Abstract

The gyrator transform is a useful tool for optical information processing applications. In this work we propose a multi-stage phase retrieval approach based on this operation as well as on the well-known Gerchberg-Saxton algorithm. It results in an iterative algorithm able to retrieve the phase information using several measurements of the gyrator transform power spectrum. The viability and performance of the proposed algorithm is demonstrated by means of several numerical simulations and experimental results.

© 2010 Optical Society of America

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  14. D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope wavefront sensing and control algorithms," Proc. SPIE 5487, 887 (2004).
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2007 (1)

2006 (3)

2004 (1)

D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope wavefront sensing and control algorithms," Proc. SPIE 5487, 887 (2004).

1998 (1)

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

1997 (1)

T. E. Gureyev and K. A. Nugent, "Rapid quantitative phase imaging using the transport of intensity equation," Opt. Commun. 133, 339 - 346 (1997).
[CrossRef]

1996 (1)

1993 (1)

1990 (1)

1988 (1)

1983 (1)

1977 (1)

J. P. Guigay, "Fourier-transrorm analysis of Fresnel diffraction patterns and in-line holograms," Optik 49, 121-125 (1977).

1973 (1)

D. L. Misell, "A method for the solution of the phase problem in electron microscopy," J. Phys. D: Applied Physics 6, L6-L9 (1973).
[CrossRef]

1972 (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

1964 (1)

1963 (1)

1962 (1)

1948 (1)

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef]

Acton, D. S.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase retrieval algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511 (2006).

D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope wavefront sensing and control algorithms," Proc. SPIE 5487, 887 (2004).

Alieva, T.

Aronstein, D. L.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase retrieval algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511 (2006).

Atcheson, P. D.

D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope wavefront sensing and control algorithms," Proc. SPIE 5487, 887 (2004).

Basinger, S.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Bely, P.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Brady, G. R.

Burg, R.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Calvo, M. L.

Cermak, M.

D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope wavefront sensing and control algorithms," Proc. SPIE 5487, 887 (2004).

Craig, L.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Dean, B. H.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase retrieval algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511 (2006).

Dorsch, R. G.

Femiano, M.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Fienup, J. R.

Fuentes, F. J.

Gabor, D.

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Guigay, J. P.

J. P. Guigay, "Fourier-transrorm analysis of Fresnel diffraction patterns and in-line holograms," Optik 49, 121-125 (1977).

Gureyev, T. E.

T. E. Gureyev and K. A. Nugent, "Rapid quantitative phase imaging using the transport of intensity equation," Opt. Commun. 133, 339 - 346 (1997).
[CrossRef]

Hadaway, J.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Jacobson, D.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Kingsbury, L. K.

D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope wavefront sensing and control algorithms," Proc. SPIE 5487, 887 (2004).

Kissil, A.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Leith, E. N.

Lowman, A.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Lyon, R.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Mendlovic, D.

Misell, D. L.

D. L. Misell, "A method for the solution of the phase problem in electron microscopy," J. Phys. D: Applied Physics 6, L6-L9 (1973).
[CrossRef]

Mosier, G.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Navarro, R.

Nieto-Vesperinas, M.

Nugent, K. A.

T. E. Gureyev and K. A. Nugent, "Rapid quantitative phase imaging using the transport of intensity equation," Opt. Commun. 133, 339 - 346 (1997).
[CrossRef]

Rakoczy, J.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Redding, D. C.

D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope wavefront sensing and control algorithms," Proc. SPIE 5487, 887 (2004).

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Rodrigo, J. A.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Schunk, R. G.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Seldin, J. H.

Shi, F.

D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope wavefront sensing and control algorithms," Proc. SPIE 5487, 887 (2004).

Shiri, R.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase retrieval algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511 (2006).

Smith, J. S.

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase retrieval algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511 (2006).

Teague, M. R.

Upatnieks, J.

Wilson, M.

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

Zalevsky, Z.

Appl. Opt. (1)

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (4)

J. Phys. D: Applied Physics (1)

D. L. Misell, "A method for the solution of the phase problem in electron microscopy," J. Phys. D: Applied Physics 6, L6-L9 (1973).
[CrossRef]

Nature (1)

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef]

Opt. Commun. (1)

T. E. Gureyev and K. A. Nugent, "Rapid quantitative phase imaging using the transport of intensity equation," Opt. Commun. 133, 339 - 346 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optik (2)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

J. P. Guigay, "Fourier-transrorm analysis of Fresnel diffraction patterns and in-line holograms," Optik 49, 121-125 (1977).

Proc. SPIE (3)

B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, "Phase retrieval algorithm for JWST Flight and Testbed Telescope," Proc. SPIE 6265, 626511 (2006).

D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M. Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, "Wavefront Sensing and Control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758 (1998).

D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, "James Webb Space Telescope wavefront sensing and control algorithms," Proc. SPIE 5487, 887 (2004).

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