Abstract

We propose a maximum a posteriori-based method that solves an important practical problem in the deconvolution of 4Pi images by simultaneously delivering an estimate of both the object and the unknown phase. The method was tested in simulations and on data from both test samples and biological specimen. It generates object estimates that are free from interference artifacts and reliably recovers arbitrary relative phases. Based on vectorial focusing theory, our theoretical analysis allowed for a simple and efficient implementation of the algorithm. Taking several 4Pi images at different relative phases of the interfering beams is shown to improve the robustness of the approach.

© 2009 Optical Society of America

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2009

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, J. Microsc. 234, 47 (2009).
[CrossRef]

2007

2006

2002

C. M. Blanca, J. Bewersdorf, and S. W. Hell, Opt. Commun. 206, 281 (2002).
[CrossRef]

S. W. Hell, C. M. Blanca, and J. Bewersdorf, Opt. Lett. 27, 888 (2002).
[CrossRef]

2001

1999

1992

1991

I. Csiszár, Ann. Stat. 19, 2032 (1991).

1987

J. C. Bezdek, R. J. Hathaway, R. E. Howard, C. A. Wilson, and M. P. Windham, J. Optim. Theory Appl. 54, 471 (1987).
[CrossRef]

Baddeley, D.

Bertero, M.

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, J. Microsc. 234, 47 (2009).
[CrossRef]

Bewersdorf, J.

S. W. Hell, C. M. Blanca, and J. Bewersdorf, Opt. Lett. 27, 888 (2002).
[CrossRef]

C. M. Blanca, J. Bewersdorf, and S. W. Hell, Opt. Commun. 206, 281 (2002).
[CrossRef]

Bezdek, J. C.

J. C. Bezdek, R. J. Hathaway, R. E. Howard, C. A. Wilson, and M. P. Windham, J. Optim. Theory Appl. 54, 471 (1987).
[CrossRef]

Blanca, C. M.

C. M. Blanca, J. Bewersdorf, and S. W. Hell, Opt. Commun. 206, 281 (2002).
[CrossRef]

S. W. Hell, C. M. Blanca, and J. Bewersdorf, Opt. Lett. 27, 888 (2002).
[CrossRef]

Boccacci, P.

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, J. Microsc. 234, 47 (2009).
[CrossRef]

Carl, C.

Conchello, J.-A.

Cremer, C.

Csiszár, I.

I. Csiszár, Ann. Stat. 19, 2032 (1991).

Diaspro, A.

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, J. Microsc. 234, 47 (2009).
[CrossRef]

Engelhardt, J.

Hathaway, R. J.

J. C. Bezdek, R. J. Hathaway, R. E. Howard, C. A. Wilson, and M. P. Windham, J. Optim. Theory Appl. 54, 471 (1987).
[CrossRef]

Hell, S.

Hell, S. W.

Howard, R. E.

J. C. Bezdek, R. J. Hathaway, R. E. Howard, C. A. Wilson, and M. P. Windham, J. Optim. Theory Appl. 54, 471 (1987).
[CrossRef]

Kelley, C.

C. Kelley, Iterative Method for Optimization (SIAM, 1999), Vol. 18.

Lang, M.

Markham, J.

Müller, T.

Nagorni, M.

Stelzer, E. H. K.

Vicidomini, G.

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, J. Microsc. 234, 47 (2009).
[CrossRef]

Wilson, C. A.

J. C. Bezdek, R. J. Hathaway, R. E. Howard, C. A. Wilson, and M. P. Windham, J. Optim. Theory Appl. 54, 471 (1987).
[CrossRef]

Windham, M. P.

J. C. Bezdek, R. J. Hathaway, R. E. Howard, C. A. Wilson, and M. P. Windham, J. Optim. Theory Appl. 54, 471 (1987).
[CrossRef]

Ann. Stat.

I. Csiszár, Ann. Stat. 19, 2032 (1991).

Appl. Opt.

J. Microsc.

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, J. Microsc. 234, 47 (2009).
[CrossRef]

J. Opt. Soc. Am. A

J. Optim. Theory Appl.

J. C. Bezdek, R. J. Hathaway, R. E. Howard, C. A. Wilson, and M. P. Windham, J. Optim. Theory Appl. 54, 471 (1987).
[CrossRef]

Opt. Commun.

C. M. Blanca, J. Bewersdorf, and S. W. Hell, Opt. Commun. 206, 281 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Other

C. Kelley, Iterative Method for Optimization (SIAM, 1999), Vol. 18.

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