Abstract

Ultrahigh contrast imaging with giant segmented-mirror telescopes will involve light levels of order 10-6 times that of the central diffraction spike or less. At these levels it is important to quantify accurately various diffraction effects, including segmentation geometry, intersegment gaps, obscuration by the secondary mirror and its supports, and segment alignment and figure errors. We describe an accurate method for performing such calculations and present preliminary results in the context of the California Extremely Large Telescope.

© 2003 Optical Society of America

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References

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  1. J. Nelson, T. Mast, eds., California Extremely Large Telescope: conceptual design for a thirty-meter telescope, CELT report 34 (University of California, California Institute of Technology, Pasadena, Calif., 2002).
  2. J. Angel, “Ground-based imaging of extrasolar planets using adaptive optics,” Nature 368, 203–207 (1994).
    [CrossRef]
  3. R. A. Brown, C. J. Burrows, “On the feasibility of detecting extrasolar planets by reflected starlight using the Hubble Space Telescope,” Icarus 87, 484–497 (1990).
    [CrossRef]
  4. A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
    [CrossRef]
  5. N. Yaitskova, K. Dohlen, P. Dierickx, “Diffraction effects in OWL: effects of segmentation and segments edge misfigure,” in Future Giant Telescopes, J. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 171–182 (2002).
    [CrossRef]
  6. G. A. 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]
  7. M. DiVittorio, Naval Observatory Flagstaff, Ariz. 86002 (personal communication, 2002).
  8. D. MacMartin, G. Chanan, “Control of the California Extremely Large Telescope primary mirror,” in Future Giant Telescopes, J. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 69–80 (2002).
    [CrossRef]
  9. G. A. Chanan, M. Troy, F. G. Dekens, S. Michaels, J. Nelson, T. Mast, D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
    [CrossRef]
  10. G. A. Chanan, C. Ohara, M. Troy, “Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm,” Appl. Opt. 39, 4706–4714 (2000).
    [CrossRef]
  11. M. Troy, G. A. Chanan, E. Sirko, E. Leffert, “Residual misalignments of the Keck telescope primary mirror segments: classification of modes and implications for adaptive optics,” in Advanced Technology Optical/IR Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 307–317 (1998).
    [CrossRef]
  12. A. Sivaramakrishnan, C. Koresko, R. Makidon, T. Berkefeld, M. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Ap. J. 552, 397–408 (2001).
    [CrossRef]

2001 (1)

A. Sivaramakrishnan, C. Koresko, R. Makidon, T. Berkefeld, M. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Ap. J. 552, 397–408 (2001).
[CrossRef]

2000 (1)

1999 (1)

1998 (1)

1997 (1)

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

1994 (1)

J. Angel, “Ground-based imaging of extrasolar planets using adaptive optics,” Nature 368, 203–207 (1994).
[CrossRef]

1990 (1)

R. A. Brown, C. J. Burrows, “On the feasibility of detecting extrasolar planets by reflected starlight using the Hubble Space Telescope,” Icarus 87, 484–497 (1990).
[CrossRef]

Angel, J.

J. Angel, “Ground-based imaging of extrasolar planets using adaptive optics,” Nature 368, 203–207 (1994).
[CrossRef]

Berkefeld, T.

A. Sivaramakrishnan, C. Koresko, R. Makidon, T. Berkefeld, M. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Ap. J. 552, 397–408 (2001).
[CrossRef]

Brown, R. A.

R. A. Brown, C. J. Burrows, “On the feasibility of detecting extrasolar planets by reflected starlight using the Hubble Space Telescope,” Icarus 87, 484–497 (1990).
[CrossRef]

Burrows, A.

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

Burrows, C. J.

R. A. Brown, C. J. Burrows, “On the feasibility of detecting extrasolar planets by reflected starlight using the Hubble Space Telescope,” Icarus 87, 484–497 (1990).
[CrossRef]

Chanan, G.

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

Chanan, G. A.

Dekens, F. G.

Dierickx, P.

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

DiVittorio, M.

M. DiVittorio, Naval Observatory Flagstaff, Ariz. 86002 (personal communication, 2002).

Dohlen, K.

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

Freedman, R.

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

Guillot, T.

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

Hubbard, W.

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

Kirkman, D.

Koresko, C.

A. Sivaramakrishnan, C. Koresko, R. Makidon, T. Berkefeld, M. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Ap. J. 552, 397–408 (2001).
[CrossRef]

Kuchner, M.

A. Sivaramakrishnan, C. Koresko, R. Makidon, T. Berkefeld, M. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Ap. J. 552, 397–408 (2001).
[CrossRef]

Leffert, E.

M. Troy, G. A. Chanan, E. Sirko, E. Leffert, “Residual misalignments of the Keck telescope primary mirror segments: classification of modes and implications for adaptive optics,” in Advanced Technology Optical/IR Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 307–317 (1998).
[CrossRef]

Lunine, J.

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

MacMartin, D.

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

Makidon, R.

A. Sivaramakrishnan, C. Koresko, R. Makidon, T. Berkefeld, M. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Ap. J. 552, 397–408 (2001).
[CrossRef]

Marley, M.

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

Mast, T.

Michaels, S.

Nelson, J.

Ohara, C.

Saumon, D.

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

Sharp, C.

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

Sirko, E.

M. Troy, G. A. Chanan, E. Sirko, E. Leffert, “Residual misalignments of the Keck telescope primary mirror segments: classification of modes and implications for adaptive optics,” in Advanced Technology Optical/IR Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 307–317 (1998).
[CrossRef]

Sivaramakrishnan, A.

A. Sivaramakrishnan, C. Koresko, R. Makidon, T. Berkefeld, M. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Ap. J. 552, 397–408 (2001).
[CrossRef]

Sudarsky, D.

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

Troy, M.

Yaitskova, N.

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

Ap. J. (2)

A. Burrows, M. Marley, W. Hubbard, J. Lunine, T. Guillot, D. Saumon, R. Freedman, D. Sudarsky, C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Ap. J. 491, 856–875 (1997).
[CrossRef]

A. Sivaramakrishnan, C. Koresko, R. Makidon, T. Berkefeld, M. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Ap. J. 552, 397–408 (2001).
[CrossRef]

Appl. Opt. (3)

Icarus (1)

R. A. Brown, C. J. Burrows, “On the feasibility of detecting extrasolar planets by reflected starlight using the Hubble Space Telescope,” Icarus 87, 484–497 (1990).
[CrossRef]

Nature (1)

J. Angel, “Ground-based imaging of extrasolar planets using adaptive optics,” Nature 368, 203–207 (1994).
[CrossRef]

Other (5)

J. Nelson, T. Mast, eds., California Extremely Large Telescope: conceptual design for a thirty-meter telescope, CELT report 34 (University of California, California Institute of Technology, Pasadena, Calif., 2002).

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

M. Troy, G. A. Chanan, E. Sirko, E. Leffert, “Residual misalignments of the Keck telescope primary mirror segments: classification of modes and implications for adaptive optics,” in Advanced Technology Optical/IR Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 307–317 (1998).
[CrossRef]

M. DiVittorio, Naval Observatory Flagstaff, Ariz. 86002 (personal communication, 2002).

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

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Figures (16)

Fig. 1
Fig. 1

Diffraction limits for 10- and 30-m circular telescopes at a wavelength of 1 μm and a Gaussian bandpass of 3% FWHM. (The finite bandpass smooths out the structure of these curves beyond approximately 0.5 arcsec.) Beyond approximately 0.2 arcsec the diffraction wings of the 30-m telescope are 30 times lower than those of the 10-m telescope.

Fig. 2
Fig. 2

Proposed aperture of the 30-m CELT, showing the segmentation geometry and the approximately circular outline. The thickness of the intersegment gaps has been exaggerated for clarity.

Fig. 3
Fig. 3

Convergence of the GPA for phase effects (λ = 1 μm, 3% bandpass). Here the effects are 100 nm each of the three second-order surface aberrations. Within 2 arcsec excellent convergence is obtained for an array of 4096 pixels on a side, but not for 1024 pixels on a side.

Fig. 4
Fig. 4

Proposed aperture of the 30-m CELT, including the typical obscuration due to the secondary mirror and its supports. The thickness of the intersegment gaps has been exaggerated for clarity.

Fig. 5
Fig. 5

Convergence of the GPA for amplitude effects (λ = 1 μm, 3% bandpass). Here the effects involve the obscuration associated with the secondary mirror and its supports as shown in Fig. 4. Within 2 arcsec excellent convergence is obtained for an array of 8192 pixels on a side, but not for 2048 pixels on a side. Note that these amplitude effects require approximately twice as many pixels (in each dimension) as do the phase effects for comparable convergence.

Fig. 6
Fig. 6

Monochromatic logarithmic point source image (λ = 1 μm; 1 arcsec × 1 arcsec) for CELT showing the characteristic hexagonal symmetry. No intersegment gaps or obscurations are included.

Fig. 7
Fig. 7

Image profiles (λ = 1 μm, 3% bandpass) for a circular 30-m telescope, for CELT with the nominal circularized design (Fig. 2; see also Fig. 6), and for an uncircularized CELT with 1122 segments in 19 rings. For the latter two, the profiles are in the direction parallel to the segment edges. In this direction, the circularized CELT backgrounds are virtually always lower than for the uncircularized CELT, often significantly so. Differences between the curves in other directions are more modest.

Fig. 8
Fig. 8

CELT radial profiles in the y direction (perpendicular to the segment edges) for various bandpasses showing the effects of 4-mm gaps. The zero-gap case (at 0 and 3% bandwidth) is also shown for comparison. Note that the features at intervals of 0.5 arcsec are strongly attenuated as the bandpass is increased.

Fig. 9
Fig. 9

Monochromatic logarithmic point source image (λ = 1 μm; 1 arcsec × 1 arcsec) for CELT showing the characteristic hexagonal symmetry. The effects of the obscuration due to the secondary mirror and its supports are readily apparent. (The relatively minor effects due to intersegment gaps are also included.)

Fig. 10
Fig. 10

CELT radial x profiles (λ = 1 μm, 3% bandpass) with and without obscuration, showing the substantial increase due to the secondary mirror and its supports.

Fig. 11
Fig. 11

CELT radial y profiles (λ = 1 μm, 3% bandpass) with and without obscuration, showing the substantial increase due to the secondary mirror and its supports. The strong increase in the y-profile background below 0.5 arcsec is due to the compression members (46 cm in diameter) that support the secondary and run along the x axis.

Fig. 12
Fig. 12

CELT radial profiles (λ = 1 μm, 3% bandpass) along the line x = y for a 5% reflectivity variation from segment to segment. This profile is barely distinguishable from that of a uniform aperture.

Fig. 13
Fig. 13

Aperture function for typical active control system noise, assuming a sensor noise of 1-nm rms. The corresponding actuator noise (roughly equal to the surface error) is 20 nm. Because of the low spatial frequency associated with aberrations of this type, these effects should be strongly attenuated by the AO system and thus are not considered further in this study.

Fig. 14
Fig. 14

CELT radial profile (λ = 1 μm, 3% bandpass) along the line x = y for piston errors of 10 nm (surface, rms), approximately equal to the best Keck phasing results. Piston errors of this magnitude produce an image profile that has only minor differences from that of a perfect mirror.

Fig. 15
Fig. 15

CELT radial profile (λ = 1 μm, 3% bandpass) along the line x = y for segment tip-tilt errors of 10 nm [surface Zernike coefficients, equal to angular errors on the sky of 0.017 arcsec (one-dimensional, rms)], approximately a factor of 2 better than the best Keck tip-tilt alignments.

Fig. 16
Fig. 16

CELT radial profiles (λ = 1 μm, 3% bandpass) along the line x = y showing the effects of 10-nm (rms) aberrations in each of the three second-order terms, as well as the cumulative effects of these and the zeroth- and first-order effects considered in Figs. 14 and 15.

Equations (3)

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fˆw=expikρ · wfρρdρdθ.
fˆw=hˆwiexpikρi · w,
fˆw=hˆwicoskxiucoskyiv.

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