X

Fig. 8.20 Mirror thickness geometries T(p) or T(p, 6) for atmospheric field stabilization holed mirrors. (A): Moderately lightweight axisymmetric mirror with conical edges optimized for a minimal axisymmetric flexure - as part of a torus surface - with a ring support. (B): Increased lightweight three-fold symmetry mirror with linear prismatic edges

From this statement, one can derive thickness distributions for minimal flexures in kg gravity cases such as for holed field stabilization mirrors.

One may distinguish two possible alternative thickness families: (i) an axisym-metrical distribution with inner and outer conical edges, or (ii) a three-fold symmetry distribution with inner and outer linear prismatic edges (Fig. 8.20).

8.8.4 Design of Low Weight Wobbling Mirrors

Infrared or far-infrared observations generally require use of a wobbling mirror. When this mirror is the telescope secondary mirror, it is appropriate to locate the telescope input pupil on it. At the detector, the rotation generated by the wobbling mirror allows a single pixel to alternatively receive a target position beam and a reference position beam. Because the reference beam must be free from any emitting astronomical object - black sky -, the rotation angle of the wobbling mirror must reach a large off-target value, such as 2-5 arcmin. Thus, contrarily to field stabilization mirrors, wobbling mirrors must provide a large rotation angle at low frequency. Typical values are 2 arcmin at 10 Hz.

If, as usual, a wobbling mirror only provides a rotation about a single axis, then a best rigid geometry for its substrate should differ from the axi- or three-fold symmetry in Fig. 8.20. If the tip motion is about the x-axis, the rigidity in the x-direction can be somewhat decreased. In both cases, the thickness geometries can be derived from those in Fig. 8.20 by use, for instance, of the transformation T(x) ^ (1 - k2) T(x) where k2 < 1, while T(y) is unchanged. Hence, this again decreases the total weight of the mirror.

References

1. J.R.P. Angel, B. Martin, D. Sandler et al., The next generation space telescope: a monolithic mirror candidate, SPIE Proc., 2807, 354 (1996) 418

2. L. Arnold, Influence functions of a thin shallow meniscus-shaped mirror, Appl. Opt., 36(10),

2019-2028 (1997) 434

3. L. Arnold, Optimized axial support topologies for thin telescope mirrors, Opt. Eng., 34, 567-574 (1995) 434

4. L. Arnold, Optimized mirror supports and active primary mirrors, SPIE Proc., 2199, 239-250 (1994) 434

5. L. Arnold, Uniform-load and actuator influence functions of a thin annular mirror: application to active mirror support optimization, Appl. Opt., 35(7), 1095-1106 (1996) 436

6. Y.Y. Balega, private communication (2007) 415

7. A. Baranne, G.R. Lemaitre, Combinaison optique pour tres grands telescopes: le concept Temos, C.R. Acad. Sc. Paris, 305, Serie II, 445-450 (1987) 448

8. P.Y. Bely, The Design and Construction of Large Optical Telescopes, Springer edt., New York, 221 (2002) 415

9. I.S. Bowen, The 200-inch Hale Telescope, in Telescopes, G.P. Kuiper & B.M. Midlehurst edts., The University of Chicago Press, Chicago, 2nd issue, 1-15 (1962) 415

10. I.S. Bowen, The 200-inch Hale telescope, IAU Proc., vol. VIII, 5,750-754 (1953) 415

11. G. Chanan, C. Ohara, M. Troy, Phasing the primary mirror of the Keck telescopes II, Appl. Opt., 39(25), 4706-4714 (2000) 450

12. G. Chanan, J. Nelson, T. Mast, P. Wisinowich, B. Schaefer, The Keck telescope phasing camera system, SPIEProc., 2198, 1139-1150 (1994) 450

13. G. Chanan, M. Troy, Strehl ratio and modulation transfer function for segmented mirror telescopes as function of the segment phase error, Appl. Opt., 38(31), 6642-6647 (2000) 450

14. G. Chanan, T. Mast, J. Nelson, Phasing the mirror segments of the Keck Telescope, SPIE Proc., 2199, 622-637 (1994) 450

15. J.-P. Chevillard, P. Connes et al., Near infrared astronomical light collector, Appl. Opt., 16(7), 1817-1833 (1977) 448

16. P. Connes, G. Michel, Astronomical Fourier spectrometer, Appl. Opt., 14(9), 2067-2084 (1975) 448

17. A. Couder, Recherches sur les deformations des grands miroirs - Effets thermiques: Deformations des miroirs, agitation de l'air, Bull. Astronomique Obs. Paris, VII, Fasc. 7, 19-312 (1932). [Cf. also transl. E.T. Pearson, Kpno Library (1966)] 417, 420

18. A. Couder, Recherches sur les deformations des grands miroirs employes aux observations astronomiques, Bull. Astronomique Obs. Paris, VII, Fasc. 6, 201-281 (1931). [Cf. also transl. E.T. Pearson, Kpno Library (1966)] 429, 431

19. J.F. Creedon, A.G. Lindgren, Automatica, 6(5), 643 (1970) 444

20. S. Cuevas, V.G. Orlov, F. Garfias et al., Curvature equation for a segmented telescope, SPIE Proc., 4003, 291-302 (2000) 452

21. X. Cui, D.-q. Su, G. Li et al., Experiment system of LAMOST active optics, SPIE Proc., 5489, 974-985 (2004) 451

22. X. Cui, Y. Li, X. Ni et al., The active support of LAMOST reflective Schmidt plate, SPIE Proc., 4837, 928-636 (2002) 451

23. P. Dierickx, D. Enard, R. Geyl, J. Paseri, M. Cayrel, P. Beraud, The VLT primary mirrors, SPIE Proc., 2871, 385-392 (1996) (see also www.eso.org/projects/vlt/unit-tel/m1unit.html) 416

24. D. Enard, ESO-VLT: status of the main 8-m telescopes, SPIE Proc., 2199, 394-403 (1994) 416

25. S. Esposito, E. Pinna, A. Puglisi, A. Tozzi, P. Stefanini, Pyramid sensor for segmented mirror alignment, Opt. Lett., 30(19), 2572-2574 (2005) 452

26. L. Foucault, Annales de l'Observatoire de Paris, 5, 197-237 (1859) 414

27. P. Giordano, Internal ESO report, Paranal (2002) 418

28. J.M. Hill, J.R.P. Angel, R.D. Lutz et al., Casting the first 8.4 m borosilicate honeycomb mirror for the Large Binocular Telescope, SPIE Proc., 3352, 172 (1998) 418

29. W.E. Howell, J.F. Creedon, NASA Technical Note, NASA TN D-7090 (Jan. 1973) 444

30. http://grus.berkeley.edu/~jrg/MIDDLE/ 414

31. http://w0.sao.ru/Doc-en/Telescopes/bta/descrip.html 415

32. N. Itoh, I. Mikami et al., Active optics experiments II, Publ. Natl. Astron. Obs. Japan., 1, 57-61 (1989) 448

33. M. Iye, K. Kodaira, Primary support system for the SUBARU telescope, SPIE Proc., 2199, 762-772 (1994) 448

34. M. Iye, R. Noguchi, Y. Toiii et al., Active optics experiments with a 62 cm thin mirror, SPIE Proc., 1236, 929-939 (1990) 448

35. N. Kaifu, SUBARU project: current status, SPIE Proc., 2199, 56-63 (1994) 416, 418

36. V.L. Krabbendam, T.A. Sebring, F.B. Ray, S.R. Fowler, Development and performance of Hooby-Herberly Telescope 11 meter segmented mirror, SPIE Proc., 3352, 436-445 (1998) 451

37. L.D. Landau, E.M. Lifshitz, Theory of Elasticity in Course of Theoretical Physics - Vol. 7, USSR Acad. of Sc., Butterworth & Heinemann eds, 3rd edition, Pergaman press, Oxford, 67 (1986) 454

38. W. Lassell, Mem. Roy. Astron. Soc., XII, 265 (1842) 414

39. G.R. Lemaitre, M. Wang, Optical results with TEMOS 4 and a metal secondary mirror actively aspherized, SPIE Proc., 1931, 43-52 (1992) 449

40. G.R. Lemaitre, R.N. Wilson, S. Mazzanti, Proposal for a 1.8 m meter metal meniscus mirror at once actively aspherized and actively supported, SPIE Proc., 1931, 67-75 (1992)

41. G.R. Lemaitre, Sur la flexion des miroirs secondaires de telescopes, Nouv. Rev. Optique, 7(6), 389-397 (1976) 455,456,457

42. G.R. Lemaitre, Sur la flexion du grand miroir de 3.6 m ESO, ESO Bull., 8, 21-31 (1971) 431

43. A.E.H. Love, Mathematical Theory of Elasticity, first and second edition. See also fourth revised enlarged issue (1927). Reissued by Dover publ., New York, Sects. 299, 309 and 312c (1944) 432

44. A.F. Möbius, in Lehrbuch der Statik, 2 vols., Leipzig, Vol. 2, Chaps. 4 and 5 (1837) 445

45. B. Mack, Deflection and stress analysis of a 4.2 m primary mirror of an alt-azimuth mounted telescope, Appl. Opt., 19(6), 1000-1010 (1980) 441

46. A.J. Malvick, E.T. Pearson, Theoretical elastic deformation of a 4-m diameter optical mirror using dynamic relaxation, Appl. Opt., 7(6), 1207-1212 (1968) 437,443

47. J-P. Marioge, C. Mahe, Contribution au controle des surfaces planes non traitees, Journ. Mod. Optics, Taylor & Francis publ., 20(6), 413-433 (1973) 420

48. T. Mast, G. Nelson, SPIE Proc., 1236, 670 (1990)

49. J.H. Michell, London Math. Soc. Proc., 31, 100 (1900) 432

50. L. Montoya-Martinez, N. Yaitskova, P. Dierickx, K. Dohlen, Mach-Zender wavefront sensor for phasing of segmented telescopes, SPIE Proc., 4840, 564-573 (2003) 452

51. L. Montoya-Martinez, M. Reyes, A. Schumacher, E. Hernandez, DIPSI: the diffraction image phase sensing instrument for Ape, SPIE Proc., 6267, (2006) 452

52. C.M. Mountain, R. Kurz, J. Oschmann, GEMINI 8-m telescope project, SPIE Proc., 2199, 41-55(1994) 416,418

53. J.E. Nelson, J. Lubliner, T.S. Mast, Telescope mirror supports: Mirror deflection on point supports, Spie Proc., 332, 212 (1982) 434

54. J.E. Nelson, J. Lubliner, T.S. Mast, Telescope mirror supports, SPIE Proc., 332, 212-228 (1982) 415

55. C. Neufeld, V. Bennet, T. Sebring, V. Krabbendam et al., Development of an active optics system for the SOAR telescope, SPIE Proc., 5489, 1052-1060 (2004) 457

56. L. Noethe et al., Proc. ESO Conf. on Progress in Telescope and Instrumentation technologies, ESO, Garching, 195 (1992) 448

57. L. Noethe, Active optics in modern large optical telescopes, Progress in Optics, Elsevier publ., 43, 1-13 (2002) 446,447

58. L. Noethe, F. Franza, P. Giorgano, R.N. Wilson, Active Optics II. Results of an experiment with a thin 1 m test mirror, J. Mod. Opt., 35, 1427-1457 (1988) 446

59. L. Noethe, private communication (2006) 452

60. L. Noethe, Use of minimum-energy modes for modal-active optics corrections of thin meniscus mirrors, J. Mod. Opt., 38(6), 1043-1046 (1991) 448

61. D. O'Donoghue, The correction of spherical aberration in the Southern African Large Telescope (Salt), Spie Proc., 4003, 363-370 (2000) 451

62. G. Parodi, G.C. Cerra, J.M. Hill, W.B. Davison, P. Salinari, Lbt primary mirror: the final design of the supporting system, SPIE Proc., 2871, 352-359 (1997) 416

63. A. Rakich, Use of field aberrations in the alignment of the Large Binocular Telescope optics, SPIE Proc., 7012, in press (2008) 445

64. E. Reissner, J. Appl. Mech., 12, A-69 (1945) 433

65. E. Reissner, Quart. Appl. Math., 5, 55 (1947) 433

66. C. Roddier, F. Roddier, Wavefront reconstruction from defocused images and the testing of ground-based optical telescopes, J. Opt. Soc. Am., A, 10(11), 3433-3436 (1988) 452

67. A. Saint-Venant (Barre de), Flamant, Théorie de l'Elasticité des Corps Solides de Clebsch, Dunod edt., Paris, 858-859 (1881). (French transl. of Clebsch's book including important annotations and complements; sometimes referred to as "Clebsch Annoted Version") 432

68. M. Schneermann, X. Cui et al., SPIE Proc., 1236, 920 (1990) 447

69. G. Schwesinger, An analytical determination of the flexure of the 3.5 m primary and 1 m mirror of the ESO New Technology Telescope for passive support and active control, J. Mod. Opt., 35, 1117-1149 (1988) 440,441

70. G. Schwesinger, Comparative assessment of aberrations originating in telescope mirrors from the edge support. Astron. J., 74, 1243-1254 (1969) 439

71. G. Schwesinger, E.D. Knol, Comments on a series of articles by L.A. Selke, Appl. Opt., 11, 200-201 (1972) 434

72. G. Schwesinger, General characteristics of elastic mirror flexure in theory and applications, Symposium Proc. on Support and Testing of Large Astronomical Mirrors, Kpno, Tucson, 10-23 (1966) 431,439

73. G. Schwesinger, Lateral support of very large telescope mirrors by edge forces only, J. Mod. Opt., 38, 1507-1516 (1991) 442

74. G. Schwesinger, Non-distorting lateral edge support of large telescope mirrors, Appl. Opt., 33(7), 1198-1202 (1994) 442

75. G. Schwesinger, Optical effect of flexure in vertically mounted precision mirrors, J. Opt. Soc. Am., 44, 417 (1954) 437,439,440

76. G. Schwesinger, Support configuration and elastic deformation of the 1.5 m prime mirror of the ESO Coude Auxiliary Telescope (CAT), European Southern Observatory Tech. Rep. 9, Garching (1972) 420,434

77. L.A. Selke, Theoretical elastic deflections of a thick horizontal circular mirror on a double-ring support, Appl. Opt., 9(6), 1453-1456 (1970) 434

78. S. Stanghellini, E. Manil, M. Schmid, K.Dost, Design and preliminary tests of the VLT secondary mirror unit, SPIE Proc., 2871, 105-116 (1996) 449

79. L. Stepp, Conceptual design of the primary mirror cell assembly, GEMINI Report 0-G0025 (1993) 415

80. L. Stepp, E. Huang, M. Cho, GEMINI primary mirror support system, SPIE Proc., 2199, 223-238 (1994) 415,448

81. B. Stobie, K. Meiring, D.A.H. Buckley, Design of the Southern African Large Telescope, in Optical Design, Material, Fabrication and Maintenance, SPIE Proc., 4003, 355-362 (2000) 451

82. D.-q. Su, S.-t. Jiang, W.-y. Zou et al., Experiment system of thin-mirror active optics, SPIE Proc., 2199, 609-621 (1994) 451

83. D-q. Su, W-j. Zou, Z-c. Zhang et al., Experiment system of segmented-mirror active optics, Spie Proc., 4003, 417-425 (2000) 451

84. D.-q. Su, X. Cui, Y.-n. Wang, Z. Yao, LAMOST and its key technology, SPIE Proc., 3352, 76-90 (1998) 420,450

85. D.-q. Su, Y.-n. Wang, A computational study of the star-image displacement due to differential atmospheric refraction during observations, Acta Astrophysica Sinica, 17, 202-212 (1997) 450

86. H. Tafelmaier, Diinnschicht-Tecknik Co., www.tafelmaier.de/eng/default.asp 418

87. S.P. Timoshenko, in History of Strength of Materials, Dover Publ. Inc., New York, 304 (1983) 445

88. S.P. Timoshenko, S. Woinowsky-Krieger, in Theory of Plates and Shells, McGraw-Hill edt., New York, second issue, Sect. 20, 74 (1959) 432

89. D.S. Wan, J.P.R. Angel, R.E. Parks, Mirror deflection on multiple axial supports, Appl. Opt., 28, 354-362 (1989) 434

90. R.N. Wilson, F. Franza, L. Noethe, Active optics I. A system for optimizing the optical quality and reducing the costs of large telescopes, J. Mod. Opt., 34, 485-509 (1987) 444, 445

91. R.N. Wilson, F. Franza, L. Noethe, G. Andreoni, Active Optics IV. Set-up and performance of the optics of the ESO New Technology Telescope (NTT) in the observatory, J. Mod. Opt., 38, 219-243 (1991) 446

92. R.N. Wilson, F. Franza, P. Giordano, L. Noethe, M. Tarenghi, Active Optics III. Final results with the 1 m test mirror and Ntt 3.56 m primary in the workshop, J. Mod. Opt., 36, 1415-1425 (1989) 446

93. R.N. Wilson, Reflecting Telescope Optics II, Springer-Verlag edt., New York, (1999) 444, 445

94. S. Woinowsky-Krieger, Ingr. Arch., 4, 305 (1933) 432, 452

96. www.telescopengineering.com/company/DmitriMaksutov.html 417,420

97. N. Yaitskova, K. Dohlen, P. Dierickx, Analytical study of diffraction effects in extremely large segmented telescopes, JOSA A, 20(8), 1563-1575 (2003)

98. N. Yaitskova, K. Dohlen, Tip-tilt error for extremely large segmented telescopes: detailed theoretical point-spread-function analysis and numerical simulation results, JOSA A, 19(7), 1274-1285 (2002) 452

99. N. Yaitskova, L.-M. Montoya-Martinez, K. Dohlen, P. Dierickx, A Mack-Zender phasing sensor for extremely large segmented telescopes, SPIE Proc., 5489, 1139-1151 (2004) 452

Chapter 9

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