Abstract

An approach for wave-front sensing using reflected laser light from a rough object is proposed. Light from a single laser beam is split into two beams, and the beams are launched from spatially separated apertures to illuminate an object. The reflected laser light is measured in the pupil plane of a receive telescope and in a plane conjugate to the object. By modulation of one of the two illuminator beams, the intensity pattern associated with each beam, as well as the field cross product of the two beams, is measured in each plane. A phase-retrieval algorithm is formulated by using projections onto constraint sets to recover the complex field associated with each illuminator. The algorithm is found to converge rapidly to the correct solution, particularly when compared with the convergence rates of more conventional phase-retrieval approaches. The new algorithm exhibits excellent performance in strong scintillation and is very tolerant to noise, exhibiting only a very small noise gain.

© 2003 Optical Society of America

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2002 (8)

D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2002).
[CrossRef]

J. D. Barchers, “Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation,” J. Opt. Soc. Am. A 19, 54–63 (2002).
[CrossRef]

J. D. Barchers, D. L. Fried, D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012–1021 (2002).
[CrossRef] [PubMed]

R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, A. Smith, “Description and simulation of an active imaging technique utilizing two speckle fields: iterative reconstructors,” J. Opt. Soc. Am. A 19, 458–471 (2002).
[CrossRef]

R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, A. Smith, “Description and simulation of an active imaging technique utilizing two speckle fields: root reconstructors,” J. Opt. Soc. Am. A 19, 444–457 (2002).
[CrossRef]

J. D. Barchers, D. L. Fried, D. J. Link, “Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise,” Appl. Opt. 41, 3674–3684 (2002).
[CrossRef] [PubMed]

H. H. Bauschke, P. L. Combettes, D. R. Luke, “Phase retrieval and error reduction algorithm, and Fienup variants: a view from convex optimization,” J. Opt. Soc. Am. A 19, 1334–1345 (2002).
[CrossRef]

J. D. Barchers, T. A. Rhoadarmer, “Evaluation of phase-shifting approaches for a point-diffraction interferometer with the mutual coherence function,” Appl. Opt. 41, 7499–7509 (2002).
[CrossRef]

2001 (1)

2000 (1)

1999 (1)

1998 (2)

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
[CrossRef]

D. L. Fried, “Scaling laws for propagation through turbulence,” J. Atmos. Ocean. Opt. 11, 982–990 (1998).

1995 (1)

1994 (1)

1993 (1)

1992 (2)

1991 (3)

C. C. Wackerman, A. E. Yagle, “Use of Fourier domain real-plane zeros to overcome phase retrieval stagnation,” J. Opt. Soc. Am. A 8, 1898–1904 (1991).
[CrossRef]

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353, 141–143 (1991).
[CrossRef]

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

1990 (1)

1987 (1)

1986 (1)

1984 (1)

1982 (2)

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982).
[CrossRef]

J. R. Fienup, “Phase-retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

1979 (1)

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
[CrossRef]

1977 (3)

1975 (1)

1974 (1)

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
[CrossRef]

1973 (3)

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D Appl. Phys. 6, L6–L9 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D Appl. Phys. 6, 2200–2216 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D Appl. Phys. 6, 2217–2225 (1973).
[CrossRef]

1972 (2)

D. Y. Gezari, A. Labeyrie, R. V. Stachnik, “Speckle interferometry: diffraction-limited measurements of nine stars with the 200-inch telescope,” Astrophys. J. 173, L1–L5 (1972).
[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).

1971 (1)

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

1967 (1)

L. G. Gubin, B. T. Polyak, E. V. Raik, “The method of projections for finding the common point in convex sets,” USSR Comput. Math. Math. Phys. 7, 1–24 (1967).
[CrossRef]

Allen, J. G.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Ameer, G. A.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Baliunar, S. L.

J. C. Shelton, T. G. Schneider, D. McKenna, S. L. Baliunar, “First tests of the Cassegrain adaptive optics system of the Mount Wilson 100-inch telescope,” in Adaptive Optical Systems and Technologies, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 72–77 (1995).

Barchers, J. D.

Barclay, H. T.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353, 141–143 (1991).
[CrossRef]

Bauschke, H. H.

Boeke, B. R.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

Brown, J. M.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Browne, S. L.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

Bruck, Y. M.

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
[CrossRef]

Christou, J. C.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Combettes, P. L.

Duncan, T. S.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Eager, R. J.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Ealey, M. A.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Ellerbroek, B. L.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Fairchild, P.

Fienup, J. R.

Fried, D. L.

J. D. Barchers, D. L. Fried, D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012–1021 (2002).
[CrossRef] [PubMed]

J. D. Barchers, D. L. Fried, D. J. Link, “Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise,” Appl. Opt. 41, 3674–3684 (2002).
[CrossRef] [PubMed]

D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2002).
[CrossRef]

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
[CrossRef]

D. L. Fried, “Scaling laws for propagation through turbulence,” J. Atmos. Ocean. Opt. 11, 982–990 (1998).

D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
[CrossRef] [PubMed]

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

D. L. Fried, “Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–374 (1977).
[CrossRef]

D. L. Fried, P.O. Box 680, Moss Landing,Calif. 95038 (personal communication, 2000).

Fugate, R. Q.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).

Gezari, D. Y.

D. Y. Gezari, A. Labeyrie, R. V. Stachnik, “Speckle interferometry: diffraction-limited measurements of nine stars with the 200-inch telescope,” Astrophys. J. 173, L1–L5 (1972).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gubin, L. G.

L. G. Gubin, B. T. Polyak, E. V. Raik, “The method of projections for finding the common point in convex sets,” USSR Comput. Math. Math. Phys. 7, 1–24 (1967).
[CrossRef]

Gurkan, D.

Hardy, J.

Holmes, R. B.

Hughes, K.

Jones, G. W.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Knox, K. T.

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
[CrossRef]

Koliopouosis, C.

Kotzer, T.

Kowalczyk, A. M.

Kuhns, R. M.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Labeyrie, A.

D. Y. Gezari, A. Labeyrie, R. V. Stachnik, “Speckle interferometry: diffraction-limited measurements of nine stars with the 200-inch telescope,” Astrophys. J. 173, L1–L5 (1972).
[CrossRef]

Lee, D. J.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Lefebvre, J.

Levi, A.

Link, D. J.

J. D. Barchers, D. L. Fried, D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012–1021 (2002).
[CrossRef] [PubMed]

J. D. Barchers, D. L. Fried, D. J. Link, “Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise,” Appl. Opt. 41, 3674–3684 (2002).
[CrossRef] [PubMed]

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Lowrey, W. H.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Luke, D. R.

McKenna, D.

J. C. Shelton, T. G. Schneider, D. McKenna, S. L. Baliunar, “First tests of the Cassegrain adaptive optics system of the Mount Wilson 100-inch telescope,” in Adaptive Optical Systems and Technologies, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 72–77 (1995).

Misell, D. L.

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D Appl. Phys. 6, L6–L9 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D Appl. Phys. 6, 2200–2216 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D Appl. Phys. 6, 2217–2225 (1973).
[CrossRef]

Murphy, D. V.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353, 141–143 (1991).
[CrossRef]

O’Meara, T. R.

Oliker, M. D.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Page, D. A.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353, 141–143 (1991).
[CrossRef]

Paxman, R. G.

Platt, B. C.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Polyak, B. T.

L. G. Gubin, B. T. Polyak, E. V. Raik, “The method of projections for finding the common point in convex sets,” USSR Comput. Math. Math. Phys. 7, 1–24 (1967).
[CrossRef]

Primmerman, C. A.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353, 141–143 (1991).
[CrossRef]

Raik, E. V.

L. G. Gubin, B. T. Polyak, E. V. Raik, “The method of projections for finding the common point in convex sets,” USSR Comput. Math. Math. Phys. 7, 1–24 (1967).
[CrossRef]

Rhoadarmer, T. A.

Roberts, P. H.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

Rosen, J.

Ruane, R. E.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).

Schneider, T. G.

J. C. Shelton, T. G. Schneider, D. McKenna, S. L. Baliunar, “First tests of the Cassegrain adaptive optics system of the Mount Wilson 100-inch telescope,” in Adaptive Optical Systems and Technologies, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 72–77 (1995).

Schulz, T. J.

Shack, R. V.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Shamir, J.

Shelton, J. C.

J. C. Shelton, T. G. Schneider, D. McKenna, S. L. Baliunar, “First tests of the Cassegrain adaptive optics system of the Mount Wilson 100-inch telescope,” in Adaptive Optical Systems and Technologies, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 72–77 (1995).

Smith, A.

Sodin, L. G.

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
[CrossRef]

Spinhirne, J. M.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Spivey, B.

Stachnik, R. V.

D. Y. Gezari, A. Labeyrie, R. V. Stachnik, “Speckle interferometry: diffraction-limited measurements of nine stars with the 200-inch telescope,” Astrophys. J. 173, L1–L5 (1972).
[CrossRef]

Stark, H.

Swindle, D. W.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Thompson, B. J.

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
[CrossRef]

Tyler, G. A.

G. A. Tyler, “Reconstruction and assessment of the least-squares and slope discrepancy components of the phase,” J. Opt. Soc. Am. A 17, 1828–1839 (2000).
[CrossRef]

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

Vaughn, J. L.

Voas, J. K.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Von Neumann, J.

J. Von Neumann, Functional Operators, Vol. II of Annals Mathematical Studies (Princeton U. Press, Princeton, N.J., 1950).

Wackerman, C. C.

Webb, H.

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982).
[CrossRef]

Wild, W. J.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Wilson, K. B.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Wopat, L. M.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

Wyant, J. C.

Wynia, J. L.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

Yagle, A. E.

Yang, Y.

Youla, D. C.

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982).
[CrossRef]

Zollars, B. G.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353, 141–143 (1991).
[CrossRef]

Appl. Opt. (8)

Astrophys. J. (2)

D. Y. Gezari, A. Labeyrie, R. V. Stachnik, “Speckle interferometry: diffraction-limited measurements of nine stars with the 200-inch telescope,” Astrophys. J. 173, L1–L5 (1972).
[CrossRef]

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
[CrossRef]

IEEE Trans. Med. Imaging (1)

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982).
[CrossRef]

J. Atmos. Ocean. Opt. (1)

D. L. Fried, “Scaling laws for propagation through turbulence,” J. Atmos. Ocean. Opt. 11, 982–990 (1998).

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (15)

G. A. Tyler, “Reconstruction and assessment of the least-squares and slope discrepancy components of the phase,” J. Opt. Soc. Am. A 17, 1828–1839 (2000).
[CrossRef]

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
[CrossRef]

J. D. Barchers, “Evaluation of the impact of finite resolution effects on scintillation compensation using two deformable mirrors,” J. Opt. Soc. Am. A 18, 3098–3109 (2001).
[CrossRef]

J. D. Barchers, “Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation,” J. Opt. Soc. Am. A 19, 54–63 (2002).
[CrossRef]

H. H. Bauschke, P. L. Combettes, D. R. Luke, “Phase retrieval and error reduction algorithm, and Fienup variants: a view from convex optimization,” J. Opt. Soc. Am. A 19, 1334–1345 (2002).
[CrossRef]

R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, A. Smith, “Description and simulation of an active imaging technique utilizing two speckle fields: iterative reconstructors,” J. Opt. Soc. Am. A 19, 458–471 (2002).
[CrossRef]

R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, A. Smith, “Description and simulation of an active imaging technique utilizing two speckle fields: root reconstructors,” J. Opt. Soc. Am. A 19, 444–457 (2002).
[CrossRef]

C. C. Wackerman, A. E. Yagle, “Phase retrieval and estimation with use of real-plane zeros,” J. Opt. Soc. Am. A 11, 2016–2026 (1994).
[CrossRef]

A. Levi, H. Stark, “Image restoration by the method of generalized projections with application to restoration from magnitude,” J. Opt. Soc. Am. A 1, 932–943 (1984).
[CrossRef]

H. Stark, Y. Yang, D. Gurkan, “Factors affecting convergence in the design of diffractive optics by iterative vector-space methods,” J. Opt. Soc. Am. A 16, 149–159 (1999).
[CrossRef]

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
[CrossRef]

J. R. Fienup, C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986).
[CrossRef]

J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of it Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987).
[CrossRef]

J. R. Fienup, A. M. Kowalczyk, “Phase retrieval for a complex-valued object by using a low-resolution image,” J. Opt. Soc. Am. A 7, 450–458 (1990).
[CrossRef]

C. C. Wackerman, A. E. Yagle, “Use of Fourier domain real-plane zeros to overcome phase retrieval stagnation,” J. Opt. Soc. Am. A 8, 1898–1904 (1991).
[CrossRef]

J. Phys. D Appl. Phys. (3)

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D Appl. Phys. 6, L6–L9 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D Appl. Phys. 6, 2200–2216 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D Appl. Phys. 6, 2217–2225 (1973).
[CrossRef]

Nature (2)

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353, 141–143 (1991).
[CrossRef]

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991).
[CrossRef]

Opt. Commun. (2)

D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2002).
[CrossRef]

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
[CrossRef]

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).

USSR Comput. Math. Math. Phys. (1)

L. G. Gubin, B. T. Polyak, E. V. Raik, “The method of projections for finding the common point in convex sets,” USSR Comput. Math. Math. Phys. 7, 1–24 (1967).
[CrossRef]

Other (6)

J. Von Neumann, Functional Operators, Vol. II of Annals Mathematical Studies (Princeton U. Press, Princeton, N.J., 1950).

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998).

J. C. Shelton, T. G. Schneider, D. McKenna, S. L. Baliunar, “First tests of the Cassegrain adaptive optics system of the Mount Wilson 100-inch telescope,” in Adaptive Optical Systems and Technologies, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 72–77 (1995).

H. Stark, Y. Yang, Vector Space Projections (Wiley, New York, 1998).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

D. L. Fried, P.O. Box 680, Moss Landing,Calif. 95038 (personal communication, 2000).

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