Abstract

A system is described to control the figure of a large telescope primary mirror that is composed of many individual segments. The geometry considered, employing hexagonal mirrors, allows a simple and economical control system. The system is shown to be reliable and effective in continuously maintaining the figure to the precision required for optical astronomy.

© 1982 Optical Society of America

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References

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  1. J. E. Nelson, “The Proposed University of California Ten-Meter Telescope,” in Proceedings, Conference on Optical Telescopes of the Future, December 1977 (Geneva 23: ESO c/o CERN, 1978), p. 133.
  2. J. E. Nelson, Proc. Soc. Photo-Opt. Instrum. Eng. 172, 31 (1979).
  3. J. E. Nelson, “The University of California Ten Meter Telescope Project—the Segmented Design,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 11.
  4. T. S. Mast, J. E. Nelson, “Figure Control for a Segmented Telescope Mirror,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 508.
  5. R. Crane, “Figure Sensing Techniques,” in Optical Telescope Technology Workshop, NASA Spec. Publ. 233 (Apr.1969), p. 297.
  6. J. W. Hardy, “Role of Active Optics in Large Telescopes,” in Proceedings, Conference on Optical Telescopes of the Future, December 1977 (Geneva 23: ESO c/o CERN, 1978), p. 455.
  7. J. E. Nelson, T. S. Mast, “Mirror Segment Motions from Gravitational Deformation of the Cell,” in Ten Meter Telescope Report 48 (Oct.1980), unpublished.
  8. J. E. Nelson, “The Size and Number of Primary Mirror Segments,” in Ten Meter Telescope Report 41 (1980), unpublished.
  9. J. Lubliner, J. E. Nelson, Appl. Opt. 19, 2332 (1980).
    [CrossRef] [PubMed]
  10. J. E. Nelson, G. Gabor, L. K. Hunt, J. Lubliner, T. S. Mast, Appl. Opt. 19, 2341 (1980).
    [CrossRef] [PubMed]
  11. G. Gabor, Proc. Soc. Photo-Opt. Instrum. Eng. 172, 39 (1979).
  12. G. Gabor, “Displacement Sensors and Acutators Needed to Control a Segmented Primary Mirror,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 587.
  13. G.H. Golub, C. Reinsch, Numerische Mathematik 14, 403 (1970).
    [CrossRef]
  14. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  15. T. S. Mast, J. E. Nelson, W. J. Welch, “The Effects of Primary Mirror Segmentation on Image Quality,” in Ten Meter Telescope Report 68 (Jan.1982), unpublished.

1980 (2)

1979 (2)

G. Gabor, Proc. Soc. Photo-Opt. Instrum. Eng. 172, 39 (1979).

J. E. Nelson, Proc. Soc. Photo-Opt. Instrum. Eng. 172, 31 (1979).

1970 (1)

G.H. Golub, C. Reinsch, Numerische Mathematik 14, 403 (1970).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Crane, R.

R. Crane, “Figure Sensing Techniques,” in Optical Telescope Technology Workshop, NASA Spec. Publ. 233 (Apr.1969), p. 297.

Gabor, G.

J. E. Nelson, G. Gabor, L. K. Hunt, J. Lubliner, T. S. Mast, Appl. Opt. 19, 2341 (1980).
[CrossRef] [PubMed]

G. Gabor, Proc. Soc. Photo-Opt. Instrum. Eng. 172, 39 (1979).

G. Gabor, “Displacement Sensors and Acutators Needed to Control a Segmented Primary Mirror,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 587.

Golub, G.H.

G.H. Golub, C. Reinsch, Numerische Mathematik 14, 403 (1970).
[CrossRef]

Hardy, J. W.

J. W. Hardy, “Role of Active Optics in Large Telescopes,” in Proceedings, Conference on Optical Telescopes of the Future, December 1977 (Geneva 23: ESO c/o CERN, 1978), p. 455.

Hunt, L. K.

Lubliner, J.

Mast, T. S.

J. E. Nelson, G. Gabor, L. K. Hunt, J. Lubliner, T. S. Mast, Appl. Opt. 19, 2341 (1980).
[CrossRef] [PubMed]

J. E. Nelson, T. S. Mast, “Mirror Segment Motions from Gravitational Deformation of the Cell,” in Ten Meter Telescope Report 48 (Oct.1980), unpublished.

T. S. Mast, J. E. Nelson, “Figure Control for a Segmented Telescope Mirror,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 508.

T. S. Mast, J. E. Nelson, W. J. Welch, “The Effects of Primary Mirror Segmentation on Image Quality,” in Ten Meter Telescope Report 68 (Jan.1982), unpublished.

Nelson, J. E.

J. Lubliner, J. E. Nelson, Appl. Opt. 19, 2332 (1980).
[CrossRef] [PubMed]

J. E. Nelson, G. Gabor, L. K. Hunt, J. Lubliner, T. S. Mast, Appl. Opt. 19, 2341 (1980).
[CrossRef] [PubMed]

J. E. Nelson, Proc. Soc. Photo-Opt. Instrum. Eng. 172, 31 (1979).

J. E. Nelson, “The University of California Ten Meter Telescope Project—the Segmented Design,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 11.

T. S. Mast, J. E. Nelson, “Figure Control for a Segmented Telescope Mirror,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 508.

J. E. Nelson, “The Size and Number of Primary Mirror Segments,” in Ten Meter Telescope Report 41 (1980), unpublished.

J. E. Nelson, T. S. Mast, “Mirror Segment Motions from Gravitational Deformation of the Cell,” in Ten Meter Telescope Report 48 (Oct.1980), unpublished.

T. S. Mast, J. E. Nelson, W. J. Welch, “The Effects of Primary Mirror Segmentation on Image Quality,” in Ten Meter Telescope Report 68 (Jan.1982), unpublished.

J. E. Nelson, “The Proposed University of California Ten-Meter Telescope,” in Proceedings, Conference on Optical Telescopes of the Future, December 1977 (Geneva 23: ESO c/o CERN, 1978), p. 133.

Reinsch, C.

G.H. Golub, C. Reinsch, Numerische Mathematik 14, 403 (1970).
[CrossRef]

Welch, W. J.

T. S. Mast, J. E. Nelson, W. J. Welch, “The Effects of Primary Mirror Segmentation on Image Quality,” in Ten Meter Telescope Report 68 (Jan.1982), unpublished.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Appl. Opt. (2)

Numerische Mathematik (1)

G.H. Golub, C. Reinsch, Numerische Mathematik 14, 403 (1970).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

G. Gabor, Proc. Soc. Photo-Opt. Instrum. Eng. 172, 39 (1979).

J. E. Nelson, Proc. Soc. Photo-Opt. Instrum. Eng. 172, 31 (1979).

Other (10)

J. E. Nelson, “The University of California Ten Meter Telescope Project—the Segmented Design,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 11.

T. S. Mast, J. E. Nelson, “Figure Control for a Segmented Telescope Mirror,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 508.

R. Crane, “Figure Sensing Techniques,” in Optical Telescope Technology Workshop, NASA Spec. Publ. 233 (Apr.1969), p. 297.

J. W. Hardy, “Role of Active Optics in Large Telescopes,” in Proceedings, Conference on Optical Telescopes of the Future, December 1977 (Geneva 23: ESO c/o CERN, 1978), p. 455.

J. E. Nelson, T. S. Mast, “Mirror Segment Motions from Gravitational Deformation of the Cell,” in Ten Meter Telescope Report 48 (Oct.1980), unpublished.

J. E. Nelson, “The Size and Number of Primary Mirror Segments,” in Ten Meter Telescope Report 41 (1980), unpublished.

G. Gabor, “Displacement Sensors and Acutators Needed to Control a Segmented Primary Mirror,” in Proceedings, Kitt Peak National Observatory Conference on Optical and Infrared Telescopes for the 1990s (Tucson, Ariz., Jan. 1980), p. 587.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

T. S. Mast, J. E. Nelson, W. J. Welch, “The Effects of Primary Mirror Segmentation on Image Quality,” in Ten Meter Telescope Report 68 (Jan.1982), unpublished.

J. E. Nelson, “The Proposed University of California Ten-Meter Telescope,” in Proceedings, Conference on Optical Telescopes of the Future, December 1977 (Geneva 23: ESO c/o CERN, 1978), p. 133.

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Figures (13)

Fig. 1
Fig. 1

Geometry of the segmented primary mirror with three rings of hexagonal segments and a total of thirty-six segments. The area is equal to that of 10-m diam circular mirror.

Fig. 2
Fig. 2

Location of some of the 108 actuators shown schematically on the backs of the mirror segments. The actuators control the orientation of the segments by moving normal to the segments.

Fig. 3
Fig. 3

Positions of the 168 displacement sensors and three tilt sensors used for sensing the relative orientations of the mirror segments.

Fig. 4
Fig. 4

Schematic plan and oblique views of three mirror segments illustrating the displacement measurements made by the sensors.

Fig. 5
Fig. 5

Definition of the mirror segment types labeled according to their distance from the center of the primary.

Fig. 6
Fig. 6

Typical image spot diagram generated by 50-nm displacement sensor noise and 0.0-sec of arc tilt sensor noise.

Fig. 7
Fig. 7

The 1-D Gaussian width δ (sec of arc) of the image spot distribution for a 50-nm noise level in displacement sensors as a function of tilt sensor noise. The straight line is the width for a system with no displacement sensor noise.

Fig. 8
Fig. 8

Contour plot of equal level of radius (sec of arc) enclosing 80% of the energy as a function of noise in the tilt sensor (sec of arc) and noise in the displacement sensors (nm).

Fig. 9
Fig. 9

Image width parameter δ (sec of arc) for systems with two, three, and four rings of segments. The lower points are for systems with (a) tilt sensor noise alone (0.1 sec of arc) and (b) displacement sensor noise alone (50 nm). The upper points (c) are for both types of noise together.

Fig. 10
Fig. 10

Gaussian width parameter δ in sec of arc as a function of mirror type for primary mirrors of two, three, and four rings of segments. We assume σd = 50 nm and σt = 0.1 sec of arc.

Fig. 11
Fig. 11

The rms surface error (μm) for systems with two, three, and four rings of segments. The lower points are for systems with (a) tilt sensor noise alone (0.1 sec of arc) and (b) displacement sensor noise alone (50 nm). The upper points (c) are for both types of noise together.

Fig. 12
Fig. 12

Radius (sec of arc) enclosing 80% of the energy as a function of wavelength determined from a diffraction calculation. A displacement sensor noise of 50 nm and a tilt sensor noise of 0.1 sec of arc have been assumed. The straight diagonal line is the image size expected from a perfect mirror.

Fig. 13
Fig. 13

Schematic showing the relative orientations of the displacement sensors.

Equations (4)

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s j exp = n A j n p n ,
X 2 = j ( n A j n p n s j meas ) 2 ( σ j ) 2 ,
p k = n B k n s n meas ,
P ( θ ) θ d θ d ϕ = 1 2 π δ 2 exp ( θ 2 / 2 δ 2 ) θ d θ d ϕ .

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