Abstract

Phase retrieval is widely used in phase contrast microscopy. Here we present an autofocus algorithm that allows the phase of the exit wave function, from a single-material object, to be reconstructed at medium resolution from a single phase contrast image without any a priori knowledge of the imaging system or object. The algorithm is demonstrated on coherent out-of-focus electron micrographs of 30nm latex sphere calibration standards, giving <10% RMS error over a large defocus range.

© 2011 Optical Society of America

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References

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2010 (1)

2007 (1)

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, Philos. Mag. 87, 3565 (2007).
[CrossRef]

2004 (1)

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef] [PubMed]

2003 (2)

P. N. H. Nakashima and A. W. S. Johnson, Ultramicroscopy 94, 135 (2003).
[CrossRef]

N. Kehtarnavaz and H. J. Oh, Real-Time Imaging 9, 197 (2003).
[CrossRef]

2002 (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef] [PubMed]

2001 (1)

D. Paganin and K. A. Nugent, Adv. Imaging Electr. Phys. 118, 85 (2001).
[CrossRef]

2000 (1)

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef] [PubMed]

1998 (1)

Y. C. Wang, T. M. Chou, M. Libera, E. Voelkl, and B. G. Frost, Microsc. Microanal. 4, 146 (1998).

1982 (1)

Bajt, S.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef] [PubMed]

Barty, A.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef] [PubMed]

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef] [PubMed]

Beltran, M. A.

Carter, C. B.

D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science, 2nd ed. (Springer Science, 2009).

Chou, T. M.

Y. C. Wang, T. M. Chou, M. Libera, E. Voelkl, and B. G. Frost, Microsc. Microanal. 4, 146 (1998).

Cowley, J. M.

J. M. Cowley, Diffraction Physics, 3rd ed. (Elsevier Science, 1995).

De Graef, M.

M. De Graef, Introduction to Conventional Transmission Electron Microscopy (Cambridge University, 2003).
[CrossRef]

Duvall, S.

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, Philos. Mag. 87, 3565 (2007).
[CrossRef]

Frost, B. G.

Y. C. Wang, T. M. Chou, M. Libera, E. Voelkl, and B. G. Frost, Microsc. Microanal. 4, 146 (1998).

Gureyev, T. E.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef] [PubMed]

Johnson, A. W. S.

P. N. H. Nakashima and A. W. S. Johnson, Ultramicroscopy 94, 135 (2003).
[CrossRef]

Johnson, K.

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, Philos. Mag. 87, 3565 (2007).
[CrossRef]

Keast, V. J.

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, Philos. Mag. 87, 3565 (2007).
[CrossRef]

Kehtarnavaz, N.

N. Kehtarnavaz and H. J. Oh, Real-Time Imaging 9, 197 (2003).
[CrossRef]

Kitchen, M. J.

Libera, M.

Y. C. Wang, T. M. Chou, M. Libera, E. Voelkl, and B. G. Frost, Microsc. Microanal. 4, 146 (1998).

Mayo, S. C.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef] [PubMed]

McCartney, M.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef] [PubMed]

McMahon, P. J.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef] [PubMed]

Miller, P. R.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef] [PubMed]

Nakashima, P. N. H.

P. N. H. Nakashima and A. W. S. Johnson, Ultramicroscopy 94, 135 (2003).
[CrossRef]

Nugent, K. A.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef] [PubMed]

D. Paganin and K. A. Nugent, Adv. Imaging Electr. Phys. 118, 85 (2001).
[CrossRef]

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef] [PubMed]

Oh, H. J.

N. Kehtarnavaz and H. J. Oh, Real-Time Imaging 9, 197 (2003).
[CrossRef]

Paganin, D.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef] [PubMed]

D. Paganin and K. A. Nugent, Adv. Imaging Electr. Phys. 118, 85 (2001).
[CrossRef]

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef] [PubMed]

Paganin, D. M.

Petersen, T. C.

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, Philos. Mag. 87, 3565 (2007).
[CrossRef]

Teague, M. R.

Uesugi, K.

Voelkl, E.

Y. C. Wang, T. M. Chou, M. Libera, E. Voelkl, and B. G. Frost, Microsc. Microanal. 4, 146 (1998).

Wall, M.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef] [PubMed]

Wang, Y. C.

Y. C. Wang, T. M. Chou, M. Libera, E. Voelkl, and B. G. Frost, Microsc. Microanal. 4, 146 (1998).

Wilkins, S. W.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef] [PubMed]

Williams, D. B.

D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science, 2nd ed. (Springer Science, 2009).

Adv. Imaging Electr. Phys. (1)

D. Paganin and K. A. Nugent, Adv. Imaging Electr. Phys. 118, 85 (2001).
[CrossRef]

J. Microsc. (2)

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Microsc. Microanal. (1)

Y. C. Wang, T. M. Chou, M. Libera, E. Voelkl, and B. G. Frost, Microsc. Microanal. 4, 146 (1998).

Opt. Express (1)

Philos. Mag. (1)

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, Philos. Mag. 87, 3565 (2007).
[CrossRef]

Real-Time Imaging (1)

N. Kehtarnavaz and H. J. Oh, Real-Time Imaging 9, 197 (2003).
[CrossRef]

Ultramicroscopy (2)

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef] [PubMed]

P. N. H. Nakashima and A. W. S. Johnson, Ultramicroscopy 94, 135 (2003).
[CrossRef]

Other (3)

D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science, 2nd ed. (Springer Science, 2009).

J. M. Cowley, Diffraction Physics, 3rd ed. (Elsevier Science, 1995).

M. De Graef, Introduction to Conventional Transmission Electron Microscopy (Cambridge University, 2003).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) In-focus image of a pentagon. Out-of-focus images of (a) under (b) incoherent and (c) coherent illumination. (d) Coherent waves illuminate a phase object. Density variations perturb the phase of the wave field giving rise to intensity variations in the image.

Fig. 2
Fig. 2

(a) Phase contrast image of 30 nm latex spheres ( δ = 74 nm ). (b) Reconstructed projected thickness of (a). (c) AC of T ( x , y ) using correct and underestimated values for τ. Note the appearance of a local minimum for the incorrect reconstruction at fridge length scales.

Fig. 3
Fig. 3

Schematic of the APR algorithm.

Fig. 4
Fig. 4

E 1 and E 2 versus defocus.

Equations (3)

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

T ( x , y ) = 1 μ ln ( F 1 { F { I δ ( x , y ) / I in } 1 τ ( k x 2 + k y 2 ) } ) .
E 2 = T af ( i , j ) T c ( i , j ) T c ( i , j ) × 100 % ,
T ( i , j ) = 1 N M i = 1 N j = 1 M | T ( i , j ) | 2 ,

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