Abstract

Wide-field astronomy requires the development of larger aperture telescopes. The optical properties of a three-mirror modified-Rumsey design provide significant advantages when compared to other telescope designs: (i) at any wavelength, the design has a flat field and is anastigmatic; (ii) the system is extremely compact, i.e., it is almost four times shorter than a Schmidt. Compared to the equally compact flat-field Ritchey–Chrétien with a doublet-lens corrector, as developed for the Sloan digital sky survey—and which requires the polishing of six optical surfaces—the proposed modified-Rumsey design requires only a two-surface polishing and provides a better imaging quality. All the mirrors are spheroids of the hyper-boloid type. Starting from the classical Rumsey design, it is shown that the use of all eight available free parameters allows the simultaneous aspherization of the primary and tertiary mirrors by active optics methods from a single deformable substrate. The continuity conditions between the primary and the tertiary hyperbolizations are achieved by an intermediate narrow ring of constant thickness that is not optically used. After the polishing of a double vase form in a spherical shape, the primary–tertiary hyperbolizations are achieved by in situ stressing. The tulip-form secondary is hyperbolized by stress polishing. Other active optics alternatives are possible for a space telescope. The modified-Rumsey design is of interest for developing large space- and ground-based survey telescopes in UV, visible, or IR ranges, such as currently demonstrated with the construction of identical telescopes MINITRUST-1 and -2, f/5 − 2° field of view. Double-pass optical tests show diffraction-limited images.

© 2005 Optical Society of America

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    [CrossRef]
  2. G. R. Lemaître, “Active optics and aberration correction with multimode deformable mirrors (MDMs)–vase form and meniscus form,” in Laser Optics 2003, V. E. Sherstobitov, L. N. Soms, eds., Proc. SPIE5481, 70–81 (2003).
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. M. C. E. Huber, E. Jannitti, G. R. Lemaître, G. Tondello, “Toroidal grating obtained on elastic substrate: SOHO Mission,” Appl. Opt. 20, 2139–2142 (1981).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. H.-J. Su, X. Cui, “Lamost project and its current status,” in Large Ground-Based Telescopes, J. M. Oschmann, L. M. Stepp, eds., Proc. SPIE4837, 26–35 (2003).
    [CrossRef]
  11. R. N. Wilson, “Active optics control systems,” in Reflecting Telescope Optics II (Springer, Berlin, 1999), pp. 274–314.
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. N. J. Rumsey, “A compact three-reflection astronomical camera,” in Optical Instruments and Techniques, Ico 8 Meeting, London, H. Dickson, ed. (Oriel, Newcastle, 1969), pp. 514–520.
  15. R. V. Willstrop, “The Mersenne-Schmidt: a three reflection survey telescope,” Mon. Not. R. Astron. Soc. 210, 597–609 (1984).
  16. M. Paul, “Systèmes correcteurs pour réflecteurs astronomiques,” Rev. Opt. Theor. Instrum. 14, 169–202 (1935).
  17. J. R. P. Angel, N. J. Woolf, H. W. Epps, “A 1.8-m three mirror telescope proposal for survey with CCDs,” in Advanced Technology Optical Telescopes, G. Burbidge, L. Barr, eds., Proc. SPIE332, 134–142 (1982).
    [CrossRef]
  18. K. Dohlen, M. Saisse, G. Claeysen, P. Lamy, J.-L. Boit, “Optical designs for the Rosetta camera,” Opt. Eng. 35, 1150–1157 (1996).
    [CrossRef]
  19. G. R. Lemaître, M. Wang, “Optical results with segmented Témos 4,” in Metal Mirrors, R. G. Bingham, D. D. Walker, eds., Proc. SPIE1931, 43–52 (1992).
  20. G. R. Lemaître, “A diffraction limited 20 m telescope with an active and adaptive tertiary,” in Advanced Technology Optical/IR Telescopes, L. N. Stepp, ed., Proc. SPIE3352, 766–777 (1998).
    [CrossRef]
  21. E. Reissner, “General theory of shallow spherical shells–I,” J. Math. Phys. (Cambridge, Mass.) 25, 80–85 (1946).
  22. E. Reissner, “General theory of shallow spherical shells–II,” J. Math. Phys. (Cambridge, Mass.) 25, 279–300 (1947).
  23. H. B. Dwight, in Table of Integrals and Other Mathematical Data, 3rded. (Macmillan, New York, 1957), pp. 184–188, 276–279.
  24. M. Abramovitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 2003), pp. 374–384 and 430–431.
  25. S. P. Timoshenko, S. Woinowsky-Kieger, in Theory of Plates and Shells (McGraw-Hill, New York, 1959), pp. 558 and 466.Note: In this book, the following representation is used for the ψi functions: ψ1= ber, ψ2= − bei, ψ3= −(2/π)kei, ψ4= –(2/π)ker on p. 560 and in the Tables on pp. 491–494. Reissner (Refs. 20 and 21) represents these functions directly by ψ = ber, ψ2= bei, ψ3= ker, ψ4= kei.
  26. G. Molodij, J. Rayrole, P. Y. Madec, F. Colson, “Thémis: Télescope héliographique pour l’étude du magnétisme et des instabilités solaires,” Astron. Astrophys. Suppl. Ser. 118, 169–179 (1996), and http://arthemis.na.astro.it/themis .
    [CrossRef]
  27. G. R. Lemaître, “Sur la flexion des miroirs secondaires de télescopes,” Nouv. Rev. Opt. 7, 389–397 (1976).
    [CrossRef]
  28. C. D. La Padula, A. Carusi, R. F. Viotti, A. Vignato, G. R. Lemaître, “Proposal for a mini-satellite with a wide-field TRT,” Mem. Soc. Astron. Ital. 74, 63 (2003).
  29. R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).
  30. M. Ferrari, G. R. Lemaître, R. F. Viotti, C. La Padula, G. Comtes, M. Blanc, M. Boer, “Three reflection telescope proposal as flat-field anastigmat for wide field observations at Dome C,” in Astronomie et Astrophysique au Dome C, Cesr Toulouse, Cnrs-Insu Proc., in press (2005).

2005 (1)

G. R. Lemaître, “Active optics: vase or meniscus multimode mirrors and degenerated monomode configurations,” Meccanica 40, 233–249 (2005).
[CrossRef]

2003 (2)

C. D. La Padula, A. Carusi, R. F. Viotti, A. Vignato, G. R. Lemaître, “Proposal for a mini-satellite with a wide-field TRT,” Mem. Soc. Astron. Ital. 74, 63 (2003).

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

1998 (1)

M. Ferrari, “Development of variable curvature mirrors for the delay lines of the VLTI,” Astron. Astrophys. Suppl. Ser. 128, 221–227 (1998).
[CrossRef]

1996 (2)

K. Dohlen, M. Saisse, G. Claeysen, P. Lamy, J.-L. Boit, “Optical designs for the Rosetta camera,” Opt. Eng. 35, 1150–1157 (1996).
[CrossRef]

G. Molodij, J. Rayrole, P. Y. Madec, F. Colson, “Thémis: Télescope héliographique pour l’étude du magnétisme et des instabilités solaires,” Astron. Astrophys. Suppl. Ser. 118, 169–179 (1996), and http://arthemis.na.astro.it/themis .
[CrossRef]

1994 (1)

1984 (1)

R. V. Willstrop, “The Mersenne-Schmidt: a three reflection survey telescope,” Mon. Not. R. Astron. Soc. 210, 597–609 (1984).

1981 (1)

1980 (2)

1976 (1)

G. R. Lemaître, “Sur la flexion des miroirs secondaires de télescopes,” Nouv. Rev. Opt. 7, 389–397 (1976).
[CrossRef]

1972 (1)

1935 (1)

M. Paul, “Systèmes correcteurs pour réflecteurs astronomiques,” Rev. Opt. Theor. Instrum. 14, 169–202 (1935).

Angel, J. R. P.

J. R. P. Angel, N. J. Woolf, H. W. Epps, “A 1.8-m three mirror telescope proposal for survey with CCDs,” in Advanced Technology Optical Telescopes, G. Burbidge, L. Barr, eds., Proc. SPIE332, 134–142 (1982).
[CrossRef]

Badiali, M.

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

Blanc, M.

M. Ferrari, G. R. Lemaître, R. F. Viotti, C. La Padula, G. Comtes, M. Blanc, M. Boer, “Three reflection telescope proposal as flat-field anastigmat for wide field observations at Dome C,” in Astronomie et Astrophysique au Dome C, Cesr Toulouse, Cnrs-Insu Proc., in press (2005).

Boattini, A.

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

Boer, M.

M. Ferrari, G. R. Lemaître, R. F. Viotti, C. La Padula, G. Comtes, M. Blanc, M. Boer, “Three reflection telescope proposal as flat-field anastigmat for wide field observations at Dome C,” in Astronomie et Astrophysique au Dome C, Cesr Toulouse, Cnrs-Insu Proc., in press (2005).

Boit, J.-L.

K. Dohlen, M. Saisse, G. Claeysen, P. Lamy, J.-L. Boit, “Optical designs for the Rosetta camera,” Opt. Eng. 35, 1150–1157 (1996).
[CrossRef]

Carusi, A.

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

C. D. La Padula, A. Carusi, R. F. Viotti, A. Vignato, G. R. Lemaître, “Proposal for a mini-satellite with a wide-field TRT,” Mem. Soc. Astron. Ital. 74, 63 (2003).

Claeysen, G.

K. Dohlen, M. Saisse, G. Claeysen, P. Lamy, J.-L. Boit, “Optical designs for the Rosetta camera,” Opt. Eng. 35, 1150–1157 (1996).
[CrossRef]

Claudi, R. U.

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

Colson, F.

G. Molodij, J. Rayrole, P. Y. Madec, F. Colson, “Thémis: Télescope héliographique pour l’étude du magnétisme et des instabilités solaires,” Astron. Astrophys. Suppl. Ser. 118, 169–179 (1996), and http://arthemis.na.astro.it/themis .
[CrossRef]

Comtes, G.

M. Ferrari, G. R. Lemaître, R. F. Viotti, C. La Padula, G. Comtes, M. Blanc, M. Boer, “Three reflection telescope proposal as flat-field anastigmat for wide field observations at Dome C,” in Astronomie et Astrophysique au Dome C, Cesr Toulouse, Cnrs-Insu Proc., in press (2005).

Cui, X.

H.-J. Su, X. Cui, “Lamost project and its current status,” in Large Ground-Based Telescopes, J. M. Oschmann, L. M. Stepp, eds., Proc. SPIE4837, 26–35 (2003).
[CrossRef]

Di Lellis, A.

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

Dohlen, K.

K. Dohlen, M. Saisse, G. Claeysen, P. Lamy, J.-L. Boit, “Optical designs for the Rosetta camera,” Opt. Eng. 35, 1150–1157 (1996).
[CrossRef]

Dwight, H. B.

H. B. Dwight, in Table of Integrals and Other Mathematical Data, 3rded. (Macmillan, New York, 1957), pp. 184–188, 276–279.

Epps, H. W.

J. R. P. Angel, N. J. Woolf, H. W. Epps, “A 1.8-m three mirror telescope proposal for survey with CCDs,” in Advanced Technology Optical Telescopes, G. Burbidge, L. Barr, eds., Proc. SPIE332, 134–142 (1982).
[CrossRef]

Ferrari, M.

M. Ferrari, “Development of variable curvature mirrors for the delay lines of the VLTI,” Astron. Astrophys. Suppl. Ser. 128, 221–227 (1998).
[CrossRef]

M. Ferrari, G. R. Lemaître, R. F. Viotti, C. La Padula, G. Comtes, M. Blanc, M. Boer, “Three reflection telescope proposal as flat-field anastigmat for wide field observations at Dome C,” in Astronomie et Astrophysique au Dome C, Cesr Toulouse, Cnrs-Insu Proc., in press (2005).

Frutti, M.

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

Gabor, G.

Huber, M. C. E.

Hunt, L. K.

Jannitti, E.

La Padula, C.

M. Ferrari, G. R. Lemaître, R. F. Viotti, C. La Padula, G. Comtes, M. Blanc, M. Boer, “Three reflection telescope proposal as flat-field anastigmat for wide field observations at Dome C,” in Astronomie et Astrophysique au Dome C, Cesr Toulouse, Cnrs-Insu Proc., in press (2005).

La Padula, C. D.

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

C. D. La Padula, A. Carusi, R. F. Viotti, A. Vignato, G. R. Lemaître, “Proposal for a mini-satellite with a wide-field TRT,” Mem. Soc. Astron. Ital. 74, 63 (2003).

Lamy, P.

K. Dohlen, M. Saisse, G. Claeysen, P. Lamy, J.-L. Boit, “Optical designs for the Rosetta camera,” Opt. Eng. 35, 1150–1157 (1996).
[CrossRef]

Lemaître, G. R.

G. R. Lemaître, “Active optics: vase or meniscus multimode mirrors and degenerated monomode configurations,” Meccanica 40, 233–249 (2005).
[CrossRef]

C. D. La Padula, A. Carusi, R. F. Viotti, A. Vignato, G. R. Lemaître, “Proposal for a mini-satellite with a wide-field TRT,” Mem. Soc. Astron. Ital. 74, 63 (2003).

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

M. C. E. Huber, E. Jannitti, G. R. Lemaître, G. Tondello, “Toroidal grating obtained on elastic substrate: SOHO Mission,” Appl. Opt. 20, 2139–2142 (1981).
[CrossRef] [PubMed]

G. R. Lemaître, “Sur la flexion des miroirs secondaires de télescopes,” Nouv. Rev. Opt. 7, 389–397 (1976).
[CrossRef]

G. R. Lemaître, “New procedure for making Schmidt corrector plates,” Appl. Opt. 11, 1630–1636 (1972).
[CrossRef] [PubMed]

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, “Active optics and aberration correction with multimode deformable mirrors (MDMs)–vase form and meniscus form,” in Laser Optics 2003, V. E. Sherstobitov, L. N. Soms, eds., Proc. SPIE5481, 70–81 (2003).

G. R. Lemaître, M. Wang, “Optical results with segmented Témos 4,” in Metal Mirrors, R. G. Bingham, D. D. Walker, eds., Proc. SPIE1931, 43–52 (1992).

M. Ferrari, G. R. Lemaître, R. F. Viotti, C. La Padula, G. Comtes, M. Blanc, M. Boer, “Three reflection telescope proposal as flat-field anastigmat for wide field observations at Dome C,” in Astronomie et Astrophysique au Dome C, Cesr Toulouse, Cnrs-Insu Proc., in press (2005).

G. R. Lemaître, “A diffraction limited 20 m telescope with an active and adaptive tertiary,” in Advanced Technology Optical/IR Telescopes, L. N. Stepp, ed., Proc. SPIE3352, 766–777 (1998).
[CrossRef]

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

Lubliner, J.

Madec, P. Y.

G. Molodij, J. Rayrole, P. Y. Madec, F. Colson, “Thémis: Télescope héliographique pour l’étude du magnétisme et des instabilités solaires,” Astron. Astrophys. Suppl. Ser. 118, 169–179 (1996), and http://arthemis.na.astro.it/themis .
[CrossRef]

Mast, T. S.

Molodij, G.

G. Molodij, J. Rayrole, P. Y. Madec, F. Colson, “Thémis: Télescope héliographique pour l’étude du magnétisme et des instabilités solaires,” Astron. Astrophys. Suppl. Ser. 118, 169–179 (1996), and http://arthemis.na.astro.it/themis .
[CrossRef]

Nelson, J. E.

Noethe, L.

L. Noethe, “Active optics in modern large optical telescopes,” in Progress in Optics, Vol. XLIII, E. Wolf, ed. (Elsevier-North-Holland, Amsterdam, 2002), pp. 1–69.
[CrossRef]

Paul, M.

M. Paul, “Systèmes correcteurs pour réflecteurs astronomiques,” Rev. Opt. Theor. Instrum. 14, 169–202 (1935).

Rayrole, J.

G. Molodij, J. Rayrole, P. Y. Madec, F. Colson, “Thémis: Télescope héliographique pour l’étude du magnétisme et des instabilités solaires,” Astron. Astrophys. Suppl. Ser. 118, 169–179 (1996), and http://arthemis.na.astro.it/themis .
[CrossRef]

Reissner, E.

E. Reissner, “General theory of shallow spherical shells–II,” J. Math. Phys. (Cambridge, Mass.) 25, 279–300 (1947).

E. Reissner, “General theory of shallow spherical shells–I,” J. Math. Phys. (Cambridge, Mass.) 25, 80–85 (1946).

Rumsey, N. J.

N. J. Rumsey, “A compact three-reflection astronomical camera,” in Optical Instruments and Techniques, Ico 8 Meeting, London, H. Dickson, ed. (Oriel, Newcastle, 1969), pp. 514–520.

Saisse, M.

K. Dohlen, M. Saisse, G. Claeysen, P. Lamy, J.-L. Boit, “Optical designs for the Rosetta camera,” Opt. Eng. 35, 1150–1157 (1996).
[CrossRef]

Schwesinger, G.

Su, H.-J.

H.-J. Su, X. Cui, “Lamost project and its current status,” in Large Ground-Based Telescopes, J. M. Oschmann, L. M. Stepp, eds., Proc. SPIE4837, 26–35 (2003).
[CrossRef]

Timoshenko, S. P.

S. P. Timoshenko, S. Woinowsky-Kieger, in Theory of Plates and Shells (McGraw-Hill, New York, 1959), pp. 558 and 466.Note: In this book, the following representation is used for the ψi functions: ψ1= ber, ψ2= − bei, ψ3= −(2/π)kei, ψ4= –(2/π)ker on p. 560 and in the Tables on pp. 491–494. Reissner (Refs. 20 and 21) represents these functions directly by ψ = ber, ψ2= bei, ψ3= ker, ψ4= kei.

Tondello, G.

Vignato, A.

C. D. La Padula, A. Carusi, R. F. Viotti, A. Vignato, G. R. Lemaître, “Proposal for a mini-satellite with a wide-field TRT,” Mem. Soc. Astron. Ital. 74, 63 (2003).

Vignatto, A.

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

Viotti, R. F.

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

C. D. La Padula, A. Carusi, R. F. Viotti, A. Vignato, G. R. Lemaître, “Proposal for a mini-satellite with a wide-field TRT,” Mem. Soc. Astron. Ital. 74, 63 (2003).

M. Ferrari, G. R. Lemaître, R. F. Viotti, C. La Padula, G. Comtes, M. Blanc, M. Boer, “Three reflection telescope proposal as flat-field anastigmat for wide field observations at Dome C,” in Astronomie et Astrophysique au Dome C, Cesr Toulouse, Cnrs-Insu Proc., in press (2005).

Wang, M.

G. R. Lemaître, M. Wang, “Optical results with segmented Témos 4,” in Metal Mirrors, R. G. Bingham, D. D. Walker, eds., Proc. SPIE1931, 43–52 (1992).

Willstrop, R. V.

R. V. Willstrop, “The Mersenne-Schmidt: a three reflection survey telescope,” Mon. Not. R. Astron. Soc. 210, 597–609 (1984).

Wilson, R. N.

R. N. Wilson, “Active optics control systems,” in Reflecting Telescope Optics II (Springer, Berlin, 1999), pp. 274–314.

Woinowsky-Kieger, S.

S. P. Timoshenko, S. Woinowsky-Kieger, in Theory of Plates and Shells (McGraw-Hill, New York, 1959), pp. 558 and 466.Note: In this book, the following representation is used for the ψi functions: ψ1= ber, ψ2= − bei, ψ3= −(2/π)kei, ψ4= –(2/π)ker on p. 560 and in the Tables on pp. 491–494. Reissner (Refs. 20 and 21) represents these functions directly by ψ = ber, ψ2= bei, ψ3= ker, ψ4= kei.

Woolf, N. J.

J. R. P. Angel, N. J. Woolf, H. W. Epps, “A 1.8-m three mirror telescope proposal for survey with CCDs,” in Advanced Technology Optical Telescopes, G. Burbidge, L. Barr, eds., Proc. SPIE332, 134–142 (1982).
[CrossRef]

Appl. Opt. (5)

Astron. Astrophys. Suppl. Ser. (2)

M. Ferrari, “Development of variable curvature mirrors for the delay lines of the VLTI,” Astron. Astrophys. Suppl. Ser. 128, 221–227 (1998).
[CrossRef]

G. Molodij, J. Rayrole, P. Y. Madec, F. Colson, “Thémis: Télescope héliographique pour l’étude du magnétisme et des instabilités solaires,” Astron. Astrophys. Suppl. Ser. 118, 169–179 (1996), and http://arthemis.na.astro.it/themis .
[CrossRef]

Meccanica (1)

G. R. Lemaître, “Active optics: vase or meniscus multimode mirrors and degenerated monomode configurations,” Meccanica 40, 233–249 (2005).
[CrossRef]

Mem. Soc. Astron. Ital. (1)

C. D. La Padula, A. Carusi, R. F. Viotti, A. Vignato, G. R. Lemaître, “Proposal for a mini-satellite with a wide-field TRT,” Mem. Soc. Astron. Ital. 74, 63 (2003).

Mem. Soc. Astron. Ital. Suppl. (1)

R. F. Viotti, M. Badiali, A. Boattini, A. Carusi, R. U. Claudi, A. Di Lellis, C. D. La Padula, M. Frutti, A. Vignatto, G. R. Lemaître, “Wide field observations at Dome C, Antartica,” Mem. Soc. Astron. Ital. Suppl. 2, 177–180 (2003).

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

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[CrossRef]

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[CrossRef]

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Other (16)

J. R. P. Angel, N. J. Woolf, H. W. Epps, “A 1.8-m three mirror telescope proposal for survey with CCDs,” in Advanced Technology Optical Telescopes, G. Burbidge, L. Barr, eds., Proc. SPIE332, 134–142 (1982).
[CrossRef]

L. Noethe, “Active optics in modern large optical telescopes,” in Progress in Optics, Vol. XLIII, E. Wolf, ed. (Elsevier-North-Holland, Amsterdam, 2002), pp. 1–69.
[CrossRef]

N. J. Rumsey, “A compact three-reflection astronomical camera,” in Optical Instruments and Techniques, Ico 8 Meeting, London, H. Dickson, ed. (Oriel, Newcastle, 1969), pp. 514–520.

M. Ferrari, G. R. Lemaître, R. F. Viotti, C. La Padula, G. Comtes, M. Blanc, M. Boer, “Three reflection telescope proposal as flat-field anastigmat for wide field observations at Dome C,” in Astronomie et Astrophysique au Dome C, Cesr Toulouse, Cnrs-Insu Proc., in press (2005).

G. R. Lemaître, M. Wang, “Optical results with segmented Témos 4,” in Metal Mirrors, R. G. Bingham, D. D. Walker, eds., Proc. SPIE1931, 43–52 (1992).

G. R. Lemaître, “A diffraction limited 20 m telescope with an active and adaptive tertiary,” in Advanced Technology Optical/IR Telescopes, L. N. Stepp, ed., Proc. SPIE3352, 766–777 (1998).
[CrossRef]

E. Reissner, “General theory of shallow spherical shells–I,” J. Math. Phys. (Cambridge, Mass.) 25, 80–85 (1946).

E. Reissner, “General theory of shallow spherical shells–II,” J. Math. Phys. (Cambridge, Mass.) 25, 279–300 (1947).

H. B. Dwight, in Table of Integrals and Other Mathematical Data, 3rded. (Macmillan, New York, 1957), pp. 184–188, 276–279.

M. Abramovitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 2003), pp. 374–384 and 430–431.

S. P. Timoshenko, S. Woinowsky-Kieger, in Theory of Plates and Shells (McGraw-Hill, New York, 1959), pp. 558 and 466.Note: In this book, the following representation is used for the ψi functions: ψ1= ber, ψ2= − bei, ψ3= −(2/π)kei, ψ4= –(2/π)ker on p. 560 and in the Tables on pp. 491–494. Reissner (Refs. 20 and 21) represents these functions directly by ψ = ber, ψ2= bei, ψ3= ker, ψ4= kei.

G. R. Lemaître, “Active optics and aberration correction with multimode deformable mirrors (MDMs)–vase form and meniscus form,” in Laser Optics 2003, V. E. Sherstobitov, L. N. Soms, eds., Proc. SPIE5481, 70–81 (2003).

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.

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[CrossRef]

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[CrossRef]

R. N. Wilson, “Active optics control systems,” in Reflecting Telescope Optics II (Springer, Berlin, 1999), pp. 274–314.

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Figures (13)

Fig. 1
Fig. 1

Comparison of wide-field telescopes having an identical input beam diameter, focal length, and field of view (2°): A, Schmidt with refractive corrector—convex FOV, 1 aspheric, length ≃ 2F, 3 polished surfaces; B, Mersenne–Schmidt by Willstrop—concave FOV, 2 aspherics, length ≃ F, 3 polished surfaces; C, paraboloid and triplet-lens corrector—flat FOV, 1 aspheric, length = F, 7 polished surfaces; D, Ritchey–Chrétien + doublet corrector—flat FOV, 2 aspherics, length ≃ F/2, 6 polished surfaces; E, modified-Rumsey continuous M1–M3—flat FOV, 3 aspherics, length ≃ F/2, 2 polished surfaces.

Fig. 2
Fig. 2

MINITRUST layout with on-axis beams.

Fig. 3
Fig. 3

Residual blur images from Table 1 parameters. 2° FOV, λλ. (380–900 nm) and window–filter flat plate. Top 10 mm thick plate; bottom 5 mm thick plate. Barr = 20 µm. Spherochromatism of plates dominate.

Fig. 4
Fig. 4

Geometric parameters of an element ring.

Fig. 5
Fig. 5

Elasticity design of the M1–M3 double vase form. Design (A), according to Table 4; design (B), equivalent to design (A) but more compact with an L-shaped outer ring.

Fig. 6
Fig. 6

Rear view of the M1–M3 double vase form.

Fig. 7
Fig. 7

He–Ne Fizeau interferograms of M1 and M3. For each mirror the autocollimation is achieved at 3 / 2 of its clear aperture radius rmax with respect to a sphere. These are r1max = 220 and r3max = 90 mm. From the M1 interferogram, the source is moved 13.32 mm toward the substrate to get the M3 interferogram.

Fig. 8
Fig. 8

Elasticity design of the M2 substrate.

Fig. 9
Fig. 9

Rear view of the M2 tulip form.

Fig. 10
Fig. 10

He–Ne Fizeau interferograms of M2. Top, mirror shape during stress; bottom, shape after elastic relaxation.

Fig. 11
Fig. 11

MINITRUST on-axis beam and substrates. The entrance pupil is on M2.

Fig. 12
Fig. 12

View of MINITRUST-1 under alignment and double-pass testing by autocollimation on a plane.

Fig. 13
Fig. 13

MINITRUST-1 He–Ne wave front after a telescope double pass. Left: decentering coma before the M2 setup, right: after the M2 setup.

Tables (5)

Tables Icon

Table 1 Modified-Rumsey Design of MINITRUST-f/4.9-2° FOV-λλ[380–900 nm]

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Table 2 Thickness Distribution of the M1 Substrate—Single Vase Form

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Table 3 Thickness Distribution of the M3 Substrate—Single Vase Form

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Table 4 Geometry of the M1–M3 Global Substrate—Double Vase Form

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Table 5 Thickness Distribution of the M2 Substrate—Tulip Form

Equations (31)

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D n = E t n 3 / [ 12 ( 1 ν 2 ) ] , l n = < R > t n / 12 ( 1 ν 2 ) .
( d z d r ) max r max < R > 1 .
w ( r ) = l n [ C 1 , n ψ 1 ( x ) + C 2 , n ψ 2 ( x ) + C 3 , n ψ 3 ( x ) + C 4 , n ψ 4 ( x ) + C 5 , n ] ,
u ( r ) = r F ( ψ i , ψ i , p ) + r w / < R > ,
x = r / l n ,
ψ 1 = ber ( r / l n ) , ψ 2 = bei ( r / l n ) , ψ 3 = ker ( r / l n ) , ψ 4 = kei ( r / l n ) ,
2 2 ψ i + 1 l n 4 ψ i = 0 .
ber x = 1 ( x 2 / 4 ) 2 ( 2 ! ) 2 + ( x 2 / 4 ) 2 ( 4 ! ) 2 ,
bei x = x 2 / 4 ( 1 ! ) 2 ( x 2 / 4 ) 3 ( 3 ! ) 2 + ( x 2 / 4 ) 5 ( 5 ! ) 2 ,
ker x = [ ln ( x 2 ) + γ ] ber x + π 4 bei x ( 1 + 1 2 ) ( x 2 / 4 ) 3 ( 2 ! ) 2 + ( 1 + 1 2 + 1 3 + 1 4 ) × ( x 2 / 4 ) 4 ( 4 ! ) 2 ,
kei x = [ ln ( x 2 ) + γ ] bei x π 4 ber x + x 2 / 4 ( 1 ! ) 2 ( 1 + 1 2 + 1 3 + 1 4 ) ( x 2 / 4 ) 3 ( 3 ! ) 2 + ,
i = 1 4 C i , n d ψ i d x = invariant for n n + 1 ;
l n 5 i = 1 4 C i , n ( d 2 ψ i d x 2 + ν x d ψ i d x ) = inv . ;
l n 3 ( i = 1 , 3 C i , n d ψ i + 1 d x i = 2 , 4 C i , n d ψ i + 1 d x ) = inv . ;
l n [ i = 1 , 3 C i , n ( d 2 ψ i + 1 d x 2 ν x d ψ i + 1 d x ) i = 1 , 4 C i , n ( d 2 ψ i 1 d x 2 ν x d ψ i 1 d x ) ( 1 ν ) p l n 3 2 D n ] = inv . ;
δ z = w cos tan 1 ( r < R > ) + u sin tan 1 ( r < R > ) ,
δ r = w cos tan 1 ( r < R > ) + u cos tan 1 ( r < R > ) ,
z flex { r + δ r } = δ z .
z flex { r } = i = 1 , 2 , 3 , a 2 i r 2 i .
{ t n } C i , n { w n } , { u n } z flex ( r ) .
z opt = z sphe + z flex
z 1 Sphe = 0.223984 × 10 3 r 2 + 0.112371 × 10 10 r 4 + 0.112750 × 10 17 r 6 + 0.141414 × 10 24 r 8 , z flex = 0.002463 × 10 3 r 2 0.176276 × 10 10 r 4 0.144077 × 10 17 r 6 0.141414 × 10 24 r 8 , z 1 SUM = 0.226448 × 10 3 r 2 0.639050 × 10 11 r 4 0.313270 × 10 18 r 6 + 0.201621 × 10 51 r 8 , z 1 opt = 0.226448 × 10 3 r 2 0.639050 × 10 11 r 4 0.313270 × 10 18 r 6 + 0.000000 × 10 00 r 8 ,
z opt = z sphe + z flex + z rota ,
z rota = 2 r l ( d z 1 d r ) r = r l r 2 .
z 3 Sphe = 0.223984 × 10 3 r 2 + 0.112371 × 10 10 r 4 + 0.112750 × 10 17 r 6 + 0.141414 × 10 24 r 8 , z 3 flex = 0.001400 × 10 3 r 2 0.870471 × 10 10 r 4 + 0.680245 × 10 16 r 6 0.141414 × 10 24 r 8 , z 3 rota = 0.002178 × 10 3 r 2 + 0 + 0 + 0 , z 3 SUM = 0.227562 × 10 3 r 2 0.758100 × 10 10 r 4 + 0.691520 × 10 16 r 6 + 0.139328 × 10 48 r 8 , z 3 opt = 0.227562 × 10 3 r 2 0.758100 × 10 10 r 4 + 0.691520 × 10 16 r 6 + 0.000000 × 10 + 00 r 8 ,
Q r = P 2 ( 14 r 2 r ext 2 ) r ,
z opt = z sphe + z flex ,
d z sphe / d r | r min = d z sphe / d r | r min ,
D d d r ( d 2 z d r 2 + 1 d r d z d r ) + d D d r ( d 2 z d r 2 + ν r d z d r ) = Q r ,
z 2 Sphe = 0.454340 × 10 3 r 2 + 0.937868 × 10 10 r 4 + 0.387198 × 10 16 r 6 + 0.199820 × 10 23 r 8 , z 2 flex = 0.001864 × 10 3 r 2 0.373737 × 10 09 r 4 + 0.203131 × 10 15 r 6 0.199521 × 10 23 r 8 , z 2 SUM = 0.456204 × 10 3 r 2 0.279950 × 10 09 r 4 + 0.241851 × 10 15 r 6 + 0.299163 × 10 26 r 8 , z 2 opt = 0.456204 × 10 3 r 2 0.279950 × 10 09 r 4 + 0.241840 × 10 15 r 6 + 0.000000 × 10 + 00 r 8 ,
Sphe 3 = 0.06 λ , Coma 3 = 0.07 λ , Astm 3 = 0.42 λ .

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