Abstract

Design concepts for future large optical telescopes have highly segmented primary mirrors, with the out-of-plane degrees of freedom actively controlled. We estimate the contribution to errors in controlling the primary mirror that results from sensor noise and, in particular, compare mechanical measurements of relative segment motion with optical wave-front information. Data from the Keck telescopes are used to obtain realistic estimates of the achievable noise due to mechanical sensors. On the basis of these estimates, mechanical sensors will be more accurate than wave-front information for any of the telescope design concepts currently under consideration, and therefore supplemental wave-front sensors are not required for real-time figure control. Furthermore, control system errors due to sensor noise will not significantly degrade either seeing-limited or diffraction-limited observations.

© 2004 Optical Society of America

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References

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  1. J. Nelson, T. Mast, eds., “Conceptual design for a 30-meter telescope,” CELT Rep. 34 (California Institute of Technology, Pasadena, Calif., and University of California, Irvine, Calif., 2002), available at http://celt.ucolick.org .
  2. S. E. Strom, L. Stepp, B. Gregory, “Giant Segmented Mirror Telescope: a point design based on science drivers,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
    [CrossRef]
  3. T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
    [CrossRef]
  4. P. Dierickx, B. Delabre, L. Noethe, “OWL optical design, active optics, and error budget,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 203–211 (2000).
    [CrossRef]
  5. R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
    [CrossRef]
  6. R. Cohen, T. Mast, J. Nelson, “Performance of the W.M. Keck telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
    [CrossRef]
  7. S. Padin, “Wind-induced deformations in a segmented mirror,” Appl. Opt. 41, 2381–2389 (2002).
    [CrossRef] [PubMed]
  8. R. N. Wilson, L. Noethe, “Closed-loop active optics: its advantages and limitations for correction of wind-buffet deformations of large flexible mirrors,” in Active Telescope Systems, F. J. Roddier, ed., Proc. SPIE1114, 290–301 (1989).
    [CrossRef]
  9. G. Chanan, D. G. MacMartin, J. Nelson, T. Mast, “Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation,” Appl. Opt. (to be published).
  10. T. Mast, J. Nelson, “Segmented mirror control system hardware for CELT,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 226–240 (2000).
    [CrossRef]
  11. D. G. MacMartin, “Control challenges for extremely large telescopes,” in Smart Structures and Materials 2003: Industrial and Commercial Applications of Smart Structures Technology, E. H. Anderson, ed., Proc. SPIE5054, 275–286 (2003).
    [CrossRef]
  12. D. G. MacMartin, T. S. Mast, G. Chanan, J. E. Nelson, “Active control issues for the California Extremely Large Telescope,” paper AIAA-2001-4035, presented at the Guidance, Navigation, and Control Conference, Montreal, Canada, 6–9 August 2001 (American Institute of Aeronautics and Astronautics, Reston, Va., 2001).
  13. S. Padin, W. Davison, “Model of image degradation due to wind buffeting on an extremely large telescope,” Appl. Opt. 42, 592–600 (2004).
    [CrossRef]
  14. D. G. MacMartin, G. Chanan, “Control of the California Extremely Large Telescope Primary Mirror,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 69–80 (2002).
    [CrossRef]

2004 (1)

2002 (1)

Andersen, T.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Andreae, S.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Ardeberg, A.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Arthur, A. A.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Beckers, J.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Biocca, A.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Chanan, G.

G. Chanan, D. G. MacMartin, J. Nelson, T. Mast, “Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation,” Appl. Opt. (to be published).

D. G. MacMartin, T. S. Mast, G. Chanan, J. E. Nelson, “Active control issues for the California Extremely Large Telescope,” paper AIAA-2001-4035, presented at the Guidance, Navigation, and Control Conference, Montreal, Canada, 6–9 August 2001 (American Institute of Aeronautics and Astronautics, Reston, Va., 2001).

D. G. MacMartin, G. Chanan, “Control of the California Extremely Large Telescope Primary Mirror,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 69–80 (2002).
[CrossRef]

Cohen, R.

R. Cohen, T. Mast, J. Nelson, “Performance of the W.M. Keck telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
[CrossRef]

Cohen, R. W.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Davison, W.

Delabre, B.

P. Dierickx, B. Delabre, L. Noethe, “OWL optical design, active optics, and error budget,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 203–211 (2000).
[CrossRef]

Dierickx, P.

P. Dierickx, B. Delabre, L. Noethe, “OWL optical design, active optics, and error budget,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 203–211 (2000).
[CrossRef]

Franck, J.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Fuertes, J. M.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Gabor, G.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Goncharov, A.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Gregory, B.

S. E. Strom, L. Stepp, B. Gregory, “Giant Segmented Mirror Telescope: a point design based on science drivers,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
[CrossRef]

Jared, R. C.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Llacer, J.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

MacMartin, D. G.

D. G. MacMartin, G. Chanan, “Control of the California Extremely Large Telescope Primary Mirror,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 69–80 (2002).
[CrossRef]

D. G. MacMartin, “Control challenges for extremely large telescopes,” in Smart Structures and Materials 2003: Industrial and Commercial Applications of Smart Structures Technology, E. H. Anderson, ed., Proc. SPIE5054, 275–286 (2003).
[CrossRef]

D. G. MacMartin, T. S. Mast, G. Chanan, J. E. Nelson, “Active control issues for the California Extremely Large Telescope,” paper AIAA-2001-4035, presented at the Guidance, Navigation, and Control Conference, Montreal, Canada, 6–9 August 2001 (American Institute of Aeronautics and Astronautics, Reston, Va., 2001).

G. Chanan, D. G. MacMartin, J. Nelson, T. Mast, “Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation,” Appl. Opt. (to be published).

Mast, T.

G. Chanan, D. G. MacMartin, J. Nelson, T. Mast, “Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation,” Appl. Opt. (to be published).

T. Mast, J. Nelson, “Segmented mirror control system hardware for CELT,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 226–240 (2000).
[CrossRef]

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

R. Cohen, T. Mast, J. Nelson, “Performance of the W.M. Keck telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
[CrossRef]

Mast, T. S.

D. G. MacMartin, T. S. Mast, G. Chanan, J. E. Nelson, “Active control issues for the California Extremely Large Telescope,” paper AIAA-2001-4035, presented at the Guidance, Navigation, and Control Conference, Montreal, Canada, 6–9 August 2001 (American Institute of Aeronautics and Astronautics, Reston, Va., 2001).

Meng, J.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Merrick, T.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Minor, R.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Nelson, J.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

R. Cohen, T. Mast, J. Nelson, “Performance of the W.M. Keck telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
[CrossRef]

T. Mast, J. Nelson, “Segmented mirror control system hardware for CELT,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 226–240 (2000).
[CrossRef]

G. Chanan, D. G. MacMartin, J. Nelson, T. Mast, “Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation,” Appl. Opt. (to be published).

Nelson, J. E.

D. G. MacMartin, T. S. Mast, G. Chanan, J. E. Nelson, “Active control issues for the California Extremely Large Telescope,” paper AIAA-2001-4035, presented at the Guidance, Navigation, and Control Conference, Montreal, Canada, 6–9 August 2001 (American Institute of Aeronautics and Astronautics, Reston, Va., 2001).

Noethe, L.

R. N. Wilson, L. Noethe, “Closed-loop active optics: its advantages and limitations for correction of wind-buffet deformations of large flexible mirrors,” in Active Telescope Systems, F. J. Roddier, ed., Proc. SPIE1114, 290–301 (1989).
[CrossRef]

P. Dierickx, B. Delabre, L. Noethe, “OWL optical design, active optics, and error budget,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 203–211 (2000).
[CrossRef]

Orayani, M.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Owner-Petersen, M.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Padin, S.

Riewaldt, H.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Salz, P.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Schaefer, B.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Snel, R.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Stepp, L.

S. E. Strom, L. Stepp, B. Gregory, “Giant Segmented Mirror Telescope: a point design based on science drivers,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
[CrossRef]

Strom, S. E.

S. E. Strom, L. Stepp, B. Gregory, “Giant Segmented Mirror Telescope: a point design based on science drivers,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
[CrossRef]

Walker, D.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Wilson, R. N.

R. N. Wilson, L. Noethe, “Closed-loop active optics: its advantages and limitations for correction of wind-buffet deformations of large flexible mirrors,” in Active Telescope Systems, F. J. Roddier, ed., Proc. SPIE1114, 290–301 (1989).
[CrossRef]

Witebsky, C.

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

Appl. Opt. (2)

Other (12)

D. G. MacMartin, G. Chanan, “Control of the California Extremely Large Telescope Primary Mirror,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 69–80 (2002).
[CrossRef]

R. N. Wilson, L. Noethe, “Closed-loop active optics: its advantages and limitations for correction of wind-buffet deformations of large flexible mirrors,” in Active Telescope Systems, F. J. Roddier, ed., Proc. SPIE1114, 290–301 (1989).
[CrossRef]

G. Chanan, D. G. MacMartin, J. Nelson, T. Mast, “Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation,” Appl. Opt. (to be published).

T. Mast, J. Nelson, “Segmented mirror control system hardware for CELT,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 226–240 (2000).
[CrossRef]

D. G. MacMartin, “Control challenges for extremely large telescopes,” in Smart Structures and Materials 2003: Industrial and Commercial Applications of Smart Structures Technology, E. H. Anderson, ed., Proc. SPIE5054, 275–286 (2003).
[CrossRef]

D. G. MacMartin, T. S. Mast, G. Chanan, J. E. Nelson, “Active control issues for the California Extremely Large Telescope,” paper AIAA-2001-4035, presented at the Guidance, Navigation, and Control Conference, Montreal, Canada, 6–9 August 2001 (American Institute of Aeronautics and Astronautics, Reston, Va., 2001).

J. Nelson, T. Mast, eds., “Conceptual design for a 30-meter telescope,” CELT Rep. 34 (California Institute of Technology, Pasadena, Calif., and University of California, Irvine, Calif., 2002), available at http://celt.ucolick.org .

S. E. Strom, L. Stepp, B. Gregory, “Giant Segmented Mirror Telescope: a point design based on science drivers,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
[CrossRef]

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, R. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

P. Dierickx, B. Delabre, L. Noethe, “OWL optical design, active optics, and error budget,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 203–211 (2000).
[CrossRef]

R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 996–1008 (1990).
[CrossRef]

R. Cohen, T. Mast, J. Nelson, “Performance of the W.M. Keck telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Segmentation geometry for the CELT 15-m radius primary mirror, with 1080 segments of circumscribed radius a = 0.5 m.

Fig. 2
Fig. 2

Control block diagram. For the control, we estimate the displacement from sensors y and use this to determine the desired control command u.

Fig. 3
Fig. 3

Detail of a generic estimate of the relative displacement sensor response at the intersection of three hexagonal segments. The vertical gap d i between a segment corner and a smooth deflection shape is proportional to the segment radius squared and the curvature. The difference between these gaps is measured by relative displacement sensors at the segment corners. The mean-square response of the three sensors at a segment intersection is given by Eq. (6).

Fig. 4
Fig. 4

Theoretical modal error multipliers for relative displacement sensors. The solid curve is the error multiplier N i from sensor noise to displacement, divided by (R/ a) (dimensionless). The dashed curve is the rotational error multiplier (N θ) i from sensor noise to rms segment rotation, divided by 1/a (in mas/nm for a in m). Modes are Zernike basis functions sorted by error multiplier.

Fig. 5
Fig. 5

Average spectrum from Keck 1 displacement sensors, plotted in physical (dotted curve) and unphysical (solid curve) components. The estimated low-frequency noise PSD (see text) is shown by a dotted line.

Fig. 6
Fig. 6

Low-frequency energy in physical and unphysical directions, Keck 1. Circles are 0–2.5 Hz, dots are 2.5–5 Hz. The dashed line corresponds to equal covariance. The slope of the best-fit line (solid line) is α-1 ∼ 6, and the intercept with 〈y p 2〉 = 〈y u 2〉 is at ∼0.42 nm/Hz.

Fig. 7
Fig. 7

Closed-loop rms displacement error in nanometers due to measurement noise as a function of the Zernike radial degree for atmospheric turbulence corrupted wave-front information (upper curve, λ = 0.55 μm, r 0 = 0.2 m, L 0 = 2R = 30 m) and relative displacement sensors (crosses, R = 15 m, a = 0.5 m). A control bandwidth of 0.05 Hz was assumed; higher control bandwidth results in higher errors from either sensor set.

Equations (17)

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y=Ax+δ+n,
xˆ=A#y-δ,
A#=limρ0ATA+ρI-1AT.
Δu=βxˆ.
N2=i=1nact Ni2=i=1nactσi-2nact.
Ψf= 14πaR40102π2fx22+2fy22rdrdθ,
Θf= 1πR20102πfx2+fy2rdrdθ.
Nθ2=i=1nactNθi2= 1nacti=1nactΘiΨi.
yp= AA#y-δ,
yu= I-AA#y-δ.
AA#=UI105000UT,
I-AA#=U000I63UT.
σx21/2=0.35 RaΦ π2 fc1/2.
θ 80=2.540.4amasnmΦ π2 fc1/2.
σwf=2η241/212Φ π2 fc1/2.
FnfRv=0.023Rr05/3n+1π2×-Jn+12πμ2μ2μ2+R/L011/6dk,
σ2fc, n=011+f/fc2 FnfRvdf.

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