995).
    [CrossRef] [PubMed]
  7. E. F. Borra, M. Beauchemin, R. Arsenault, R. Lalande, “Optical shop testing of liquid mirrors,” Publ. Astron. Soc. Pac. 97, 454–464 (1985).
    [CrossRef]
  8. E. F. Borra, R. Content, M. Drinkwater, S. Szapiel, “A diffraction-limited f/2 1.5-meter diameter liquid mirror,” Astrophys. J. 346, L41–L44 (1989).
    [CrossRef]
  9. E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).
  10. E. F. Borra, R. Content, L. Girard, “Optical shop tests of a f/1.2 2.5-meter diameter liquid mirror,” Astrophys. J. 418, 943–946 (1993).
    [CrossRef]
  11. F. Biesel, “Calcul de l'amortissement d'une houle dans un liquide visqueux de profondeur finie,” Houille Blanche 5, 630–634 (1949).
    [CrossRef]
  12. Ph. M. Gerhart, R. J. Gross, J. I. Hoschstein, “Mechanics of nonflowing fluids,” in Fundamentals of Fluid Mechanics (Addison-Wesley, New York, 1992), pp. 88–93.
  13. 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]
  14. B. Gibson, P. Hickson, “Liquid mirror surface aberrations. I. Wavefront analysis,” Astrophys. J. 391, 409–417 (1992).
    [CrossRef]
  15. M. Alonso, E. J. Finn, “Mouvement relatif,” in Physique Générale (InterEdition, Paris, 1977), pp. 133–135.
  16. I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 88–93.
  17. J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 323–349 (1964).
    [CrossRef]
  18. V. N. Mahajan, ed., Aberration Theory Made Simple, Vol. TT06 of SPIE Tutorial Text Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1991).
    [CrossRef]
  19. J. M. Sasian, “Design of null lens correctors for the testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).
  20. J. M. Sasian, “Optimum configuration of the Offner null corrector: testing an F/1 paraboloid,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 8–12 (1989).
  21. M. C. Ruda, Optical Alignment Techniques, (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).
  22. W. Walter, “High precision antenna structures, FIRST related technology programme,” Final Rep. of ESA contract 8556/89/NL/PP(SC) RST 121-31/92 (European Space Agency, Noordwijk, 1992).
  23. N. Ninane, A. Orban, “Far Infrared and Submillimeter Space Telescope: on ground verification of high precision antenna structures,” Final Rep. of ESA contract 9939/92/NL/BS Task 93/CSL/01/04/61C (European Space Agency, Noordwijk, 1994).

1995 (1)

1994 (1)

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

1993 (1)

E. F. Borra, R. Content, L. Girard, “Optical shop tests of a f/1.2 2.5-meter diameter liquid mirror,” Astrophys. J. 418, 943–946 (1993).
[CrossRef]

1992 (2)

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

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

1989 (1)

E. F. Borra, R. Content, M. Drinkwater, S. Szapiel, “A diffraction-limited f/2 1.5-meter diameter liquid mirror,” Astrophys. J. 346, L41–L44 (1989).
[CrossRef]

1988 (1)

J. M. Sasian, “Design of null lens correctors for the testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).

1985 (2)

E. F. Borra, M. Beauchemin, R. Arsenault, R. Lalande, “Optical shop testing of liquid mirrors,” Publ. Astron. Soc. Pac. 97, 454–464 (1985).
[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]

1982 (1)

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

1964 (1)

J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 323–349 (1964).
[CrossRef]

1949 (1)

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

1893 (1)

Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
[CrossRef]

Alonso, M.

M. Alonso, E. J. Finn, “Mouvement relatif,” in Physique Générale (InterEdition, Paris, 1977), pp. 133–135.

Anderson, D. S.

D. A. Kestelsen, D. S. Anderson, “Optical testing with large liquid flats,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 365–371 (1988).

Argall, P. S.

Arsenault, R.

E. F. Borra, M. Beauchemin, R. Arsenault, R. Lalande, “Optical shop testing of liquid mirrors,” Publ. Astron. Soc. Pac. 97, 454–464 (1985).
[CrossRef]

Beauchemin, M.

E. F. Borra, M. Beauchemin, R. Arsenault, R. Lalande, “Optical shop testing of liquid mirrors,” Publ. Astron. Soc. Pac. 97, 454–464 (1985).
[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 houle dans un liquide visqueux de profondeur finie,” Houille Blanche 5, 630–634 (1949).
[CrossRef]

Boily, E.

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

Borra, E.

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

Borra, E. F.

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

E. F. Borra, R. Content, L. Girard, “Optical shop tests of a f/1.2 2.5-meter diameter liquid mirror,” Astrophys. J. 418, 943–946 (1993).
[CrossRef]

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

E. F. Borra, R. Content, M. Drinkwater, S. Szapiel, “A diffraction-limited f/2 1.5-meter diameter liquid mirror,” Astrophys. J. 346, L41–L44 (1989).
[CrossRef]

E. F. Borra, M. Beauchemin, R. Arsenault, R. Lalande, “Optical shop testing of liquid mirrors,” Publ. Astron. Soc. Pac. 97, 454–464 (1985).
[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).

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

Cabanac, R.

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

Content, R.

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

E. F. Borra, R. Content, L. Girard, “Optical shop tests of a f/1.2 2.5-meter diameter liquid mirror,” Astrophys. J. 418, 943–946 (1993).
[CrossRef]

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

E. F. Borra, R. Content, M. Drinkwater, S. Szapiel, “A diffraction-limited f/2 1.5-meter diameter liquid mirror,” Astrophys. J. 346, L41–L44 (1989).
[CrossRef]

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

Drinkwater, M.

E. F. Borra, R. Content, M. Drinkwater, S. Szapiel, “A diffraction-limited f/2 1.5-meter diameter liquid mirror,” Astrophys. J. 346, L41–L44 (1989).
[CrossRef]

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

Finn, E. J.

M. Alonso, E. J. Finn, “Mouvement relatif,” in Physique Générale (InterEdition, Paris, 1977), pp. 133–135.

Flatt, S.

Gerhart, Ph. M.

Ph. M. Gerhart, R. J. Gross, J. I. Hoschstein, “Mechanics of nonflowing fluids,” in Fundamentals of Fluid Mechanics (Addison-Wesley, New York, 1992), pp. 88–93.

Ghozeil, I.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 88–93.

Gibson, B.

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

Gibson, B. K.

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

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

Girard, L.

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

E. F. Borra, R. Content, L. Girard, “Optical shop tests of a f/1.2 2.5-meter diameter liquid mirror,” Astrophys. J. 418, 943–946 (1993).
[CrossRef]

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

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

Gross, R. J.

Ph. M. Gerhart, R. J. Gross, J. I. Hoschstein, “Mechanics of nonflowing fluids,” in Fundamentals of Fluid Mechanics (Addison-Wesley, New York, 1992), pp. 88–93.

Hickson, P.

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

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

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

Hoschstein, J. I.

Ph. M. Gerhart, R. J. Gross, J. I. Hoschstein, “Mechanics of nonflowing fluids,” in Fundamentals of Fluid Mechanics (Addison-Wesley, New York, 1992), pp. 88–93.

Kestelsen, D. A.

D. A. Kestelsen, D. S. Anderson, “Optical testing with large liquid flats,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 365–371 (1988).

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]

E. F. Borra, M. Beauchemin, R. Arsenault, R. Lalande, “Optical shop testing of liquid mirrors,” Publ. Astron. Soc. Pac. 97, 454–464 (1985).
[CrossRef]

Morbey, C.

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

Ninane, N.

N. Ninane, A. Orban, “Far Infrared and Submillimeter Space Telescope: on ground verification of high precision antenna structures,” Final Rep. of ESA contract 9939/92/NL/BS Task 93/CSL/01/04/61C (European Space Agency, Noordwijk, 1994).

Orban, A.

N. Ninane, A. Orban, “Far Infrared and Submillimeter Space Telescope: on ground verification of high precision antenna structures,” Final Rep. of ESA contract 9939/92/NL/BS Task 93/CSL/01/04/61C (European Space Agency, Noordwijk, 1994).

Rayces, J. L.

J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 323–349 (1964).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
[CrossRef]

Ruda, M. C.

M. C. Ruda, Optical Alignment Techniques, (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).

Sargoytchev, S.

Sasian, J. M.

J. M. Sasian, “Design of null lens correctors for the testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).

J. M. Sasian, “Optimum configuration of the Offner null corrector: testing an F/1 paraboloid,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 8–12 (1989).

Sica, R. J.

Sparrow, C. T.

Szapiel, S.

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

E. F. Borra, R. Content, M. Drinkwater, S. Szapiel, “A diffraction-limited f/2 1.5-meter diameter liquid mirror,” Astrophys. J. 346, L41–L44 (1989).
[CrossRef]

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

Tremblay, L. M.

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

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

Walker, G. A. H.

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

Walter, W.

W. Walter, “High precision antenna structures, FIRST related technology programme,” Final Rep. of ESA contract 8556/89/NL/PP(SC) RST 121-31/92 (European Space Agency, Noordwijk, 1992).

Appl. Opt. (1)

Astrophys. J. (6)

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

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

E. F. Borra, R. Content, M. Drinkwater, S. Szapiel, “A diffraction-limited f/2 1.5-meter diameter liquid mirror,” Astrophys. J. 346, L41–L44 (1989).
[CrossRef]

E. F. Borra, R. Content, L. Girard, “Optical shop tests of a f/1.2 2.5-meter diameter liquid mirror,” Astrophys. J. 418, 943–946 (1993).
[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. Gibson, P. Hickson, “Liquid mirror surface aberrations. I. Wavefront analysis,” Astrophys. J. 391, 409–417 (1992).
[CrossRef]

Houille Blanche (1)

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

Nature (London) (1)

Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
[CrossRef]

Opt. Acta (1)

J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 323–349 (1964).
[CrossRef]

Opt. Eng. (1)

J. M. Sasian, “Design of null lens correctors for the testing of astronomical optics,” Opt. Eng. 27, 1051–1056 (1988).

Publ. Astron. Soc. Pac. (1)

E. F. Borra, M. Beauchemin, R. Arsenault, R. Lalande, “Optical shop testing of liquid mirrors,” Publ. Astron. Soc. Pac. 97, 454–464 (1985).
[CrossRef]

Other (10)

J. M. Sasian, “Optimum configuration of the Offner null corrector: testing an F/1 paraboloid,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 8–12 (1989).

M. C. Ruda, Optical Alignment Techniques, (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).

W. Walter, “High precision antenna structures, FIRST related technology programme,” Final Rep. of ESA contract 8556/89/NL/PP(SC) RST 121-31/92 (European Space Agency, Noordwijk, 1992).

N. Ninane, A. Orban, “Far Infrared and Submillimeter Space Telescope: on ground verification of high precision antenna structures,” Final Rep. of ESA contract 9939/92/NL/BS Task 93/CSL/01/04/61C (European Space Agency, Noordwijk, 1994).

V. N. Mahajan, ed., Aberration Theory Made Simple, Vol. TT06 of SPIE Tutorial Text Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1991).
[CrossRef]

D. A. Kestelsen, D. S. Anderson, “Optical testing with large liquid flats,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 365–371 (1988).

Ph. M. Gerhart, R. J. Gross, J. I. Hoschstein, “Mechanics of nonflowing fluids,” in Fundamentals of Fluid Mechanics (Addison-Wesley, New York, 1992), pp. 88–93.

E. F. Borra, R. Content, M. Drinkwater, L. Girard, L. M. Tremblay, S. Szapiel, B. K. Gibson, P. Hickson, C. Morbey, “Liquid mirrors: a progress report,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 653–662 (1990).

M. Alonso, E. J. Finn, “Mouvement relatif,” in Physique Générale (InterEdition, Paris, 1977), pp. 133–135.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 88–93.

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Figures (11)

Fig. 1
Fig. 1

Expanded view of the liquid-mirror system.

Fig. 2
Fig. 2

Section of the liquid-mirror container.

Fig. 3
Fig. 3

Hartmann test setup.

Fig. 4
Fig. 4

Amplitude of the spherical aberration W4 that results from an error of the focal length Δf versus the F-number when a corrector is tested with a reference mirror. ×, Δf = 0.5 mm; +, Δf = 1 mm; *, Δf = 1.5 mm. The curves are computed with the formula W4 = −17.2 × 10−4 Δf/F 4 for the respective values of Δf.

Fig. 5
Fig. 5

Interferogram of the parabolic liquid mirror with a mercury layer thickness of 1.4 mm.

Fig. 6
Fig. 6

Interferograms of the liquid mirror for two different mercury layer thicknesses t: top, t = 1.7 mm; bottom, t = 0.8 mm.

Fig. 7
Fig. 7

Radial profile of the surface error when the rotation axis is tilted with respect to the direction of the gravity force by approximately 5 arc sec.

Fig. 8
Fig. 8

WFE three-dimensional plot of an average of 106 interferometric measurements taken at regular intervals during one period of rotation of the liquid mirror.

Fig. 9
Fig. 9

WFE map of a CFRP antenna measured with a null lens. WFE rms = 8 μm, Z(9) = −13.1 μm.

Fig. 10
Fig. 10

WFE map of the null lens, adapted to the CFRP antenna, measured with the liquid mirror. WFE rms = 0.6 μm, Z(9) = 1 μm.

Fig. 11
Fig. 11

Profile of the WFE of the CFRP mirror and of its null lens.

Tables (4)

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Table 1 Primary Mirror of Different Telescopes with Their Diameter and Conic Constant a

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Table 2 Basic Parameters of the Liquid Mirror

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Table 3 The Hartmann Test: the Average, the Standard Deviation, and the Estimated Accuracy of the Measurements

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Table 4 Zernike Coefficients of the Liquid-Mirror WFE a

Equations (19)

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f = g 2 ω 2
z = ω 2 r 2 2 g ,
f = g 2 ω 2 .
a = a 2 Ω × ν Ω × ( Ω × r ) ,
f = ( g Ω 2 R E cos 2 l ) ( 2 ω 2 + 4 ω Ω sin l ) ,
W ( r ) r = TA ( r ) YP ,
W ( u ) = W 0 + W 1 u + W 2 u 2 + W 3 u 3 + W 4 u 4 + W 5 u 5 ,
Δ f = W 2 R 2 2 r 2 ,
Z ( 9 ) = ( W 4 ) / 6 .
W 4 = 3 2 Δ f ( r R ) 4 .
W 4 = 17.2 × 10 4 Δ f F 4 = 0.44 Δ f ( r R ) 4 ,
z = R 1 + K { 1 [ 1 r 2 R 2 ( 1 + K ) ] 1 / 2 } ,
z = r 2 2 R
z a z p = r 2 2 R a r 2 2 ( R a + d R ) + ( 1 + K a ) r 4 8 R a 3 + ( 1 + K a ) 2 r 6 16 R a 5 + , ,
z a z p r 2 d R 2 R a 2 + r 4 ( 1 + K a ) 8 R a 3 .
d ( z a z p ) d r | r = a = d ( z a z p ) d r | r = b ;
d 2 ( z a z p ) d r 2 | b = 0 ,
d R = 3 a 2 K a 8 R a .
s = 1 8 r 3 ( 1 + K a ) R a 3 .

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