Abstract

We investigate a family of two-mirror correctors to compensate for the aberrations of a parabolic mirror observing at a large angle from the zenith. We constrain our designs to optical elements that can be built with currently available technology. The secondary and the tertiary mirrors are warped by Zernike polynomials, which we know can be generated with active vase mirrors. The performances of these corrector designs are usable for imagery.

© 1997 Optical Society of America

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References

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  1. E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
    [CrossRef]
  2. 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]
  3. 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. 436, L201–L204 (1994).
    [CrossRef]
  4. 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]
  5. B. Iannotta, “Spinning mages from mercury mirrors,” New Sci. 147(1986), 38–41 (1995).
  6. E. H. Richardson, C. L. Morbey, “Fifteen degree correcting optics for a 10-meter liquid mirror telescope,” in Instrumentation for Ground-Based Optical Astronomy Present and Future, L. B. Robinson, ed. (Springer, New York, 1987), pp. 720–723.
  7. E. F. Borra, “On the correction of the aberrations of a liquid mirror telescope observing at large zenith angles,” Astron. Astrophys. 278, 665–668 (1993).
  8. M. Paul, “Systèmes connecteurs pour réflecteurs astronomique,” Rev. Opt. 14, 169 (1935).
  9. N. J. Rumsey, Optical Instruments and Techniques (Oriel, Newcastle, 1970).
  10. J. G. Baker, “On improving the effectiveness of large telescopes,” IEEE Trans. Aerosp. Electron. Syst. AES-5, 261 (1969).
  11. J. R. P. Angel, N. J. Woolf, H. W. Epps, “Good images with very fast paraboloidal primaries: an optical solutionand some applications,” in Advanced Technology Optical Telescopes I, L. D. Barr, G. Burbidge, eds., Proc. SPIE332, 134–140 (1982).
    [CrossRef]
  12. E. F. Borra, G. Moretto, M. Wang, “An optical corrector design that allows a fixed telescope to access a large region of the sky,” Astron. Astrophys. Suppl. Ser. 109, 563–570 (1995).
  13. G. R. Lemaître, “Active optics and elastic relaxation methods,” Vol. 135 of Current Trends in Optics Series (Taylor & Francis, London, 1981).
  14. G. R. Lemaître, “Various aspects of active optics,” in Telescopes and Active Systems, F. J. Roddier, ed., Proc. SPIE1114, 328–341 (1989).
    [CrossRef]
  15. G. R. Lemaître, M. Wang, “Active vase mirrors warped by Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 1—Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).
  16. G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).
  17. S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959), pp. 282–286.
  18. G. Moretto, “Optical corrector design for fixed primary mirrors observing off-axis,” Ph.D. dissertation (Laval University, Québec, Canada, 1996).
  19. M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1964).
  20. D. Malacara, Optical Shop Testing (Wiley, New York, 1978), pp. 489–505.
  21. We use the software CodeV for the optical optimizations. CodeV is a trademark of Optical Research Associates, Pasadena, Calif.
  22. C. R. Benn, R. Martin, “Isaac Newton Observations 1984–1986,” Q. J. R. Astron. Soc. 28, 481–496 (1987).
  23. E. H. Richardson, “Corrector lens design for UBC 5-metre liquid mirror telescope,” Department of Mechanical Engineering, University of Victoria, Victoria, BC V8N 3P6, Canada (personal communication, 1995).
  24. D. Zaritsky, S. A. Shectman, G. Bredthauer, “The great circle camera: a new drift-scanning instrument,” Pub. Astron. Soc. Pac. 108, 104–109 (1996).
    [CrossRef]

1996

D. Zaritsky, S. A. Shectman, G. Bredthauer, “The great circle camera: a new drift-scanning instrument,” Pub. Astron. Soc. Pac. 108, 104–109 (1996).
[CrossRef]

1995

B. Iannotta, “Spinning mages from mercury mirrors,” New Sci. 147(1986), 38–41 (1995).

E. F. Borra, G. Moretto, M. Wang, “An optical corrector design that allows a fixed telescope to access a large region of the sky,” Astron. Astrophys. Suppl. Ser. 109, 563–570 (1995).

G. R. Lemaître, M. Wang, “Active vase mirrors warped by Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 1—Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

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]

1994

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. 436, L201–L204 (1994).
[CrossRef]

1993

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, “On the correction of the aberrations of a liquid mirror telescope observing at large zenith angles,” Astron. Astrophys. 278, 665–668 (1993).

1992

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

1987

C. R. Benn, R. Martin, “Isaac Newton Observations 1984–1986,” Q. J. R. Astron. Soc. 28, 481–496 (1987).

1969

J. G. Baker, “On improving the effectiveness of large telescopes,” IEEE Trans. Aerosp. Electron. Syst. AES-5, 261 (1969).

1935

M. Paul, “Systèmes connecteurs pour réflecteurs astronomique,” Rev. Opt. 14, 169 (1935).

Angel, J. R. P.

J. R. P. Angel, N. J. Woolf, H. W. Epps, “Good images with very fast paraboloidal primaries: an optical solutionand some applications,” in Advanced Technology Optical Telescopes I, L. D. Barr, G. Burbidge, eds., Proc. SPIE332, 134–140 (1982).
[CrossRef]

Argall, P. S.

Bactivelane, T.

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

Baker, J. G.

J. G. Baker, “On improving the effectiveness of large telescopes,” IEEE Trans. Aerosp. Electron. Syst. AES-5, 261 (1969).

Benn, C. R.

C. R. Benn, R. Martin, “Isaac Newton Observations 1984–1986,” Q. J. R. Astron. Soc. 28, 481–496 (1987).

Boily, E.

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

Born, M.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1964).

Borra, E. F.

E. F. Borra, G. Moretto, M. Wang, “An optical corrector design that allows a fixed telescope to access a large region of the sky,” Astron. Astrophys. Suppl. Ser. 109, 563–570 (1995).

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]

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

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. 436, L201–L204 (1994).
[CrossRef]

E. F. Borra, “On the correction of the aberrations of a liquid mirror telescope observing at large zenith angles,” Astron. Astrophys. 278, 665–668 (1993).

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 contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

Bredthauer, G.

D. Zaritsky, S. A. Shectman, G. Bredthauer, “The great circle camera: a new drift-scanning instrument,” Pub. Astron. Soc. Pac. 108, 104–109 (1996).
[CrossRef]

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. 436, L201–L204 (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. 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 contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

Di Biagio, B.

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

Epps, H. W.

J. R. P. Angel, N. J. Woolf, H. W. Epps, “Good images with very fast paraboloidal primaries: an optical solutionand some applications,” in Advanced Technology Optical Telescopes I, L. D. Barr, G. Burbidge, eds., Proc. SPIE332, 134–140 (1982).
[CrossRef]

Ferrari, M.

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

Flatt, S.

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. 436, L201–L204 (1994).
[CrossRef]

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 contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

Hickson, P.

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. 436, L201–L204 (1994).
[CrossRef]

Iannotta, B.

B. Iannotta, “Spinning mages from mercury mirrors,” New Sci. 147(1986), 38–41 (1995).

Lemaître, G. R.

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

G. R. Lemaître, M. Wang, “Active vase mirrors warped by Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 1—Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).

G. R. Lemaître, “Active optics and elastic relaxation methods,” Vol. 135 of Current Trends in Optics Series (Taylor & Francis, London, 1981).

G. R. Lemaître, “Various aspects of active optics,” in Telescopes and Active Systems, F. J. Roddier, ed., Proc. SPIE1114, 328–341 (1989).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), pp. 489–505.

Martin, R.

C. R. Benn, R. Martin, “Isaac Newton Observations 1984–1986,” Q. J. R. Astron. Soc. 28, 481–496 (1987).

Mazzanti, S.

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

Morbey, C. L.

E. H. Richardson, C. L. Morbey, “Fifteen degree correcting optics for a 10-meter liquid mirror telescope,” in Instrumentation for Ground-Based Optical Astronomy Present and Future, L. B. Robinson, ed. (Springer, New York, 1987), pp. 720–723.

Moretto, G.

E. F. Borra, G. Moretto, M. Wang, “An optical corrector design that allows a fixed telescope to access a large region of the sky,” Astron. Astrophys. Suppl. Ser. 109, 563–570 (1995).

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

G. Moretto, “Optical corrector design for fixed primary mirrors observing off-axis,” Ph.D. dissertation (Laval University, Québec, Canada, 1996).

Paul, M.

M. Paul, “Systèmes connecteurs pour réflecteurs astronomique,” Rev. Opt. 14, 169 (1935).

Richardson, E. H.

E. H. Richardson, “Corrector lens design for UBC 5-metre liquid mirror telescope,” Department of Mechanical Engineering, University of Victoria, Victoria, BC V8N 3P6, Canada (personal communication, 1995).

E. H. Richardson, C. L. Morbey, “Fifteen degree correcting optics for a 10-meter liquid mirror telescope,” in Instrumentation for Ground-Based Optical Astronomy Present and Future, L. B. Robinson, ed. (Springer, New York, 1987), pp. 720–723.

Rumsey, N. J.

N. J. Rumsey, Optical Instruments and Techniques (Oriel, Newcastle, 1970).

Sargoytchev, S.

Shectman, S. A.

D. Zaritsky, S. A. Shectman, G. Bredthauer, “The great circle camera: a new drift-scanning instrument,” Pub. Astron. Soc. Pac. 108, 104–109 (1996).
[CrossRef]

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 contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[CrossRef]

Timoshenko, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959), pp. 282–286.

Tremblay, L. M.

E. F. Borra, R. Content, L. Girard, S. Szapiel, L. M. Tremblay, E. Boily, “Liquid mirrors: optical shop tests and contributions to the technology,” Astrophys. J. 393, 829–847 (1992).
[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. 436, L201–L204 (1994).
[CrossRef]

Wang, M.

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

E. F. Borra, G. Moretto, M. Wang, “An optical corrector design that allows a fixed telescope to access a large region of the sky,” Astron. Astrophys. Suppl. Ser. 109, 563–570 (1995).

G. R. Lemaître, M. Wang, “Active vase mirrors warped by Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 1—Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).

Woinowsky-Krieger, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959), pp. 282–286.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1964).

Woolf, N. J.

J. R. P. Angel, N. J. Woolf, H. W. Epps, “Good images with very fast paraboloidal primaries: an optical solutionand some applications,” in Advanced Technology Optical Telescopes I, L. D. Barr, G. Burbidge, eds., Proc. SPIE332, 134–140 (1982).
[CrossRef]

Zaritsky, D.

D. Zaritsky, S. A. Shectman, G. Bredthauer, “The great circle camera: a new drift-scanning instrument,” Pub. Astron. Soc. Pac. 108, 104–109 (1996).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

E. F. Borra, “On the correction of the aberrations of a liquid mirror telescope observing at large zenith angles,” Astron. Astrophys. 278, 665–668 (1993).

Astron. Astrophys. Suppl. Ser.

E. F. Borra, G. Moretto, M. Wang, “An optical corrector design that allows a fixed telescope to access a large region of the sky,” Astron. Astrophys. Suppl. Ser. 109, 563–570 (1995).

G. R. Lemaître, M. Wang, “Active vase mirrors warped by Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 1—Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).

G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, B. Di Biagio, E. F. Borra, “Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors.—Part 2—Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

Astrophys. J.

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

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. 436, L201–L204 (1994).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

J. G. Baker, “On improving the effectiveness of large telescopes,” IEEE Trans. Aerosp. Electron. Syst. AES-5, 261 (1969).

New Sci.

B. Iannotta, “Spinning mages from mercury mirrors,” New Sci. 147(1986), 38–41 (1995).

Pub. Astron. Soc. Pac.

D. Zaritsky, S. A. Shectman, G. Bredthauer, “The great circle camera: a new drift-scanning instrument,” Pub. Astron. Soc. Pac. 108, 104–109 (1996).
[CrossRef]

Q. J. R. Astron. Soc.

C. R. Benn, R. Martin, “Isaac Newton Observations 1984–1986,” Q. J. R. Astron. Soc. 28, 481–496 (1987).

Rev. Opt.

M. Paul, “Systèmes connecteurs pour réflecteurs astronomique,” Rev. Opt. 14, 169 (1935).

Other

N. J. Rumsey, Optical Instruments and Techniques (Oriel, Newcastle, 1970).

E. H. Richardson, C. L. Morbey, “Fifteen degree correcting optics for a 10-meter liquid mirror telescope,” in Instrumentation for Ground-Based Optical Astronomy Present and Future, L. B. Robinson, ed. (Springer, New York, 1987), pp. 720–723.

J. R. P. Angel, N. J. Woolf, H. W. Epps, “Good images with very fast paraboloidal primaries: an optical solutionand some applications,” in Advanced Technology Optical Telescopes I, L. D. Barr, G. Burbidge, eds., Proc. SPIE332, 134–140 (1982).
[CrossRef]

G. R. Lemaître, “Active optics and elastic relaxation methods,” Vol. 135 of Current Trends in Optics Series (Taylor & Francis, London, 1981).

G. R. Lemaître, “Various aspects of active optics,” in Telescopes and Active Systems, F. J. Roddier, ed., Proc. SPIE1114, 328–341 (1989).
[CrossRef]

E. H. Richardson, “Corrector lens design for UBC 5-metre liquid mirror telescope,” Department of Mechanical Engineering, University of Victoria, Victoria, BC V8N 3P6, Canada (personal communication, 1995).

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959), pp. 282–286.

G. Moretto, “Optical corrector design for fixed primary mirrors observing off-axis,” Ph.D. dissertation (Laval University, Québec, Canada, 1996).

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1964).

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), pp. 489–505.

We use the software CodeV for the optical optimizations. CodeV is a trademark of Optical Research Associates, Pasadena, Calif.

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Figures (9)

Fig. 1
Fig. 1

Solutions of Eq. (1) when the value of the load q is zero or constant. The shaded terms are the classes of the deformation terms that are feasible for vase mirrors.

Fig. 2
Fig. 2

Layout of the angular FOV with nine positions f1…9 defined on the plane X(XAN) and Y(YAN). On this plane we have the focal plane or surface image (Si) defined by the axes XLocal and YLocal with the XLocal axis displaced in the Y(YAN) direction. The quantities Δ(Xn - Xm) and Δ(Yn - Ym) are the differences, in millimeters, of the chief ray’s X and Y coordinates for the positions fn and fm.

Fig. 3
Fig. 3

Schematic design for a 4-m-diameter f/4.5 mirror observing at θ = 5.0° from the zenith and with a FOV of 12 arc min. ϕ represents the diameter in millimeters of each mirror and Rn is the radius of curvature for the nth surface. The system is symmetrical in the XZ plane. The dimensions are given in millimeters. The human figure at the bottom right of the telescope gives a handy reference scale. THI’s, distances between subsequent surfaces measured along the optical axis of the optical element; ADE’s, tilts of the lenses’ Y axis in the YZ plane; YDE’s, surface decenters along the Y direction of the lens (these abbreviations are also used in the figures below).

Fig. 4
Fig. 4

Spot diagrams for point sources observed at 4.90°, 5.00°, and 5.10° from the zenith and displaced by ±0.10° in the orthogonal direction. The parameters of the corrector have been optimized to give good images simultaneously for the nine spots.

Fig. 5
Fig. 5

Schematic design for a 4-m-diameter f/5.25 mirror with the correctors observing at θ = 7.50° from the zenith and a FOV of 18 arc min. ϕ represents the diameter for each mirror, and Rn is the radius of curvature for the nth surface. The dimensions are given in millimeters. Note that the system is symmetrical in the XZ plane. The details for the three-lens sets are shown in Figs. 6 and 7. The human figure at the bottom right of the telescope gives a handy reference scale. EFL, effective focal length.

Fig. 6
Fig. 6

Details of the three-lens group and the active secondary and tertiary mirrors for the 4-m-diameter f/5.25 mirror observing at θ = 7.50° from the zenith and with a FOV of 18 arc min.

Fig. 7
Fig. 7

Details of the three-lens group for the system. Each decenter defines a subsequent surface displaced or rotated from the preceding surface. The dimensions are given in millimeters.

Fig. 8
Fig. 8

Spot diagrams for point sources observed at 7.35°, 7.50°, and 7.65° from the zenith and displaced by ±0.15° in the orthogonal direction, at wavelengths of (a) 600 nm, (b) 700 nm, (c) 800 nm. The parameters of the corrector have been optimized for the 800–600-nm wavelength band.

Fig. 9
Fig. 9

EED for point sources observed at 7.35°, 7.50°, and 7.65° from the zenith and displaced by ±0.15° in the orthogonal direction. Because of the bilateral symmetry, the curves for +0.15° are the same as those for -0.15°.

Tables (12)

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Table 1 Standard Zernike Polynomials Used in the Optical Optimizations

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Table 2 Values of Zernike Coefficients for the Secondary and the Tertiary vase mirrors for the 5.00° ± 0.10° Design

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Table 3 Parameters that Characterize the Correction at 5.0° from the Zenith: a Single Two-Mirror Corrector Corrects at ±0.1° and at the 632.8-nm Wavelength

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Table 4 Corrector Distortion at 632.8 nm for each Section of FOV that Characterizes the Corrections for the Selected Zenith Angles: θ = 5.00 ± 0.10a

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Table 5 Values of Zernike Coefficients for the Secondary and the Tertiary Vase Mirrors for 7.50° ± 0.15° Design

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Table 6 Geometric Parameters for the Three-Lens Set, Surfaces S4 to S9a

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Table 7 Values of Aspherical terms for the Second (S6 and S7) and the Third (S8 and S9) Lensesa

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Table 8 Parameters that Characterize the Correction at 7.50° from the Zenith: A Single Two-Mirror Corrector Corrects at ±0.15°

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Table 9 Corrector Distortion at Two Wavelengths for each Section of FOV that Characterizes the Correction at Selected Zenith Anglesa

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Table 10 Radial Energy Distributions for the Spot Diagrams that Characterize the Corrections at Selected Zenith Anglesa

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Table 11 Maximum Amplitudes of Deflection wmax for the 7.50° ± 0.15° Design, in Millimeters, for each Zernike Term Zia

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Table 12 Maximum Amplitudes of Deflection wmax for the 5.00° ± 0.10° Design, in millimeters, for each Zernike term Zia

Equations (3)

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22wr, θ=q/D,
Z=cρ21+1-1-Kc2ρ21/2+Aρ4+Bρ6+Cρ8+Dρ10,
C51+νσmax/Et2,

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