Abstract

Through-focus phase retrieval methods aim to retrieve the phase of an optical field from its intensity distribution measured at different planes in the focal region. By using the concept of spatial correlation for propagating fields, for both the complex amplitude and the intensity of a field, we can infer which planes are suitable to retrieve the phase and which are not. Our analysis also reveals why all techniques based on measuring the intensity at two Fourier-conjugated planes usually lead to a good reconstruction of the phase. The findings presented in this work are important for aberration characterization of optical systems, adaptive optics and wavefront metrology.

© 2012 OSA

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2011 (1)

2009 (1)

2005 (1)

H. M. Faulkner and J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy,” Ultramicroscopy103153–164 (2005).
[CrossRef] [PubMed]

2004 (1)

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett.93, 023903 (2004).
[CrossRef] [PubMed]

2003 (1)

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400342–344 (1999).
[CrossRef]

1998 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

1985 (1)

1982 (2)

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

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21, 829–832 (1982).
[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 (Stuttgart)35, 237–246 (1972).

Agard, D.

Alieva, T.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 2007), 883–891.

Brady, G. R.

Calvo, M. L.

Chapman, H. N.

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400342–344 (1999).
[CrossRef]

Cristbal, G.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

Faulkner, H. M.

H. M. Faulkner and J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy,” Ultramicroscopy103153–164 (2005).
[CrossRef] [PubMed]

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett.93, 023903 (2004).
[CrossRef] [PubMed]

Fienup, J.

Fienup, J. R.

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 (Stuttgart)35, 237–246 (1972).

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21, 829–832 (1982).
[CrossRef]

Guizar-Sicairos, M.

Gustafsson, M.

Hanser, B.

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400342–344 (1999).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).

Miao, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400342–344 (1999).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A15, 1662–1669 (1998).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

Rodenburg, J. M.

H. M. Faulkner and J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy,” Ultramicroscopy103153–164 (2005).
[CrossRef] [PubMed]

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett.93, 023903 (2004).
[CrossRef] [PubMed]

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 (Stuttgart)35, 237–246 (1972).

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400342–344 (1999).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A15, 1662–1669 (1998).
[CrossRef]

Sedat, J.

Teague, M. R.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 2007), 883–891.

Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

Nature (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400342–344 (1999).
[CrossRef]

Opt. Eng. (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21, 829–832 (1982).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Optik (Stuttgart) (1)

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

Phys. Rev. Lett. (2)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett.93, 023903 (2004).
[CrossRef] [PubMed]

Ultramicroscopy (1)

H. M. Faulkner and J. M. Rodenburg, “Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy,” Ultramicroscopy103153–164 (2005).
[CrossRef] [PubMed]

Other (2)

R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 2007), 883–891.

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