Abstract

We present an analysis of the diffraction effects from a segmented aperture with a very large number of segments—prototype of the next generation of extremely large telescopes. This analysis is based on the point-spread-function analytical calculation for Keck-type hexagonal segmentation geometry. We concentrate on the effects that lead to the appearance of speckles and/or a regular pattern of diffraction peaks. These effects are related to random piston and tip–tilt errors on each segment, gaps between segments, and segment edge distortion. We deliver formulas and the typical numerical values for the Strehl ratio, the relative intensity of higher-order diffraction peaks, and the averaged intensity of speckles associated with each particular case of segmentation error.

© 2003 Optical Society of America

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  1. H. M. Martin, J. R. P. Angel, J. H. Burge, S. M. Miller, J. M. Sasian, P. A. Strittmatter, “Optics for the 20/20 telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 194–205 (2002).
    [CrossRef]
  2. P. Dierickx, R. Gilmozzi, “Progress of the OWL 100-m telescope conceptual design,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. Sebring, T. Andersen, eds., Proc. SPIE4004, 290–299 (2000).
    [CrossRef]
  3. D. Burgarella, K. Dohlen, M. Ferrari, F. Sayede, F. Hammer, F. Zamkotsian, “Next generation Canada–France–Hawaii telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 93–103 (2002).
    [CrossRef]
  4. J. Nelson, T. Mast, S. Faber, “The design of the Keck Observatory and telescope,” (W. M. Keck Library, Kamuela Hawaii, 1985), pp. 5-1 to 5-44.
  5. V. L. Krabbendam, T. A. Sebring, F. B. Ray, S. R. Fowler, “Development and performance of Hobby–Eberly Telescope 11 meter segmented mirror,” in Advanced Technology Optical/IR Telescopes VI, L. Stepp, ed., Proc. SPIE3352, 436–445 (1998).
    [CrossRef]
  6. F. J. Castro, N. Devaney, L. Jochum, B. Ronquillo, L. Cavaller, “The status of the design and fabrication of the GTC Mirrors,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 24–33 (2000).
    [CrossRef]
  7. J. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. Sebring, T. Andersen, eds. Proc. SPIE4004, 282–289 (2000).
    [CrossRef]
  8. S. Strom, L. Stepp, M. Mountain, B. Gregory, “Giant segmented mirror telescope: a point design based on science drivers,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
    [CrossRef]
  9. A. L. Ardeberg, T. Andersen, M. Rodriguez-Espinosa, “Euro50 extremely large telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
  10. G. Zeider, E. Montgomery, “Diffraction effect with segmented aperture,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 799–809 (1998).
    [CrossRef]
  11. G. Zeider, “Image-based alignment of large segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 241–249 (2000).
    [CrossRef]
  12. N. Yaitskova, K. Dohlen, “Simulation of imaging performance for extremely large segmented telescopes,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 279–290 (2000).
    [CrossRef]
  13. M. Troy, G. A. Chanan, “Diffraction effects from giant segmented mirror telescopes,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 81–92 (2002).
    [CrossRef]
  14. J. R. Kurn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concept for a large-aperture, high dynamic range telescope,” Publ. Astron. Soc. Pac. 113, 1486–1510 (2001).
    [CrossRef]
  15. N. Yaitskova, K. Dohlen, P. Dierickx, “Diffraction in OWL: effects of segmentation and segments edge misfigure,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 171–182 (2002).
    [CrossRef]
  16. N. Yaitskova, K. Dohlen, “Tip–tilt error for extremely large segmented telescope: detailed theoretical analysis and numerical simulation,” J. Opt. Soc. Am. A 19, 1274–1285 (2002).
    [CrossRef]
  17. G. Chanan, M. Troy, “Strehl ratio and modulation transfer function for segmented mirror telescopes as functions of segment phase error,” Appl. Opt. 38, 6642–6647 (1999).
    [CrossRef]
  18. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1986).
  19. G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, D. Kirkman, “Phasing the mirror segments of the Keck telescope: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
    [CrossRef]
  20. A. Schumacher, N. Devaney, L. Montoya Martinez, “Phasing segmented mirrors: a modification of the Keck narrow-band technique and its application to extremely large telescopes,” Appl. Opt. 41, 1297–1307 (2002).
    [CrossRef] [PubMed]
  21. S. Esposito, N. Devaney, “Segmented telescope co-phasing using pyramid sensor,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds., in ESO Conference Workshop Proceedings (European Southern Observatory, Garching, Germany, 2002), Vol. 58, pp. 161–166.
  22. S. Cuevas, V. G. Orlov, F. Garfias, V. Voitsekhovich, L. Sanchez, “Curvature equation for a segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 291–302 (2000).
    [CrossRef]
  23. L. Montoya Martinez, N. Yaitskova, P. Dierickx, K. Dohlen, “Mach–Zehnder wave front sensor for phasing of segmented telescopes,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 564–573 (2002).
    [CrossRef]

2002

2001

J. R. Kurn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concept for a large-aperture, high dynamic range telescope,” Publ. Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

1999

1998

Andersen, T.

A. L. Ardeberg, T. Andersen, M. Rodriguez-Espinosa, “Euro50 extremely large telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).

Angel, J. R. P.

H. M. Martin, J. R. P. Angel, J. H. Burge, S. M. Miller, J. M. Sasian, P. A. Strittmatter, “Optics for the 20/20 telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 194–205 (2002).
[CrossRef]

Ardeberg, A. L.

A. L. Ardeberg, T. Andersen, M. Rodriguez-Espinosa, “Euro50 extremely large telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).

Burgarella, D.

D. Burgarella, K. Dohlen, M. Ferrari, F. Sayede, F. Hammer, F. Zamkotsian, “Next generation Canada–France–Hawaii telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 93–103 (2002).
[CrossRef]

Burge, J. H.

H. M. Martin, J. R. P. Angel, J. H. Burge, S. M. Miller, J. M. Sasian, P. A. Strittmatter, “Optics for the 20/20 telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 194–205 (2002).
[CrossRef]

Castro, F. J.

F. J. Castro, N. Devaney, L. Jochum, B. Ronquillo, L. Cavaller, “The status of the design and fabrication of the GTC Mirrors,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 24–33 (2000).
[CrossRef]

Cavaller, L.

F. J. Castro, N. Devaney, L. Jochum, B. Ronquillo, L. Cavaller, “The status of the design and fabrication of the GTC Mirrors,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 24–33 (2000).
[CrossRef]

Chanan, G.

Chanan, G. A.

M. Troy, G. A. Chanan, “Diffraction effects from giant segmented mirror telescopes,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 81–92 (2002).
[CrossRef]

Coulter, R.

J. R. Kurn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concept for a large-aperture, high dynamic range telescope,” Publ. Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Cuevas, S.

S. Cuevas, V. G. Orlov, F. Garfias, V. Voitsekhovich, L. Sanchez, “Curvature equation for a segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 291–302 (2000).
[CrossRef]

Dekens, F.

Devaney, N.

A. Schumacher, N. Devaney, L. Montoya Martinez, “Phasing segmented mirrors: a modification of the Keck narrow-band technique and its application to extremely large telescopes,” Appl. Opt. 41, 1297–1307 (2002).
[CrossRef] [PubMed]

S. Esposito, N. Devaney, “Segmented telescope co-phasing using pyramid sensor,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds., in ESO Conference Workshop Proceedings (European Southern Observatory, Garching, Germany, 2002), Vol. 58, pp. 161–166.

F. J. Castro, N. Devaney, L. Jochum, B. Ronquillo, L. Cavaller, “The status of the design and fabrication of the GTC Mirrors,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 24–33 (2000).
[CrossRef]

Dierickx, P.

P. Dierickx, R. Gilmozzi, “Progress of the OWL 100-m telescope conceptual design,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. Sebring, T. Andersen, eds., Proc. SPIE4004, 290–299 (2000).
[CrossRef]

N. Yaitskova, K. Dohlen, P. Dierickx, “Diffraction in OWL: effects of segmentation and segments edge misfigure,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 171–182 (2002).
[CrossRef]

L. Montoya Martinez, N. Yaitskova, P. Dierickx, K. Dohlen, “Mach–Zehnder wave front sensor for phasing of segmented telescopes,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 564–573 (2002).
[CrossRef]

Dohlen, K.

N. Yaitskova, K. Dohlen, “Tip–tilt error for extremely large segmented telescope: detailed theoretical analysis and numerical simulation,” J. Opt. Soc. Am. A 19, 1274–1285 (2002).
[CrossRef]

N. Yaitskova, K. Dohlen, P. Dierickx, “Diffraction in OWL: effects of segmentation and segments edge misfigure,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 171–182 (2002).
[CrossRef]

N. Yaitskova, K. Dohlen, “Simulation of imaging performance for extremely large segmented telescopes,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 279–290 (2000).
[CrossRef]

D. Burgarella, K. Dohlen, M. Ferrari, F. Sayede, F. Hammer, F. Zamkotsian, “Next generation Canada–France–Hawaii telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 93–103 (2002).
[CrossRef]

L. Montoya Martinez, N. Yaitskova, P. Dierickx, K. Dohlen, “Mach–Zehnder wave front sensor for phasing of segmented telescopes,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 564–573 (2002).
[CrossRef]

Esposito, S.

S. Esposito, N. Devaney, “Segmented telescope co-phasing using pyramid sensor,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds., in ESO Conference Workshop Proceedings (European Southern Observatory, Garching, Germany, 2002), Vol. 58, pp. 161–166.

Faber, S.

J. Nelson, T. Mast, S. Faber, “The design of the Keck Observatory and telescope,” (W. M. Keck Library, Kamuela Hawaii, 1985), pp. 5-1 to 5-44.

Ferrari, M.

D. Burgarella, K. Dohlen, M. Ferrari, F. Sayede, F. Hammer, F. Zamkotsian, “Next generation Canada–France–Hawaii telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 93–103 (2002).
[CrossRef]

Fowler, S. R.

V. L. Krabbendam, T. A. Sebring, F. B. Ray, S. R. Fowler, “Development and performance of Hobby–Eberly Telescope 11 meter segmented mirror,” in Advanced Technology Optical/IR Telescopes VI, L. Stepp, ed., Proc. SPIE3352, 436–445 (1998).
[CrossRef]

Garfias, F.

S. Cuevas, V. G. Orlov, F. Garfias, V. Voitsekhovich, L. Sanchez, “Curvature equation for a segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 291–302 (2000).
[CrossRef]

Gilmozzi, R.

P. Dierickx, R. Gilmozzi, “Progress of the OWL 100-m telescope conceptual design,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. Sebring, T. Andersen, eds., Proc. SPIE4004, 290–299 (2000).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1986).

Gregory, B.

S. Strom, L. Stepp, M. Mountain, B. Gregory, “Giant segmented mirror telescope: a point design based on science drivers,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
[CrossRef]

Hammer, F.

D. Burgarella, K. Dohlen, M. Ferrari, F. Sayede, F. Hammer, F. Zamkotsian, “Next generation Canada–France–Hawaii telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 93–103 (2002).
[CrossRef]

Jochum, L.

F. J. Castro, N. Devaney, L. Jochum, B. Ronquillo, L. Cavaller, “The status of the design and fabrication of the GTC Mirrors,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 24–33 (2000).
[CrossRef]

Kirkman, D.

Krabbendam, V. L.

V. L. Krabbendam, T. A. Sebring, F. B. Ray, S. R. Fowler, “Development and performance of Hobby–Eberly Telescope 11 meter segmented mirror,” in Advanced Technology Optical/IR Telescopes VI, L. Stepp, ed., Proc. SPIE3352, 436–445 (1998).
[CrossRef]

Kurn, J. R.

J. R. Kurn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concept for a large-aperture, high dynamic range telescope,” Publ. Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Martin, H. M.

H. M. Martin, J. R. P. Angel, J. H. Burge, S. M. Miller, J. M. Sasian, P. A. Strittmatter, “Optics for the 20/20 telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 194–205 (2002).
[CrossRef]

Mast, T.

G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, D. Kirkman, “Phasing the mirror segments of the Keck telescope: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
[CrossRef]

J. Nelson, T. Mast, S. Faber, “The design of the Keck Observatory and telescope,” (W. M. Keck Library, Kamuela Hawaii, 1985), pp. 5-1 to 5-44.

Michaels, S.

Miller, S. M.

H. M. Martin, J. R. P. Angel, J. H. Burge, S. M. Miller, J. M. Sasian, P. A. Strittmatter, “Optics for the 20/20 telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 194–205 (2002).
[CrossRef]

Montgomery, E.

G. Zeider, E. Montgomery, “Diffraction effect with segmented aperture,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 799–809 (1998).
[CrossRef]

Montoya Martinez, L.

A. Schumacher, N. Devaney, L. Montoya Martinez, “Phasing segmented mirrors: a modification of the Keck narrow-band technique and its application to extremely large telescopes,” Appl. Opt. 41, 1297–1307 (2002).
[CrossRef] [PubMed]

L. Montoya Martinez, N. Yaitskova, P. Dierickx, K. Dohlen, “Mach–Zehnder wave front sensor for phasing of segmented telescopes,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 564–573 (2002).
[CrossRef]

Moretto, G.

J. R. Kurn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concept for a large-aperture, high dynamic range telescope,” Publ. Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Mountain, M.

S. Strom, L. Stepp, M. Mountain, B. Gregory, “Giant segmented mirror telescope: a point design based on science drivers,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
[CrossRef]

Nelson, J.

G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, D. Kirkman, “Phasing the mirror segments of the Keck telescope: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
[CrossRef]

J. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. Sebring, T. Andersen, eds. Proc. SPIE4004, 282–289 (2000).
[CrossRef]

J. Nelson, T. Mast, S. Faber, “The design of the Keck Observatory and telescope,” (W. M. Keck Library, Kamuela Hawaii, 1985), pp. 5-1 to 5-44.

Orlov, V. G.

S. Cuevas, V. G. Orlov, F. Garfias, V. Voitsekhovich, L. Sanchez, “Curvature equation for a segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 291–302 (2000).
[CrossRef]

Racine, R.

J. R. Kurn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concept for a large-aperture, high dynamic range telescope,” Publ. Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Ray, F. B.

V. L. Krabbendam, T. A. Sebring, F. B. Ray, S. R. Fowler, “Development and performance of Hobby–Eberly Telescope 11 meter segmented mirror,” in Advanced Technology Optical/IR Telescopes VI, L. Stepp, ed., Proc. SPIE3352, 436–445 (1998).
[CrossRef]

Roddier, F.

J. R. Kurn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concept for a large-aperture, high dynamic range telescope,” Publ. Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Rodriguez-Espinosa, M.

A. L. Ardeberg, T. Andersen, M. Rodriguez-Espinosa, “Euro50 extremely large telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).

Ronquillo, B.

F. J. Castro, N. Devaney, L. Jochum, B. Ronquillo, L. Cavaller, “The status of the design and fabrication of the GTC Mirrors,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 24–33 (2000).
[CrossRef]

Sanchez, L.

S. Cuevas, V. G. Orlov, F. Garfias, V. Voitsekhovich, L. Sanchez, “Curvature equation for a segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 291–302 (2000).
[CrossRef]

Sasian, J. M.

H. M. Martin, J. R. P. Angel, J. H. Burge, S. M. Miller, J. M. Sasian, P. A. Strittmatter, “Optics for the 20/20 telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 194–205 (2002).
[CrossRef]

Sayede, F.

D. Burgarella, K. Dohlen, M. Ferrari, F. Sayede, F. Hammer, F. Zamkotsian, “Next generation Canada–France–Hawaii telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 93–103 (2002).
[CrossRef]

Schumacher, A.

Sebring, T. A.

V. L. Krabbendam, T. A. Sebring, F. B. Ray, S. R. Fowler, “Development and performance of Hobby–Eberly Telescope 11 meter segmented mirror,” in Advanced Technology Optical/IR Telescopes VI, L. Stepp, ed., Proc. SPIE3352, 436–445 (1998).
[CrossRef]

Stepp, L.

S. Strom, L. Stepp, M. Mountain, B. Gregory, “Giant segmented mirror telescope: a point design based on science drivers,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
[CrossRef]

Strittmatter, P. A.

H. M. Martin, J. R. P. Angel, J. H. Burge, S. M. Miller, J. M. Sasian, P. A. Strittmatter, “Optics for the 20/20 telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 194–205 (2002).
[CrossRef]

Strom, S.

S. Strom, L. Stepp, M. Mountain, B. Gregory, “Giant segmented mirror telescope: a point design based on science drivers,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
[CrossRef]

Troy, M.

Voitsekhovich, V.

S. Cuevas, V. G. Orlov, F. Garfias, V. Voitsekhovich, L. Sanchez, “Curvature equation for a segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 291–302 (2000).
[CrossRef]

Yaitskova, N.

N. Yaitskova, K. Dohlen, “Tip–tilt error for extremely large segmented telescope: detailed theoretical analysis and numerical simulation,” J. Opt. Soc. Am. A 19, 1274–1285 (2002).
[CrossRef]

N. Yaitskova, K. Dohlen, P. Dierickx, “Diffraction in OWL: effects of segmentation and segments edge misfigure,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 171–182 (2002).
[CrossRef]

N. Yaitskova, K. Dohlen, “Simulation of imaging performance for extremely large segmented telescopes,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 279–290 (2000).
[CrossRef]

L. Montoya Martinez, N. Yaitskova, P. Dierickx, K. Dohlen, “Mach–Zehnder wave front sensor for phasing of segmented telescopes,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 564–573 (2002).
[CrossRef]

Zamkotsian, F.

D. Burgarella, K. Dohlen, M. Ferrari, F. Sayede, F. Hammer, F. Zamkotsian, “Next generation Canada–France–Hawaii telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 93–103 (2002).
[CrossRef]

Zeider, G.

G. Zeider, E. Montgomery, “Diffraction effect with segmented aperture,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 799–809 (1998).
[CrossRef]

G. Zeider, “Image-based alignment of large segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 241–249 (2000).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Publ. Astron. Soc. Pac.

J. R. Kurn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concept for a large-aperture, high dynamic range telescope,” Publ. Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Other

N. Yaitskova, K. Dohlen, P. Dierickx, “Diffraction in OWL: effects of segmentation and segments edge misfigure,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 171–182 (2002).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1986).

S. Esposito, N. Devaney, “Segmented telescope co-phasing using pyramid sensor,” in Beyond Conventional Adaptive Optics, E. Vernet, R. Ragazzoni, S. Esposito, N. Hubin, eds., in ESO Conference Workshop Proceedings (European Southern Observatory, Garching, Germany, 2002), Vol. 58, pp. 161–166.

S. Cuevas, V. G. Orlov, F. Garfias, V. Voitsekhovich, L. Sanchez, “Curvature equation for a segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 291–302 (2000).
[CrossRef]

L. Montoya Martinez, N. Yaitskova, P. Dierickx, K. Dohlen, “Mach–Zehnder wave front sensor for phasing of segmented telescopes,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 564–573 (2002).
[CrossRef]

H. M. Martin, J. R. P. Angel, J. H. Burge, S. M. Miller, J. M. Sasian, P. A. Strittmatter, “Optics for the 20/20 telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 194–205 (2002).
[CrossRef]

P. Dierickx, R. Gilmozzi, “Progress of the OWL 100-m telescope conceptual design,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. Sebring, T. Andersen, eds., Proc. SPIE4004, 290–299 (2000).
[CrossRef]

D. Burgarella, K. Dohlen, M. Ferrari, F. Sayede, F. Hammer, F. Zamkotsian, “Next generation Canada–France–Hawaii telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 93–103 (2002).
[CrossRef]

J. Nelson, T. Mast, S. Faber, “The design of the Keck Observatory and telescope,” (W. M. Keck Library, Kamuela Hawaii, 1985), pp. 5-1 to 5-44.

V. L. Krabbendam, T. A. Sebring, F. B. Ray, S. R. Fowler, “Development and performance of Hobby–Eberly Telescope 11 meter segmented mirror,” in Advanced Technology Optical/IR Telescopes VI, L. Stepp, ed., Proc. SPIE3352, 436–445 (1998).
[CrossRef]

F. J. Castro, N. Devaney, L. Jochum, B. Ronquillo, L. Cavaller, “The status of the design and fabrication of the GTC Mirrors,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 24–33 (2000).
[CrossRef]

J. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. Sebring, T. Andersen, eds. Proc. SPIE4004, 282–289 (2000).
[CrossRef]

S. Strom, L. Stepp, M. Mountain, B. Gregory, “Giant segmented mirror telescope: a point design based on science drivers,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 116–128 (2002).
[CrossRef]

A. L. Ardeberg, T. Andersen, M. Rodriguez-Espinosa, “Euro50 extremely large telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).

G. Zeider, E. Montgomery, “Diffraction effect with segmented aperture,” in Space Telescopes and Instruments V, P. Y. Bely, J. B. Breckinridge, eds., Proc. SPIE3356, 799–809 (1998).
[CrossRef]

G. Zeider, “Image-based alignment of large segmented telescope,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 241–249 (2000).
[CrossRef]

N. Yaitskova, K. Dohlen, “Simulation of imaging performance for extremely large segmented telescopes,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 279–290 (2000).
[CrossRef]

M. Troy, G. A. Chanan, “Diffraction effects from giant segmented mirror telescopes,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 81–92 (2002).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Segmented mirror with segmentation order M=5 consisting of N=90 segments. Solid and dashed arrows illustrate the double π/3 symmetry of the system.

Fig. 2
Fig. 2

a, Grid factor (regular spots) and the segment PSFs for a perfect telescope without gaps. Except for the central peak, all peaks of the grid factor fall into zeros of the segment PSFs. Solid and dashed arrows illustrate the same double π/3 symmetry as observed in the pupil plane (Fig. 1). b, The same, but with gaps between segments (relative gap size ω=0.1). Higher-order peaks are no longer coincident with PSFs zeros. The same effect is seen for tip–tilt errors and segment-edge misfigure.

Fig. 3
Fig. 3

Illustration of the classification scheme for higher-order peaks. Angular separation is calculated assuming segment size d=1.5 m and wavelength λ=0.5 μm.

Fig. 4
Fig. 4

Strehl ratio as a function of tip–tilt rms in units of wavelength, for different numbers of segments: 1, N=37; 2, N=217; 3, N=817.

Fig. 5
Fig. 5

Relative intensity of higher-order peaks as a function of tip–tilt rms. N=217. The curve numbers indicate peak classification: 1, A1; 2, B1; 3, A2; 4, C1; 5, A3; 6, B2; 7, D1; 8, A4.

Fig. 6
Fig. 6

Relative intensity of higher-order peaks as a function of relative gap size ω plotted over a large range (a) and as a function of gap size in millimeters for d=1.5 m plotted over a small range (b). The curve numbers indicate peak classification: 1, A1; 2, B1; 3, A2; 4, C1; 5, A3; 6, B2; 7, D1; 8, A4.

Fig. 7
Fig. 7

Turned-down edge. Dashed line, linear model; solid line, quadratic model; dotted line, exponential model.

Fig. 8
Fig. 8

For PSF calculation in a case of segment-edge misfigure. The turned edge is split into K hexagonal zones, within which the phase is settled accordingly to the edge profile.

Fig. 9
Fig. 9

Strehl ratio for turned-down edges as a function of misfigure depth. The curve parameter is misfigure width: 1, η=5 mm; 2, η=10 mm; 3, η=20 mm. Segment size d=1.5 m. Dotted lines are the saturation level (1-2η/d)4.

Fig. 10
Fig. 10

Relative intensity of the A1 higher-order maxima: 1, η=5 mm; 2, η=10 mm; 3, η=20 mm. Segment size d=1.5 m. Dotted lines are the saturation level 0.68×(2η/d)2.

Tables (3)

Tables Icon

Table 1 Ensemble-Averaged Relative Intensity of the Higher-Order Peaks Due to Random Tip–Tilt Errors with rms = 2π/30

Tables Icon

Table 2 Relative Intensity of the Higher-Order Peaks Due to 12-mm Gap Size with Segments d = 1.5 m

Tables Icon

Table 3 Upper Limits for Higher-Order-Peak Relative Intensity Due to Turned-Down Edges with Segments d = 1.5  m

Equations (48)

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F(x)=j=1Nfj(x-rj)=j=1Nθj(x-rj)exp[iϕj(x-rj)],
θj(x-rj)=1insidethesegmentaperture0outsidethesegmentaperture.
U(w)=1λzF(x)expi 2πλzwxd2x=1λzj=1Nθj(x-rj)exp[iϕj(x-rj)]×expi 2πλzwxd2x,
U(w)=1λzj=1Nexpi 2πλzwrjθj(x-rj)×exp[iϕj(x-rj)]expi 2πλzw(x-rj)d2x=ANλz1Nj=1Nexpi 2πλzwrjAjA1Aj×θj(ξ)exp[iϕj(ξ)]expi 2πλzwξd2ξ,
A=32 d2.
PSF(w)=|U(w)|2=ANλz21Nj=1Nexpi 2πλzwrjAjA1Aj×θj(ξ)exp[iϕj(ξ)]×expi 2πλzwξd2ξ2.
PSF(w)=ANλz21Nj=1Nexpi 2πλzwrj2×1Aθ(ξ)expi 2πλzwξd2ξ2=ANλz2GF(w)PSFs(w).
I0=PSF(0)=ANλz2.
GF(w)=sin[(3M+1)β+(M+1)3α] ×sin[M(β-3α)]Nsin(2β)sin(β-3α)+sin[(3M+2)β-M3α] sin[(M+1)(β+3α)]Nsin(2β)sin(β+3α)2,
2β=mπβ±3α=nπ or wy=mλz/dwy±3wx=n2λz/d ,
t(w)=1Aθ(ξ)expi 2πλzwξd2ξ=sin(3α-β)sinc(α/3+β)+sin(3α+β)sinc(α/3-β)23α.
tx(α)=sin(α/3)sin(α3)α2,
ty(β)=1-cos(2β)+2β sin(2β)6β2.
PSF(w)=ANλz21Nj=1Nexpi 2πλzwrjexp(iδj)2×1Aθ(ξ)expi 2πλzwξd2ξ2=ANλz2GF(w)PSFs(w).
speckle 2.9λ/πd.
S=1N1+2Nj>1Ncos(δj-δ1).
S=1N [1+(N-1)exp(-rms2)],
R=1-exp(-rms2)1+(N-1)exp(-rms2).
PSF(w, rms)ANλz2GF(w)PSFs(w, rms).
PSFs(w, rms)=t(w)Q(rms, w-w)d2w2,
Q(rms, w-w)=2πλz2d22π(2.7rms)2×exp-2πλz2(w-w)2d22(2.7rms)2.
S(rms)1-rms2+rms442.34+2N.
IAI(rms)0.01rms4.
ω=d-dd=1-d/d.
PSF(w)=ANλz21Nj=1Nexpi 2πλzw  rj2×(1-ω)41Aθ(ξ)×expi 2πλzwξd2ξ2=ANλz2GF(w)[(1-ω)4|t(w, d)|2]=ANλz2GF(w)PSFs(w, d),
PSF(0)=ANλz2(1-ω)4.
S=PSF(0)/I0=(1-ω)41-4ω+6ω2.
IAn(ω)tXπn3dd2=3 sin[nπ(1-ω)]sin[nπ(1-ω)/3](nπ)2(1-ω)22,
IBm(ω)tyπm dd2=1-cos[m2πω]+mπ(1-ω)sin[m2πω]6(mπ)2(1-ω)22.
IAn(ω)ω2sinc2(nπ/3)+ω4cos2(nπ/3),
IBm(ω)ω2/9.
IA1(ω)0.68ω2.
ϕ(x, , η)=-x/η,
ϕ(x, , η)=-(x/η)2,
ϕ(x, , η)=2{exp[-(x/η)2ln 2]-1},
PSF(w)=ANλz21Nj=1Nexpi 2πλzwrj2×1Aθ(ξ)exp[iϕ(ξ, η, )]×expi 2πλzwξd2ξ2=ANλz2GF(w)PSFs(w, η, ),
PSFs(w, η, )1Aθ0(ξ)exp[iϕ0(η, )]+n=1K[θn(ξ)-θn-1(ξ)]×exp[iϕn(η, )]×expi 2πλzwξd2ξ2,
PSFs(w, η, )A0A1A0θ0(ξ)expi 2πλzwξd2ξ+n=1Kexp[iϕn(η, )]AnA1Anθn(ξ)×expi 2πλzwξd2ξ-An-1A1An-1θn-1(ξ)×expi 2πλzwξd2ξ2=A0A t0(w)+n=1Kexp[iϕn(η, )]×AnA tn(w)-An-1A tn-1(w)2,
tn(w)=1Anθn(ξ)expi 2πλzwξd2ξ.
d(x)=d-2η+2x,
PSFs(w, η, )=d-2ηd2t(w, 0, η)+0ηexp[iϕ(x, η, )] x×d-2η+2xd2t(w, x, η)dx2.
S(η, )=d-2ηd2+0ηexp[iϕ(x, η, )]4 d-2η+2xd2dx2.
S(η, )1-42ηd1-π2C()+2ηd26-12π2C()-2sin()+4 π2 [C2()+S2()],
C(x)=2π0xcos(t2)dt;S(x)=2π0xsin(t2)dt.
S(η, )>1-3.32ηd+4.52ηd2.
PSFs(w, η, )d-2ηd2t(w, 0)2.
IA1(η, )2ηd2sinc2π31-π2C()+π2 [C2()+S2()],
IA1(η, )<0.52ηd2.

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