Abstract

Phase discontinuity sensing (PDS) is one of two successful approaches to segment phasing that are currently in use at the Keck telescopes, but it has only a limited capture range. We describe and present numerical simulations of a broadband version of the current (narrowband) PDS algorithm that can extend the capture range from 0.4 to 40 μm. Like the original algorithm, the new broadband PDS algorithm requires no special-purpose hardware but only a high-resolution area detector operating in the 2–3-μm range. The potential application of this algorithm to extremely large telescopes is also discussed.

© 2004 Optical Society of America

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2001 (1)

M. Löfdahl, H. Eriksson, “An algorithm for resolving 2π ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40, 984–990 (2001).
[CrossRef]

2000 (1)

1999 (1)

1998 (1)

1987 (1)

Andersen, T.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro-50 Extremely Large Telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Anderson, E.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Ardeberg, A. L.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro-50 Extremely Large Telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Bai, Z.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Beckers, J.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro-50 Extremely Large Telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Beckers, J. L.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Bischof, C.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Brunetto, E.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Carlberg, R.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Chanan, G.

G. Chanan, M. Troy, E. Sirko, “Phase discontinuity sensing: a method for phasing segmented mirrors in the infrared,” Appl. Opt. 38, 704–713 (1999).
[CrossRef]

M. Troy, G. 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 Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 307–316 (1998).
[CrossRef]

T. Mast, J. Nelson, G. Chanan, “Sampling segment phases: minimal spanning sets of zero-sum triplets,” Keck Observatory Tech. Note 208 (Keck Library, Kamuela, Hawaii, 1986).

Chanan, G. A.

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]

Conan, R.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Crabtree, D. R.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Crampton, D.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Creath, K.

Croz, J. D.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Davidge, T. J.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Dekens, F. G.

Demmel, J.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Dierickx, P.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Dongarra, J.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Eriksson, H.

M. Löfdahl, H. Eriksson, “An algorithm for resolving 2π ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40, 984–990 (2001).
[CrossRef]

Faber, S. M.

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” Keck Observatory Rep. 90 (Keck Observatory, Kamuela, Hawaii, 1985).

Fedrigo, E.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Fitzsimmons, J. T.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Flannery, B.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing, 1st ed. (Cambridge U. Press, New York, 1989), pp. 484–487.

Gedig, M. H.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Gilmozzi, R.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Goncharov, A.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro-50 Extremely Large Telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Greenbaum, A.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Gregory, B.

S. E. Strom, L. M. Stepp, 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]

Halliday, D. J.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Hammarling, S.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Herriot, R. G.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Hesse, J. E.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Hubin, N.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Kirkman, D.

Koch, F.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Leffert, E.

M. Troy, G. 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 Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 307–316 (1998).
[CrossRef]

Lelouarn, M.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Löfdahl, M.

M. Löfdahl, H. Eriksson, “An algorithm for resolving 2π ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40, 984–990 (2001).
[CrossRef]

Marchetti, E.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Mast, T.

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]

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, G. Chanan, “Sampling segment phases: minimal spanning sets of zero-sum triplets,” Keck Observatory Tech. Note 208 (Keck Library, Kamuela, Hawaii, 1986).

Mast, T. S.

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” Keck Observatory Rep. 90 (Keck Observatory, Kamuela, Hawaii, 1985).

Matthews, K.

K. Matthews, B. T. Soifer, “The near infrared camera on the W. M. Keck Telescope,” in Infrared Astronomy with Arrays: The Next Generation, I. S. McLean, ed. (Kluwer Academic, Boston, Mass., 1994), pp. 239–246.
[CrossRef]

McKenney, A.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Michaels, S.

Monnet, G. J.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Morbey, C. L.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Nelson, J.

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]

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, G. Chanan, “Sampling segment phases: minimal spanning sets of zero-sum triplets,” Keck Observatory Tech. Note 208 (Keck Library, Kamuela, Hawaii, 1986).

Nelson, J. E.

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” Keck Observatory Rep. 90 (Keck Observatory, Kamuela, Hawaii, 1985).

J. E. Nelson, “Progress on the California Extremely Large Telescope (CELT),” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 47–59 (2002).
[CrossRef]

Noethe, L.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Ohara, C.

Oke, J. B.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Ostrouchov, S.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Owner-Petersen, M.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro-50 Extremely Large Telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Pazder, J. S.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Press, W.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing, 1st ed. (Cambridge U. Press, New York, 1989), pp. 484–487.

Quattri, M.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Riewaldt, H.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro-50 Extremely Large Telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Roberts, S. C.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Sarazin, M. S.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Sirko, E.

G. Chanan, M. Troy, E. Sirko, “Phase discontinuity sensing: a method for phasing segmented mirrors in the infrared,” Appl. Opt. 38, 704–713 (1999).
[CrossRef]

M. Troy, G. 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 Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 307–316 (1998).
[CrossRef]

Snel, R.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro-50 Extremely Large Telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Soifer, B. T.

K. Matthews, B. T. Soifer, “The near infrared camera on the W. M. Keck Telescope,” in Infrared Astronomy with Arrays: The Next Generation, I. S. McLean, ed. (Kluwer Academic, Boston, Mass., 1994), pp. 239–246.
[CrossRef]

Sorensen, D.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

Spyromilio, J.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Stepp, L. M.

S. E. Strom, L. M. Stepp, 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]

Strom, S. E.

S. E. Strom, L. M. Stepp, 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]

Szeto, K.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Teukolsky, S.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing, 1st ed. (Cambridge U. Press, New York, 1989), pp. 484–487.

Troy, M.

Veran, J.-P.

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

Vetterling, W.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing, 1st ed. (Cambridge U. Press, New York, 1989), pp. 484–487.

Walker, D.

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro-50 Extremely Large Telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

Yaitskova, N.

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

Appl. Opt. (4)

Opt. Eng. (1)

M. Löfdahl, H. Eriksson, “An algorithm for resolving 2π ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40, 984–990 (2001).
[CrossRef]

Other (14)

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, G. Chanan, “Sampling segment phases: minimal spanning sets of zero-sum triplets,” Keck Observatory Tech. Note 208 (Keck Library, Kamuela, Hawaii, 1986).

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing, 1st ed. (Cambridge U. Press, New York, 1989), pp. 484–487.

E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, “LAPACK User’s Guide,” 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1995).

M. Troy, G. 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 Telescopes VI, L. M. Stepp, ed., Proc. SPIE3352, 307–316 (1998).
[CrossRef]

K. Matthews, B. T. Soifer, “The near infrared camera on the W. M. Keck Telescope,” in Infrared Astronomy with Arrays: The Next Generation, I. S. McLean, ed. (Kluwer Academic, Boston, Mass., 1994), pp. 239–246.
[CrossRef]

J. E. Nelson, “Progress on the California Extremely Large Telescope (CELT),” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 47–59 (2002).
[CrossRef]

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, D. Walker, “The Euro-50 Extremely Large Telescope,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 214–225 (2002).
[CrossRef]

P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Lelouarn, E. Marchetti, G. J. Monnet, L. Noethe, M. Quattri, M. S. Sarazin, J. Spyromilio, N. Yaitskova, “The eye of the beholder: designing the OWL,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 151–170 (2002).
[CrossRef]

S. C. Roberts, C. L. Morbey, D. R. Crabtree, R. Carlberg, D. Crampton, T. J. Davidge, J. T. Fitzsimmons, M. H. Gedig, D. J. Halliday, J. E. Hesse, R. G. Herriot, J. B. Oke, J. S. Pazder, K. Szeto, J.-P. Veran, “Canadian Very Large Optical Telescope technology studies,” in Future Giant Telescopes, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4840, 104–115 (2002).
[CrossRef]

S. E. Strom, L. M. Stepp, 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]

J. Nelson, ed., “The California Extremely Large Telescope,” CELT Rep. 34 (University of California and California Institute of Technology, Santa Cruz, Calif., 2002).

G. A. Chanan, “Design of the Keck Observatory alignment camera,” in Precision Instrument Design, T. C. Bristow, A. E. Hathaway, eds., Proc. SPIE1036, 59–70 (1988).
[CrossRef]

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” Keck Observatory Rep. 90 (Keck Observatory, Kamuela, Hawaii, 1985).

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Figures (5)

Fig. 1
Fig. 1

Numerically generated inside-of-focus image of a star formed by the Keck telescope at a monochromatic wavelength of 3.3 μm. The upper segment in the middle ring has been pistoned out of the page by λ/8. The diffraction pattern has an obvious correspondence with the position of the mispistoned segment in the primary mirror.

Fig. 2
Fig. 2

Numerically generated difference images for the Keck telescope with two mispistoned segments, through a filter with λ = 3.3 μm and Δλ = 0.063 μm. The piston error of the upper and lower segments (positive and negative values, respectively, are as follows: (a) ±λ/8, (b) ±(5λ + λ/8), (c) ±(10λ + λ/8), (d) ±(15λ + λ/8), (e) ±(20λ + λ/8), and (f) ±(25λ + λ/8). The fading of the difference image with increasing piston error is the physical effect that is exploited by the BPDS algorithm.

Fig. 3
Fig. 3

Numerically generated template for λ = 3.3 μm. Each rectangle measures 1.5 arc sec by 1.2 arc sec and is centered on one of the intersegment edges.

Fig. 4
Fig. 4

Modulation of the difference image in the neighborhood of an intersegment edge for a filter with λ = 2.2 μm and Δλ = 0.59 μm. This theoretical quantity should be equal to the experimentally determined correlation coefficient defined in Eq. (11). The filled diamonds show the typical sampling of the modulation curve by the BPDS algorithm. These data points were determined by means of the Monte Carlo technique described in the text, without reference to the equation for the plotted curve. The points do not land exactly on the theoretical curve because the bandwidth was not small compared with the central wavelength (as assumed in the derivation of the theoretical expression). The numerically generated curve used in the data analysis does not suffer from this discrepancy.

Fig. 5
Fig. 5

Convergence of the BPDS algorithm for 10 typical simulations with aberrated segments and one with aberration-free segments. The filter bandwidth for iterations 1 and 2 was 0.06 μm, for which the limiting rms piston error is ∼1 μm. The filter bandwidth for iterations 3 and 4 was 0.6 μm, for which the limiting rms piston error is the size of the segment aberrations, or essentially zero in the absence of aberrations.

Tables (2)

Tables Icon

Table 1 Properties of NIRC Filters Suitable for BPDS

Tables Icon

Table 2 Convergence of the (Simulated) BPDS Algorithm

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

fλ/a  al/f,
λ/a  p/206265,
S=I+-I-,
lc=λ22Δλ.
Aω, k= Px, yexp2ikexp-ik lρ24f2×expikρ · ωdxdy,
Iω= Gk|Aω, k|2dk.
Sδ, Δk=MδΔkSλ/8, 0,
MδΔk=exp-2σk2δ2sin 2kδ,
lcσk=π8 ln 2=1.334
MδΔk=sinδΔkδΔksin 2kδ.
cδ, Δk Sijδ, ΔkSijλ/8, 0 Sij2λ/8, 0=MδΔk,
Δs=λ08+m λ04,
AB=Nλ,
N=9.25×10-5an/λ,

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