Abstract

Recording methods for making aberration-corrected holographic gratings are greatly simplified by use of a plane multimode deformable mirror (MDM) upon one of the two recording beams. It is shown that MDM compensators easily provide the superposition of many interesting active optics modes, which we have named Clebsch–Zernike modes. When we apply only a uniform loading or no loading at all onto the rear side of the MDM clear aperture, the available Clebsch–Zernike modes are made to belong to a subclass of the Zernike modes that includes the three modes of the third-order aberration theory as well as a well-defined part of the Zernike higher-order modes. Such a recording method is considered to be universal, since it does not require the use of a sophisticated optical system such as a compensator. Active optics 12-arm MDM’s in the vase form have been designed from the elasticity theory. The design of six-arm MDM’s is currently carried out with theoretical results. As an example of the method, the recording of three holographic gratings of the Hubble Space Telescope Cosmic Origins Spectrograph has been investigated. Substantial improvements in image quality have been found by use of a six-arm MDM as recording compensator. The result is that aberrations of much higher order can simultaneously be corrected so that the residual blur images of the spectra occupy areas approximately 10 (direction of dispersion) × 3 (cross dispersion) = 30 times smaller—also in terms of pixel number—than those obtained by our American colleagues. Therefore the active optics recording method appears to provide substantial gains in resolving power and in sensitivity: (i) For all three gratings the spectral resolution would be increased by a factor of 10, and (ii), in addition, for the two higher dispersion gratings, the limiting magnitude on the sky appears to be increased by a magnitude of approximately 1–1.2.

© 2001 Optical Society of America

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  1. M. Duban, “Holographic aspheric gratings printed with aberration waves,” Appl. Opt. 26, 4263–4273 (1987).
    [CrossRef] [PubMed]
  2. M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
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  3. M. Duban, “Third-generation holographic Rowland mounting: fourth-order theory,” Appl. Opt. 38, 3443–3449 (1999).
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  4. M. Duban, G. R. Lemaître, R. Malina, “Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors,” Appl. Opt. 37, 3438–3439 (1998).
    [CrossRef]
  5. M. Duban, K. Dohlen, G. R. Lemaître, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope,” Appl. Opt. 37, 7214–7217 (1998).
    [CrossRef]
  6. M. Duban, “Theory and computation of three Cosmic Origins Spectrograph aspheric gratings recorded with a multimode deformable mirror,” Appl. Opt. 38, 1096–1102 (1999).
    [CrossRef]
  7. G. R. Lemaître, M. Wang, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. I. Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).
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    [CrossRef]
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    [CrossRef]
  10. J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
    [CrossRef]
  11. M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213 (1998).
    [CrossRef]
  12. G. R. Lemaître, M. Duban, “A general method of holographic grating recording with a null-powered multimode deformable mirror,” Astron. Astrophys. 339, L89–L93 (1998).
  13. S. Osterman, E. Wilkinson, J. C. Green, K. Redman, “FUV grating performance for the Cosmic origins spectrograph, in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 360–366 (2000).
    [CrossRef]
  14. G. R. Lemaître, “Various aspects of active optics,” in Active Telescope Systems, F. J. Roddier, eds., Proc. SPIE1114, 328–341 (1989).
    [CrossRef]
  15. G. R. Lemaître, M. Wang, “Témos 4: optical results with a segmented spherical primary and an actively aspherized secondary, in Metal Mirrors, R. G. Bingham, D. D. Walker, eds., Proc. SPIE1931, 43–52 (1992).
  16. A. Couder, “Sur les miroirs de télescopes,” Bull. Astronom.2nd ed., Tome VII, Fasc. VI, 219 et seq. (1931).
  17. G. Moretto, G. R. Lemaître, T. Bactivelane, M. Wang, M. Ferrari, S. Mazzanti, E. F. Borra, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. II. Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).
  18. A. R. F. Clebsch, in Theorie der Elasticität fester Körper (Teubner, Leipzig, 1862) [French translation, Théorie de l’Élasticité des Corps Solides, with annotations and complements by Saint-Venant and Flamant (Dunod, Paris, 1881)].
  19. B. Schmidt, “A coma-free telescope,” Mitt. Hamburg Strenv. 7, 15 (1932).
  20. E. Schmidt, in Optical Illusions: The Life Story of Bernhard Schmidt the Great Stellar Optician of the Twentieth Century (Estonian Academy Publishers, Tallinn, Estonia, 1995) (ISBN 9985-50-102-0).
  21. J. Kross, in L’Oeil du Grand Tout (Laffont, Paris, 1997). French translation of the Estonian book Vastutuulelaev, Kirjastus Eesti Raamat, Estonia, 1987. This book is about the life of Bernhard Schmidt, 1879–1935.
  22. R. N. Wilson, in Reflecting Telescope Optics II (Springer, Berlin, 1999), Chap. 3.
  23. R. N. Wilson, F. Franza, L. Noethe, “The ESO 3.5 meter Ntt-Active optics I: a system for optimizing the optical quality and reducing the cost of large telescopes,” J. Mod. Opt. 34, 485–511 (1987).
    [CrossRef]
  24. G. R. Lemaître, “In situ active reshaping of the CFHT Cassegrain mirror,” available from the author.
  25. G. R. Lemaître, “Asphérisation par relaxation élastique—Miroirs de forme en vase,” Comptes Rendus Acad. Sci. Ser. B 290, 171–174 (1980).
  26. G. R. Lemaître, “Active optics and elastic relaxation methods,” in Current Trends in Optics, International Commission for Optics 12 (Taylor & Francis, London, 1981), pp. 135–149.
  27. W. Min, “Instrumentation astrophysique et optique active: evaluation de Témos 4,” Ph.D. dissertation, (Observatoire de Marseille, Université de Provence Aix-Marseille I, Aix-en-Provence, 1992).
  28. J. Lubliner, J. E. Nelson, “Keck Telescope: stressed mirror polishing,” Appl. Opt. 19, 2332–2340 (1980).
    [CrossRef] [PubMed]
  29. D. Su, X. Cui, Y. Wang, Z. Yao, “Large-sky-area multiobject fiber spectroscopic telescope (LAMOST) and its key technology, in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed., Proc. SPIE3352, 76–90 (1998).
    [CrossRef]
  30. S. Wang, D. Su, Y. Chu, X. Cui, Y. Wang, “Special configuration of a very large Schmidt telescope for extensive astronomical spectroscopic observation,” Appl. Opt. 35, 5155–5161 (1996).
    [CrossRef] [PubMed]
  31. X. Cui, D. Yang, “Support structure of LAMOST Schmidt plate MA,” in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed. Proc. SPIE3352, 378–385 (1998).
    [CrossRef]
  32. G. R. Lemaître, “Elasticité et miroirs à courbure variable,” Comptes Rendus Acad. Sci. Series B 282, 87–89 (1976).
  33. M. Ferrari, G. R. Lemaître, “Analysis of large deflection variable curvature mirrors,” Astron. Astrophys. 274, 12–18 (1993).
  34. M. Ferrari, “Optique active et grandes déformations élastiques,” Ph.D. dissertation (Observatoire de Marseille, Université de Provence Aix-Marseille I, Aix-en-Provence, 1994).
  35. A. Saint-Venant (Barré de), in Résumé des Leçons de Navier sur l’Application à la Mécanique, 3rd. ed. (Dunod, Paris, 1864), p. 40.
  36. P. Germain, P. Muller, in Introduction à la Mécanique des Milieux Continus (Masson, Paris, 1994), pp. 140–141.
  37. S. P. Timoshenko, S. Woinowsky-Krieger, in Theory of Plates and Shells (McGraw-Hill, New York, 1959), p. 248.

1999 (2)

1998 (4)

1996 (1)

1995 (2)

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

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

1993 (1)

M. Ferrari, G. R. Lemaître, “Analysis of large deflection variable curvature mirrors,” Astron. Astrophys. 274, 12–18 (1993).

1991 (1)

1987 (2)

M. Duban, “Holographic aspheric gratings printed with aberration waves,” Appl. Opt. 26, 4263–4273 (1987).
[CrossRef] [PubMed]

R. N. Wilson, F. Franza, L. Noethe, “The ESO 3.5 meter Ntt-Active optics I: a system for optimizing the optical quality and reducing the cost of large telescopes,” J. Mod. Opt. 34, 485–511 (1987).
[CrossRef]

1980 (2)

G. R. Lemaître, “Asphérisation par relaxation élastique—Miroirs de forme en vase,” Comptes Rendus Acad. Sci. Ser. B 290, 171–174 (1980).

J. Lubliner, J. E. Nelson, “Keck Telescope: stressed mirror polishing,” Appl. Opt. 19, 2332–2340 (1980).
[CrossRef] [PubMed]

1976 (1)

G. R. Lemaître, “Elasticité et miroirs à courbure variable,” Comptes Rendus Acad. Sci. Series B 282, 87–89 (1976).

1932 (1)

B. Schmidt, “A coma-free telescope,” Mitt. Hamburg Strenv. 7, 15 (1932).

Andrews, J. P.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Bactivelane, T.

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

Borra, E. F.

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

Chu, Y.

Clebsch, A. R. F.

A. R. F. Clebsch, in Theorie der Elasticität fester Körper (Teubner, Leipzig, 1862) [French translation, Théorie de l’Élasticité des Corps Solides, with annotations and complements by Saint-Venant and Flamant (Dunod, Paris, 1881)].

Couder, A.

A. Couder, “Sur les miroirs de télescopes,” Bull. Astronom.2nd ed., Tome VII, Fasc. VI, 219 et seq. (1931).

Cui, X.

S. Wang, D. Su, Y. Chu, X. Cui, Y. Wang, “Special configuration of a very large Schmidt telescope for extensive astronomical spectroscopic observation,” Appl. Opt. 35, 5155–5161 (1996).
[CrossRef] [PubMed]

X. Cui, D. Yang, “Support structure of LAMOST Schmidt plate MA,” in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed. Proc. SPIE3352, 378–385 (1998).
[CrossRef]

D. Su, X. Cui, Y. Wang, Z. Yao, “Large-sky-area multiobject fiber spectroscopic telescope (LAMOST) and its key technology, in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed., Proc. SPIE3352, 76–90 (1998).
[CrossRef]

Dohlen, K.

Duban, M.

Ebbets, D. C.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Ferrari, M.

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

M. Ferrari, G. R. Lemaître, “Analysis of large deflection variable curvature mirrors,” Astron. Astrophys. 274, 12–18 (1993).

M. Ferrari, “Optique active et grandes déformations élastiques,” Ph.D. dissertation (Observatoire de Marseille, Université de Provence Aix-Marseille I, Aix-en-Provence, 1994).

Franza, F.

R. N. Wilson, F. Franza, L. Noethe, “The ESO 3.5 meter Ntt-Active optics I: a system for optimizing the optical quality and reducing the cost of large telescopes,” J. Mod. Opt. 34, 485–511 (1987).
[CrossRef]

Germain, P.

P. Germain, P. Muller, in Introduction à la Mécanique des Milieux Continus (Masson, Paris, 1994), pp. 140–141.

Green, J. C.

J. C. Green, “The cosmic origins spectrograph: a Hubble replacement instrument for the 2002 reservicing mission,” in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 265–270 (1998).
[CrossRef]

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

J. C. Green, “The cosmic origins spectrograph,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 352–359 (2000).
[CrossRef]

S. Osterman, E. Wilkinson, J. C. Green, K. Redman, “FUV grating performance for the Cosmic origins spectrograph, in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 360–366 (2000).
[CrossRef]

Heap, S. R.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Kross, J.

J. Kross, in L’Oeil du Grand Tout (Laffont, Paris, 1997). French translation of the Estonian book Vastutuulelaev, Kirjastus Eesti Raamat, Estonia, 1987. This book is about the life of Bernhard Schmidt, 1879–1935.

Leitherer, C.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Lemaître, G. R.

M. Duban, G. R. Lemaître, R. Malina, “Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors,” Appl. Opt. 37, 3438–3439 (1998).
[CrossRef]

G. R. Lemaître, M. Duban, “A general method of holographic grating recording with a null-powered multimode deformable mirror,” Astron. Astrophys. 339, L89–L93 (1998).

M. Duban, K. Dohlen, G. R. Lemaître, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope,” Appl. Opt. 37, 7214–7217 (1998).
[CrossRef]

G. R. Lemaître, M. Wang, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. I. 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, E. F. Borra, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. II. Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

M. Ferrari, G. R. Lemaître, “Analysis of large deflection variable curvature mirrors,” Astron. Astrophys. 274, 12–18 (1993).

G. R. Lemaître, “Asphérisation par relaxation élastique—Miroirs de forme en vase,” Comptes Rendus Acad. Sci. Ser. B 290, 171–174 (1980).

G. R. Lemaître, “Elasticité et miroirs à courbure variable,” Comptes Rendus Acad. Sci. Series B 282, 87–89 (1976).

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

G. R. Lemaître, “Active optics and elastic relaxation methods,” in Current Trends in Optics, International Commission for Optics 12 (Taylor & Francis, London, 1981), pp. 135–149.

G. R. Lemaître, “In situ active reshaping of the CFHT Cassegrain mirror,” available from the author.

G. R. Lemaître, M. Wang, “Témos 4: optical results with a segmented spherical primary and an actively aspherized secondary, in Metal Mirrors, R. G. Bingham, D. D. Walker, eds., Proc. SPIE1931, 43–52 (1992).

Linsky, J. L.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Lubliner, J.

Malina, R.

Mazzanti, S.

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

Min, W.

W. Min, “Instrumentation astrophysique et optique active: evaluation de Témos 4,” Ph.D. dissertation, (Observatoire de Marseille, Université de Provence Aix-Marseille I, Aix-en-Provence, 1992).

Moretto, G.

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

Morse, J. A.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Muller, P.

P. Germain, P. Muller, in Introduction à la Mécanique des Milieux Continus (Masson, Paris, 1994), pp. 140–141.

Nelson, J. E.

Noethe, L.

R. N. Wilson, F. Franza, L. Noethe, “The ESO 3.5 meter Ntt-Active optics I: a system for optimizing the optical quality and reducing the cost of large telescopes,” J. Mod. Opt. 34, 485–511 (1987).
[CrossRef]

Osterman, S.

S. Osterman, E. Wilkinson, J. C. Green, K. Redman, “FUV grating performance for the Cosmic origins spectrograph, in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 360–366 (2000).
[CrossRef]

Redman, K.

S. Osterman, E. Wilkinson, J. C. Green, K. Redman, “FUV grating performance for the Cosmic origins spectrograph, in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 360–366 (2000).
[CrossRef]

Saint-Venant (Barré de), A.

A. Saint-Venant (Barré de), in Résumé des Leçons de Navier sur l’Application à la Mécanique, 3rd. ed. (Dunod, Paris, 1864), p. 40.

Savage, B. D.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Schmidt, B.

B. Schmidt, “A coma-free telescope,” Mitt. Hamburg Strenv. 7, 15 (1932).

Schmidt, E.

E. Schmidt, in Optical Illusions: The Life Story of Bernhard Schmidt the Great Stellar Optician of the Twentieth Century (Estonian Academy Publishers, Tallinn, Estonia, 1995) (ISBN 9985-50-102-0).

Shull, J. M.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Snow, T. P.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Stern, S. A.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Stocke, J. T.

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Su, D.

S. Wang, D. Su, Y. Chu, X. Cui, Y. Wang, “Special configuration of a very large Schmidt telescope for extensive astronomical spectroscopic observation,” Appl. Opt. 35, 5155–5161 (1996).
[CrossRef] [PubMed]

D. Su, X. Cui, Y. Wang, Z. Yao, “Large-sky-area multiobject fiber spectroscopic telescope (LAMOST) and its key technology, in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed., Proc. SPIE3352, 76–90 (1998).
[CrossRef]

Timoshenko, S. P.

S. P. Timoshenko, S. Woinowsky-Krieger, in Theory of Plates and Shells (McGraw-Hill, New York, 1959), p. 248.

Wang, M.

G. R. Lemaître, M. Wang, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. I. 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, E. F. Borra, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. II. Optical testing and performance evaluation,” Astron. Astrophys. Suppl. Ser. 114, 379–386 (1995).

G. R. Lemaître, M. Wang, “Témos 4: optical results with a segmented spherical primary and an actively aspherized secondary, in Metal Mirrors, R. G. Bingham, D. D. Walker, eds., Proc. SPIE1931, 43–52 (1992).

Wang, S.

Wang, Y.

S. Wang, D. Su, Y. Chu, X. Cui, Y. Wang, “Special configuration of a very large Schmidt telescope for extensive astronomical spectroscopic observation,” Appl. Opt. 35, 5155–5161 (1996).
[CrossRef] [PubMed]

D. Su, X. Cui, Y. Wang, Z. Yao, “Large-sky-area multiobject fiber spectroscopic telescope (LAMOST) and its key technology, in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed., Proc. SPIE3352, 76–90 (1998).
[CrossRef]

Wilkinson, E.

S. Osterman, E. Wilkinson, J. C. Green, K. Redman, “FUV grating performance for the Cosmic origins spectrograph, in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 360–366 (2000).
[CrossRef]

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Wilson, R. N.

R. N. Wilson, F. Franza, L. Noethe, “The ESO 3.5 meter Ntt-Active optics I: a system for optimizing the optical quality and reducing the cost of large telescopes,” J. Mod. Opt. 34, 485–511 (1987).
[CrossRef]

R. N. Wilson, in Reflecting Telescope Optics II (Springer, Berlin, 1999), Chap. 3.

Woinowsky-Krieger, S.

S. P. Timoshenko, S. Woinowsky-Krieger, in Theory of Plates and Shells (McGraw-Hill, New York, 1959), p. 248.

Yang, D.

X. Cui, D. Yang, “Support structure of LAMOST Schmidt plate MA,” in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed. Proc. SPIE3352, 378–385 (1998).
[CrossRef]

Yao, Z.

D. Su, X. Cui, Y. Wang, Z. Yao, “Large-sky-area multiobject fiber spectroscopic telescope (LAMOST) and its key technology, in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed., Proc. SPIE3352, 76–90 (1998).
[CrossRef]

Appl. Opt. (9)

J. Lubliner, J. E. Nelson, “Keck Telescope: stressed mirror polishing,” Appl. Opt. 19, 2332–2340 (1980).
[CrossRef] [PubMed]

M. Duban, “Holographic aspheric gratings printed with aberration waves,” Appl. Opt. 26, 4263–4273 (1987).
[CrossRef] [PubMed]

M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
[CrossRef] [PubMed]

M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213 (1998).
[CrossRef]

M. Duban, “Theory and computation of three Cosmic Origins Spectrograph aspheric gratings recorded with a multimode deformable mirror,” Appl. Opt. 38, 1096–1102 (1999).
[CrossRef]

M. Duban, “Third-generation holographic Rowland mounting: fourth-order theory,” Appl. Opt. 38, 3443–3449 (1999).
[CrossRef]

S. Wang, D. Su, Y. Chu, X. Cui, Y. Wang, “Special configuration of a very large Schmidt telescope for extensive astronomical spectroscopic observation,” Appl. Opt. 35, 5155–5161 (1996).
[CrossRef] [PubMed]

M. Duban, G. R. Lemaître, R. Malina, “Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors,” Appl. Opt. 37, 3438–3439 (1998).
[CrossRef]

M. Duban, K. Dohlen, G. R. Lemaître, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope,” Appl. Opt. 37, 7214–7217 (1998).
[CrossRef]

Astron. Astrophys. (2)

M. Ferrari, G. R. Lemaître, “Analysis of large deflection variable curvature mirrors,” Astron. Astrophys. 274, 12–18 (1993).

G. R. Lemaître, M. Duban, “A general method of holographic grating recording with a null-powered multimode deformable mirror,” Astron. Astrophys. 339, L89–L93 (1998).

Astron. Astrophys. Suppl. Ser. (2)

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

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

Comptes Rendus Acad. Sci. Ser. B (1)

G. R. Lemaître, “Asphérisation par relaxation élastique—Miroirs de forme en vase,” Comptes Rendus Acad. Sci. Ser. B 290, 171–174 (1980).

Comptes Rendus Acad. Sci. Series B (1)

G. R. Lemaître, “Elasticité et miroirs à courbure variable,” Comptes Rendus Acad. Sci. Series B 282, 87–89 (1976).

J. Mod. Opt. (1)

R. N. Wilson, F. Franza, L. Noethe, “The ESO 3.5 meter Ntt-Active optics I: a system for optimizing the optical quality and reducing the cost of large telescopes,” J. Mod. Opt. 34, 485–511 (1987).
[CrossRef]

Mitt. Hamburg Strenv. (1)

B. Schmidt, “A coma-free telescope,” Mitt. Hamburg Strenv. 7, 15 (1932).

Other (20)

E. Schmidt, in Optical Illusions: The Life Story of Bernhard Schmidt the Great Stellar Optician of the Twentieth Century (Estonian Academy Publishers, Tallinn, Estonia, 1995) (ISBN 9985-50-102-0).

J. Kross, in L’Oeil du Grand Tout (Laffont, Paris, 1997). French translation of the Estonian book Vastutuulelaev, Kirjastus Eesti Raamat, Estonia, 1987. This book is about the life of Bernhard Schmidt, 1879–1935.

R. N. Wilson, in Reflecting Telescope Optics II (Springer, Berlin, 1999), Chap. 3.

S. Osterman, E. Wilkinson, J. C. Green, K. Redman, “FUV grating performance for the Cosmic origins spectrograph, in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 360–366 (2000).
[CrossRef]

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

G. R. Lemaître, M. Wang, “Témos 4: optical results with a segmented spherical primary and an actively aspherized secondary, in Metal Mirrors, R. G. Bingham, D. D. Walker, eds., Proc. SPIE1931, 43–52 (1992).

A. Couder, “Sur les miroirs de télescopes,” Bull. Astronom.2nd ed., Tome VII, Fasc. VI, 219 et seq. (1931).

G. R. Lemaître, “In situ active reshaping of the CFHT Cassegrain mirror,” available from the author.

A. R. F. Clebsch, in Theorie der Elasticität fester Körper (Teubner, Leipzig, 1862) [French translation, Théorie de l’Élasticité des Corps Solides, with annotations and complements by Saint-Venant and Flamant (Dunod, Paris, 1881)].

J. C. Green, “The cosmic origins spectrograph: a Hubble replacement instrument for the 2002 reservicing mission,” in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 265–270 (1998).
[CrossRef]

J. C. Green, “The cosmic origins spectrograph,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 352–359 (2000).
[CrossRef]

J. A. Morse, J. C. Green, D. C. Ebbets, J. P. Andrews, S. R. Heap, C. Leitherer, J. L. Linsky, B. D. Savage, J. M. Shull, T. P. Snow, S. A. Stern, J. T. Stocke, E. Wilkinson, “Performance overview and science goals of the Cosmic Origins Spectrograph for the Hubble Space Telescope, in Space Telescopes and Instruments V, P. J. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

X. Cui, D. Yang, “Support structure of LAMOST Schmidt plate MA,” in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed. Proc. SPIE3352, 378–385 (1998).
[CrossRef]

G. R. Lemaître, “Active optics and elastic relaxation methods,” in Current Trends in Optics, International Commission for Optics 12 (Taylor & Francis, London, 1981), pp. 135–149.

W. Min, “Instrumentation astrophysique et optique active: evaluation de Témos 4,” Ph.D. dissertation, (Observatoire de Marseille, Université de Provence Aix-Marseille I, Aix-en-Provence, 1992).

M. Ferrari, “Optique active et grandes déformations élastiques,” Ph.D. dissertation (Observatoire de Marseille, Université de Provence Aix-Marseille I, Aix-en-Provence, 1994).

A. Saint-Venant (Barré de), in Résumé des Leçons de Navier sur l’Application à la Mécanique, 3rd. ed. (Dunod, Paris, 1864), p. 40.

P. Germain, P. Muller, in Introduction à la Mécanique des Milieux Continus (Masson, Paris, 1994), pp. 140–141.

S. P. Timoshenko, S. Woinowsky-Krieger, in Theory of Plates and Shells (McGraw-Hill, New York, 1959), p. 248.

D. Su, X. Cui, Y. Wang, Z. Yao, “Large-sky-area multiobject fiber spectroscopic telescope (LAMOST) and its key technology, in Advanced Technology Optical/IR Telescopes, L. M. Stepp, ed., Proc. SPIE3352, 76–90 (1998).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Elasticity design of a MDM showing a two-zone rigidity and radial arms. The clear aperture zone is built in at r = a into a thicker ring. The holosteric shape allows one to achieve the Clebsch–Zernike deformation modes, i.e., Cv1, Sphe3, Coma3, Astm3, Astm5, Tri5, Tri7, Squa7, Squa9, … , by the action of axial forces F a,k and F c,k applied to the ring inner radius r = a and to the outer end r = c of each arm (here k m = 12 arms). Except for the mode Sphe3, given by A 4,0, which is achieved by addition of uniform air pressure or depressure q, all other above modes, obtained with q = 0, belong to the central diagonal A n,n and to the upper diagonal A n,n-2, with n = 2, 3, 4, … , of the A n,m optics wave-front triangular matrix.

Fig. 2
Fig. 2

True proportion design of six-arm MDM’s in quenched FeCr13 alloy, HB300. The elastic constants are E = 205 × 109 Pa and ν = 0.305 for the Young’s modulus and the Poisson’s ratio, respectively. The mirror geometry is defined by the thicknesses t 1 = 5 mm and t 2 = 14 mm for the central plate and outer ring, respectively. The radial parameters are a = 40 mm (optical semiaperture), b = 54 mm, and c = 80 mm. This geometry provides a rigidity ratio of 1/γ = D 2/D 1 = (14/5)3≃ 22 and an aspect ratio of 2a/ t 1 = 16. The axial forces F a,k and F c,k are applied to the ring inner radius r = a and to the outer end r = c of the radial arms (k m = 6) built in to the ring.

Fig. 3
Fig. 3

Spot diagram given by grating 1, 3800 l mm-1. Nonisotropic scales. The FWHM size of the blur image at 1300 Å is 2.5 µm × 88 µm. The diffraction will increase this size in the direction of dispersion to 3.8 µm × 88 µm. Compared with the imaging and resolution tests performed by the COS team13 with the 3800 l mm-1 more classical grating at 1284 Å, which shows a FWHM image of 38 µm × 264 µm, our high-order corrected grating would provide images 10 times better in dispersion and 2.5 times better in cross dispersion. Since the pixel size of the COS detector is expected to be 2.4 µm × 33 µm, our design appears to provide the very effective gain of 10 × 3 = 30 in light concentration. Therefore (i) the resolving power λ/δλ would be increased by a factor 10, and (ii), in addition, the limiting magnitude (cross dispersion), or COS sensitivity on the sky, appears to be increased by a magnitude of approximately 1–1.2.

Fig. 4
Fig. 4

Spot diagram given by grating 2, 3052.6 l mm-1. Nonisotropic scales. The FWHM size of the blur image at 1589Å is 3 µm × 84 µm. The diffraction will increase this size in the direction of dispersion to 4.6 µm × 84 µm. As for grating 1, the image sizes at the edges of the spectrum are quite the same as at the center.

Fig. 5
Fig. 5

Spot diagram given by grating 3, 380 l mm-1. Isotropic scales. The FWHM size of the blur image at 1615 Å is 2.5 µm × 5 µm. The diffraction will increase this size in the direction of dispersion to 4.7 µm × 5 µm.

Fig. 6
Fig. 6

Basical recording mounting. The recording angles α and β of the principal rays at the vertex O of the grating from laser source points L 1 and L 2, respectively, are given by Table 3. For the case of COS grating 1, the α and the β values are shown; the incidence angle at the vertex M of the MDM is i MDM = 29.96°; the Rowland circle optical paths are L 1 O = R cos α and L 2 O = R cos β with R = 1652 mm and L 1 M = 1100 mm. The f/24 HST projects the central beam areas for all three gratings that are contained in a 73.2-mm circle, since i ≤ 20° (see Table 3); for recording 80-mm circular-aperture COS gratings, the corresponding size of the recording projected beam at the MDM is 42.9 mm × 53.3 mm for grating 1 and a little smaller for gratings 2 and 3.

Fig. 7
Fig. 7

Views of MDM 1 in its mounting, with the nine differential screws and three reference points onto the inner ring, and of MDM 2 alone. Clear optical aperture is 80 mm.

Fig. 8
Fig. 8

He–Ne interferograms of MDM 2 at full aperture, 80 mm, showing single modes Cv1, Astm3, Coma3, Tri5, and Astm5. With respect to Table 1, Sphe3 could be obtained by air pressure or depressure inside the MDM vase form.

Fig. 9
Fig. 9

Full-aperture He–Ne interferogram of six-arm MDM 1 tuned as optical path compensator for holographic recording of the COS grating 1 (3800 l mm-1). The three modes Coma3, Tri5, and Astm5 are coadded by generating forces F a,k and F c,k such as given in the final column of Table 7. (Top) obtained shape, (bottom) theoretical shape. An 80-mm circular aperture of COS gratings, which is larger than the 73.2 mm × 68.8 mm area of the f/24 HST incident beam for i = 20°, corresponds to a recording beam at the MDM of 42.9 mm × 53.3 mm for grating 1 and a little smaller for gratings 2 and 3. On this MDM recording area, the PtV deviation of the interferogram is better than 0.2λHe–Ne. This can be partly checked by the reader in making a convenient scaled up transparent from the synthetic interferogram.

Tables (7)

Tables Icon

Table 1 Axial Distribution of Forces F a,k and F c,k Applied to a Six-Arm MDMa

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Table 2 Spectral Data in Angstroms

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Table 3 Grating and Geometrical Recording Parameters

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Table 4 Substrate Coefficients (Deformations in Micrometers)

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Table 5 MDM Coefficients and Incidence Angle

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Table 6 Spectral Resolutions λ/δλ for Grating Number of Lines Equal to 68.8 mm/N cos i, Where the i Angles Are Given in Table 3a

Tables Icon

Table 7 Axial Distribution of Forces F a,k and F c,k Applied to the Six-Arm MDM for the Recording of the COS Grating 1, i.e., 3800 l/mma

Equations (17)

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22Zr, θ=q/D,
D=Et3/121-ν2=constant,
Z=znm=Anmrn cos mθ,
Anmn2-m2n-22-m2rn-4 cos mθ=q/D,
Z=znm=Rn0+m=1Rnm cos mθ+m=1Rnm sin mθ,
d2dr2+1rddr-m2r2d2 Rnmdr2+1rdRnmdr-m2r2Rnm=0.
Rn0=Bn0+Cn0 ln r+Dn0r2+En0r2 ln r, Rn1=Bn1r+Cn1r-1+Dn1r3+En1r ln r, Rnm=Bnmrm+Cnmr-m+Dnmrm+2+Enmr-m+2.
Mr=-D2zr2+ν1rzr+1r22zθ2, Qr=-Dr2z,
Anman=Rnma, Anmnan-1=dRnmdrr=a, Anmnn-1+νn-m2an-2=1γd2 Rnmdr2+νrdRnmdr-νm2r2Rnmr=a, Anmn2-m2n-2an-3=1γddrd2Rnmdr2+1rdRnmdr-m2r2Rnmr=a.
B20=1-γ1+ν1-ln a2a2A20/2, C20=1-γ1+νa2A20, D20=2-1-γ1+νA20/2, E20=0, Mrb=-D2-1-νC20/b2+21+νD20+3+νE20+1+νE20 ln b2, Qrb=-4D2E20/b.
B40=ν+γ5-ν-1+ν+γ1-νln a2×a4A40, C40=21+ν+γ1-νa4A40, D40=1-ν-γ5-ν+4 ln a2a2A40, E40=8γa2A40, Mrb=-D21-νC40/b2+21+νD40+3+νE40+1+νE40 ln b2, Qrb=-4D2E40/b.
B31=1-γ7+ν-1-νln a2a2A31/4, C31=-1-γ5+3νa4A31/8, D31=8γ+1-γ1-νA31/8, E31=1-γ1-νa2A31/2, Mrb=-D221-νC31/b3+23+νD31b+1+νE31/b, Qrb=-2D24D31-E31/b2.
B22=A22, C22=-1-γ1-νa4A22/6, D22=-1-γ1-νA22/12a2, E22=1-γ1-νa2A22/4, Mrb=-2D21-νB22+31-νC22/b4+6D22b2-2νE22/b2, Qrb=-8D23D22b+E22/b3.
B42=31-γa2A42/2, C42=-1-γa6A42/2, D42=γA42, E42=0, Mrb=-2D21-νB42+31-νC42/b4+6D42b2-2νE42/b2, Qrb=-8D23D42b+E42/b3.
B33=8+1-γ1-νA33/8, C33=-51-γ1-νa6A33/16, D33=-31-γ1-νA33/16a2, E33=31-γ1-νa4A33/8, Mrb=-2D231-νB33b+61-νC33/b5+25-νD33b3+1-5νE33/b3, Qrb=-24D22D33b2+E33/b4.
Fa,k+Fc,k=b π2k-3/kmπ2k-1/kmQrb, θdθ,
b-aFa,k+b-cFc,k=b π2k-3/kmπ2k-1/kmMrb, θdθ,

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